Mercurial > dropbear
changeset 190:d8254fc979e9 libtommath-orig LTM_0.35
Initial import of libtommath 0.35
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/TODO Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,16 @@ +things for book in order of importance... + +- Fix up pseudo-code [only] for combas that are not consistent with source +- Start in chapter 3 [basics] and work up... + - re-write to prose [less abrupt] + - clean up pseudo code [spacing] + - more examples where appropriate and figures + +Goal: + - Get sync done by mid January [roughly 8-12 hours work] + - Finish ch3-6 by end of January [roughly 12-16 hours of work] + - Finish ch7-end by mid Feb [roughly 20-24 hours of work]. + +Goal isn't "first edition" but merely cleaner to read. + +
--- a/bn.tex Sun Dec 19 11:33:56 2004 +0000 +++ b/bn.tex Fri May 06 08:59:30 2005 +0000 @@ -49,7 +49,7 @@ \begin{document} \frontmatter \pagestyle{empty} -\title{LibTomMath User Manual \\ v0.32} +\title{LibTomMath User Manual \\ v0.35} \author{Tom St Denis \\ [email protected]} \maketitle This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been @@ -263,12 +263,12 @@ \begin{center} \begin{tabular}{|l|c|c|l|} \hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\ -\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath $ = 76.04$ \\ +\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath $ = 71.97$ \\ \hline Commented function prototypes & X && GnuPG function names are cryptic. \\ \hline Speed && X & LibTomMath is slower. \\ \hline Totally free & X & & GPL has unfavourable restrictions.\\ \hline Large function base & X & & GnuPG is barebones. \\ -\hline Four modular reduction algorithms & X & & Faster modular exponentiation. \\ +\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\ \hline Portable & X & & GnuPG requires configuration to build. \\ \hline \end{tabular} @@ -284,9 +284,12 @@ So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your own application but I think there are reasons not to. While LibTomMath is slower than libraries such as GnuMP it is not normally significantly slower. On x86 machines the difference is normally a factor of two when performing modular -exponentiations. +exponentiations. It depends largely on the processor, compiler and the moduli being used. -Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern. +Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern. However, +on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library +that is very flexible, complete and performs well in resource contrained environments. Fast RSA for example can +be performed with as little as 8KB of ram for data (again depending on build options). \chapter{Getting Started with LibTomMath} \section{Building Programs} @@ -809,7 +812,7 @@ \index{mp\_cmp\_mag} \begin{alltt} -int mp_cmp(mp_int * a, mp_int * b); +int mp_cmp_mag(mp_int * a, mp_int * b); \end{alltt} This will compare $a$ to $b$ placing $a$ to the left of $b$. This function cannot fail and will return one of the three compare codes listed in figure \ref{fig:CMP}. @@ -1220,12 +1223,13 @@ \end{alltt} Will square $a$ and store it in $b$. Like the case of multiplication there are four different squaring -algorithms all which can be called from mp\_sqr(). It is ideal to use mp\_sqr over mp\_mul when squaring terms. +algorithms all which can be called from mp\_sqr(). It is ideal to use mp\_sqr over mp\_mul when squaring terms because +of the speed difference. \section{Tuning Polynomial Basis Routines} Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that -the Comba and baseline algorithms use. At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectfully they require +the Comba and baseline algorithms use. At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require considerably less work. For example, a 10000-digit multiplication would take roughly 724,000 single precision multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor of 138). @@ -1297,14 +1301,14 @@ \section{Barrett Reduction} Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve -a decent speedup over straight division. First a $mu$ value must be precomputed with the following function. +a decent speedup over straight division. First a $\mu$ value must be precomputed with the following function. \index{mp\_reduce\_setup} \begin{alltt} int mp_reduce_setup(mp_int *a, mp_int *b); \end{alltt} -Given a modulus in $b$ this produces the required $mu$ value in $a$. For any given modulus this only has to +Given a modulus in $b$ this produces the required $\mu$ value in $a$. For any given modulus this only has to be computed once. Modular reduction can now be performed with the following. \index{mp\_reduce} @@ -1312,7 +1316,7 @@ int mp_reduce(mp_int *a, mp_int *b, mp_int *c); \end{alltt} -This will reduce $a$ in place modulo $b$ with the precomputed $mu$ value in $c$. $a$ must be in the range +This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$. $a$ must be in the range $0 \le a < b^2$. \begin{alltt} @@ -1578,7 +1582,8 @@ This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly. Since the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large values of $b$. If particularly large roots are required then a factor method could be used instead. For example, -$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$. +$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply +$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$ \chapter{Prime Numbers} \section{Trial Division}
--- a/bn_fast_mp_invmod.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_fast_mp_invmod.c Fri May 06 08:59:30 2005 +0000 @@ -21,8 +21,7 @@ * Based on slow invmod except this is optimized for the case where b is * odd as per HAC Note 14.64 on pp. 610 */ -int -fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) +int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) { mp_int x, y, u, v, B, D; int res, neg; @@ -39,20 +38,20 @@ /* x == modulus, y == value to invert */ if ((res = mp_copy (b, &x)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* we need y = |a| */ - if ((res = mp_abs (a, &y)) != MP_OKAY) { - goto __ERR; + if ((res = mp_mod (a, b, &y)) != MP_OKAY) { + goto LBL_ERR; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } mp_set (&D, 1); @@ -61,17 +60,17 @@ while (mp_iseven (&u) == 1) { /* 4.1 u = u/2 */ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 4.2 if B is odd then */ if (mp_isodd (&B) == 1) { if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* B = B/2 */ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -79,18 +78,18 @@ while (mp_iseven (&v) == 1) { /* 5.1 v = v/2 */ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 5.2 if D is odd then */ if (mp_isodd (&D) == 1) { /* D = (D-x)/2 */ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* D = D/2 */ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -98,20 +97,20 @@ if (mp_cmp (&u, &v) != MP_LT) { /* u = u - v, B = B - D */ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } else { /* v - v - u, D = D - B */ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -125,21 +124,21 @@ /* if v != 1 then there is no inverse */ if (mp_cmp_d (&v, 1) != MP_EQ) { res = MP_VAL; - goto __ERR; + goto LBL_ERR; } /* b is now the inverse */ neg = a->sign; while (D.sign == MP_NEG) { if ((res = mp_add (&D, b, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } mp_exch (&D, c); c->sign = neg; res = MP_OKAY; -__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); +LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif
--- a/bn_fast_mp_montgomery_reduce.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_fast_mp_montgomery_reduce.c Fri May 06 08:59:30 2005 +0000 @@ -23,8 +23,7 @@ * * Based on Algorithm 14.32 on pp.601 of HAC. */ -int -fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) +int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) { int ix, res, olduse; mp_word W[MP_WARRAY];
--- a/bn_fast_s_mp_mul_digs.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_fast_s_mp_mul_digs.c Fri May 06 08:59:30 2005 +0000 @@ -31,8 +31,7 @@ * Based on Algorithm 14.12 on pp.595 of HAC. * */ -int -fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { int olduse, res, pa, ix, iz; mp_digit W[MP_WARRAY]; @@ -50,7 +49,7 @@ /* clear the carry */ _W = 0; - for (ix = 0; ix <= pa; ix++) { + for (ix = 0; ix < pa; ix++) { int tx, ty; int iy; mp_digit *tmpx, *tmpy; @@ -63,7 +62,7 @@ tmpx = a->dp + tx; tmpy = b->dp + ty; - /* this is the number of times the loop will iterrate, essentially its + /* this is the number of times the loop will iterrate, essentially while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); @@ -80,14 +79,17 @@ _W = _W >> ((mp_word)DIGIT_BIT); } + /* store final carry */ + W[ix] = (mp_digit)(_W & MP_MASK); + /* setup dest */ olduse = c->used; - c->used = digs; + c->used = pa; { register mp_digit *tmpc; tmpc = c->dp; - for (ix = 0; ix < digs; ix++) { + for (ix = 0; ix < pa+1; ix++) { /* now extract the previous digit [below the carry] */ *tmpc++ = W[ix]; }
--- a/bn_fast_s_mp_mul_high_digs.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_fast_s_mp_mul_high_digs.c Fri May 06 08:59:30 2005 +0000 @@ -24,8 +24,7 @@ * * Based on Algorithm 14.12 on pp.595 of HAC. */ -int -fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { int olduse, res, pa, ix, iz; mp_digit W[MP_WARRAY]; @@ -42,7 +41,7 @@ /* number of output digits to produce */ pa = a->used + b->used; _W = 0; - for (ix = digs; ix <= pa; ix++) { + for (ix = digs; ix < pa; ix++) { int tx, ty, iy; mp_digit *tmpx, *tmpy; @@ -70,6 +69,9 @@ /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); } + + /* store final carry */ + W[ix] = (mp_digit)(_W & MP_MASK); /* setup dest */ olduse = c->used;
--- a/bn_fast_s_mp_sqr.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_fast_s_mp_sqr.c Fri May 06 08:59:30 2005 +0000 @@ -15,33 +15,14 @@ * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -/* fast squaring - * - * This is the comba method where the columns of the product - * are computed first then the carries are computed. This - * has the effect of making a very simple inner loop that - * is executed the most - * - * W2 represents the outer products and W the inner. - * - * A further optimizations is made because the inner - * products are of the form "A * B * 2". The *2 part does - * not need to be computed until the end which is good - * because 64-bit shifts are slow! - * - * Based on Algorithm 14.16 on pp.597 of HAC. - * - */ /* the jist of squaring... - -you do like mult except the offset of the tmpx [one that starts closer to zero] -can't equal the offset of tmpy. So basically you set up iy like before then you min it with -(ty-tx) so that it never happens. You double all those you add in the inner loop + * you do like mult except the offset of the tmpx [one that + * starts closer to zero] can't equal the offset of tmpy. + * So basically you set up iy like before then you min it with + * (ty-tx) so that it never happens. You double all those + * you add in the inner loop After that loop you do the squares and add them in. - -Remove W2 and don't memset W - */ int fast_s_mp_sqr (mp_int * a, mp_int * b) @@ -60,7 +41,7 @@ /* number of output digits to produce */ W1 = 0; - for (ix = 0; ix <= pa; ix++) { + for (ix = 0; ix < pa; ix++) { int tx, ty, iy; mp_word _W; mp_digit *tmpy; @@ -76,7 +57,7 @@ tmpx = a->dp + tx; tmpy = a->dp + ty; - /* this is the number of times the loop will iterrate, essentially its + /* this is the number of times the loop will iterrate, essentially while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); @@ -101,7 +82,7 @@ } /* store it */ - W[ix] = _W; + W[ix] = (mp_digit)(_W & MP_MASK); /* make next carry */ W1 = _W >> ((mp_word)DIGIT_BIT);
--- a/bn_mp_div.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_div.c Fri May 06 08:59:30 2005 +0000 @@ -49,23 +49,23 @@ mp_set(&tq, 1); n = mp_count_bits(a) - mp_count_bits(b); - if (((res = mp_copy(a, &ta)) != MP_OKAY) || - ((res = mp_copy(b, &tb)) != MP_OKAY) || + if (((res = mp_abs(a, &ta)) != MP_OKAY) || + ((res = mp_abs(b, &tb)) != MP_OKAY) || ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { - goto __ERR; + goto LBL_ERR; } while (n-- >= 0) { if (mp_cmp(&tb, &ta) != MP_GT) { if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { - goto __ERR; + goto LBL_ERR; } } if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { - goto __ERR; + goto LBL_ERR; } } @@ -74,13 +74,13 @@ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); if (c != NULL) { mp_exch(c, &q); - c->sign = n2; + c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; } if (d != NULL) { mp_exch(d, &ta); - d->sign = n; + d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; } -__ERR: +LBL_ERR: mp_clear_multi(&ta, &tb, &tq, &q, NULL); return res; } @@ -129,19 +129,19 @@ q.used = a->used + 2; if ((res = mp_init (&t1)) != MP_OKAY) { - goto __Q; + goto LBL_Q; } if ((res = mp_init (&t2)) != MP_OKAY) { - goto __T1; + goto LBL_T1; } if ((res = mp_init_copy (&x, a)) != MP_OKAY) { - goto __T2; + goto LBL_T2; } if ((res = mp_init_copy (&y, b)) != MP_OKAY) { - goto __X; + goto LBL_X; } /* fix the sign */ @@ -153,10 +153,10 @@ if (norm < (int)(DIGIT_BIT-1)) { norm = (DIGIT_BIT-1) - norm; if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } } else { norm = 0; @@ -168,13 +168,13 @@ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ - goto __Y; + goto LBL_Y; } while (mp_cmp (&x, &y) != MP_LT) { ++(q.dp[n - t]); if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } } @@ -216,7 +216,7 @@ t1.dp[1] = y.dp[t]; t1.used = 2; if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* find right hand */ @@ -228,27 +228,27 @@ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ if (x.sign == MP_NEG) { if ((res = mp_copy (&y, &t1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; @@ -275,11 +275,11 @@ res = MP_OKAY; -__Y:mp_clear (&y); -__X:mp_clear (&x); -__T2:mp_clear (&t2); -__T1:mp_clear (&t1); -__Q:mp_clear (&q); +LBL_Y:mp_clear (&y); +LBL_X:mp_clear (&x); +LBL_T2:mp_clear (&t2); +LBL_T1:mp_clear (&t1); +LBL_Q:mp_clear (&q); return res; }
--- a/bn_mp_dr_reduce.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_dr_reduce.c Fri May 06 08:59:30 2005 +0000 @@ -20,7 +20,7 @@ * Based on algorithm from the paper * * "Generating Efficient Primes for Discrete Log Cryptosystems" - * Chae Hoon Lim, Pil Loong Lee, + * Chae Hoon Lim, Pil Joong Lee, * POSTECH Information Research Laboratories * * The modulus must be of a special format [see manual]
--- a/bn_mp_exptmod.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_exptmod.c Fri May 06 08:59:30 2005 +0000 @@ -61,25 +61,33 @@ return err; #else /* no invmod */ - return MP_VAL + return MP_VAL; #endif } +/* modified diminished radix reduction */ +#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) + if (mp_reduce_is_2k_l(P) == MP_YES) { + return s_mp_exptmod(G, X, P, Y, 1); + } +#endif + #ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ dr = mp_dr_is_modulus(P); #else + /* default to no */ dr = 0; #endif #ifdef BN_MP_REDUCE_IS_2K_C - /* if not, is it a uDR modulus? */ + /* if not, is it a unrestricted DR modulus? */ if (dr == 0) { dr = mp_reduce_is_2k(P) << 1; } #endif - /* if the modulus is odd or dr != 0 use the fast method */ + /* if the modulus is odd or dr != 0 use the montgomery method */ #ifdef BN_MP_EXPTMOD_FAST_C if (mp_isodd (P) == 1 || dr != 0) { return mp_exptmod_fast (G, X, P, Y, dr); @@ -87,7 +95,7 @@ #endif #ifdef BN_S_MP_EXPTMOD_C /* otherwise use the generic Barrett reduction technique */ - return s_mp_exptmod (G, X, P, Y); + return s_mp_exptmod (G, X, P, Y, 0); #else /* no exptmod for evens */ return MP_VAL;
--- a/bn_mp_exptmod_fast.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_exptmod_fast.c Fri May 06 08:59:30 2005 +0000 @@ -29,8 +29,7 @@ #define TAB_SIZE 256 #endif -int -mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) +int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) { mp_int M[TAB_SIZE], res; mp_digit buf, mp; @@ -88,11 +87,11 @@ #ifdef BN_MP_MONTGOMERY_SETUP_C /* now setup montgomery */ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { - goto __M; + goto LBL_M; } #else err = MP_VAL; - goto __M; + goto LBL_M; #endif /* automatically pick the comba one if available (saves quite a few calls/ifs) */ @@ -108,7 +107,7 @@ redux = mp_montgomery_reduce; #else err = MP_VAL; - goto __M; + goto LBL_M; #endif } } else if (redmode == 1) { @@ -118,24 +117,24 @@ redux = mp_dr_reduce; #else err = MP_VAL; - goto __M; + goto LBL_M; #endif } else { #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) /* setup DR reduction for moduli of the form 2**k - b */ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { - goto __M; + goto LBL_M; } redux = mp_reduce_2k; #else err = MP_VAL; - goto __M; + goto LBL_M; #endif } /* setup result */ if ((err = mp_init (&res)) != MP_OKAY) { - goto __M; + goto LBL_M; } /* create M table @@ -149,45 +148,45 @@ #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* now we need R mod m */ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } #else err = MP_VAL; - goto __RES; + goto LBL_RES; #endif /* now set M[1] to G * R mod m */ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } else { mp_set(&res, 1); if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } for (x = 0; x < (winsize - 1); x++) { if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* create upper table */ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&M[x], P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } @@ -227,10 +226,10 @@ /* if the bit is zero and mode == 1 then we square */ if (mode == 1 && y == 0) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } continue; } @@ -244,19 +243,19 @@ /* square first */ for (x = 0; x < winsize; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* then multiply */ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } /* empty window and reset */ @@ -271,10 +270,10 @@ /* square then multiply if the bit is set */ for (x = 0; x < bitcpy; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } /* get next bit of the window */ @@ -282,10 +281,10 @@ if ((bitbuf & (1 << winsize)) != 0) { /* then multiply */ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } } @@ -299,15 +298,15 @@ * of R. */ if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* swap res with Y */ mp_exch (&res, Y); err = MP_OKAY; -__RES:mp_clear (&res); -__M: +LBL_RES:mp_clear (&res); +LBL_M: mp_clear(&M[1]); for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]);
--- a/bn_mp_exteuclid.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_exteuclid.c Fri May 06 08:59:30 2005 +0000 @@ -59,6 +59,13 @@ if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; } } + /* make sure U3 >= 0 */ + if (u3.sign == MP_NEG) { + mp_neg(&u1, &u1); + mp_neg(&u2, &u2); + mp_neg(&u3, &u3); + } + /* copy result out */ if (U1 != NULL) { mp_exch(U1, &u1); } if (U2 != NULL) { mp_exch(U2, &u2); }
--- a/bn_mp_gcd.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_gcd.c Fri May 06 08:59:30 2005 +0000 @@ -43,7 +43,7 @@ } if ((res = mp_init_copy (&v, b)) != MP_OKAY) { - goto __U; + goto LBL_U; } /* must be positive for the remainder of the algorithm */ @@ -57,24 +57,24 @@ if (k > 0) { /* divide the power of two out */ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } /* divide any remaining factors of two out */ if (u_lsb != k) { if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } if (v_lsb != k) { if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } @@ -87,23 +87,23 @@ /* subtract smallest from largest */ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) { - goto __V; + goto LBL_V; } /* Divide out all factors of two */ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } /* multiply by 2**k which we divided out at the beginning */ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) { - goto __V; + goto LBL_V; } c->sign = MP_ZPOS; res = MP_OKAY; -__V:mp_clear (&u); -__U:mp_clear (&v); +LBL_V:mp_clear (&u); +LBL_U:mp_clear (&v); return res; } #endif
--- a/bn_mp_invmod_slow.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_invmod_slow.c Fri May 06 08:59:30 2005 +0000 @@ -33,25 +33,25 @@ } /* x = a, y = b */ - if ((res = mp_copy (a, &x)) != MP_OKAY) { - goto __ERR; + if ((res = mp_mod(a, b, &x)) != MP_OKAY) { + goto LBL_ERR; } if ((res = mp_copy (b, &y)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 2. [modified] if x,y are both even then return an error! */ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { res = MP_VAL; - goto __ERR; + goto LBL_ERR; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } mp_set (&A, 1); mp_set (&D, 1); @@ -61,24 +61,24 @@ while (mp_iseven (&u) == 1) { /* 4.1 u = u/2 */ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 4.2 if A or B is odd then */ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) { /* A = (A+y)/2, B = (B-x)/2 */ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* A = A/2, B = B/2 */ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -86,24 +86,24 @@ while (mp_iseven (&v) == 1) { /* 5.1 v = v/2 */ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 5.2 if C or D is odd then */ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) { /* C = (C+y)/2, D = (D-x)/2 */ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* C = C/2, D = D/2 */ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -111,28 +111,28 @@ if (mp_cmp (&u, &v) != MP_LT) { /* u = u - v, A = A - C, B = B - D */ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } else { /* v - v - u, C = C - A, D = D - B */ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -145,27 +145,27 @@ /* if v != 1 then there is no inverse */ if (mp_cmp_d (&v, 1) != MP_EQ) { res = MP_VAL; - goto __ERR; + goto LBL_ERR; } /* if its too low */ while (mp_cmp_d(&C, 0) == MP_LT) { if ((res = mp_add(&C, b, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* too big */ while (mp_cmp_mag(&C, b) != MP_LT) { if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* C is now the inverse */ mp_exch (&C, c); res = MP_OKAY; -__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); +LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif
--- a/bn_mp_jacobi.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_jacobi.c Fri May 06 08:59:30 2005 +0000 @@ -50,13 +50,13 @@ } if ((res = mp_init (&p1)) != MP_OKAY) { - goto __A1; + goto LBL_A1; } /* divide out larger power of two */ k = mp_cnt_lsb(&a1); if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) { - goto __P1; + goto LBL_P1; } /* step 4. if e is even set s=1 */ @@ -84,18 +84,18 @@ } else { /* n1 = n mod a1 */ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) { - goto __P1; + goto LBL_P1; } if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) { - goto __P1; + goto LBL_P1; } *c = s * r; } /* done */ res = MP_OKAY; -__P1:mp_clear (&p1); -__A1:mp_clear (&a1); +LBL_P1:mp_clear (&p1); +LBL_A1:mp_clear (&a1); return res; } #endif
--- a/bn_mp_lcm.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_lcm.c Fri May 06 08:59:30 2005 +0000 @@ -28,20 +28,20 @@ /* t1 = get the GCD of the two inputs */ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) { - goto __T; + goto LBL_T; } /* divide the smallest by the GCD */ if (mp_cmp_mag(a, b) == MP_LT) { /* store quotient in t2 such that t2 * b is the LCM */ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { - goto __T; + goto LBL_T; } res = mp_mul(b, &t2, c); } else { /* store quotient in t2 such that t2 * a is the LCM */ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { - goto __T; + goto LBL_T; } res = mp_mul(a, &t2, c); } @@ -49,7 +49,7 @@ /* fix the sign to positive */ c->sign = MP_ZPOS; -__T: +LBL_T: mp_clear_multi (&t1, &t2, NULL); return res; }
--- a/bn_mp_mod_2d.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_mod_2d.c Fri May 06 08:59:30 2005 +0000 @@ -28,7 +28,7 @@ } /* if the modulus is larger than the value than return */ - if (b > (int) (a->used * DIGIT_BIT)) { + if (b >= (int) (a->used * DIGIT_BIT)) { res = mp_copy (a, c); return res; }
--- a/bn_mp_montgomery_calc_normalization.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_montgomery_calc_normalization.c Fri May 06 08:59:30 2005 +0000 @@ -28,7 +28,6 @@ /* how many bits of last digit does b use */ bits = mp_count_bits (b) % DIGIT_BIT; - if (b->used > 1) { if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { return res;
--- a/bn_mp_mul_d.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_mul_d.c Fri May 06 08:59:30 2005 +0000 @@ -57,8 +57,9 @@ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); } - /* store final carry [if any] */ + /* store final carry [if any] and increment ix offset */ *tmpc++ = u; + ++ix; /* now zero digits above the top */ while (ix++ < olduse) {
--- a/bn_mp_n_root.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_n_root.c Fri May 06 08:59:30 2005 +0000 @@ -40,11 +40,11 @@ } if ((res = mp_init (&t2)) != MP_OKAY) { - goto __T1; + goto LBL_T1; } if ((res = mp_init (&t3)) != MP_OKAY) { - goto __T2; + goto LBL_T2; } /* if a is negative fudge the sign but keep track */ @@ -57,52 +57,52 @@ do { /* t1 = t2 */ if ((res = mp_copy (&t2, &t1)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ /* t3 = t1**(b-1) */ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* numerator */ /* t2 = t1**b */ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* t2 = t1**b - a */ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* denominator */ /* t3 = t1**(b-1) * b */ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* t3 = (t1**b - a)/(b * t1**(b-1)) */ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } } while (mp_cmp (&t1, &t2) != MP_EQ); /* result can be off by a few so check */ for (;;) { if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } if (mp_cmp (&t2, a) == MP_GT) { if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } } else { break; @@ -120,9 +120,9 @@ res = MP_OKAY; -__T3:mp_clear (&t3); -__T2:mp_clear (&t2); -__T1:mp_clear (&t1); +LBL_T3:mp_clear (&t3); +LBL_T2:mp_clear (&t2); +LBL_T1:mp_clear (&t1); return res; } #endif
--- a/bn_mp_neg.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_neg.c Fri May 06 08:59:30 2005 +0000 @@ -19,12 +19,18 @@ int mp_neg (mp_int * a, mp_int * b) { int res; - if ((res = mp_copy (a, b)) != MP_OKAY) { - return res; + if (a != b) { + if ((res = mp_copy (a, b)) != MP_OKAY) { + return res; + } } + if (mp_iszero(b) != MP_YES) { b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; + } else { + b->sign = MP_ZPOS; } + return MP_OKAY; } #endif
--- a/bn_mp_prime_fermat.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_prime_fermat.c Fri May 06 08:59:30 2005 +0000 @@ -43,7 +43,7 @@ /* compute t = b**a mod a */ if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) { - goto __T; + goto LBL_T; } /* is it equal to b? */ @@ -52,7 +52,7 @@ } err = MP_OKAY; -__T:mp_clear (&t); +LBL_T:mp_clear (&t); return err; } #endif
--- a/bn_mp_prime_is_divisible.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_prime_is_divisible.c Fri May 06 08:59:30 2005 +0000 @@ -29,8 +29,8 @@ *result = MP_NO; for (ix = 0; ix < PRIME_SIZE; ix++) { - /* what is a mod __prime_tab[ix] */ - if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) { + /* what is a mod LBL_prime_tab[ix] */ + if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) { return err; }
--- a/bn_mp_prime_is_prime.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_prime_is_prime.c Fri May 06 08:59:30 2005 +0000 @@ -37,7 +37,7 @@ /* is the input equal to one of the primes in the table? */ for (ix = 0; ix < PRIME_SIZE; ix++) { - if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) { + if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) { *result = 1; return MP_OKAY; } @@ -60,20 +60,20 @@ for (ix = 0; ix < t; ix++) { /* set the prime */ - mp_set (&b, __prime_tab[ix]); + mp_set (&b, ltm_prime_tab[ix]); if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) { - goto __B; + goto LBL_B; } if (res == MP_NO) { - goto __B; + goto LBL_B; } } /* passed the test */ *result = MP_YES; -__B:mp_clear (&b); +LBL_B:mp_clear (&b); return err; } #endif
--- a/bn_mp_prime_miller_rabin.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_prime_miller_rabin.c Fri May 06 08:59:30 2005 +0000 @@ -40,12 +40,12 @@ return err; } if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) { - goto __N1; + goto LBL_N1; } /* set 2**s * r = n1 */ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { - goto __N1; + goto LBL_N1; } /* count the number of least significant bits @@ -55,15 +55,15 @@ /* now divide n - 1 by 2**s */ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) { - goto __R; + goto LBL_R; } /* compute y = b**r mod a */ if ((err = mp_init (&y)) != MP_OKAY) { - goto __R; + goto LBL_R; } if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* if y != 1 and y != n1 do */ @@ -72,12 +72,12 @@ /* while j <= s-1 and y != n1 */ while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) { if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* if y == 1 then composite */ if (mp_cmp_d (&y, 1) == MP_EQ) { - goto __Y; + goto LBL_Y; } ++j; @@ -85,15 +85,15 @@ /* if y != n1 then composite */ if (mp_cmp (&y, &n1) != MP_EQ) { - goto __Y; + goto LBL_Y; } } /* probably prime now */ *result = MP_YES; -__Y:mp_clear (&y); -__R:mp_clear (&r); -__N1:mp_clear (&n1); +LBL_Y:mp_clear (&y); +LBL_R:mp_clear (&r); +LBL_N1:mp_clear (&n1); return err; } #endif
--- a/bn_mp_prime_next_prime.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_prime_next_prime.c Fri May 06 08:59:30 2005 +0000 @@ -35,10 +35,10 @@ a->sign = MP_ZPOS; /* simple algo if a is less than the largest prime in the table */ - if (mp_cmp_d(a, __prime_tab[PRIME_SIZE-1]) == MP_LT) { + if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) { /* find which prime it is bigger than */ for (x = PRIME_SIZE - 2; x >= 0; x--) { - if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) { + if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) { if (bbs_style == 1) { /* ok we found a prime smaller or * equal [so the next is larger] @@ -46,17 +46,17 @@ * however, the prime must be * congruent to 3 mod 4 */ - if ((__prime_tab[x + 1] & 3) != 3) { + if ((ltm_prime_tab[x + 1] & 3) != 3) { /* scan upwards for a prime congruent to 3 mod 4 */ for (y = x + 1; y < PRIME_SIZE; y++) { - if ((__prime_tab[y] & 3) == 3) { - mp_set(a, __prime_tab[y]); + if ((ltm_prime_tab[y] & 3) == 3) { + mp_set(a, ltm_prime_tab[y]); return MP_OKAY; } } } } else { - mp_set(a, __prime_tab[x + 1]); + mp_set(a, ltm_prime_tab[x + 1]); return MP_OKAY; } } @@ -94,7 +94,7 @@ /* generate the restable */ for (x = 1; x < PRIME_SIZE; x++) { - if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) { + if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) { return err; } } @@ -120,8 +120,8 @@ res_tab[x] += kstep; /* subtract the modulus [instead of using division] */ - if (res_tab[x] >= __prime_tab[x]) { - res_tab[x] -= __prime_tab[x]; + if (res_tab[x] >= ltm_prime_tab[x]) { + res_tab[x] -= ltm_prime_tab[x]; } /* set flag if zero */ @@ -133,7 +133,7 @@ /* add the step */ if ((err = mp_add_d(a, step, a)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* if didn't pass sieve and step == MAX then skip test */ @@ -143,9 +143,9 @@ /* is this prime? */ for (x = 0; x < t; x++) { - mp_set(&b, __prime_tab[t]); + mp_set(&b, ltm_prime_tab[t]); if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if (res == MP_NO) { break; @@ -158,7 +158,7 @@ } err = MP_OKAY; -__ERR: +LBL_ERR: mp_clear(&b); return err; }
--- a/bn_mp_prime_random_ex.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_prime_random_ex.c Fri May 06 08:59:30 2005 +0000 @@ -47,7 +47,7 @@ } /* calc the byte size */ - bsize = (size>>3)+(size&7?1:0); + bsize = (size>>3) + ((size&7)?1:0); /* we need a buffer of bsize bytes */ tmp = OPT_CAST(unsigned char) XMALLOC(bsize); @@ -56,19 +56,19 @@ } /* calc the maskAND value for the MSbyte*/ - maskAND = 0xFF >> (8 - (size & 7)); + maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); /* calc the maskOR_msb */ maskOR_msb = 0; - maskOR_msb_offset = (size - 2) >> 3; + maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { maskOR_msb |= 1 << ((size - 2) & 7); } else if (flags & LTM_PRIME_2MSB_OFF) { maskAND &= ~(1 << ((size - 2) & 7)); - } + } /* get the maskOR_lsb */ - maskOR_lsb = 0; + maskOR_lsb = 1; if (flags & LTM_PRIME_BBS) { maskOR_lsb |= 3; }
--- a/bn_mp_radix_size.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_radix_size.c Fri May 06 08:59:30 2005 +0000 @@ -35,22 +35,29 @@ return MP_VAL; } - /* init a copy of the input */ - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; + if (mp_iszero(a) == MP_YES) { + *size = 2; + return MP_OKAY; } /* digs is the digit count */ digs = 0; /* if it's negative add one for the sign */ - if (t.sign == MP_NEG) { + if (a->sign == MP_NEG) { ++digs; - t.sign = MP_ZPOS; } + /* init a copy of the input */ + if ((res = mp_init_copy (&t, a)) != MP_OKAY) { + return res; + } + + /* force temp to positive */ + t.sign = MP_ZPOS; + /* fetch out all of the digits */ - while (mp_iszero (&t) == 0) { + while (mp_iszero (&t) == MP_NO) { if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res;
--- a/bn_mp_rand.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_rand.c Fri May 06 08:59:30 2005 +0000 @@ -29,14 +29,14 @@ /* first place a random non-zero digit */ do { - d = ((mp_digit) abs (rand ())); + d = ((mp_digit) abs (rand ())) & MP_MASK; } while (d == 0); if ((res = mp_add_d (a, d, a)) != MP_OKAY) { return res; } - while (digits-- > 0) { + while (--digits > 0) { if ((res = mp_lshd (a, 1)) != MP_OKAY) { return res; }
--- a/bn_mp_read_radix.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_read_radix.c Fri May 06 08:59:30 2005 +0000 @@ -16,7 +16,7 @@ */ /* read a string [ASCII] in a given radix */ -int mp_read_radix (mp_int * a, char *str, int radix) +int mp_read_radix (mp_int * a, const char *str, int radix) { int y, res, neg; char ch;
--- a/bn_mp_reduce.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_reduce.c Fri May 06 08:59:30 2005 +0000 @@ -19,8 +19,7 @@ * precomputed via mp_reduce_setup. * From HAC pp.604 Algorithm 14.42 */ -int -mp_reduce (mp_int * x, mp_int * m, mp_int * mu) +int mp_reduce (mp_int * x, mp_int * m, mp_int * mu) { mp_int q; int res, um = m->used; @@ -40,11 +39,11 @@ } } else { #ifdef BN_S_MP_MUL_HIGH_DIGS_C - if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { + if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { goto CLEANUP; } #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) - if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { + if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { goto CLEANUP; } #else
--- a/bn_mp_reduce_2k.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_reduce_2k.c Fri May 06 08:59:30 2005 +0000 @@ -16,8 +16,7 @@ */ /* reduces a modulo n where n is of the form 2**p - d */ -int -mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) +int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) { mp_int q; int p, res;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_reduce_2k_l.c Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,58 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* reduces a modulo n where n is of the form 2**p - d + This differs from reduce_2k since "d" can be larger + than a single digit. +*/ +int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d) +{ + mp_int q; + int p, res; + + if ((res = mp_init(&q)) != MP_OKAY) { + return res; + } + + p = mp_count_bits(n); +top: + /* q = a/2**p, a = a mod 2**p */ + if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto ERR; + } + + /* q = q * d */ + if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { + goto ERR; + } + + /* a = a + q */ + if ((res = s_mp_add(a, &q, a)) != MP_OKAY) { + goto ERR; + } + + if (mp_cmp_mag(a, n) != MP_LT) { + s_mp_sub(a, n, a); + goto top; + } + +ERR: + mp_clear(&q); + return res; +} + +#endif
--- a/bn_mp_reduce_2k_setup.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_reduce_2k_setup.c Fri May 06 08:59:30 2005 +0000 @@ -16,8 +16,7 @@ */ /* determines the setup value */ -int -mp_reduce_2k_setup(mp_int *a, mp_digit *d) +int mp_reduce_2k_setup(mp_int *a, mp_digit *d) { int res, p; mp_int tmp;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_reduce_2k_setup_l.c Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,40 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_SETUP_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* determines the setup value */ +int mp_reduce_2k_setup_l(mp_int *a, mp_int *d) +{ + int res; + mp_int tmp; + + if ((res = mp_init(&tmp)) != MP_OKAY) { + return res; + } + + if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { + goto ERR; + } + + if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) { + goto ERR; + } + +ERR: + mp_clear(&tmp); + return res; +} +#endif
--- a/bn_mp_reduce_is_2k.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_reduce_is_2k.c Fri May 06 08:59:30 2005 +0000 @@ -22,9 +22,9 @@ mp_digit iz; if (a->used == 0) { - return 0; + return MP_NO; } else if (a->used == 1) { - return 1; + return MP_YES; } else if (a->used > 1) { iy = mp_count_bits(a); iz = 1; @@ -33,7 +33,7 @@ /* Test every bit from the second digit up, must be 1 */ for (ix = DIGIT_BIT; ix < iy; ix++) { if ((a->dp[iw] & iz) == 0) { - return 0; + return MP_NO; } iz <<= 1; if (iz > (mp_digit)MP_MASK) { @@ -42,7 +42,7 @@ } } } - return 1; + return MP_YES; } #endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_reduce_is_2k_l.c Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,40 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_IS_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* determines if reduce_2k_l can be used */ +int mp_reduce_is_2k_l(mp_int *a) +{ + int ix, iy; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + /* if more than half of the digits are -1 we're sold */ + for (iy = ix = 0; ix < a->used; ix++) { + if (a->dp[ix] == MP_MASK) { + ++iy; + } + } + return (iy >= (a->used/2)) ? MP_YES : MP_NO; + + } + return MP_NO; +} + +#endif
--- a/bn_mp_to_signed_bin.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_to_signed_bin.c Fri May 06 08:59:30 2005 +0000 @@ -16,8 +16,7 @@ */ /* store in signed [big endian] format */ -int -mp_to_signed_bin (mp_int * a, unsigned char *b) +int mp_to_signed_bin (mp_int * a, unsigned char *b) { int res;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_to_signed_bin_n.c Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,27 @@ +#include <tommath.h> +#ifdef BN_MP_TO_SIGNED_BIN_N_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* store in signed [big endian] format */ +int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) +{ + if (*outlen < (unsigned long)mp_signed_bin_size(a)) { + return MP_VAL; + } + *outlen = mp_signed_bin_size(a); + return mp_to_signed_bin(a, b); +} +#endif
--- a/bn_mp_to_unsigned_bin.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_to_unsigned_bin.c Fri May 06 08:59:30 2005 +0000 @@ -16,8 +16,7 @@ */ /* store in unsigned [big endian] format */ -int -mp_to_unsigned_bin (mp_int * a, unsigned char *b) +int mp_to_unsigned_bin (mp_int * a, unsigned char *b) { int x, res; mp_int t;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_to_unsigned_bin_n.c Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,27 @@ +#include <tommath.h> +#ifdef BN_MP_TO_UNSIGNED_BIN_N_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* store in unsigned [big endian] format */ +int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) +{ + if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { + return MP_VAL; + } + *outlen = mp_unsigned_bin_size(a); + return mp_to_unsigned_bin(a, b); +} +#endif
--- a/bn_mp_toom_mul.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_toom_mul.c Fri May 06 08:59:30 2005 +0000 @@ -17,9 +17,10 @@ /* multiplication using the Toom-Cook 3-way algorithm * - * Much more complicated than Karatsuba but has a lower asymptotic running time of - * O(N**1.464). This algorithm is only particularly useful on VERY large - * inputs (we're talking 1000s of digits here...). + * Much more complicated than Karatsuba but has a lower + * asymptotic running time of O(N**1.464). This algorithm is + * only particularly useful on VERY large inputs + * (we're talking 1000s of digits here...). */ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) {
--- a/bn_mp_unsigned_bin_size.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_unsigned_bin_size.c Fri May 06 08:59:30 2005 +0000 @@ -16,8 +16,7 @@ */ /* get the size for an unsigned equivalent */ -int -mp_unsigned_bin_size (mp_int * a) +int mp_unsigned_bin_size (mp_int * a) { int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0));
--- a/bn_mp_xor.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_xor.c Fri May 06 08:59:30 2005 +0000 @@ -37,7 +37,7 @@ } for (ix = 0; ix < px; ix++) { - + t.dp[ix] ^= x->dp[ix]; } mp_clamp (&t); mp_exch (c, &t);
--- a/bn_mp_zero.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_mp_zero.c Fri May 06 08:59:30 2005 +0000 @@ -16,11 +16,17 @@ */ /* set to zero */ -void -mp_zero (mp_int * a) +void mp_zero (mp_int * a) { + int n; + mp_digit *tmp; + a->sign = MP_ZPOS; a->used = 0; - memset (a->dp, 0, sizeof (mp_digit) * a->alloc); + + tmp = a->dp; + for (n = 0; n < a->alloc; n++) { + *tmp++ = 0; + } } #endif
--- a/bn_prime_tab.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_prime_tab.c Fri May 06 08:59:30 2005 +0000 @@ -14,7 +14,7 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -const mp_digit __prime_tab[] = { +const mp_digit ltm_prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
--- a/bn_s_mp_exptmod.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_s_mp_exptmod.c Fri May 06 08:59:30 2005 +0000 @@ -21,11 +21,12 @@ #define TAB_SIZE 256 #endif -int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) +int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) { mp_int M[TAB_SIZE], res, mu; mp_digit buf; int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + int (*redux)(mp_int*,mp_int*,mp_int*); /* find window size */ x = mp_count_bits (X); @@ -70,11 +71,20 @@ /* create mu, used for Barrett reduction */ if ((err = mp_init (&mu)) != MP_OKAY) { - goto __M; + goto LBL_M; } - if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { - goto __MU; - } + + if (redmode == 0) { + if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { + goto LBL_MU; + } + redux = mp_reduce; + } else { + if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) { + goto LBL_MU; + } + redux = mp_reduce_2k_l; + } /* create M table * @@ -85,23 +95,26 @@ * computed though accept for M[0] and M[1] */ if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) { - goto __MU; + goto LBL_MU; } /* compute the value at M[1<<(winsize-1)] by squaring * M[1] (winsize-1) times */ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __MU; + goto LBL_MU; } for (x = 0; x < (winsize - 1); x++) { + /* square it */ if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __MU; + goto LBL_MU; } - if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { - goto __MU; + + /* reduce modulo P */ + if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { + goto LBL_MU; } } @@ -110,16 +123,16 @@ */ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto __MU; + goto LBL_MU; } - if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) { - goto __MU; + if ((err = redux (&M[x], P, &mu)) != MP_OKAY) { + goto LBL_MU; } } /* setup result */ if ((err = mp_init (&res)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } mp_set (&res, 1); @@ -159,10 +172,10 @@ /* if the bit is zero and mode == 1 then we square */ if (mode == 1 && y == 0) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } continue; } @@ -176,19 +189,19 @@ /* square first */ for (x = 0; x < winsize; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } } /* then multiply */ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } /* empty window and reset */ @@ -203,20 +216,20 @@ /* square then multiply if the bit is set */ for (x = 0; x < bitcpy; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } bitbuf <<= 1; if ((bitbuf & (1 << winsize)) != 0) { /* then multiply */ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } } } @@ -224,9 +237,9 @@ mp_exch (&res, Y); err = MP_OKAY; -__RES:mp_clear (&res); -__MU:mp_clear (&mu); -__M: +LBL_RES:mp_clear (&res); +LBL_MU:mp_clear (&mu); +LBL_M: mp_clear(&M[1]); for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]);
--- a/bn_s_mp_mul_digs.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_s_mp_mul_digs.c Fri May 06 08:59:30 2005 +0000 @@ -19,8 +19,7 @@ * HAC pp. 595, Algorithm 14.12 Modified so you can control how * many digits of output are created. */ -int -s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { mp_int t; int res, pa, pb, ix, iy;
--- a/bn_s_mp_sqr.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bn_s_mp_sqr.c Fri May 06 08:59:30 2005 +0000 @@ -16,8 +16,7 @@ */ /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ -int -s_mp_sqr (mp_int * a, mp_int * b) +int s_mp_sqr (mp_int * a, mp_int * b) { mp_int t; int res, ix, iy, pa;
--- a/bncore.c Sun Dec 19 11:33:56 2004 +0000 +++ b/bncore.c Fri May 06 08:59:30 2005 +0000 @@ -20,11 +20,12 @@ CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) + AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34 */ -int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */ +int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */ + KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400;
--- a/callgraph.txt Sun Dec 19 11:33:56 2004 +0000 +++ b/callgraph.txt Fri May 06 08:59:30 2005 +0000 @@ -245,6 +245,7 @@ | | +--->BN_MP_INIT_MULTI_C | | | +--->BN_MP_CLEAR_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -298,6 +299,7 @@ | | +--->BN_MP_CLEAR_C | +--->BN_MP_SET_C | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_ABS_C | +--->BN_MP_MUL_2D_C | | +--->BN_MP_GROW_C | | +--->BN_MP_LSHD_C @@ -404,6 +406,7 @@ | | | +--->BN_MP_CLEAR_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -700,6 +703,7 @@ | | | +--->BN_MP_INIT_MULTI_C | | | | +--->BN_MP_CLEAR_C | | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_ABS_C | | | +--->BN_MP_MUL_2D_C | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_LSHD_C @@ -753,6 +757,7 @@ | | | +--->BN_MP_CLEAR_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -902,7 +907,64 @@ | | | +--->BN_MP_CLEAR_C | | +--->BN_MP_COPY_C | | | +--->BN_MP_GROW_C -| | +--->BN_MP_ABS_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C | | +--->BN_MP_SET_C | | | +--->BN_MP_ZERO_C | | +--->BN_MP_DIV_2_C @@ -933,6 +995,66 @@ | +--->BN_MP_INVMOD_SLOW_C | | +--->BN_MP_INIT_MULTI_C | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C | | +--->BN_MP_COPY_C | | | +--->BN_MP_GROW_C | | +--->BN_MP_SET_C @@ -968,6 +1090,470 @@ | +--->BN_MP_COPY_C | | +--->BN_MP_GROW_C +--->BN_MP_CLEAR_MULTI_C ++--->BN_MP_REDUCE_IS_2K_L_C ++--->BN_S_MP_EXPTMOD_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_REDUCE_SETUP_C +| | +--->BN_MP_2EXPT_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_REDUCE_C +| | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_D_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_REDUCE_2K_SETUP_L_C +| | +--->BN_MP_2EXPT_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_REDUCE_2K_L_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_SQR_C +| | +--->BN_MP_TOOM_SQR_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_KARATSUBA_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | +--->BN_FAST_S_MP_SQR_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_EXCH_C +--->BN_MP_DR_IS_MODULUS_C +--->BN_MP_REDUCE_IS_2K_C | +--->BN_MP_REDUCE_2K_C @@ -1375,122 +1961,190 @@ | | | +--->BN_MP_CLAMP_C | | | +--->BN_MP_EXCH_C | +--->BN_MP_EXCH_C -+--->BN_S_MP_EXPTMOD_C -| +--->BN_MP_COUNT_BITS_C -| +--->BN_MP_REDUCE_SETUP_C -| | +--->BN_MP_2EXPT_C -| | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_GROW_C -| | +--->BN_MP_DIV_C -| | | +--->BN_MP_CMP_MAG_C + + +BN_MP_OR_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_ZERO_C + + +BN_MP_GROW_C + + +BN_MP_COUNT_BITS_C + + +BN_MP_PRIME_FERMAT_C ++--->BN_MP_CMP_D_C ++--->BN_MP_INIT_C ++--->BN_MP_EXPTMOD_C +| +--->BN_MP_INVMOD_C +| | +--->BN_FAST_MP_INVMOD_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C | | | +--->BN_MP_COPY_C | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_INIT_MULTI_C -| | | +--->BN_MP_SET_C -| | | +--->BN_MP_MUL_2D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_SET_C +| | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_ABS_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2D_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_INIT_COPY_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C | | | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_2D_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_INIT_COPY_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_RSHD_C -| | | +--->BN_MP_RSHD_C -| | | +--->BN_MP_MUL_D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CLAMP_C -| +--->BN_MP_MOD_C -| | +--->BN_MP_DIV_C -| | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_MP_COPY_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_INIT_MULTI_C | | | +--->BN_MP_SET_C -| | | +--->BN_MP_MUL_2D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C | | | +--->BN_MP_SUB_C | | | | +--->BN_S_MP_ADD_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C | | | +--->BN_MP_ADD_C | | | | +--->BN_S_MP_ADD_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_2D_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_INIT_COPY_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_RSHD_C -| | | +--->BN_MP_RSHD_C -| | | +--->BN_MP_MUL_D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_ADD_C -| | | +--->BN_S_MP_ADD_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_S_MP_SUB_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_EXCH_C -| +--->BN_MP_COPY_C -| | +--->BN_MP_GROW_C -| +--->BN_MP_SQR_C -| | +--->BN_MP_TOOM_SQR_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INVMOD_SLOW_C | | | +--->BN_MP_INIT_MULTI_C -| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_SET_C +| | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_ABS_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2D_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_INIT_COPY_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SET_C | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_MUL_2_C -| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C | | | +--->BN_MP_ADD_C | | | | +--->BN_S_MP_ADD_C | | | | | +--->BN_MP_GROW_C @@ -1507,58 +2161,417 @@ | | | | +--->BN_S_MP_SUB_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_2_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_2D_C -| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ABS_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_REDUCE_IS_2K_L_C +| +--->BN_S_MP_EXPTMOD_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_REDUCE_SETUP_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C | | | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_C +| | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_INIT_SIZE_C | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C | | | +--->BN_MP_LSHD_C | | | | +--->BN_MP_GROW_C -| | +--->BN_MP_KARATSUBA_SQR_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_S_MP_ADD_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_2K_SETUP_L_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_2K_L_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_RSHD_C | | | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | +--->BN_FAST_S_MP_SQR_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_S_MP_SQR_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| +--->BN_MP_REDUCE_C -| | +--->BN_MP_INIT_COPY_C -| | +--->BN_MP_RSHD_C -| | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C | | +--->BN_MP_MUL_C | | | +--->BN_MP_TOOM_MUL_C | | | | +--->BN_MP_INIT_MULTI_C | | | | +--->BN_MP_MOD_2D_C | | | | | +--->BN_MP_ZERO_C | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C | | | | +--->BN_MP_MUL_2_C | | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_ADD_C @@ -1610,6 +2623,8 @@ | | | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_LSHD_C | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C | | | +--->BN_FAST_S_MP_MUL_DIGS_C | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_CLAMP_C @@ -1617,217 +2632,9 @@ | | | | +--->BN_MP_INIT_SIZE_C | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_EXCH_C -| | +--->BN_S_MP_MUL_HIGH_DIGS_C -| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_MOD_2D_C -| | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_S_MP_MUL_DIGS_C -| | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| | +--->BN_MP_SUB_C -| | | +--->BN_S_MP_ADD_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_S_MP_SUB_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_CMP_D_C | | +--->BN_MP_SET_C | | | +--->BN_MP_ZERO_C -| | +--->BN_MP_LSHD_C -| | | +--->BN_MP_GROW_C -| | +--->BN_MP_ADD_C -| | | +--->BN_S_MP_ADD_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_S_MP_SUB_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_CMP_C -| | | +--->BN_MP_CMP_MAG_C -| | +--->BN_S_MP_SUB_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| +--->BN_MP_MUL_C -| | +--->BN_MP_TOOM_MUL_C -| | | +--->BN_MP_INIT_MULTI_C -| | | +--->BN_MP_MOD_2D_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_MUL_2_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_2_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_2D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_3_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | +--->BN_MP_KARATSUBA_MUL_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_S_MP_MUL_DIGS_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| +--->BN_MP_SET_C -| | +--->BN_MP_ZERO_C -| +--->BN_MP_EXCH_C - - -BN_MP_OR_C -+--->BN_MP_INIT_COPY_C -| +--->BN_MP_COPY_C -| | +--->BN_MP_GROW_C -+--->BN_MP_CLAMP_C -+--->BN_MP_EXCH_C -+--->BN_MP_CLEAR_C - - -BN_MP_ZERO_C - - -BN_MP_GROW_C - - -BN_MP_COUNT_BITS_C - - -BN_MP_PRIME_FERMAT_C -+--->BN_MP_CMP_D_C -+--->BN_MP_INIT_C -+--->BN_MP_EXPTMOD_C -| +--->BN_MP_INVMOD_C -| | +--->BN_FAST_MP_INVMOD_C -| | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_CLEAR_C -| | | +--->BN_MP_COPY_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ABS_C -| | | +--->BN_MP_SET_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_DIV_2_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_CLEAR_MULTI_C -| | | | +--->BN_MP_CLEAR_C -| | +--->BN_MP_INVMOD_SLOW_C -| | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_CLEAR_C -| | | +--->BN_MP_COPY_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_SET_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_DIV_2_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_CLEAR_MULTI_C -| | | | +--->BN_MP_CLEAR_C -| +--->BN_MP_CLEAR_C -| +--->BN_MP_ABS_C -| | +--->BN_MP_COPY_C -| | | +--->BN_MP_GROW_C -| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_EXCH_C | +--->BN_MP_DR_IS_MODULUS_C | +--->BN_MP_REDUCE_IS_2K_C | | +--->BN_MP_REDUCE_2K_C @@ -2235,364 +3042,6 @@ | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_EXCH_C | | +--->BN_MP_EXCH_C -| +--->BN_S_MP_EXPTMOD_C -| | +--->BN_MP_COUNT_BITS_C -| | +--->BN_MP_REDUCE_SETUP_C -| | | +--->BN_MP_2EXPT_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_DIV_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_MP_COPY_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_SET_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_2D_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_INIT_COPY_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_MOD_C -| | | +--->BN_MP_DIV_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_MP_COPY_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_SET_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_2D_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_INIT_COPY_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| | +--->BN_MP_COPY_C -| | | +--->BN_MP_GROW_C -| | +--->BN_MP_SQR_C -| | | +--->BN_MP_TOOM_SQR_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_MUL_2_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_2_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_3_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_KARATSUBA_SQR_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | +--->BN_FAST_S_MP_SQR_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_S_MP_SQR_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | +--->BN_MP_REDUCE_C -| | | +--->BN_MP_INIT_COPY_C -| | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_MUL_C -| | | | +--->BN_MP_TOOM_MUL_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_3_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | +--->BN_S_MP_MUL_HIGH_DIGS_C -| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MOD_2D_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_S_MP_MUL_DIGS_C -| | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SET_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_S_MP_SUB_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_MUL_C -| | | +--->BN_MP_TOOM_MUL_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_MUL_2_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_2_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_3_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_KARATSUBA_MUL_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_S_MP_MUL_DIGS_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | +--->BN_MP_SET_C -| | | +--->BN_MP_ZERO_C -| | +--->BN_MP_EXCH_C +--->BN_MP_CMP_C | +--->BN_MP_CMP_MAG_C +--->BN_MP_CLEAR_C @@ -2618,6 +3067,7 @@ | | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -2838,6 +3288,7 @@ | | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -2894,7 +3345,65 @@ | | +--->BN_MP_CLEAR_C | +--->BN_MP_COPY_C | | +--->BN_MP_GROW_C -| +--->BN_MP_ABS_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_ABS_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C | +--->BN_MP_SET_C | | +--->BN_MP_ZERO_C | +--->BN_MP_DIV_2_C @@ -2926,6 +3435,67 @@ | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_INIT_C | | +--->BN_MP_CLEAR_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_ABS_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C | +--->BN_MP_COPY_C | | +--->BN_MP_GROW_C | +--->BN_MP_SET_C @@ -2978,7 +3548,65 @@ | +--->BN_MP_CLEAR_C +--->BN_MP_COPY_C | +--->BN_MP_GROW_C -+--->BN_MP_ABS_C ++--->BN_MP_MOD_C +| +--->BN_MP_INIT_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +--->BN_MP_SET_C | +--->BN_MP_ZERO_C +--->BN_MP_DIV_2_C @@ -3313,6 +3941,7 @@ | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_CLEAR_C | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_ABS_C | +--->BN_MP_MUL_2D_C | | +--->BN_MP_GROW_C | | +--->BN_MP_LSHD_C @@ -3465,7 +4094,55 @@ | | | | | | +--->BN_MP_CLEAR_C | | | | | +--->BN_MP_COPY_C | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ABS_C +| | | | | +--->BN_MP_MOD_C +| | | | | | +--->BN_MP_DIV_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | | | +--->BN_MP_ABS_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | | | +--->BN_MP_CLEAR_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C | | | | | +--->BN_MP_DIV_2_C | | | | | | +--->BN_MP_GROW_C | | | | | | +--->BN_MP_CLAMP_C @@ -3493,6 +4170,57 @@ | | | | +--->BN_MP_INVMOD_SLOW_C | | | | | +--->BN_MP_INIT_MULTI_C | | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_MOD_C +| | | | | | +--->BN_MP_DIV_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | | | +--->BN_MP_ABS_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | | | +--->BN_MP_CLEAR_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C | | | | | +--->BN_MP_COPY_C | | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_DIV_2_C @@ -3525,6 +4253,437 @@ | | | | +--->BN_MP_COPY_C | | | | | +--->BN_MP_GROW_C | | | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_REDUCE_IS_2K_L_C +| | | +--->BN_S_MP_EXPTMOD_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_REDUCE_SETUP_C +| | | | | +--->BN_MP_2EXPT_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_REDUCE_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_C +| | | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | | | +--->BN_MP_COPY_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_MUL_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_3_C +| | | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_REDUCE_2K_SETUP_L_C +| | | | | +--->BN_MP_2EXPT_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_REDUCE_2K_L_C +| | | | | +--->BN_MP_MUL_C +| | | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | | | +--->BN_MP_COPY_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_MUL_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_3_C +| | | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_SQR_C +| | | | | +--->BN_MP_TOOM_SQR_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_SQR_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SQR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C | | | +--->BN_MP_DR_IS_MODULUS_C | | | +--->BN_MP_REDUCE_IS_2K_C | | | | +--->BN_MP_REDUCE_2K_C @@ -3895,343 +5054,6 @@ | | | | | | +--->BN_MP_CLAMP_C | | | | | | +--->BN_MP_EXCH_C | | | | +--->BN_MP_EXCH_C -| | | +--->BN_S_MP_EXPTMOD_C -| | | | +--->BN_MP_COUNT_BITS_C -| | | | +--->BN_MP_REDUCE_SETUP_C -| | | | | +--->BN_MP_2EXPT_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_DIV_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_MP_COPY_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_MUL_D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MOD_C -| | | | | +--->BN_MP_DIV_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_MP_COPY_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_MUL_D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_COPY_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_SQR_C -| | | | | +--->BN_MP_TOOM_SQR_C -| | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | +--->BN_MP_MOD_2D_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_MUL_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_3_C -| | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_EXCH_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_KARATSUBA_SQR_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_FAST_S_MP_SQR_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SQR_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_REDUCE_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_MUL_C -| | | | | | +--->BN_MP_TOOM_MUL_C -| | | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | | +--->BN_MP_MOD_2D_C -| | | | | | | | +--->BN_MP_ZERO_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_MUL_2_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_ADD_C -| | | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_SUB_C -| | | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_DIV_2_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_LSHD_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_MUL_D_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_DIV_3_C -| | | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | | +--->BN_MP_EXCH_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_SUB_C -| | | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_ADD_C -| | | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_S_MP_MUL_HIGH_DIGS_C -| | | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_C -| | | | | +--->BN_MP_TOOM_MUL_C -| | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | +--->BN_MP_MOD_2D_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_MUL_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_3_C -| | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_EXCH_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_EXCH_C | | +--->BN_MP_CMP_C | | | +--->BN_MP_CMP_MAG_C | | +--->BN_MP_SQRMOD_C @@ -4322,6 +5144,7 @@ | | | | | +--->BN_MP_ZERO_C | | | | | +--->BN_MP_INIT_MULTI_C | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_ABS_C | | | | | +--->BN_MP_MUL_2D_C | | | | | | +--->BN_MP_GROW_C | | | | | | +--->BN_MP_LSHD_C @@ -4548,6 +5371,7 @@ | | +--->BN_MP_CLEAR_C | +--->BN_MP_SET_C | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_ABS_C | +--->BN_MP_MUL_2D_C | | +--->BN_MP_GROW_C | | +--->BN_MP_LSHD_C @@ -4743,7 +5567,55 @@ | | | | | +--->BN_MP_CLEAR_C | | | | +--->BN_MP_COPY_C | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | | +--->BN_MP_ABS_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C | | | | +--->BN_MP_DIV_2_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_CLAMP_C @@ -4771,6 +5643,57 @@ | | | +--->BN_MP_INVMOD_SLOW_C | | | | +--->BN_MP_INIT_MULTI_C | | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | | +--->BN_MP_ABS_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C | | | | +--->BN_MP_COPY_C | | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_DIV_2_C @@ -4803,6 +5726,437 @@ | | | +--->BN_MP_COPY_C | | | | +--->BN_MP_GROW_C | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_REDUCE_IS_2K_L_C +| | +--->BN_S_MP_EXPTMOD_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_REDUCE_SETUP_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_2K_SETUP_L_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_2K_L_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C | | +--->BN_MP_DR_IS_MODULUS_C | | +--->BN_MP_REDUCE_IS_2K_C | | | +--->BN_MP_REDUCE_2K_C @@ -5173,343 +6527,6 @@ | | | | | +--->BN_MP_CLAMP_C | | | | | +--->BN_MP_EXCH_C | | | +--->BN_MP_EXCH_C -| | +--->BN_S_MP_EXPTMOD_C -| | | +--->BN_MP_COUNT_BITS_C -| | | +--->BN_MP_REDUCE_SETUP_C -| | | | +--->BN_MP_2EXPT_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_DIV_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_MP_COPY_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MOD_C -| | | | +--->BN_MP_DIV_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_MP_COPY_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_COPY_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_SQR_C -| | | | +--->BN_MP_TOOM_SQR_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_MUL_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_3_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_KARATSUBA_SQR_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_FAST_S_MP_SQR_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_SQR_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_REDUCE_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_MUL_C -| | | | | +--->BN_MP_TOOM_MUL_C -| | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | +--->BN_MP_MOD_2D_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_3_C -| | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_EXCH_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C -| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_C -| | | | +--->BN_MP_TOOM_MUL_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_MUL_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_3_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_EXCH_C | +--->BN_MP_CMP_C | | +--->BN_MP_CMP_MAG_C | +--->BN_MP_SQRMOD_C @@ -5600,6 +6617,7 @@ | | | | +--->BN_MP_ZERO_C | | | | +--->BN_MP_INIT_MULTI_C | | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_ABS_C | | | | +--->BN_MP_MUL_2D_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_LSHD_C @@ -5809,6 +6827,7 @@ | | | +--->BN_MP_ZERO_C | | | +--->BN_MP_INIT_MULTI_C | | | +--->BN_MP_SET_C +| | | +--->BN_MP_ABS_C | | | +--->BN_MP_MUL_2D_C | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_LSHD_C @@ -5865,6 +6884,7 @@ | | | +--->BN_MP_GROW_C | | +--->BN_MP_ZERO_C | | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -6284,6 +7304,7 @@ | | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -6482,7 +7503,55 @@ | | | | | +--->BN_MP_CLEAR_C | | | | +--->BN_MP_COPY_C | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | | +--->BN_MP_ABS_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C | | | | +--->BN_MP_DIV_2_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_CLAMP_C @@ -6510,6 +7579,57 @@ | | | +--->BN_MP_INVMOD_SLOW_C | | | | +--->BN_MP_INIT_MULTI_C | | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COUNT_BITS_C +| | | | | | +--->BN_MP_ABS_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | | +--->BN_MP_CLEAR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C | | | | +--->BN_MP_COPY_C | | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_DIV_2_C @@ -6542,6 +7662,437 @@ | | | +--->BN_MP_COPY_C | | | | +--->BN_MP_GROW_C | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_REDUCE_IS_2K_L_C +| | +--->BN_S_MP_EXPTMOD_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_REDUCE_SETUP_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_2K_SETUP_L_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_2K_L_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C | | +--->BN_MP_DR_IS_MODULUS_C | | +--->BN_MP_REDUCE_IS_2K_C | | | +--->BN_MP_REDUCE_2K_C @@ -6912,343 +8463,6 @@ | | | | | +--->BN_MP_CLAMP_C | | | | | +--->BN_MP_EXCH_C | | | +--->BN_MP_EXCH_C -| | +--->BN_S_MP_EXPTMOD_C -| | | +--->BN_MP_COUNT_BITS_C -| | | +--->BN_MP_REDUCE_SETUP_C -| | | | +--->BN_MP_2EXPT_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_DIV_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_MP_COPY_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MOD_C -| | | | +--->BN_MP_DIV_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_MP_COPY_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_COPY_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_SQR_C -| | | | +--->BN_MP_TOOM_SQR_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_MUL_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_3_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_KARATSUBA_SQR_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_FAST_S_MP_SQR_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_SQR_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_REDUCE_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_MUL_C -| | | | | +--->BN_MP_TOOM_MUL_C -| | | | | | +--->BN_MP_INIT_MULTI_C -| | | | | | +--->BN_MP_MOD_2D_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_2_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_2D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_MUL_D_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_DIV_3_C -| | | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | | +--->BN_MP_EXCH_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_SUB_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_ADD_C -| | | | | | | +--->BN_S_MP_ADD_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | | +--->BN_S_MP_SUB_C -| | | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C -| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_C -| | | | +--->BN_MP_TOOM_MUL_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_MUL_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_3_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_EXCH_C | +--->BN_MP_CMP_C | | +--->BN_MP_CMP_MAG_C | +--->BN_MP_SQRMOD_C @@ -7339,6 +8553,7 @@ | | | | +--->BN_MP_ZERO_C | | | | +--->BN_MP_INIT_MULTI_C | | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_ABS_C | | | | +--->BN_MP_MUL_2D_C | | | | | +--->BN_MP_GROW_C | | | | | +--->BN_MP_LSHD_C @@ -7391,6 +8606,67 @@ +--->BN_MP_INIT_MULTI_C | +--->BN_MP_INIT_C | +--->BN_MP_CLEAR_C ++--->BN_MP_MOD_C +| +--->BN_MP_INIT_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +--->BN_MP_COPY_C | +--->BN_MP_GROW_C +--->BN_MP_SET_C @@ -7465,6 +8741,7 @@ | +--->BN_MP_ZERO_C | +--->BN_MP_SET_C | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_ABS_C | +--->BN_MP_MUL_2D_C | | +--->BN_MP_GROW_C | | +--->BN_MP_LSHD_C @@ -7588,6 +8865,107 @@ | +--->BN_MP_CLEAR_C +BN_MP_REDUCE_2K_L_C ++--->BN_MP_INIT_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_S_MP_ADD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C + + BN_REVERSE_C @@ -7655,6 +9033,18 @@ +--->BN_MP_CLEAR_C +BN_MP_REDUCE_2K_SETUP_L_C ++--->BN_MP_INIT_C ++--->BN_MP_2EXPT_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_GROW_C ++--->BN_MP_COUNT_BITS_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C + + BN_MP_READ_RADIX_C +--->BN_MP_ZERO_C +--->BN_MP_MUL_D_C @@ -7928,6 +9318,7 @@ | | +--->BN_MP_ZERO_C | | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_SET_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -7966,6 +9357,226 @@ | | | +--->BN_MP_GROW_C | | | +--->BN_MP_CLAMP_C | | +--->BN_MP_CLAMP_C ++--->BN_MP_REDUCE_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_S_MP_MUL_HIGH_DIGS_C +| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_D_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_REDUCE_2K_SETUP_L_C +| +--->BN_MP_2EXPT_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_GROW_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_REDUCE_2K_L_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +--->BN_MP_MOD_C | +--->BN_MP_DIV_C | | +--->BN_MP_CMP_MAG_C @@ -7974,6 +9585,7 @@ | | +--->BN_MP_ZERO_C | | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_SET_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -8092,121 +9704,6 @@ | | +--->BN_MP_INIT_SIZE_C | | +--->BN_MP_CLAMP_C | | +--->BN_MP_EXCH_C -+--->BN_MP_REDUCE_C -| +--->BN_MP_INIT_COPY_C -| +--->BN_MP_RSHD_C -| | +--->BN_MP_ZERO_C -| +--->BN_MP_MUL_C -| | +--->BN_MP_TOOM_MUL_C -| | | +--->BN_MP_INIT_MULTI_C -| | | +--->BN_MP_MOD_2D_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_2_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_2_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_2D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MUL_D_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_DIV_3_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLEAR_MULTI_C -| | +--->BN_MP_KARATSUBA_MUL_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_S_MP_MUL_DIGS_C -| | | +--->BN_MP_INIT_SIZE_C -| | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| +--->BN_S_MP_MUL_HIGH_DIGS_C -| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_INIT_SIZE_C -| | +--->BN_MP_CLAMP_C -| | +--->BN_MP_EXCH_C -| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | +--->BN_MP_GROW_C -| | +--->BN_MP_CLAMP_C -| +--->BN_MP_MOD_2D_C -| | +--->BN_MP_ZERO_C -| | +--->BN_MP_CLAMP_C -| +--->BN_S_MP_MUL_DIGS_C -| | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_INIT_SIZE_C -| | +--->BN_MP_CLAMP_C -| | +--->BN_MP_EXCH_C -| +--->BN_MP_SUB_C -| | +--->BN_S_MP_ADD_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_CMP_MAG_C -| | +--->BN_S_MP_SUB_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| +--->BN_MP_CMP_D_C -| +--->BN_MP_SET_C -| | +--->BN_MP_ZERO_C -| +--->BN_MP_LSHD_C -| | +--->BN_MP_GROW_C -| +--->BN_MP_ADD_C -| | +--->BN_S_MP_ADD_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_CMP_MAG_C -| | +--->BN_S_MP_SUB_C -| | | +--->BN_MP_GROW_C -| | | +--->BN_MP_CLAMP_C -| +--->BN_MP_CMP_C -| | +--->BN_MP_CMP_MAG_C -| +--->BN_S_MP_SUB_C -| | +--->BN_MP_GROW_C -| | +--->BN_MP_CLAMP_C +--->BN_MP_MUL_C | +--->BN_MP_TOOM_MUL_C | | +--->BN_MP_INIT_MULTI_C @@ -8372,6 +9869,7 @@ | +--->BN_MP_CLEAR_C +--->BN_MP_SET_C +--->BN_MP_COUNT_BITS_C ++--->BN_MP_ABS_C +--->BN_MP_MUL_2D_C | +--->BN_MP_GROW_C | +--->BN_MP_LSHD_C @@ -8465,6 +9963,7 @@ | | +--->BN_MP_INIT_MULTI_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -8509,6 +10008,31 @@ | +--->BN_MP_CLAMP_C +BN_MP_TO_SIGNED_BIN_N_C ++--->BN_MP_SIGNED_BIN_SIZE_C +| +--->BN_MP_UNSIGNED_BIN_SIZE_C +| | +--->BN_MP_COUNT_BITS_C ++--->BN_MP_TO_SIGNED_BIN_C +| +--->BN_MP_TO_UNSIGNED_BIN_C +| | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C + + +BN_MP_REDUCE_IS_2K_L_C + + BN_MP_RAND_C +--->BN_MP_ZERO_C +--->BN_MP_ADD_D_C @@ -8536,6 +10060,26 @@ BN_MP_SHRINK_C +BN_MP_TO_UNSIGNED_BIN_N_C ++--->BN_MP_UNSIGNED_BIN_SIZE_C +| +--->BN_MP_COUNT_BITS_C ++--->BN_MP_TO_UNSIGNED_BIN_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C + + BN_MP_REDUCE_C +--->BN_MP_REDUCE_SETUP_C | +--->BN_MP_2EXPT_C @@ -8551,6 +10095,7 @@ | | | +--->BN_MP_CLEAR_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -8766,6 +10311,7 @@ | | | +--->BN_MP_CLEAR_C | | +--->BN_MP_SET_C | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_ABS_C | | +--->BN_MP_MUL_2D_C | | | +--->BN_MP_GROW_C | | | +--->BN_MP_LSHD_C @@ -8912,6 +10458,7 @@ | +--->BN_MP_CMP_MAG_C | +--->BN_MP_ZERO_C | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_ABS_C | +--->BN_MP_MUL_2D_C | | +--->BN_MP_GROW_C | | +--->BN_MP_LSHD_C @@ -9039,6 +10586,7 @@ | +--->BN_S_MP_SUB_C | | +--->BN_MP_GROW_C | | +--->BN_MP_CLAMP_C ++--->BN_MP_NEG_C +--->BN_MP_EXCH_C +--->BN_MP_CLEAR_MULTI_C | +--->BN_MP_CLEAR_C @@ -9078,6 +10626,7 @@ | | +--->BN_MP_CLEAR_C | +--->BN_MP_SET_C | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_ABS_C | +--->BN_MP_MUL_2D_C | | +--->BN_MP_GROW_C | | +--->BN_MP_LSHD_C @@ -9245,7 +10794,56 @@ | | | | +--->BN_MP_CLEAR_C | | | +--->BN_MP_COPY_C | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ABS_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_SET_C +| | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_ABS_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C | | | +--->BN_MP_SET_C | | | | +--->BN_MP_ZERO_C | | | +--->BN_MP_DIV_2_C @@ -9275,6 +10873,58 @@ | | +--->BN_MP_INVMOD_SLOW_C | | | +--->BN_MP_INIT_MULTI_C | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_SET_C +| | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_ABS_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C | | | +--->BN_MP_COPY_C | | | | +--->BN_MP_GROW_C | | | +--->BN_MP_SET_C @@ -9309,6 +10959,443 @@ | | +--->BN_MP_COPY_C | | | +--->BN_MP_GROW_C | +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_REDUCE_IS_2K_L_C +| +--->BN_S_MP_EXPTMOD_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_REDUCE_SETUP_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_2K_SETUP_L_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_2K_L_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_EXCH_C | +--->BN_MP_DR_IS_MODULUS_C | +--->BN_MP_REDUCE_IS_2K_C | | +--->BN_MP_REDUCE_2K_C @@ -9684,349 +11771,6 @@ | | | | +--->BN_MP_CLAMP_C | | | | +--->BN_MP_EXCH_C | | +--->BN_MP_EXCH_C -| +--->BN_S_MP_EXPTMOD_C -| | +--->BN_MP_COUNT_BITS_C -| | +--->BN_MP_REDUCE_SETUP_C -| | | +--->BN_MP_2EXPT_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_DIV_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_MP_COPY_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_SET_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_MOD_C -| | | +--->BN_MP_DIV_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_MP_COPY_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_SET_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_EXCH_C -| | +--->BN_MP_COPY_C -| | | +--->BN_MP_GROW_C -| | +--->BN_MP_SQR_C -| | | +--->BN_MP_TOOM_SQR_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_MUL_2_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_2_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_3_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_KARATSUBA_SQR_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | +--->BN_FAST_S_MP_SQR_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_S_MP_SQR_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | +--->BN_MP_REDUCE_C -| | | +--->BN_MP_RSHD_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_MUL_C -| | | | +--->BN_MP_TOOM_MUL_C -| | | | | +--->BN_MP_INIT_MULTI_C -| | | | | +--->BN_MP_MOD_2D_C -| | | | | | +--->BN_MP_ZERO_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_2_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_2D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_MUL_D_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_DIV_3_C -| | | | | | +--->BN_MP_INIT_SIZE_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | | +--->BN_MP_EXCH_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_KARATSUBA_MUL_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_SUB_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_ADD_C -| | | | | | +--->BN_S_MP_ADD_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CMP_MAG_C -| | | | | | +--->BN_S_MP_SUB_C -| | | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | +--->BN_S_MP_MUL_HIGH_DIGS_C -| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_MOD_2D_C -| | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_S_MP_MUL_DIGS_C -| | | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | | +--->BN_MP_SUB_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_SET_C -| | | | +--->BN_MP_ZERO_C -| | | +--->BN_MP_LSHD_C -| | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_ADD_C -| | | | +--->BN_S_MP_ADD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | | +--->BN_S_MP_SUB_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | +--->BN_MP_CMP_C -| | | | +--->BN_MP_CMP_MAG_C -| | | +--->BN_S_MP_SUB_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | +--->BN_MP_MUL_C -| | | +--->BN_MP_TOOM_MUL_C -| | | | +--->BN_MP_INIT_MULTI_C -| | | | +--->BN_MP_MOD_2D_C -| | | | | +--->BN_MP_ZERO_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_RSHD_C -| | | | | +--->BN_MP_ZERO_C -| | | | +--->BN_MP_MUL_2_C -| | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_2_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_2D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_MUL_D_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_DIV_3_C -| | | | | +--->BN_MP_INIT_SIZE_C -| | | | | +--->BN_MP_CLAMP_C -| | | | | +--->BN_MP_EXCH_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | +--->BN_MP_KARATSUBA_MUL_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_SUB_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_ADD_C -| | | | | +--->BN_S_MP_ADD_C -| | | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_CMP_MAG_C -| | | | | +--->BN_S_MP_SUB_C -| | | | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_LSHD_C -| | | | | +--->BN_MP_GROW_C -| | | | | +--->BN_MP_RSHD_C -| | | | | | +--->BN_MP_ZERO_C -| | | +--->BN_FAST_S_MP_MUL_DIGS_C -| | | | +--->BN_MP_GROW_C -| | | | +--->BN_MP_CLAMP_C -| | | +--->BN_S_MP_MUL_DIGS_C -| | | | +--->BN_MP_INIT_SIZE_C -| | | | +--->BN_MP_CLAMP_C -| | | | +--->BN_MP_EXCH_C -| | +--->BN_MP_SET_C -| | | +--->BN_MP_ZERO_C -| | +--->BN_MP_EXCH_C +--->BN_MP_CMP_C | +--->BN_MP_CMP_MAG_C +--->BN_MP_SQRMOD_C @@ -10118,6 +11862,7 @@ | | | +--->BN_MP_INIT_MULTI_C | | | +--->BN_MP_SET_C | | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_ABS_C | | | +--->BN_MP_MUL_2D_C | | | | +--->BN_MP_GROW_C | | | | +--->BN_MP_LSHD_C
--- a/changes.txt Sun Dec 19 11:33:56 2004 +0000 +++ b/changes.txt Fri May 06 08:59:30 2005 +0000 @@ -1,3 +1,35 @@ +March 12th, 2005 +v0.35 -- Stupid XOR function missing line again... oops. + -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt] + -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ] + -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns. ;-) + -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops + -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly + -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs" + -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny] + -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code! + +February 12th, 2005 +v0.34 -- Fixed two more small errors in mp_prime_random_ex() + -- Fixed overflow in mp_mul_d() [Kevin Kenny] + -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size] + -- Added "large" diminished radix support. Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so + Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4) + -- Updated the manual a bit + -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the + end of Feb/05. Once I get back I'll have tons of free time and I plan to go to town on the book. + As of this release the API will freeze. At least until the book catches up with all the changes. I welcome + bug reports but new algorithms will have to wait. + +December 23rd, 2004 +v0.33 -- Fixed "small" variant for mp_div() which would munge with negative dividends... + -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when + no special flags were set + -- Fixed overflow [minor] bug in fast_s_mp_sqr() + -- Made the makefiles easier to configure the group/user that ltm will install as + -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan) + -- Matt Johnston pointed out a missing semi-colon in mp_exptmod + October 29th, 2004 v0.32 -- Added "makefile.shared" for shared object support -- Added more to the build options/configs in the manual
--- a/demo/demo.c Sun Dec 19 11:33:56 2004 +0000 +++ b/demo/demo.c Fri May 06 08:59:30 2005 +0000 @@ -9,15 +9,16 @@ #include "tommath.h" -void ndraw(mp_int *a, char *name) +void ndraw(mp_int * a, char *name) { - char buf[4096]; + char buf[16000]; + printf("%s: ", name); - mp_toradix(a, buf, 64); + mp_toradix(a, buf, 10); printf("%s\n", buf); } -static void draw(mp_int *a) +static void draw(mp_int * a) { ndraw(a, ""); } @@ -39,20 +40,23 @@ int myrng(unsigned char *dst, int len, void *dat) { int x; - for (x = 0; x < len; x++) dst[x] = rand() & 0xFF; + + for (x = 0; x < len; x++) + dst[x] = rand() & 0xFF; return len; } - char cmd[4096], buf[4096]; +char cmd[4096], buf[4096]; int main(void) { mp_int a, b, c, d, e, f; - unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, inv_n, - div2_n, mul2_n, add_d_n, sub_d_n, t; + unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, + gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n, t; unsigned rr; int i, n, err, cnt, ix, old_kara_m, old_kara_s; + mp_digit mp; mp_init(&a); @@ -65,108 +69,152 @@ srand(time(NULL)); #if 0 - // test mp_get_int - printf("Testing: mp_get_int\n"); - for(i=0;i<1000;++i) { - t = ((unsigned long)rand()*rand()+1)&0xFFFFFFFF; - mp_set_int(&a,t); - if (t!=mp_get_int(&a)) { + // test montgomery + printf("Testing montgomery...\n"); + for (i = 1; i < 10; i++) { + printf("Testing digit size: %d\n", i); + for (n = 0; n < 1000; n++) { + mp_rand(&a, i); + a.dp[0] |= 1; + + // let's see if R is right + mp_montgomery_calc_normalization(&b, &a); + mp_montgomery_setup(&a, &mp); + + // now test a random reduction + for (ix = 0; ix < 100; ix++) { + mp_rand(&c, 1 + abs(rand()) % (2*i)); + mp_copy(&c, &d); + mp_copy(&c, &e); + + mp_mod(&d, &a, &d); + mp_montgomery_reduce(&c, &a, mp); + mp_mulmod(&c, &b, &a, &c); + + if (mp_cmp(&c, &d) != MP_EQ) { +printf("d = e mod a, c = e MOD a\n"); +mp_todecimal(&a, buf); printf("a = %s\n", buf); +mp_todecimal(&e, buf); printf("e = %s\n", buf); +mp_todecimal(&d, buf); printf("d = %s\n", buf); +mp_todecimal(&c, buf); printf("c = %s\n", buf); +printf("compare no compare!\n"); exit(EXIT_FAILURE); } + } + } + } + printf("done\n"); + + // test mp_get_int + printf("Testing: mp_get_int\n"); + for (i = 0; i < 1000; ++i) { + t = ((unsigned long) rand() * rand() + 1) & 0xFFFFFFFF; + mp_set_int(&a, t); + if (t != mp_get_int(&a)) { + printf("mp_get_int() bad result!\n"); + return 1; + } + } + mp_set_int(&a, 0); + if (mp_get_int(&a) != 0) { + printf("mp_get_int() bad result!\n"); + return 1; + } + mp_set_int(&a, 0xffffffff); + if (mp_get_int(&a) != 0xffffffff) { printf("mp_get_int() bad result!\n"); return 1; - } - } - mp_set_int(&a,0); - if (mp_get_int(&a)!=0) - { printf("mp_get_int() bad result!\n"); - return 1; - } - mp_set_int(&a,0xffffffff); - if (mp_get_int(&a)!=0xffffffff) - { printf("mp_get_int() bad result!\n"); - return 1; - } + } + // test mp_sqrt + printf("Testing: mp_sqrt\n"); + for (i = 0; i < 1000; ++i) { + printf("%6d\r", i); + fflush(stdout); + n = (rand() & 15) + 1; + mp_rand(&a, n); + if (mp_sqrt(&a, &b) != MP_OKAY) { + printf("mp_sqrt() error!\n"); + return 1; + } + mp_n_root(&a, 2, &a); + if (mp_cmp_mag(&b, &a) != MP_EQ) { + printf("mp_sqrt() bad result!\n"); + return 1; + } + } - // test mp_sqrt - printf("Testing: mp_sqrt\n"); - for (i=0;i<1000;++i) { - printf("%6d\r", i); fflush(stdout); - n = (rand()&15)+1; - mp_rand(&a,n); - if (mp_sqrt(&a,&b) != MP_OKAY) - { printf("mp_sqrt() error!\n"); - return 1; - } - mp_n_root(&a,2,&a); - if (mp_cmp_mag(&b,&a) != MP_EQ) - { printf("mp_sqrt() bad result!\n"); - return 1; - } - } + printf("\nTesting: mp_is_square\n"); + for (i = 0; i < 1000; ++i) { + printf("%6d\r", i); + fflush(stdout); - printf("\nTesting: mp_is_square\n"); - for (i=0;i<1000;++i) { - printf("%6d\r", i); fflush(stdout); + /* test mp_is_square false negatives */ + n = (rand() & 7) + 1; + mp_rand(&a, n); + mp_sqr(&a, &a); + if (mp_is_square(&a, &n) != MP_OKAY) { + printf("fn:mp_is_square() error!\n"); + return 1; + } + if (n == 0) { + printf("fn:mp_is_square() bad result!\n"); + return 1; + } - /* test mp_is_square false negatives */ - n = (rand()&7)+1; - mp_rand(&a,n); - mp_sqr(&a,&a); - if (mp_is_square(&a,&n)!=MP_OKAY) { - printf("fn:mp_is_square() error!\n"); - return 1; - } - if (n==0) { - printf("fn:mp_is_square() bad result!\n"); - return 1; - } + /* test for false positives */ + mp_add_d(&a, 1, &a); + if (mp_is_square(&a, &n) != MP_OKAY) { + printf("fp:mp_is_square() error!\n"); + return 1; + } + if (n == 1) { + printf("fp:mp_is_square() bad result!\n"); + return 1; + } - /* test for false positives */ - mp_add_d(&a, 1, &a); - if (mp_is_square(&a,&n)!=MP_OKAY) { - printf("fp:mp_is_square() error!\n"); - return 1; - } - if (n==1) { - printf("fp:mp_is_square() bad result!\n"); - return 1; - } - - } - printf("\n\n"); + } + printf("\n\n"); /* test for size */ - for (ix = 10; ix < 256; ix++) { - printf("Testing (not safe-prime): %9d bits \r", ix); fflush(stdout); - err = mp_prime_random_ex(&a, 8, ix, (rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON, myrng, NULL); - if (err != MP_OKAY) { - printf("failed with err code %d\n", err); - return EXIT_FAILURE; - } - if (mp_count_bits(&a) != ix) { - printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); - return EXIT_FAILURE; - } + for (ix = 10; ix < 128; ix++) { + printf("Testing (not safe-prime): %9d bits \r", ix); + fflush(stdout); + err = + mp_prime_random_ex(&a, 8, ix, + (rand() & 1) ? LTM_PRIME_2MSB_OFF : + LTM_PRIME_2MSB_ON, myrng, NULL); + if (err != MP_OKAY) { + printf("failed with err code %d\n", err); + return EXIT_FAILURE; + } + if (mp_count_bits(&a) != ix) { + printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); + return EXIT_FAILURE; + } } - for (ix = 16; ix < 256; ix++) { - printf("Testing ( safe-prime): %9d bits \r", ix); fflush(stdout); - err = mp_prime_random_ex(&a, 8, ix, ((rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON)|LTM_PRIME_SAFE, myrng, NULL); - if (err != MP_OKAY) { - printf("failed with err code %d\n", err); - return EXIT_FAILURE; - } - if (mp_count_bits(&a) != ix) { - printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); - return EXIT_FAILURE; - } - /* let's see if it's really a safe prime */ - mp_sub_d(&a, 1, &a); - mp_div_2(&a, &a); - mp_prime_is_prime(&a, 8, &cnt); - if (cnt != MP_YES) { - printf("sub is not prime!\n"); - return EXIT_FAILURE; - } + for (ix = 16; ix < 128; ix++) { + printf("Testing ( safe-prime): %9d bits \r", ix); + fflush(stdout); + err = + mp_prime_random_ex(&a, 8, ix, + ((rand() & 1) ? LTM_PRIME_2MSB_OFF : + LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE, myrng, + NULL); + if (err != MP_OKAY) { + printf("failed with err code %d\n", err); + return EXIT_FAILURE; + } + if (mp_count_bits(&a) != ix) { + printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); + return EXIT_FAILURE; + } + /* let's see if it's really a safe prime */ + mp_sub_d(&a, 1, &a); + mp_div_2(&a, &a); + mp_prime_is_prime(&a, 8, &cnt); + if (cnt != MP_YES) { + printf("sub is not prime!\n"); + return EXIT_FAILURE; + } } printf("\n\n"); @@ -194,51 +242,56 @@ printf("testing mp_cnt_lsb...\n"); mp_set(&a, 1); for (ix = 0; ix < 1024; ix++) { - if (mp_cnt_lsb(&a) != ix) { - printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a)); - return 0; - } - mp_mul_2(&a, &a); + if (mp_cnt_lsb(&a) != ix) { + printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a)); + return 0; + } + mp_mul_2(&a, &a); } /* test mp_reduce_2k */ printf("Testing mp_reduce_2k...\n"); for (cnt = 3; cnt <= 128; ++cnt) { - mp_digit tmp; - mp_2expt(&a, cnt); - mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */ + mp_digit tmp; + + mp_2expt(&a, cnt); + mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */ - printf("\nTesting %4d bits", cnt); - printf("(%d)", mp_reduce_is_2k(&a)); - mp_reduce_2k_setup(&a, &tmp); - printf("(%d)", tmp); - for (ix = 0; ix < 1000; ix++) { - if (!(ix & 127)) {printf("."); fflush(stdout); } - mp_rand(&b, (cnt/DIGIT_BIT + 1) * 2); - mp_copy(&c, &b); - mp_mod(&c, &a, &c); - mp_reduce_2k(&b, &a, 1); - if (mp_cmp(&c, &b)) { - printf("FAILED\n"); - exit(0); - } - } - } + printf("\nTesting %4d bits", cnt); + printf("(%d)", mp_reduce_is_2k(&a)); + mp_reduce_2k_setup(&a, &tmp); + printf("(%d)", tmp); + for (ix = 0; ix < 1000; ix++) { + if (!(ix & 127)) { + printf("."); + fflush(stdout); + } + mp_rand(&b, (cnt / DIGIT_BIT + 1) * 2); + mp_copy(&c, &b); + mp_mod(&c, &a, &c); + mp_reduce_2k(&b, &a, 2); + if (mp_cmp(&c, &b)) { + printf("FAILED\n"); + exit(0); + } + } + } /* test mp_div_3 */ printf("Testing mp_div_3...\n"); mp_set(&d, 3); - for (cnt = 0; cnt < 10000; ) { + for (cnt = 0; cnt < 10000;) { mp_digit r1, r2; - if (!(++cnt & 127)) printf("%9d\r", cnt); + if (!(++cnt & 127)) + printf("%9d\r", cnt); mp_rand(&a, abs(rand()) % 128 + 1); mp_div(&a, &d, &b, &e); mp_div_3(&a, &c, &r2); if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) { - printf("\n\nmp_div_3 => Failure\n"); + printf("\n\nmp_div_3 => Failure\n"); } } printf("\n\nPassed div_3 testing\n"); @@ -246,270 +299,438 @@ /* test the DR reduction */ printf("testing mp_dr_reduce...\n"); for (cnt = 2; cnt < 32; cnt++) { - printf("%d digit modulus\n", cnt); - mp_grow(&a, cnt); - mp_zero(&a); - for (ix = 1; ix < cnt; ix++) { - a.dp[ix] = MP_MASK; - } - a.used = cnt; - a.dp[0] = 3; + printf("%d digit modulus\n", cnt); + mp_grow(&a, cnt); + mp_zero(&a); + for (ix = 1; ix < cnt; ix++) { + a.dp[ix] = MP_MASK; + } + a.used = cnt; + a.dp[0] = 3; - mp_rand(&b, cnt - 1); - mp_copy(&b, &c); + mp_rand(&b, cnt - 1); + mp_copy(&b, &c); rr = 0; do { - if (!(rr & 127)) { printf("%9lu\r", rr); fflush(stdout); } - mp_sqr(&b, &b); mp_add_d(&b, 1, &b); - mp_copy(&b, &c); + if (!(rr & 127)) { + printf("%9lu\r", rr); + fflush(stdout); + } + mp_sqr(&b, &b); + mp_add_d(&b, 1, &b); + mp_copy(&b, &c); - mp_mod(&b, &a, &b); - mp_dr_reduce(&c, &a, (((mp_digit)1)<<DIGIT_BIT)-a.dp[0]); + mp_mod(&b, &a, &b); + mp_dr_reduce(&c, &a, (((mp_digit) 1) << DIGIT_BIT) - a.dp[0]); - if (mp_cmp(&b, &c) != MP_EQ) { - printf("Failed on trial %lu\n", rr); exit(-1); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("Failed on trial %lu\n", rr); + exit(-1); - } + } } while (++rr < 500); printf("Passed DR test for %d digits\n", cnt); } #endif +/* test the mp_reduce_2k_l code */ +#if 0 +#if 0 +/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */ + mp_2expt(&a, 1024); + mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16); + mp_sub(&a, &b, &a); +#elif 1 +/* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */ + mp_2expt(&a, 2048); + mp_read_radix(&b, + "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F", + 16); + mp_sub(&a, &b, &a); +#endif + + mp_todecimal(&a, buf); + printf("p==%s\n", buf); +/* now mp_reduce_is_2k_l() should return */ + if (mp_reduce_is_2k_l(&a) != 1) { + printf("mp_reduce_is_2k_l() return 0, should be 1\n"); + return EXIT_FAILURE; + } + mp_reduce_2k_setup_l(&a, &d); + /* now do a million square+1 to see if it varies */ + mp_rand(&b, 64); + mp_mod(&b, &a, &b); + mp_copy(&b, &c); + printf("testing mp_reduce_2k_l..."); + fflush(stdout); + for (cnt = 0; cnt < (1UL << 20); cnt++) { + mp_sqr(&b, &b); + mp_add_d(&b, 1, &b); + mp_reduce_2k_l(&b, &a, &d); + mp_sqr(&c, &c); + mp_add_d(&c, 1, &c); + mp_mod(&c, &a, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("mp_reduce_2k_l() failed at step %lu\n", cnt); + mp_tohex(&b, buf); + printf("b == %s\n", buf); + mp_tohex(&c, buf); + printf("c == %s\n", buf); + return EXIT_FAILURE; + } + } + printf("...Passed\n"); +#endif + div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n = - sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n= 0; + sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = + sub_d_n = 0; /* force KARA and TOOM to enable despite cutoffs */ KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 110; - TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 150; + TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 150; for (;;) { - /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ - switch (abs(rand()) % 7) { - case 0: mp_clear(&a); mp_init(&a); break; - case 1: mp_clear(&b); mp_init(&b); break; - case 2: mp_clear(&c); mp_init(&c); break; - case 3: mp_clear(&d); mp_init(&d); break; - case 4: mp_clear(&e); mp_init(&e); break; - case 5: mp_clear(&f); mp_init(&f); break; - case 6: break; /* don't clear any */ - } + /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ + switch (abs(rand()) % 7) { + case 0: + mp_clear(&a); + mp_init(&a); + break; + case 1: + mp_clear(&b); + mp_init(&b); + break; + case 2: + mp_clear(&c); + mp_init(&c); + break; + case 3: + mp_clear(&d); + mp_init(&d); + break; + case 4: + mp_clear(&e); + mp_init(&e); + break; + case 5: + mp_clear(&f); + mp_init(&f); + break; + case 6: + break; /* don't clear any */ + } - printf("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ", add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n); - fgets(cmd, 4095, stdin); - cmd[strlen(cmd)-1] = 0; - printf("%s ]\r",cmd); fflush(stdout); - if (!strcmp(cmd, "mul2d")) { ++mul2d_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); sscanf(buf, "%d", &rr); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); + printf + ("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ", + add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, + expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n); + fgets(cmd, 4095, stdin); + cmd[strlen(cmd) - 1] = 0; + printf("%s ]\r", cmd); + fflush(stdout); + if (!strcmp(cmd, "mul2d")) { + ++mul2d_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + sscanf(buf, "%d", &rr); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); - mp_mul_2d(&a, rr, &a); - a.sign = b.sign; - if (mp_cmp(&a, &b) != MP_EQ) { - printf("mul2d failed, rr == %d\n",rr); - draw(&a); - draw(&b); - return 0; - } - } else if (!strcmp(cmd, "div2d")) { ++div2d_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); sscanf(buf, "%d", &rr); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); + mp_mul_2d(&a, rr, &a); + a.sign = b.sign; + if (mp_cmp(&a, &b) != MP_EQ) { + printf("mul2d failed, rr == %d\n", rr); + draw(&a); + draw(&b); + return 0; + } + } else if (!strcmp(cmd, "div2d")) { + ++div2d_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + sscanf(buf, "%d", &rr); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); - mp_div_2d(&a, rr, &a, &e); - a.sign = b.sign; - if (a.used == b.used && a.used == 0) { a.sign = b.sign = MP_ZPOS; } - if (mp_cmp(&a, &b) != MP_EQ) { - printf("div2d failed, rr == %d\n",rr); - draw(&a); - draw(&b); - return 0; - } - } else if (!strcmp(cmd, "add")) { ++add_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - mp_copy(&a, &d); - mp_add(&d, &b, &d); - if (mp_cmp(&c, &d) != MP_EQ) { - printf("add %lu failure!\n", add_n); -draw(&a);draw(&b);draw(&c);draw(&d); - return 0; - } + mp_div_2d(&a, rr, &a, &e); + a.sign = b.sign; + if (a.used == b.used && a.used == 0) { + a.sign = b.sign = MP_ZPOS; + } + if (mp_cmp(&a, &b) != MP_EQ) { + printf("div2d failed, rr == %d\n", rr); + draw(&a); + draw(&b); + return 0; + } + } else if (!strcmp(cmd, "add")) { + ++add_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_add(&d, &b, &d); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("add %lu failure!\n", add_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + return 0; + } - /* test the sign/unsigned storage functions */ + /* test the sign/unsigned storage functions */ - rr = mp_signed_bin_size(&c); - mp_to_signed_bin(&c, (unsigned char *)cmd); - memset(cmd+rr, rand()&255, sizeof(cmd)-rr); - mp_read_signed_bin(&d, (unsigned char *)cmd, rr); - if (mp_cmp(&c, &d) != MP_EQ) { - printf("mp_signed_bin failure!\n"); - draw(&c); - draw(&d); - return 0; - } + rr = mp_signed_bin_size(&c); + mp_to_signed_bin(&c, (unsigned char *) cmd); + memset(cmd + rr, rand() & 255, sizeof(cmd) - rr); + mp_read_signed_bin(&d, (unsigned char *) cmd, rr); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("mp_signed_bin failure!\n"); + draw(&c); + draw(&d); + return 0; + } - rr = mp_unsigned_bin_size(&c); - mp_to_unsigned_bin(&c, (unsigned char *)cmd); - memset(cmd+rr, rand()&255, sizeof(cmd)-rr); - mp_read_unsigned_bin(&d, (unsigned char *)cmd, rr); - if (mp_cmp_mag(&c, &d) != MP_EQ) { - printf("mp_unsigned_bin failure!\n"); - draw(&c); - draw(&d); - return 0; - } + rr = mp_unsigned_bin_size(&c); + mp_to_unsigned_bin(&c, (unsigned char *) cmd); + memset(cmd + rr, rand() & 255, sizeof(cmd) - rr); + mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr); + if (mp_cmp_mag(&c, &d) != MP_EQ) { + printf("mp_unsigned_bin failure!\n"); + draw(&c); + draw(&d); + return 0; + } - } else if (!strcmp(cmd, "sub")) { ++sub_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - mp_copy(&a, &d); - mp_sub(&d, &b, &d); - if (mp_cmp(&c, &d) != MP_EQ) { - printf("sub %lu failure!\n", sub_n); -draw(&a);draw(&b);draw(&c);draw(&d); - return 0; - } - } else if (!strcmp(cmd, "mul")) { ++mul_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - mp_copy(&a, &d); - mp_mul(&d, &b, &d); - if (mp_cmp(&c, &d) != MP_EQ) { - printf("mul %lu failure!\n", mul_n); -draw(&a);draw(&b);draw(&c);draw(&d); - return 0; - } - } else if (!strcmp(cmd, "div")) { ++div_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&d, buf, 64); + } else if (!strcmp(cmd, "sub")) { + ++sub_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_sub(&d, &b, &d); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("sub %lu failure!\n", sub_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + return 0; + } + } else if (!strcmp(cmd, "mul")) { + ++mul_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_mul(&d, &b, &d); + if (mp_cmp(&c, &d) != MP_EQ) { + printf("mul %lu failure!\n", mul_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + return 0; + } + } else if (!strcmp(cmd, "div")) { + ++div_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&d, buf, 64); - mp_div(&a, &b, &e, &f); - if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) { - printf("div %lu failure!\n", div_n); -draw(&a);draw(&b);draw(&c);draw(&d); draw(&e); draw(&f); - return 0; - } + mp_div(&a, &b, &e, &f); + if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) { + printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e), + mp_cmp(&d, &f)); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + draw(&e); + draw(&f); + return 0; + } - } else if (!strcmp(cmd, "sqr")) { ++sqr_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - mp_copy(&a, &c); - mp_sqr(&c, &c); - if (mp_cmp(&b, &c) != MP_EQ) { - printf("sqr %lu failure!\n", sqr_n); -draw(&a);draw(&b);draw(&c); - return 0; - } - } else if (!strcmp(cmd, "gcd")) { ++gcd_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - mp_copy(&a, &d); - mp_gcd(&d, &b, &d); - d.sign = c.sign; - if (mp_cmp(&c, &d) != MP_EQ) { - printf("gcd %lu failure!\n", gcd_n); -draw(&a);draw(&b);draw(&c);draw(&d); - return 0; - } - } else if (!strcmp(cmd, "lcm")) { ++lcm_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - mp_copy(&a, &d); - mp_lcm(&d, &b, &d); - d.sign = c.sign; - if (mp_cmp(&c, &d) != MP_EQ) { - printf("lcm %lu failure!\n", lcm_n); - draw(&a);draw(&b);draw(&c);draw(&d); - return 0; - } - } else if (!strcmp(cmd, "expt")) { ++expt_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&d, buf, 64); - mp_copy(&a, &e); - mp_exptmod(&e, &b, &c, &e); - if (mp_cmp(&d, &e) != MP_EQ) { - printf("expt %lu failure!\n", expt_n); - draw(&a);draw(&b);draw(&c);draw(&d); draw(&e); - return 0; - } - } else if (!strcmp(cmd, "invmod")) { ++inv_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 64); - mp_invmod(&a, &b, &d); - mp_mulmod(&d,&a,&b,&e); - if (mp_cmp_d(&e, 1) != MP_EQ) { - printf("inv [wrong value from MPI?!] failure\n"); - draw(&a);draw(&b);draw(&c);draw(&d); - mp_gcd(&a, &b, &e); - draw(&e); - return 0; - } + } else if (!strcmp(cmd, "sqr")) { + ++sqr_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_copy(&a, &c); + mp_sqr(&c, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("sqr %lu failure!\n", sqr_n); + draw(&a); + draw(&b); + draw(&c); + return 0; + } + } else if (!strcmp(cmd, "gcd")) { + ++gcd_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_gcd(&d, &b, &d); + d.sign = c.sign; + if (mp_cmp(&c, &d) != MP_EQ) { + printf("gcd %lu failure!\n", gcd_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + return 0; + } + } else if (!strcmp(cmd, "lcm")) { + ++lcm_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_copy(&a, &d); + mp_lcm(&d, &b, &d); + d.sign = c.sign; + if (mp_cmp(&c, &d) != MP_EQ) { + printf("lcm %lu failure!\n", lcm_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + return 0; + } + } else if (!strcmp(cmd, "expt")) { + ++expt_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&d, buf, 64); + mp_copy(&a, &e); + mp_exptmod(&e, &b, &c, &e); + if (mp_cmp(&d, &e) != MP_EQ) { + printf("expt %lu failure!\n", expt_n); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + draw(&e); + return 0; + } + } else if (!strcmp(cmd, "invmod")) { + ++inv_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&c, buf, 64); + mp_invmod(&a, &b, &d); + mp_mulmod(&d, &a, &b, &e); + if (mp_cmp_d(&e, 1) != MP_EQ) { + printf("inv [wrong value from MPI?!] failure\n"); + draw(&a); + draw(&b); + draw(&c); + draw(&d); + mp_gcd(&a, &b, &e); + draw(&e); + return 0; + } - } else if (!strcmp(cmd, "div2")) { ++div2_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - mp_div_2(&a, &c); - if (mp_cmp(&c, &b) != MP_EQ) { - printf("div_2 %lu failure\n", div2_n); - draw(&a); - draw(&b); - draw(&c); - return 0; - } - } else if (!strcmp(cmd, "mul2")) { ++mul2_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - mp_mul_2(&a, &c); - if (mp_cmp(&c, &b) != MP_EQ) { - printf("mul_2 %lu failure\n", mul2_n); - draw(&a); - draw(&b); - draw(&c); - return 0; - } - } else if (!strcmp(cmd, "add_d")) { ++add_d_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); sscanf(buf, "%d", &ix); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - mp_add_d(&a, ix, &c); - if (mp_cmp(&b, &c) != MP_EQ) { - printf("add_d %lu failure\n", add_d_n); - draw(&a); - draw(&b); - draw(&c); - printf("d == %d\n", ix); - return 0; - } - } else if (!strcmp(cmd, "sub_d")) { ++sub_d_n; - fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 64); - fgets(buf, 4095, stdin); sscanf(buf, "%d", &ix); - fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 64); - mp_sub_d(&a, ix, &c); - if (mp_cmp(&b, &c) != MP_EQ) { - printf("sub_d %lu failure\n", sub_d_n); - draw(&a); - draw(&b); - draw(&c); - printf("d == %d\n", ix); - return 0; - } - } + } else if (!strcmp(cmd, "div2")) { + ++div2_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_div_2(&a, &c); + if (mp_cmp(&c, &b) != MP_EQ) { + printf("div_2 %lu failure\n", div2_n); + draw(&a); + draw(&b); + draw(&c); + return 0; + } + } else if (!strcmp(cmd, "mul2")) { + ++mul2_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_mul_2(&a, &c); + if (mp_cmp(&c, &b) != MP_EQ) { + printf("mul_2 %lu failure\n", mul2_n); + draw(&a); + draw(&b); + draw(&c); + return 0; + } + } else if (!strcmp(cmd, "add_d")) { + ++add_d_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + sscanf(buf, "%d", &ix); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_add_d(&a, ix, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("add_d %lu failure\n", add_d_n); + draw(&a); + draw(&b); + draw(&c); + printf("d == %d\n", ix); + return 0; + } + } else if (!strcmp(cmd, "sub_d")) { + ++sub_d_n; + fgets(buf, 4095, stdin); + mp_read_radix(&a, buf, 64); + fgets(buf, 4095, stdin); + sscanf(buf, "%d", &ix); + fgets(buf, 4095, stdin); + mp_read_radix(&b, buf, 64); + mp_sub_d(&a, ix, &c); + if (mp_cmp(&b, &c) != MP_EQ) { + printf("sub_d %lu failure\n", sub_d_n); + draw(&a); + draw(&b); + draw(&c); + printf("d == %d\n", ix); + return 0; + } + } } return 0; } -
--- a/demo/timing.c Sun Dec 19 11:33:56 2004 +0000 +++ b/demo/timing.c Fri May 06 08:59:30 2005 +0000 @@ -11,15 +11,16 @@ #endif -void ndraw(mp_int *a, char *name) +void ndraw(mp_int * a, char *name) { char buf[4096]; + printf("%s: ", name); mp_toradix(a, buf, 64); printf("%s\n", buf); } -static void draw(mp_int *a) +static void draw(mp_int * a) { ndraw(a, ""); } @@ -38,40 +39,39 @@ } } -#if defined(__i386__) || defined(_M_IX86) || defined(_M_AMD64) /* RDTSC from Scott Duplichan */ -static ulong64 TIMFUNC (void) - { - #if defined __GNUC__ - #ifdef __i386__ - ulong64 a; - __asm__ __volatile__ ("rdtsc ":"=A" (a)); - return a; - #else /* gcc-IA64 version */ - unsigned long result; - __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); - while (__builtin_expect ((int) result == -1, 0)) - __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); - return result; - #endif +static ulong64 TIMFUNC(void) +{ +#if defined __GNUC__ +#if defined(__i386__) || defined(__x86_64__) + unsigned long long a; + __asm__ __volatile__("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n":: + "m"(a):"%eax", "%edx"); + return a; +#else /* gcc-IA64 version */ + unsigned long result; + __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory"); + + while (__builtin_expect((int) result == -1, 0)) + __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory"); + + return result; +#endif // Microsoft and Intel Windows compilers - #elif defined _M_IX86 - __asm rdtsc - #elif defined _M_AMD64 - return __rdtsc (); - #elif defined _M_IA64 - #if defined __INTEL_COMPILER - #include <ia64intrin.h> - #endif - return __getReg (3116); - #else - #error need rdtsc function for this build - #endif - } +#elif defined _M_IX86 + __asm rdtsc +#elif defined _M_AMD64 + return __rdtsc(); +#elif defined _M_IA64 +#if defined __INTEL_COMPILER +#include <ia64intrin.h> +#endif + return __getReg(3116); #else -#define TIMFUNC clock +#error need rdtsc function for this build #endif +} #define DO(x) x; x; //#define DO4(x) DO2(x); DO2(x); @@ -81,7 +81,7 @@ int main(void) { ulong64 tt, gg, CLK_PER_SEC; - FILE *log, *logb, *logc; + FILE *log, *logb, *logc, *logd; mp_int a, b, c, d, e, f; int n, cnt, ix, old_kara_m, old_kara_s; unsigned rr; @@ -94,168 +94,191 @@ mp_init(&f); srand(time(NULL)); - + + + /* temp. turn off TOOM */ + TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000; + + CLK_PER_SEC = TIMFUNC(); + sleep(1); + CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC; - /* temp. turn off TOOM */ - TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000; - - CLK_PER_SEC = TIMFUNC(); - sleep(1); - CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC; + printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC); + goto exptmod; + log = fopen("logs/add.log", "w"); + for (cnt = 8; cnt <= 128; cnt += 8) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_add(&a, &b, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100000); + printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt); + fflush(log); + } + fclose(log); - printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC); - - log = fopen("logs/add.log", "w"); - for (cnt = 8; cnt <= 128; cnt += 8) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - rr = 0; - tt = -1; - do { - gg = TIMFUNC(); - DO(mp_add(&a,&b,&c)); - gg = (TIMFUNC() - gg)>>1; - if (tt > gg) tt = gg; - } while (++rr < 100000); - printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); - fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log); + log = fopen("logs/sub.log", "w"); + for (cnt = 8; cnt <= 128; cnt += 8) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_sub(&a, &b, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100000); + + printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt); + fflush(log); + } + fclose(log); + + /* do mult/square twice, first without karatsuba and second with */ + multtest: + old_kara_m = KARATSUBA_MUL_CUTOFF; + old_kara_s = KARATSUBA_SQR_CUTOFF; + for (ix = 0; ix < 2; ix++) { + printf("With%s Karatsuba\n", (ix == 0) ? "out" : ""); + + KARATSUBA_MUL_CUTOFF = (ix == 0) ? 9999 : old_kara_m; + KARATSUBA_SQR_CUTOFF = (ix == 0) ? 9999 : old_kara_s; + + log = fopen((ix == 0) ? "logs/mult.log" : "logs/mult_kara.log", "w"); + for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_mul(&a, &b, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100); + printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); + fflush(log); } fclose(log); - log = fopen("logs/sub.log", "w"); - for (cnt = 8; cnt <= 128; cnt += 8) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - rr = 0; - tt = -1; - do { - gg = TIMFUNC(); - DO(mp_sub(&a,&b,&c)); - gg = (TIMFUNC() - gg)>>1; - if (tt > gg) tt = gg; - } while (++rr < 100000); - - printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); - fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log); - } - fclose(log); - - /* do mult/square twice, first without karatsuba and second with */ - old_kara_m = KARATSUBA_MUL_CUTOFF; - old_kara_s = KARATSUBA_SQR_CUTOFF; - for (ix = 0; ix < 1; ix++) { - printf("With%s Karatsuba\n", (ix==0)?"out":""); - - KARATSUBA_MUL_CUTOFF = (ix==0)?9999:old_kara_m; - KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s; - - log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w"); - for (cnt = 4; cnt <= 288; cnt += 2) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - rr = 0; - tt = -1; - do { - gg = TIMFUNC(); - DO(mp_mul(&a, &b, &c)); - gg = (TIMFUNC() - gg)>>1; - if (tt > gg) tt = gg; - } while (++rr < 100); - printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); - fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); fflush(log); - } - fclose(log); - - log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w"); - for (cnt = 4; cnt <= 288; cnt += 2) { - SLEEP; - mp_rand(&a, cnt); - rr = 0; - tt = -1; - do { - gg = TIMFUNC(); - DO(mp_sqr(&a, &b)); - gg = (TIMFUNC() - gg)>>1; - if (tt > gg) tt = gg; - } while (++rr < 100); - printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); - fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); fflush(log); + log = fopen((ix == 0) ? "logs/sqr.log" : "logs/sqr_kara.log", "w"); + for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) { + SLEEP; + mp_rand(&a, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_sqr(&a, &b)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 100); + printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); + fflush(log); } fclose(log); } + exptmod: - { + { char *primes[] = { - /* 2K moduli mersenne primes */ - "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", - "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127", - "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087", - "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007", - "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071", - "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991", + /* 2K large moduli */ + "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217", + "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169", + "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283", + /* 2K moduli mersenne primes */ + "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", + "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127", + "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087", + "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007", + "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071", + "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991", - /* DR moduli */ - "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079", - "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039", - "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431", - 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+ /* DR moduli */ + "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079", + "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039", + "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431", + 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- /* generic unrestricted moduli */ - "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203", - "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487", - "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319", - 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+ NULL }; - log = fopen("logs/expt.log", "w"); - logb = fopen("logs/expt_dr.log", "w"); - logc = fopen("logs/expt_2k.log", "w"); - for (n = 0; primes[n]; n++) { - SLEEP; - mp_read_radix(&a, primes[n], 10); - mp_zero(&b); - for (rr = 0; rr < (unsigned)mp_count_bits(&a); rr++) { - mp_mul_2(&b, &b); - b.dp[0] |= lbit(); - b.used += 1; + log = fopen("logs/expt.log", "w"); + logb = fopen("logs/expt_dr.log", "w"); + logc = fopen("logs/expt_2k.log", "w"); + logd = fopen("logs/expt_2kl.log", "w"); + for (n = 0; primes[n]; n++) { + SLEEP; + mp_read_radix(&a, primes[n], 10); + mp_zero(&b); + for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) { + mp_mul_2(&b, &b); + b.dp[0] |= lbit(); + b.used += 1; + } + mp_sub_d(&a, 1, &c); + mp_mod(&b, &c, &b); + mp_set(&c, 3); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_exptmod(&c, &b, &a, &d)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; + } while (++rr < 10); + mp_sub_d(&a, 1, &e); + mp_sub(&e, &b, &b); + mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */ + mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */ + if (mp_cmp_d(&d, 1)) { + printf("Different (%d)!!!\n", mp_count_bits(&a)); + draw(&d); + exit(0); + } + printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + fprintf(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log, + "%d %9llu\n", mp_count_bits(&a), tt); } - mp_sub_d(&a, 1, &c); - mp_mod(&b, &c, &b); - mp_set(&c, 3); - rr = 0; - tt = -1; - do { - gg = TIMFUNC(); - DO(mp_exptmod(&c, &b, &a, &d)); - gg = (TIMFUNC() - gg)>>1; - if (tt > gg) tt = gg; - } while (++rr < 10); - mp_sub_d(&a, 1, &e); - mp_sub(&e, &b, &b); - mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */ - mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */ - if (mp_cmp_d(&d, 1)) { - printf("Different (%d)!!!\n", mp_count_bits(&a)); - draw(&d); - exit(0); - } - printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); - fprintf((n < 6) ? logc : (n < 13) ? logb : log, "%d %9llu\n", mp_count_bits(&a), tt); - } } fclose(log); fclose(logb); fclose(logc); + fclose(logd); log = fopen("logs/invmod.log", "w"); for (cnt = 4; cnt <= 128; cnt += 4) { @@ -264,28 +287,29 @@ mp_rand(&b, cnt); do { - mp_add_d(&b, 1, &b); - mp_gcd(&a, &b, &c); + mp_add_d(&b, 1, &b); + mp_gcd(&a, &b, &c); } while (mp_cmp_d(&c, 1) != MP_EQ); - rr = 0; - tt = -1; + rr = 0; + tt = -1; do { - gg = TIMFUNC(); - DO(mp_invmod(&b, &a, &c)); - gg = (TIMFUNC() - gg)>>1; - if (tt > gg) tt = gg; + gg = TIMFUNC(); + DO(mp_invmod(&b, &a, &c)); + gg = (TIMFUNC() - gg) >> 1; + if (tt > gg) + tt = gg; } while (++rr < 1000); mp_mulmod(&b, &c, &a, &d); if (mp_cmp_d(&d, 1) != MP_EQ) { - printf("Failed to invert\n"); - return 0; + printf("Failed to invert\n"); + return 0; } - printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); - fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); + printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n", + mp_count_bits(&a), CLK_PER_SEC / tt, tt); + fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt); } fclose(log); return 0; } -
--- a/dep.pl Sun Dec 19 11:33:56 2004 +0000 +++ b/dep.pl Fri May 06 08:59:30 2005 +0000 @@ -13,6 +13,8 @@ foreach my $filename (glob "bn*.c") { my $define = $filename; +print "Processing $filename\n"; + # convert filename to upper case so we can use it as a define $define =~ tr/[a-z]/[A-Z]/; $define =~ tr/\./_/;
--- a/etc/mersenne.c Sun Dec 19 11:33:56 2004 +0000 +++ b/etc/mersenne.c Fri May 06 08:59:30 2005 +0000 @@ -18,15 +18,15 @@ } if ((res = mp_init (&u)) != MP_OKAY) { - goto __N; + goto LBL_N; } /* n = 2^s - 1 */ if ((res = mp_2expt(&n, s)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } /* set u=4 */ @@ -36,22 +36,22 @@ for (k = 1; k <= s - 2; k++) { /* u = u^2 - 2 mod n */ if ((res = mp_sqr (&u, &u)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } /* make sure u is positive */ while (u.sign == MP_NEG) { if ((res = mp_add (&u, &n, &u)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } } /* reduce */ if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } } @@ -62,8 +62,8 @@ } res = MP_OKAY; -__MU:mp_clear (&u); -__N:mp_clear (&n); +LBL_MU:mp_clear (&u); +LBL_N:mp_clear (&n); return res; }
--- a/etc/pprime.c Sun Dec 19 11:33:56 2004 +0000 +++ b/etc/pprime.c Fri May 06 08:59:30 2005 +0000 @@ -189,7 +189,7 @@ } if ((res = mp_init (&v)) != MP_OKAY) { - goto __C; + goto LBL_C; } /* product of first 50 primes */ @@ -197,34 +197,34 @@ mp_read_radix (&v, "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190", 10)) != MP_OKAY) { - goto __V; + goto LBL_V; } if ((res = mp_init (&a)) != MP_OKAY) { - goto __V; + goto LBL_V; } /* set the prime */ mp_set (&a, prime_digit ()); if ((res = mp_init (&b)) != MP_OKAY) { - goto __A; + goto LBL_A; } if ((res = mp_init (&n)) != MP_OKAY) { - goto __B; + goto LBL_B; } if ((res = mp_init (&x)) != MP_OKAY) { - goto __N; + goto LBL_N; } if ((res = mp_init (&y)) != MP_OKAY) { - goto __X; + goto LBL_X; } if ((res = mp_init (&z)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* now loop making the single digit */ @@ -236,25 +236,25 @@ /* now compute z = a * b * 2 */ if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) { /* z = a * b */ - goto __Z; + goto LBL_Z; } if ((res = mp_copy (&z, &c)) != MP_OKAY) { /* c = a * b */ - goto __Z; + goto LBL_Z; } if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) { /* z = 2 * a * b */ - goto __Z; + goto LBL_Z; } /* n = z + 1 */ if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */ - goto __Z; + goto LBL_Z; } /* check (n, v) == 1 */ if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */ - goto __Z; + goto LBL_Z; } if (mp_cmp_d (&y, 1) != MP_EQ) @@ -266,7 +266,7 @@ /* compute x^a mod n */ if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */ - goto __Z; + goto LBL_Z; } /* if y == 1 loop */ @@ -275,7 +275,7 @@ /* now x^2a mod n */ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */ - goto __Z; + goto LBL_Z; } if (mp_cmp_d (&y, 1) == MP_EQ) @@ -283,7 +283,7 @@ /* compute x^b mod n */ if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */ - goto __Z; + goto LBL_Z; } /* if y == 1 loop */ @@ -292,7 +292,7 @@ /* now x^2b mod n */ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */ - goto __Z; + goto LBL_Z; } if (mp_cmp_d (&y, 1) == MP_EQ) @@ -300,7 +300,7 @@ /* compute x^c mod n == x^ab mod n */ if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */ - goto __Z; + goto LBL_Z; } /* if y == 1 loop */ @@ -309,7 +309,7 @@ /* now compute (x^c mod n)^2 */ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */ - goto __Z; + goto LBL_Z; } /* y should be 1 */ @@ -346,14 +346,14 @@ mp_exch (&n, p); res = MP_OKAY; -__Z:mp_clear (&z); -__Y:mp_clear (&y); -__X:mp_clear (&x); -__N:mp_clear (&n); -__B:mp_clear (&b); -__A:mp_clear (&a); -__V:mp_clear (&v); -__C:mp_clear (&c); +LBL_Z:mp_clear (&z); +LBL_Y:mp_clear (&y); +LBL_X:mp_clear (&x); +LBL_N:mp_clear (&n); +LBL_B:mp_clear (&b); +LBL_A:mp_clear (&a); +LBL_V:mp_clear (&v); +LBL_C:mp_clear (&c); return res; }
--- a/etc/tune.c Sun Dec 19 11:33:56 2004 +0000 +++ b/etc/tune.c Fri May 06 08:59:30 2005 +0000 @@ -10,13 +10,44 @@ */ #define TIMES (1UL<<14UL) +/* RDTSC from Scott Duplichan */ +static ulong64 TIMFUNC (void) + { + #if defined __GNUC__ + #if defined(__i386__) || defined(__x86_64__) + unsigned long long a; + __asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx"); + return a; + #else /* gcc-IA64 version */ + unsigned long result; + __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); + while (__builtin_expect ((int) result == -1, 0)) + __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); + return result; + #endif + + // Microsoft and Intel Windows compilers + #elif defined _M_IX86 + __asm rdtsc + #elif defined _M_AMD64 + return __rdtsc (); + #elif defined _M_IA64 + #if defined __INTEL_COMPILER + #include <ia64intrin.h> + #endif + return __getReg (3116); + #else + #error need rdtsc function for this build + #endif + } + #ifndef X86_TIMER /* generic ISO C timer */ -ulong64 __T; -void t_start(void) { __T = clock(); } -ulong64 t_read(void) { return clock() - __T; } +ulong64 LBL_T; +void t_start(void) { LBL_T = TIMFUNC(); } +ulong64 t_read(void) { return TIMFUNC() - LBL_T; } #else extern void t_start(void);
--- a/logs/add.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/add.log Fri May 06 08:59:30 2005 +0000 @@ -1,16 +1,16 @@ -224 222 -448 330 -672 436 -896 520 -1120 612 -1344 696 -1568 810 -1792 912 -2016 1006 -2240 1116 -2464 1152 -2688 1284 -2912 1348 -3136 1486 -3360 1580 -3584 1636 +480 87 +960 111 +1440 135 +1920 159 +2400 200 +2880 224 +3360 248 +3840 272 +4320 296 +4800 320 +5280 344 +5760 368 +6240 392 +6720 416 +7200 440 +7680 464
--- a/logs/expt.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/expt.log Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,7 @@ +513 1489160 +769 3688476 +1025 8162061 +2049 49260015 +2561 89579052 +3073 148797060 +4097 324449263
--- a/logs/expt_2k.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/expt_2k.log Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,5 @@ +607 2272809 +1279 9557382 +2203 36250309 +3217 87666486 +4253 174168369
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/logs/expt_2kl.log Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,4 @@ +1024 6954080 +2048 35993987 +4096 176068521 +521 1683720
--- a/logs/expt_dr.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/expt_dr.log Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,7 @@ +532 1989592 +784 3898697 +1036 6519700 +1540 15676650 +2072 33128187 +3080 82963362 +4116 168358337
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--- a/logs/mult_kara.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/mult_kara.log Fri May 06 08:59:30 2005 +0000 @@ -1,33 +1,84 @@ -924 16686 -1146 25334 -1371 35304 -1591 47122 -1820 61500 -2044 75254 -2266 91732 -2492 111656 -2716 129428 -2937 147508 -3164 167758 -3388 188248 -3612 210826 -3836 233814 -4059 256898 -4284 280210 -4508 310372 -4731 333902 -4955 376502 -5179 402854 -5404 432004 -5626 459010 -5849 491868 -6076 520550 -6300 547400 -6524 575968 -6747 608482 -6971 642850 -7196 673670 -7419 710680 -7644 743942 -7868 780394 -8092 817342 +271 560 +391 870 +511 1159 +631 1605 +750 2111 +871 2737 +991 3361 +1111 4054 +1231 4778 +1351 5600 +1471 6404 +1591 7323 +1710 8255 +1831 9239 +1948 10257 +2070 11397 +2190 12531 +2308 13665 +2429 14870 +2550 16175 +2671 17539 +2787 18879 +2911 20350 +3031 21807 +3150 23415 +3270 24897 +3388 26567 +3511 28205 +3627 30076 +3751 31744 +3869 33657 +3991 35425 +4111 37522 +4229 39363 +4351 41503 +4470 43491 +4590 45827 +4711 47795 +4828 50166 +4951 52318 +5070 54911 +5191 57036 +5308 58237 +5431 60248 +5551 62678 +5671 64786 +5791 67294 +5908 69343 +6031 71607 +6151 74166 +6271 76590 +6391 78734 +6511 81175 +6631 83742 +6750 86403 +6868 88873 +6990 91150 +7110 94211 +7228 96922 +7351 99445 +7469 102216 +7589 104968 +7711 108113 +7827 110758 +7950 113714 +8071 116511 +8186 119643 +8310 122679 +8425 125581 +8551 128715 +8669 131778 +8788 135116 +8910 138138 +9031 141628 +9148 144754 +9268 148367 +9391 151551 +9511 155033 +9631 158652 +9751 162125 +9871 165248 +9988 168627 +10111 172427 +10231 176412
--- a/logs/sqr.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/sqr.log Fri May 06 08:59:30 2005 +0000 @@ -1,143 +1,84 @@ -139 806 -195 1212 -252 1604 -307 2260 -364 2892 -420 3308 -476 4152 -532 4814 -588 5754 -644 6684 -700 7226 -756 8324 -808 9092 -866 10068 -924 11204 -976 12918 -1036 13656 -1092 15248 -1148 15956 -1204 17270 -1260 19894 -1316 20516 -1370 21864 -1428 25554 -1483 26138 -1540 27086 -1596 29246 -1652 32210 -1707 32704 -1764 35142 -1820 39050 -1876 39256 -1931 41574 -1985 45070 -2044 46352 -2099 48114 -2155 51332 -2212 53268 -2267 55890 -2324 59054 -2380 60206 -2434 63540 -2491 66084 -2547 68590 -2604 74332 -2660 74784 -2715 77974 -2772 79924 -2826 82914 -2884 87210 -2929 89076 -2996 92480 -3052 96814 -3108 99990 -3162 102550 -3219 105396 -3276 109284 -3332 113752 -3387 116628 -3444 120782 -3500 122938 -3556 127940 -3612 303656 -3667 312212 -3724 324376 -3779 329204 -3833 340910 -3892 353850 -3943 362348 -4003 367780 -4056 380448 -4114 393616 -4172 404104 -4227 415148 -4284 409770 -4339 436648 -4394 442970 -4451 463096 -4507 472056 -4564 485780 -4616 496286 -4675 507612 -4732 519524 -4788 536768 -4843 542754 -4899 553090 -4956 571986 -5012 586340 -5068 599606 -5124 613670 -5179 624256 -5235 636266 -5292 655518 -5348 668142 -5403 677266 -5460 696040 -5516 712772 -5570 723942 -5628 739052 -5684 755350 -5739 769962 -5790 775258 -5851 790128 -5908 814536 -5962 827278 -6018 844510 -6076 851606 -6130 865748 -6188 894752 -6244 900474 -6300 928174 -6356 928440 -6410 957758 -6468 981134 -6524 994088 -6580 1011124 -6636 1027178 -6692 1045466 -6747 1056910 -6804 1083784 -6860 1104706 -6915 1116450 -6972 1137894 -7028 1154670 -7084 1158064 -7138 1188734 -7196 1214218 -7249 1226822 -7307 1247528 -7363 1255338 -7420 1291104 -7475 1297940 -7532 1324994 -7587 1340274 -7644 1342596 -7698 1381418 -7756 1382904 -7812 1432588 -7867 1443632 -7922 1465092 -7979 1496804 -8036 1520142 -8092 1539566 +265 562 +389 882 +509 1207 +631 1572 +750 1990 +859 2433 +991 2894 +1109 3555 +1230 4228 +1350 5018 +1471 5805 +1591 6579 +1709 7415 +1829 8329 +1949 9225 +2071 10139 +2188 11239 +2309 12178 +2431 13212 +2551 14294 +2671 15551 +2791 16512 +2911 17718 +3030 18876 +3150 20259 +3270 21374 +3391 22650 +3511 23948 +3631 25493 +3750 26756 +3870 28225 +3989 29705 +4110 31409 +4230 32834 +4351 34327 +4471 35818 +4591 37636 +4711 39228 +4830 40868 +4949 42393 +5070 44541 +5191 46269 +5310 48162 +5429 49728 +5548 51985 +5671 53948 +5791 55885 +5910 57584 +6031 60082 +6150 62239 +6270 64309 +6390 66014 +6511 68766 +6631 71012 +6750 73172 +6871 74952 +6991 77909 +7111 80371 +7231 82666 +7351 84531 +7469 87698 +7589 90318 +7711 225384 +7830 232428 +7950 240009 +8070 246522 +8190 253662 +8310 260961 +8431 269253 +8549 275743 +8671 283769 +8789 290811 +8911 300034 +9030 306873 +9149 315085 +9270 323944 +9390 332390 +9508 337519 +9631 348986 +9749 356904 +9871 367013 +9989 373831 +10108 381033 +10230 393475
--- a/logs/sqr_kara.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/sqr_kara.log Fri May 06 08:59:30 2005 +0000 @@ -1,33 +1,84 @@ -922 11272 -1148 16004 -1370 21958 -1596 28684 -1817 37832 -2044 46386 -2262 56218 -2492 66388 -2716 77478 -2940 89380 -3163 103680 -3385 116274 -3612 135334 -3836 151332 -4057 164938 -4284 183178 -4508 198864 -4731 215222 -4954 231986 -5180 251660 -5404 269414 -5626 288454 -5850 307806 -6076 329458 -6299 347726 -6523 369864 -6748 387832 -6971 413010 -7194 453310 -7415 476936 -7643 497118 -7867 521394 -8091 540224 +271 560 +388 878 +511 1179 +629 1625 +751 1988 +871 2423 +989 2896 +1111 3561 +1231 4209 +1350 5015 +1470 5804 +1591 6556 +1709 7420 +1831 8263 +1951 9173 +2070 10153 +2191 11229 +2310 12167 +2431 13211 +2550 14309 +2671 15524 +2788 16525 +2910 17712 +3028 18822 +3148 20220 +3271 21343 +3391 22652 +3511 23944 +3630 25485 +3750 26778 +3868 28201 +3990 29653 +4111 31393 +4225 32841 +4350 34328 +4471 35786 +4590 37652 +4711 39245 +4830 40876 +4951 42433 +5068 44547 +5191 46321 +5311 48140 +5430 49727 +5550 52034 +5671 53954 +5791 55921 +5908 57597 +6031 60084 +6148 62226 +6270 64295 +6390 66045 +6511 68779 +6629 71003 +6751 73169 +6871 74992 +6991 77895 +7110 80376 +7231 82628 +7351 84468 +7470 87664 +7591 90284 +7711 91352 +7828 93995 +7950 96276 +8071 98691 +8190 101256 +8308 103631 +8431 105222 +8550 108343 +8671 110281 +8787 112764 +8911 115397 +9031 117690 +9151 120266 +9271 122715 +9391 124624 +9510 127937 +9630 130313 +9750 132914 +9871 136129 +9991 138517 +10108 141525 +10231 144225
--- a/logs/sub.log Sun Dec 19 11:33:56 2004 +0000 +++ b/logs/sub.log Fri May 06 08:59:30 2005 +0000 @@ -1,16 +1,16 @@ -224 216 -448 324 -672 428 -896 532 -1120 648 -1344 766 -1568 862 -1792 928 -2016 1070 -2240 1128 -2464 1250 -2688 1344 -2912 1436 -3136 1542 -3360 1628 -3584 1696 +480 94 +960 116 +1440 140 +1920 164 +2400 205 +2880 229 +3360 253 +3840 277 +4320 299 +4800 321 +5280 345 +5760 371 +6240 395 +6720 419 +7200 441 +7680 465
--- a/makefile Sun Dec 19 11:33:56 2004 +0000 +++ b/makefile Fri May 06 08:59:30 2005 +0000 @@ -1,10 +1,14 @@ #Makefile for GCC # #Tom St Denis + +#version of library +VERSION=0.35 + CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare #for speed -CFLAGS += -O3 -funroll-loops +CFLAGS += -O3 -funroll-all-loops #for size #CFLAGS += -Os @@ -15,13 +19,15 @@ #debug #CFLAGS += -g3 -VERSION=0.32 +#install as this user +USER=root +GROUP=root default: libtommath.a #default files to install LIBNAME=libtommath.a -HEADERS=tommath.h +HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. @@ -51,17 +57,18 @@ bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \ bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ -bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ +bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o libtommath.a: $(OBJECTS) $(AR) $(ARFLAGS) libtommath.a $(OBJECTS) ranlib libtommath.a - #make a profiled library (takes a while!!!) # # This will build the library with profile generation @@ -86,19 +93,19 @@ ranlib libtommath.a install: libtommath.a - install -d -g root -o root $(DESTDIR)$(LIBPATH) - install -d -g root -o root $(DESTDIR)$(INCPATH) - install -g root -o root $(LIBNAME) $(DESTDIR)$(LIBPATH) - install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH) + install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH) + install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH) + install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH) + install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH) test: libtommath.a demo/demo.o - $(CC) demo/demo.o libtommath.a -o test + $(CC) $(CFLAGS) demo/demo.o libtommath.a -o test mtest: test - cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest -s + cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest timing: libtommath.a - $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s + $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest # makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think] docdvi: tommath.src
--- a/makefile.bcc Sun Dec 19 11:33:56 2004 +0000 +++ b/makefile.bcc Fri May 06 08:59:30 2005 +0000 @@ -27,11 +27,13 @@ bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \ bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \ bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \ +bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \ bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \ bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \ bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ -bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj +bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \ +bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj TARGET = libtommath.lib
--- a/makefile.cygwin_dll Sun Dec 19 11:33:56 2004 +0000 +++ b/makefile.cygwin_dll Fri May 06 08:59:30 2005 +0000 @@ -32,11 +32,13 @@ bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \ bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ -bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ +bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o # make a Windows DLL via Cygwin windll: $(OBJECTS)
--- a/makefile.icc Sun Dec 19 11:33:56 2004 +0000 +++ b/makefile.icc Fri May 06 08:59:30 2005 +0000 @@ -21,6 +21,10 @@ # Default to just generic max opts CFLAGS += -O3 -xN +#install as this user +USER=root +GROUP=root + default: libtommath.a #default files to install @@ -55,11 +59,13 @@ bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \ bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ -bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ +bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o libtommath.a: $(OBJECTS) $(AR) $(ARFLAGS) libtommath.a $(OBJECTS) @@ -89,10 +95,10 @@ ranlib libtommath.a install: libtommath.a - install -d -g root -o root $(DESTDIR)$(LIBPATH) - install -d -g root -o root $(DESTDIR)$(INCPATH) - install -g root -o root $(LIBNAME) $(DESTDIR)$(LIBPATH) - install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH) + install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH) + install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH) + install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH) + install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH) test: libtommath.a demo/demo.o $(CC) demo/demo.o libtommath.a -o test
--- a/makefile.msvc Sun Dec 19 11:33:56 2004 +0000 +++ b/makefile.msvc Fri May 06 08:59:30 2005 +0000 @@ -26,11 +26,13 @@ bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \ bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \ bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \ +bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \ bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \ bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \ bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ -bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj +bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \ +bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj library: $(OBJECTS) lib /out:tommath.lib $(OBJECTS)
--- a/makefile.shared Sun Dec 19 11:33:56 2004 +0000 +++ b/makefile.shared Fri May 06 08:59:30 2005 +0000 @@ -1,10 +1,9 @@ #Makefile for GCC # #Tom St Denis -VERSION=0:32 +VERSION=0:35 CC = libtool --mode=compile gcc - CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare #for speed @@ -16,11 +15,15 @@ #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer +#install as this user +USER=root +GROUP=root + default: libtommath.la #default files to install LIBNAME=libtommath.la -HEADERS=tommath.h +HEADERS=tommath.h tommath_class.h tommath_superclass.h #LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. @@ -50,18 +53,21 @@ bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \ bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ +bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ -bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \ +bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o + libtommath.la: $(OBJECTS) libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info $(VERSION) libtool --mode=link gcc *.o -o libtommath.a libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la - install -d -g root -o root $(DESTDIR)$(INCPATH) - install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH) + install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH) + install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH) test: libtommath.a demo/demo.o gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
--- a/mtest/mtest.c Sun Dec 19 11:33:56 2004 +0000 +++ b/mtest/mtest.c Fri May 06 08:59:30 2005 +0000 @@ -46,7 +46,7 @@ int n, size; unsigned char buf[2048]; - size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 1031; + size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 101; buf[0] = (fgetc(rng)&1)?1:0; fread(buf+1, 1, size, rng); while (buf[1] == 0) buf[1] = fgetc(rng); @@ -58,7 +58,7 @@ int n, size; unsigned char buf[2048]; - size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 97; + size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 101; buf[0] = (fgetc(rng)&1)?1:0; fread(buf+1, 1, size, rng); while (buf[1] == 0) buf[1] = fgetc(rng);
--- a/pre_gen/mpi.c Sun Dec 19 11:33:56 2004 +0000 +++ b/pre_gen/mpi.c Fri May 06 08:59:30 2005 +0000 @@ -69,8 +69,7 @@ * Based on slow invmod except this is optimized for the case where b is * odd as per HAC Note 14.64 on pp. 610 */ -int -fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) +int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) { mp_int x, y, u, v, B, D; int res, neg; @@ -87,20 +86,20 @@ /* x == modulus, y == value to invert */ if ((res = mp_copy (b, &x)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* we need y = |a| */ - if ((res = mp_abs (a, &y)) != MP_OKAY) { - goto __ERR; + if ((res = mp_mod (a, b, &y)) != MP_OKAY) { + goto LBL_ERR; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } mp_set (&D, 1); @@ -109,17 +108,17 @@ while (mp_iseven (&u) == 1) { /* 4.1 u = u/2 */ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 4.2 if B is odd then */ if (mp_isodd (&B) == 1) { if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* B = B/2 */ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -127,18 +126,18 @@ while (mp_iseven (&v) == 1) { /* 5.1 v = v/2 */ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 5.2 if D is odd then */ if (mp_isodd (&D) == 1) { /* D = (D-x)/2 */ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* D = D/2 */ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -146,20 +145,20 @@ if (mp_cmp (&u, &v) != MP_LT) { /* u = u - v, B = B - D */ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } else { /* v - v - u, D = D - B */ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -173,21 +172,21 @@ /* if v != 1 then there is no inverse */ if (mp_cmp_d (&v, 1) != MP_EQ) { res = MP_VAL; - goto __ERR; + goto LBL_ERR; } /* b is now the inverse */ neg = a->sign; while (D.sign == MP_NEG) { if ((res = mp_add (&D, b, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } mp_exch (&D, c); c->sign = neg; res = MP_OKAY; -__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); +LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } #endif @@ -220,8 +219,7 @@ * * Based on Algorithm 14.32 on pp.601 of HAC. */ -int -fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) +int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) { int ix, res, olduse; mp_word W[MP_WARRAY]; @@ -401,8 +399,7 @@ * Based on Algorithm 14.12 on pp.595 of HAC. * */ -int -fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { int olduse, res, pa, ix, iz; mp_digit W[MP_WARRAY]; @@ -420,7 +417,7 @@ /* clear the carry */ _W = 0; - for (ix = 0; ix <= pa; ix++) { + for (ix = 0; ix < pa; ix++) { int tx, ty; int iy; mp_digit *tmpx, *tmpy; @@ -433,7 +430,7 @@ tmpx = a->dp + tx; tmpy = b->dp + ty; - /* this is the number of times the loop will iterrate, essentially its + /* this is the number of times the loop will iterrate, essentially while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); @@ -450,14 +447,17 @@ _W = _W >> ((mp_word)DIGIT_BIT); } + /* store final carry */ + W[ix] = (mp_digit)(_W & MP_MASK); + /* setup dest */ olduse = c->used; - c->used = digs; + c->used = pa; { register mp_digit *tmpc; tmpc = c->dp; - for (ix = 0; ix < digs; ix++) { + for (ix = 0; ix < pa+1; ix++) { /* now extract the previous digit [below the carry] */ *tmpc++ = W[ix]; } @@ -501,8 +501,7 @@ * * Based on Algorithm 14.12 on pp.595 of HAC. */ -int -fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { int olduse, res, pa, ix, iz; mp_digit W[MP_WARRAY]; @@ -519,7 +518,7 @@ /* number of output digits to produce */ pa = a->used + b->used; _W = 0; - for (ix = digs; ix <= pa; ix++) { + for (ix = digs; ix < pa; ix++) { int tx, ty, iy; mp_digit *tmpx, *tmpy; @@ -547,6 +546,9 @@ /* make next carry */ _W = _W >> ((mp_word)DIGIT_BIT); } + + /* store final carry */ + W[ix] = (mp_digit)(_W & MP_MASK); /* setup dest */ olduse = c->used; @@ -591,33 +593,14 @@ * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -/* fast squaring - * - * This is the comba method where the columns of the product - * are computed first then the carries are computed. This - * has the effect of making a very simple inner loop that - * is executed the most - * - * W2 represents the outer products and W the inner. - * - * A further optimizations is made because the inner - * products are of the form "A * B * 2". The *2 part does - * not need to be computed until the end which is good - * because 64-bit shifts are slow! - * - * Based on Algorithm 14.16 on pp.597 of HAC. - * - */ /* the jist of squaring... - -you do like mult except the offset of the tmpx [one that starts closer to zero] -can't equal the offset of tmpy. So basically you set up iy like before then you min it with -(ty-tx) so that it never happens. You double all those you add in the inner loop + * you do like mult except the offset of the tmpx [one that + * starts closer to zero] can't equal the offset of tmpy. + * So basically you set up iy like before then you min it with + * (ty-tx) so that it never happens. You double all those + * you add in the inner loop After that loop you do the squares and add them in. - -Remove W2 and don't memset W - */ int fast_s_mp_sqr (mp_int * a, mp_int * b) @@ -636,7 +619,7 @@ /* number of output digits to produce */ W1 = 0; - for (ix = 0; ix <= pa; ix++) { + for (ix = 0; ix < pa; ix++) { int tx, ty, iy; mp_word _W; mp_digit *tmpy; @@ -652,7 +635,7 @@ tmpx = a->dp + tx; tmpy = a->dp + ty; - /* this is the number of times the loop will iterrate, essentially its + /* this is the number of times the loop will iterrate, essentially while (tx++ < a->used && ty-- >= 0) { ... } */ iy = MIN(a->used-tx, ty+1); @@ -677,7 +660,7 @@ } /* store it */ - W[ix] = _W; + W[ix] = (mp_digit)(_W & MP_MASK); /* make next carry */ W1 = _W >> ((mp_word)DIGIT_BIT); @@ -1539,23 +1522,23 @@ mp_set(&tq, 1); n = mp_count_bits(a) - mp_count_bits(b); - if (((res = mp_copy(a, &ta)) != MP_OKAY) || - ((res = mp_copy(b, &tb)) != MP_OKAY) || + if (((res = mp_abs(a, &ta)) != MP_OKAY) || + ((res = mp_abs(b, &tb)) != MP_OKAY) || ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { - goto __ERR; + goto LBL_ERR; } while (n-- >= 0) { if (mp_cmp(&tb, &ta) != MP_GT) { if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { - goto __ERR; + goto LBL_ERR; } } if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { - goto __ERR; + goto LBL_ERR; } } @@ -1564,13 +1547,13 @@ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); if (c != NULL) { mp_exch(c, &q); - c->sign = n2; + c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; } if (d != NULL) { mp_exch(d, &ta); - d->sign = n; - } -__ERR: + d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; + } +LBL_ERR: mp_clear_multi(&ta, &tb, &tq, &q, NULL); return res; } @@ -1619,19 +1602,19 @@ q.used = a->used + 2; if ((res = mp_init (&t1)) != MP_OKAY) { - goto __Q; + goto LBL_Q; } if ((res = mp_init (&t2)) != MP_OKAY) { - goto __T1; + goto LBL_T1; } if ((res = mp_init_copy (&x, a)) != MP_OKAY) { - goto __T2; + goto LBL_T2; } if ((res = mp_init_copy (&y, b)) != MP_OKAY) { - goto __X; + goto LBL_X; } /* fix the sign */ @@ -1643,10 +1626,10 @@ if (norm < (int)(DIGIT_BIT-1)) { norm = (DIGIT_BIT-1) - norm; if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } } else { norm = 0; @@ -1658,13 +1641,13 @@ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ - goto __Y; + goto LBL_Y; } while (mp_cmp (&x, &y) != MP_LT) { ++(q.dp[n - t]); if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } } @@ -1706,7 +1689,7 @@ t1.dp[1] = y.dp[t]; t1.used = 2; if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* find right hand */ @@ -1718,27 +1701,27 @@ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ if (x.sign == MP_NEG) { if ((res = mp_copy (&y, &t1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; @@ -1765,11 +1748,11 @@ res = MP_OKAY; -__Y:mp_clear (&y); -__X:mp_clear (&x); -__T2:mp_clear (&t2); -__T1:mp_clear (&t1); -__Q:mp_clear (&q); +LBL_Y:mp_clear (&y); +LBL_X:mp_clear (&x); +LBL_T2:mp_clear (&t2); +LBL_T1:mp_clear (&t1); +LBL_Q:mp_clear (&q); return res; } @@ -2199,7 +2182,7 @@ * Based on algorithm from the paper * * "Generating Efficient Primes for Discrete Log Cryptosystems" - * Chae Hoon Lim, Pil Loong Lee, + * Chae Hoon Lim, Pil Joong Lee, * POSTECH Information Research Laboratories * * The modulus must be of a special format [see manual] @@ -2457,25 +2440,33 @@ return err; #else /* no invmod */ - return MP_VAL -#endif - } + return MP_VAL; +#endif + } + +/* modified diminished radix reduction */ +#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) + if (mp_reduce_is_2k_l(P) == MP_YES) { + return s_mp_exptmod(G, X, P, Y, 1); + } +#endif #ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ dr = mp_dr_is_modulus(P); #else + /* default to no */ dr = 0; #endif #ifdef BN_MP_REDUCE_IS_2K_C - /* if not, is it a uDR modulus? */ + /* if not, is it a unrestricted DR modulus? */ if (dr == 0) { dr = mp_reduce_is_2k(P) << 1; } #endif - /* if the modulus is odd or dr != 0 use the fast method */ + /* if the modulus is odd or dr != 0 use the montgomery method */ #ifdef BN_MP_EXPTMOD_FAST_C if (mp_isodd (P) == 1 || dr != 0) { return mp_exptmod_fast (G, X, P, Y, dr); @@ -2483,7 +2474,7 @@ #endif #ifdef BN_S_MP_EXPTMOD_C /* otherwise use the generic Barrett reduction technique */ - return s_mp_exptmod (G, X, P, Y); + return s_mp_exptmod (G, X, P, Y, 0); #else /* no exptmod for evens */ return MP_VAL; @@ -2529,8 +2520,7 @@ #define TAB_SIZE 256 #endif -int -mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) +int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) { mp_int M[TAB_SIZE], res; mp_digit buf, mp; @@ -2588,11 +2578,11 @@ #ifdef BN_MP_MONTGOMERY_SETUP_C /* now setup montgomery */ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { - goto __M; + goto LBL_M; } #else err = MP_VAL; - goto __M; + goto LBL_M; #endif /* automatically pick the comba one if available (saves quite a few calls/ifs) */ @@ -2608,7 +2598,7 @@ redux = mp_montgomery_reduce; #else err = MP_VAL; - goto __M; + goto LBL_M; #endif } } else if (redmode == 1) { @@ -2618,24 +2608,24 @@ redux = mp_dr_reduce; #else err = MP_VAL; - goto __M; + goto LBL_M; #endif } else { #if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) /* setup DR reduction for moduli of the form 2**k - b */ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { - goto __M; + goto LBL_M; } redux = mp_reduce_2k; #else err = MP_VAL; - goto __M; + goto LBL_M; #endif } /* setup result */ if ((err = mp_init (&res)) != MP_OKAY) { - goto __M; + goto LBL_M; } /* create M table @@ -2649,45 +2639,45 @@ #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* now we need R mod m */ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } #else err = MP_VAL; - goto __RES; + goto LBL_RES; #endif /* now set M[1] to G * R mod m */ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } else { mp_set(&res, 1); if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } for (x = 0; x < (winsize - 1); x++) { if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* create upper table */ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&M[x], P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } @@ -2727,10 +2717,10 @@ /* if the bit is zero and mode == 1 then we square */ if (mode == 1 && y == 0) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } continue; } @@ -2744,19 +2734,19 @@ /* square first */ for (x = 0; x < winsize; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* then multiply */ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } /* empty window and reset */ @@ -2771,10 +2761,10 @@ /* square then multiply if the bit is set */ for (x = 0; x < bitcpy; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } /* get next bit of the window */ @@ -2782,10 +2772,10 @@ if ((bitbuf & (1 << winsize)) != 0) { /* then multiply */ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } } @@ -2799,15 +2789,15 @@ * of R. */ if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } } /* swap res with Y */ mp_exch (&res, Y); err = MP_OKAY; -__RES:mp_clear (&res); -__M: +LBL_RES:mp_clear (&res); +LBL_M: mp_clear(&M[1]); for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); @@ -2881,6 +2871,13 @@ if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; } } + /* make sure U3 >= 0 */ + if (u3.sign == MP_NEG) { + mp_neg(&u1, &u1); + mp_neg(&u2, &u2); + mp_neg(&u3, &u3); + } + /* copy result out */ if (U1 != NULL) { mp_exch(U1, &u1); } if (U2 != NULL) { mp_exch(U2, &u2); } @@ -3059,7 +3056,7 @@ } if ((res = mp_init_copy (&v, b)) != MP_OKAY) { - goto __U; + goto LBL_U; } /* must be positive for the remainder of the algorithm */ @@ -3073,24 +3070,24 @@ if (k > 0) { /* divide the power of two out */ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } /* divide any remaining factors of two out */ if (u_lsb != k) { if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } if (v_lsb != k) { if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } @@ -3103,23 +3100,23 @@ /* subtract smallest from largest */ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) { - goto __V; + goto LBL_V; } /* Divide out all factors of two */ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) { - goto __V; + goto LBL_V; } } /* multiply by 2**k which we divided out at the beginning */ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) { - goto __V; + goto LBL_V; } c->sign = MP_ZPOS; res = MP_OKAY; -__V:mp_clear (&u); -__U:mp_clear (&v); +LBL_V:mp_clear (&u); +LBL_U:mp_clear (&v); return res; } #endif @@ -3555,25 +3552,25 @@ } /* x = a, y = b */ - if ((res = mp_copy (a, &x)) != MP_OKAY) { - goto __ERR; + if ((res = mp_mod(a, b, &x)) != MP_OKAY) { + goto LBL_ERR; } if ((res = mp_copy (b, &y)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 2. [modified] if x,y are both even then return an error! */ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { res = MP_VAL; - goto __ERR; + goto LBL_ERR; } /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } mp_set (&A, 1); mp_set (&D, 1); @@ -3583,24 +3580,24 @@ while (mp_iseven (&u) == 1) { /* 4.1 u = u/2 */ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 4.2 if A or B is odd then */ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) { /* A = (A+y)/2, B = (B-x)/2 */ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* A = A/2, B = B/2 */ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -3608,24 +3605,24 @@ while (mp_iseven (&v) == 1) { /* 5.1 v = v/2 */ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* 5.2 if C or D is odd then */ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) { /* C = (C+y)/2, D = (D-x)/2 */ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* C = C/2, D = D/2 */ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -3633,28 +3630,28 @@ if (mp_cmp (&u, &v) != MP_LT) { /* u = u - v, A = A - C, B = B - D */ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } else { /* v - v - u, C = C - A, D = D - B */ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } @@ -3667,27 +3664,27 @@ /* if v != 1 then there is no inverse */ if (mp_cmp_d (&v, 1) != MP_EQ) { res = MP_VAL; - goto __ERR; + goto LBL_ERR; } /* if its too low */ while (mp_cmp_d(&C, 0) == MP_LT) { if ((res = mp_add(&C, b, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* too big */ while (mp_cmp_mag(&C, b) != MP_LT) { if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } } /* C is now the inverse */ mp_exch (&C, c); res = MP_OKAY; -__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); +LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } #endif @@ -3856,13 +3853,13 @@ } if ((res = mp_init (&p1)) != MP_OKAY) { - goto __A1; + goto LBL_A1; } /* divide out larger power of two */ k = mp_cnt_lsb(&a1); if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) { - goto __P1; + goto LBL_P1; } /* step 4. if e is even set s=1 */ @@ -3890,18 +3887,18 @@ } else { /* n1 = n mod a1 */ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) { - goto __P1; + goto LBL_P1; } if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) { - goto __P1; + goto LBL_P1; } *c = s * r; } /* done */ res = MP_OKAY; -__P1:mp_clear (&p1); -__A1:mp_clear (&a1); +LBL_P1:mp_clear (&p1); +LBL_A1:mp_clear (&a1); return res; } #endif @@ -4227,20 +4224,20 @@ /* t1 = get the GCD of the two inputs */ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) { - goto __T; + goto LBL_T; } /* divide the smallest by the GCD */ if (mp_cmp_mag(a, b) == MP_LT) { /* store quotient in t2 such that t2 * b is the LCM */ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) { - goto __T; + goto LBL_T; } res = mp_mul(b, &t2, c); } else { /* store quotient in t2 such that t2 * a is the LCM */ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) { - goto __T; + goto LBL_T; } res = mp_mul(a, &t2, c); } @@ -4248,7 +4245,7 @@ /* fix the sign to positive */ c->sign = MP_ZPOS; -__T: +LBL_T: mp_clear_multi (&t1, &t2, NULL); return res; } @@ -4402,7 +4399,7 @@ } /* if the modulus is larger than the value than return */ - if (b > (int) (a->used * DIGIT_BIT)) { + if (b >= (int) (a->used * DIGIT_BIT)) { res = mp_copy (a, c); return res; } @@ -4484,7 +4481,6 @@ /* how many bits of last digit does b use */ bits = mp_count_bits (b) % DIGIT_BIT; - if (b->used > 1) { if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { return res; @@ -4983,8 +4979,9 @@ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); } - /* store final carry [if any] */ + /* store final carry [if any] and increment ix offset */ *tmpc++ = u; + ++ix; /* now zero digits above the top */ while (ix++ < olduse) { @@ -5085,11 +5082,11 @@ } if ((res = mp_init (&t2)) != MP_OKAY) { - goto __T1; + goto LBL_T1; } if ((res = mp_init (&t3)) != MP_OKAY) { - goto __T2; + goto LBL_T2; } /* if a is negative fudge the sign but keep track */ @@ -5102,52 +5099,52 @@ do { /* t1 = t2 */ if ((res = mp_copy (&t2, &t1)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ /* t3 = t1**(b-1) */ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* numerator */ /* t2 = t1**b */ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* t2 = t1**b - a */ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* denominator */ /* t3 = t1**(b-1) * b */ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } /* t3 = (t1**b - a)/(b * t1**(b-1)) */ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } } while (mp_cmp (&t1, &t2) != MP_EQ); /* result can be off by a few so check */ for (;;) { if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } if (mp_cmp (&t2, a) == MP_GT) { if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) { - goto __T3; + goto LBL_T3; } } else { break; @@ -5165,9 +5162,9 @@ res = MP_OKAY; -__T3:mp_clear (&t3); -__T2:mp_clear (&t2); -__T1:mp_clear (&t1); +LBL_T3:mp_clear (&t3); +LBL_T2:mp_clear (&t2); +LBL_T1:mp_clear (&t1); return res; } #endif @@ -5196,12 +5193,18 @@ int mp_neg (mp_int * a, mp_int * b) { int res; - if ((res = mp_copy (a, b)) != MP_OKAY) { - return res; - } + if (a != b) { + if ((res = mp_copy (a, b)) != MP_OKAY) { + return res; + } + } + if (mp_iszero(b) != MP_YES) { b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; - } + } else { + b->sign = MP_ZPOS; + } + return MP_OKAY; } #endif @@ -5304,7 +5307,7 @@ /* compute t = b**a mod a */ if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) { - goto __T; + goto LBL_T; } /* is it equal to b? */ @@ -5313,7 +5316,7 @@ } err = MP_OKAY; -__T:mp_clear (&t); +LBL_T:mp_clear (&t); return err; } #endif @@ -5352,8 +5355,8 @@ *result = MP_NO; for (ix = 0; ix < PRIME_SIZE; ix++) { - /* what is a mod __prime_tab[ix] */ - if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) { + /* what is a mod LBL_prime_tab[ix] */ + if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) { return err; } @@ -5410,7 +5413,7 @@ /* is the input equal to one of the primes in the table? */ for (ix = 0; ix < PRIME_SIZE; ix++) { - if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) { + if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) { *result = 1; return MP_OKAY; } @@ -5433,20 +5436,20 @@ for (ix = 0; ix < t; ix++) { /* set the prime */ - mp_set (&b, __prime_tab[ix]); + mp_set (&b, ltm_prime_tab[ix]); if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) { - goto __B; + goto LBL_B; } if (res == MP_NO) { - goto __B; + goto LBL_B; } } /* passed the test */ *result = MP_YES; -__B:mp_clear (&b); +LBL_B:mp_clear (&b); return err; } #endif @@ -5496,12 +5499,12 @@ return err; } if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) { - goto __N1; + goto LBL_N1; } /* set 2**s * r = n1 */ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { - goto __N1; + goto LBL_N1; } /* count the number of least significant bits @@ -5511,15 +5514,15 @@ /* now divide n - 1 by 2**s */ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) { - goto __R; + goto LBL_R; } /* compute y = b**r mod a */ if ((err = mp_init (&y)) != MP_OKAY) { - goto __R; + goto LBL_R; } if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* if y != 1 and y != n1 do */ @@ -5528,12 +5531,12 @@ /* while j <= s-1 and y != n1 */ while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) { if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) { - goto __Y; + goto LBL_Y; } /* if y == 1 then composite */ if (mp_cmp_d (&y, 1) == MP_EQ) { - goto __Y; + goto LBL_Y; } ++j; @@ -5541,15 +5544,15 @@ /* if y != n1 then composite */ if (mp_cmp (&y, &n1) != MP_EQ) { - goto __Y; + goto LBL_Y; } } /* probably prime now */ *result = MP_YES; -__Y:mp_clear (&y); -__R:mp_clear (&r); -__N1:mp_clear (&n1); +LBL_Y:mp_clear (&y); +LBL_R:mp_clear (&r); +LBL_N1:mp_clear (&n1); return err; } #endif @@ -5594,10 +5597,10 @@ a->sign = MP_ZPOS; /* simple algo if a is less than the largest prime in the table */ - if (mp_cmp_d(a, __prime_tab[PRIME_SIZE-1]) == MP_LT) { + if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) { /* find which prime it is bigger than */ for (x = PRIME_SIZE - 2; x >= 0; x--) { - if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) { + if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) { if (bbs_style == 1) { /* ok we found a prime smaller or * equal [so the next is larger] @@ -5605,17 +5608,17 @@ * however, the prime must be * congruent to 3 mod 4 */ - if ((__prime_tab[x + 1] & 3) != 3) { + if ((ltm_prime_tab[x + 1] & 3) != 3) { /* scan upwards for a prime congruent to 3 mod 4 */ for (y = x + 1; y < PRIME_SIZE; y++) { - if ((__prime_tab[y] & 3) == 3) { - mp_set(a, __prime_tab[y]); + if ((ltm_prime_tab[y] & 3) == 3) { + mp_set(a, ltm_prime_tab[y]); return MP_OKAY; } } } } else { - mp_set(a, __prime_tab[x + 1]); + mp_set(a, ltm_prime_tab[x + 1]); return MP_OKAY; } } @@ -5653,7 +5656,7 @@ /* generate the restable */ for (x = 1; x < PRIME_SIZE; x++) { - if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) { + if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) { return err; } } @@ -5679,8 +5682,8 @@ res_tab[x] += kstep; /* subtract the modulus [instead of using division] */ - if (res_tab[x] >= __prime_tab[x]) { - res_tab[x] -= __prime_tab[x]; + if (res_tab[x] >= ltm_prime_tab[x]) { + res_tab[x] -= ltm_prime_tab[x]; } /* set flag if zero */ @@ -5692,7 +5695,7 @@ /* add the step */ if ((err = mp_add_d(a, step, a)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } /* if didn't pass sieve and step == MAX then skip test */ @@ -5702,9 +5705,9 @@ /* is this prime? */ for (x = 0; x < t; x++) { - mp_set(&b, __prime_tab[t]); + mp_set(&b, ltm_prime_tab[t]); if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { - goto __ERR; + goto LBL_ERR; } if (res == MP_NO) { break; @@ -5717,7 +5720,7 @@ } err = MP_OKAY; -__ERR: +LBL_ERR: mp_clear(&b); return err; } @@ -5828,7 +5831,7 @@ } /* calc the byte size */ - bsize = (size>>3)+(size&7?1:0); + bsize = (size>>3) + ((size&7)?1:0); /* we need a buffer of bsize bytes */ tmp = OPT_CAST(unsigned char) XMALLOC(bsize); @@ -5837,19 +5840,19 @@ } /* calc the maskAND value for the MSbyte*/ - maskAND = 0xFF >> (8 - (size & 7)); + maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7))); /* calc the maskOR_msb */ maskOR_msb = 0; - maskOR_msb_offset = (size - 2) >> 3; + maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0; if (flags & LTM_PRIME_2MSB_ON) { maskOR_msb |= 1 << ((size - 2) & 7); } else if (flags & LTM_PRIME_2MSB_OFF) { maskAND &= ~(1 << ((size - 2) & 7)); - } + } /* get the maskOR_lsb */ - maskOR_lsb = 0; + maskOR_lsb = 1; if (flags & LTM_PRIME_BBS) { maskOR_lsb |= 3; } @@ -5943,22 +5946,29 @@ return MP_VAL; } - /* init a copy of the input */ - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; + if (mp_iszero(a) == MP_YES) { + *size = 2; + return MP_OKAY; } /* digs is the digit count */ digs = 0; /* if it's negative add one for the sign */ - if (t.sign == MP_NEG) { + if (a->sign == MP_NEG) { ++digs; - t.sign = MP_ZPOS; - } + } + + /* init a copy of the input */ + if ((res = mp_init_copy (&t, a)) != MP_OKAY) { + return res; + } + + /* force temp to positive */ + t.sign = MP_ZPOS; /* fetch out all of the digits */ - while (mp_iszero (&t) == 0) { + while (mp_iszero (&t) == MP_NO) { if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { mp_clear (&t); return res; @@ -6032,14 +6042,14 @@ /* first place a random non-zero digit */ do { - d = ((mp_digit) abs (rand ())); + d = ((mp_digit) abs (rand ())) & MP_MASK; } while (d == 0); if ((res = mp_add_d (a, d, a)) != MP_OKAY) { return res; } - while (digits-- > 0) { + while (--digits > 0) { if ((res = mp_lshd (a, 1)) != MP_OKAY) { return res; } @@ -6074,7 +6084,7 @@ */ /* read a string [ASCII] in a given radix */ -int mp_read_radix (mp_int * a, char *str, int radix) +int mp_read_radix (mp_int * a, const char *str, int radix) { int y, res, neg; char ch; @@ -6257,8 +6267,7 @@ * precomputed via mp_reduce_setup. * From HAC pp.604 Algorithm 14.42 */ -int -mp_reduce (mp_int * x, mp_int * m, mp_int * mu) +int mp_reduce (mp_int * x, mp_int * m, mp_int * mu) { mp_int q; int res, um = m->used; @@ -6278,11 +6287,11 @@ } } else { #ifdef BN_S_MP_MUL_HIGH_DIGS_C - if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { + if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { goto CLEANUP; } #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) - if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { + if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { goto CLEANUP; } #else @@ -6355,8 +6364,7 @@ */ /* reduces a modulo n where n is of the form 2**p - d */ -int -mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) +int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) { mp_int q; int p, res; @@ -6398,6 +6406,68 @@ /* End: bn_mp_reduce_2k.c */ +/* Start: bn_mp_reduce_2k_l.c */ +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* reduces a modulo n where n is of the form 2**p - d + This differs from reduce_2k since "d" can be larger + than a single digit. +*/ +int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d) +{ + mp_int q; + int p, res; + + if ((res = mp_init(&q)) != MP_OKAY) { + return res; + } + + p = mp_count_bits(n); +top: + /* q = a/2**p, a = a mod 2**p */ + if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) { + goto ERR; + } + + /* q = q * d */ + if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { + goto ERR; + } + + /* a = a + q */ + if ((res = s_mp_add(a, &q, a)) != MP_OKAY) { + goto ERR; + } + + if (mp_cmp_mag(a, n) != MP_LT) { + s_mp_sub(a, n, a); + goto top; + } + +ERR: + mp_clear(&q); + return res; +} + +#endif + +/* End: bn_mp_reduce_2k_l.c */ + /* Start: bn_mp_reduce_2k_setup.c */ #include <tommath.h> #ifdef BN_MP_REDUCE_2K_SETUP_C @@ -6417,8 +6487,7 @@ */ /* determines the setup value */ -int -mp_reduce_2k_setup(mp_int *a, mp_digit *d) +int mp_reduce_2k_setup(mp_int *a, mp_digit *d) { int res, p; mp_int tmp; @@ -6446,6 +6515,50 @@ /* End: bn_mp_reduce_2k_setup.c */ +/* Start: bn_mp_reduce_2k_setup_l.c */ +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_SETUP_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* determines the setup value */ +int mp_reduce_2k_setup_l(mp_int *a, mp_int *d) +{ + int res; + mp_int tmp; + + if ((res = mp_init(&tmp)) != MP_OKAY) { + return res; + } + + if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { + goto ERR; + } + + if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) { + goto ERR; + } + +ERR: + mp_clear(&tmp); + return res; +} +#endif + +/* End: bn_mp_reduce_2k_setup_l.c */ + /* Start: bn_mp_reduce_is_2k.c */ #include <tommath.h> #ifdef BN_MP_REDUCE_IS_2K_C @@ -6471,9 +6584,9 @@ mp_digit iz; if (a->used == 0) { - return 0; + return MP_NO; } else if (a->used == 1) { - return 1; + return MP_YES; } else if (a->used > 1) { iy = mp_count_bits(a); iz = 1; @@ -6482,7 +6595,7 @@ /* Test every bit from the second digit up, must be 1 */ for (ix = DIGIT_BIT; ix < iy; ix++) { if ((a->dp[iw] & iz) == 0) { - return 0; + return MP_NO; } iz <<= 1; if (iz > (mp_digit)MP_MASK) { @@ -6491,13 +6604,57 @@ } } } - return 1; + return MP_YES; } #endif /* End: bn_mp_reduce_is_2k.c */ +/* Start: bn_mp_reduce_is_2k_l.c */ +#include <tommath.h> +#ifdef BN_MP_REDUCE_IS_2K_L_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* determines if reduce_2k_l can be used */ +int mp_reduce_is_2k_l(mp_int *a) +{ + int ix, iy; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + /* if more than half of the digits are -1 we're sold */ + for (iy = ix = 0; ix < a->used; ix++) { + if (a->dp[ix] == MP_MASK) { + ++iy; + } + } + return (iy >= (a->used/2)) ? MP_YES : MP_NO; + + } + return MP_NO; +} + +#endif + +/* End: bn_mp_reduce_is_2k_l.c */ + /* Start: bn_mp_reduce_setup.c */ #include <tommath.h> #ifdef BN_MP_REDUCE_SETUP_C @@ -7132,8 +7289,7 @@ */ /* store in signed [big endian] format */ -int -mp_to_signed_bin (mp_int * a, unsigned char *b) +int mp_to_signed_bin (mp_int * a, unsigned char *b) { int res; @@ -7147,6 +7303,37 @@ /* End: bn_mp_to_signed_bin.c */ +/* Start: bn_mp_to_signed_bin_n.c */ +#include <tommath.h> +#ifdef BN_MP_TO_SIGNED_BIN_N_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* store in signed [big endian] format */ +int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) +{ + if (*outlen < (unsigned long)mp_signed_bin_size(a)) { + return MP_VAL; + } + *outlen = mp_signed_bin_size(a); + return mp_to_signed_bin(a, b); +} +#endif + +/* End: bn_mp_to_signed_bin_n.c */ + /* Start: bn_mp_to_unsigned_bin.c */ #include <tommath.h> #ifdef BN_MP_TO_UNSIGNED_BIN_C @@ -7166,8 +7353,7 @@ */ /* store in unsigned [big endian] format */ -int -mp_to_unsigned_bin (mp_int * a, unsigned char *b) +int mp_to_unsigned_bin (mp_int * a, unsigned char *b) { int x, res; mp_int t; @@ -7196,6 +7382,37 @@ /* End: bn_mp_to_unsigned_bin.c */ +/* Start: bn_mp_to_unsigned_bin_n.c */ +#include <tommath.h> +#ifdef BN_MP_TO_UNSIGNED_BIN_N_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* store in unsigned [big endian] format */ +int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen) +{ + if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) { + return MP_VAL; + } + *outlen = mp_unsigned_bin_size(a); + return mp_to_unsigned_bin(a, b); +} +#endif + +/* End: bn_mp_to_unsigned_bin_n.c */ + /* Start: bn_mp_toom_mul.c */ #include <tommath.h> #ifdef BN_MP_TOOM_MUL_C @@ -7216,9 +7433,10 @@ /* multiplication using the Toom-Cook 3-way algorithm * - * Much more complicated than Karatsuba but has a lower asymptotic running time of - * O(N**1.464). This algorithm is only particularly useful on VERY large - * inputs (we're talking 1000s of digits here...). + * Much more complicated than Karatsuba but has a lower + * asymptotic running time of O(N**1.464). This algorithm is + * only particularly useful on VERY large inputs + * (we're talking 1000s of digits here...). */ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) { @@ -7888,8 +8106,7 @@ */ /* get the size for an unsigned equivalent */ -int -mp_unsigned_bin_size (mp_int * a) +int mp_unsigned_bin_size (mp_int * a) { int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); @@ -7938,7 +8155,7 @@ } for (ix = 0; ix < px; ix++) { - + t.dp[ix] ^= x->dp[ix]; } mp_clamp (&t); mp_exch (c, &t); @@ -7968,12 +8185,18 @@ */ /* set to zero */ -void -mp_zero (mp_int * a) -{ +void mp_zero (mp_int * a) +{ + int n; + mp_digit *tmp; + a->sign = MP_ZPOS; a->used = 0; - memset (a->dp, 0, sizeof (mp_digit) * a->alloc); + + tmp = a->dp; + for (n = 0; n < a->alloc; n++) { + *tmp++ = 0; + } } #endif @@ -7996,7 +8219,7 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -const mp_digit __prime_tab[] = { +const mp_digit ltm_prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, @@ -8212,11 +8435,12 @@ #define TAB_SIZE 256 #endif -int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) +int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) { mp_int M[TAB_SIZE], res, mu; mp_digit buf; int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + int (*redux)(mp_int*,mp_int*,mp_int*); /* find window size */ x = mp_count_bits (X); @@ -8261,11 +8485,20 @@ /* create mu, used for Barrett reduction */ if ((err = mp_init (&mu)) != MP_OKAY) { - goto __M; - } - if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { - goto __MU; - } + goto LBL_M; + } + + if (redmode == 0) { + if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { + goto LBL_MU; + } + redux = mp_reduce; + } else { + if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) { + goto LBL_MU; + } + redux = mp_reduce_2k_l; + } /* create M table * @@ -8276,23 +8509,26 @@ * computed though accept for M[0] and M[1] */ if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) { - goto __MU; + goto LBL_MU; } /* compute the value at M[1<<(winsize-1)] by squaring * M[1] (winsize-1) times */ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __MU; + goto LBL_MU; } for (x = 0; x < (winsize - 1); x++) { + /* square it */ if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto __MU; - } - if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { - goto __MU; + goto LBL_MU; + } + + /* reduce modulo P */ + if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { + goto LBL_MU; } } @@ -8301,16 +8537,16 @@ */ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto __MU; - } - if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) { - goto __MU; + goto LBL_MU; + } + if ((err = redux (&M[x], P, &mu)) != MP_OKAY) { + goto LBL_MU; } } /* setup result */ if ((err = mp_init (&res)) != MP_OKAY) { - goto __MU; + goto LBL_MU; } mp_set (&res, 1); @@ -8350,10 +8586,10 @@ /* if the bit is zero and mode == 1 then we square */ if (mode == 1 && y == 0) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } continue; } @@ -8367,19 +8603,19 @@ /* square first */ for (x = 0; x < winsize; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } } /* then multiply */ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } /* empty window and reset */ @@ -8394,20 +8630,20 @@ /* square then multiply if the bit is set */ for (x = 0; x < bitcpy; x++) { if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } bitbuf <<= 1; if ((bitbuf & (1 << winsize)) != 0) { /* then multiply */ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto __RES; + goto LBL_RES; } - if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) { - goto __RES; + if ((err = redux (&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; } } } @@ -8415,9 +8651,9 @@ mp_exch (&res, Y); err = MP_OKAY; -__RES:mp_clear (&res); -__MU:mp_clear (&mu); -__M: +LBL_RES:mp_clear (&res); +LBL_MU:mp_clear (&mu); +LBL_M: mp_clear(&M[1]); for (x = 1<<(winsize-1); x < (1 << winsize); x++) { mp_clear (&M[x]); @@ -8450,8 +8686,7 @@ * HAC pp. 595, Algorithm 14.12 Modified so you can control how * many digits of output are created. */ -int -s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { mp_int t; int res, pa, pb, ix, iy; @@ -8619,8 +8854,7 @@ */ /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ -int -s_mp_sqr (mp_int * a, mp_int * b) +int s_mp_sqr (mp_int * a, mp_int * b) { mp_int t; int res, ix, iy, pa; @@ -8797,11 +9031,12 @@ CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) + AMD Athlon64 /GCC v3.4.4 / 74/ 124/LTM 0.34 */ -int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */ +int KARATSUBA_MUL_CUTOFF = 74, /* Min. number of digits before Karatsuba multiplication is used. */ + KARATSUBA_SQR_CUTOFF = 124, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/tombc/grammar.txt Fri May 06 08:59:30 2005 +0000 @@ -0,0 +1,35 @@ +program := program statement | statement | empty +statement := { statement } | + identifier = numexpression; | + identifier[numexpression] = numexpression; | + function(expressionlist); | + for (identifer = numexpression; numexpression; identifier = numexpression) { statement } | + while (numexpression) { statement } | + if (numexpresion) { statement } elif | + break; | + continue; + +elif := else statement | empty +function := abs | countbits | exptmod | jacobi | print | isprime | nextprime | issquare | readinteger | exit +expressionlist := expressionlist, expression | expression + +// LR(1) !!!? +expression := string | numexpression +numexpression := cmpexpr && cmpexpr | cmpexpr \|\| cmpexpr | cmpexpr +cmpexpr := boolexpr < boolexpr | boolexpr > boolexpr | boolexpr == boolexpr | + boolexpr <= boolexpr | boolexpr >= boolexpr | boolexpr +boolexpr := shiftexpr & shiftexpr | shiftexpr ^ shiftexpr | shiftexpr \| shiftexpr | shiftexpr +shiftexpr := addsubexpr << addsubexpr | addsubexpr >> addsubexpr | addsubexpr +addsubexpr := mulexpr + mulexpr | mulexpr - mulexpr | mulexpr +mulexpr := expr * expr | expr / expr | expr % expr | expr +expr := -nexpr | nexpr +nexpr := integer | identifier | ( numexpression ) | identifier[numexpression] + +identifier := identifer digits | identifier alpha | alpha +alpha := a ... z | A ... Z +integer := hexnumber | digits +hexnumber := 0xhexdigits +hexdigits := hexdigits hexdigit | hexdigit +hexdigit := 0 ... 9 | a ... f | A ... F +digits := digits digit | digit +digit := 0 ... 9
--- a/tommath.h Sun Dec 19 11:33:56 2004 +0000 +++ b/tommath.h Fri May 06 08:59:30 2005 +0000 @@ -429,6 +429,15 @@ /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); +/* returns true if a can be reduced with mp_reduce_2k_l */ +int mp_reduce_is_2k_l(mp_int *a); + +/* determines k value for 2k reduction */ +int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); + +/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ +int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); + /* d = a**b (mod c) */ int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); @@ -442,7 +451,7 @@ #endif /* table of first PRIME_SIZE primes */ -extern const mp_digit __prime_tab[]; +extern const mp_digit ltm_prime_tab[]; /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ int mp_prime_is_divisible(mp_int *a, int *result); @@ -511,12 +520,14 @@ int mp_unsigned_bin_size(mp_int *a); int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c); int mp_to_unsigned_bin(mp_int *a, unsigned char *b); +int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); int mp_signed_bin_size(mp_int *a); int mp_read_signed_bin(mp_int *a, unsigned char *b, int c); int mp_to_signed_bin(mp_int *a, unsigned char *b); +int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); -int mp_read_radix(mp_int *a, char *str, int radix); +int mp_read_radix(mp_int *a, const char *str, int radix); int mp_toradix(mp_int *a, char *str, int radix); int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); int mp_radix_size(mp_int *a, int radix, int *size); @@ -554,7 +565,7 @@ int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); -int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y); +int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); void bn_reverse(unsigned char *s, int len); extern const char *mp_s_rmap;
--- a/tommath.src Sun Dec 19 11:33:56 2004 +0000 +++ b/tommath.src Fri May 06 08:59:30 2005 +0000 @@ -49,7 +49,7 @@ \begin{document} \frontmatter \pagestyle{empty} -\title{Implementing Multiple Precision Arithmetic \\ ~ \\ Draft Edition } +\title{Multi--Precision Math} \author{\mbox{ %\begin{small} \begin{tabular}{c} @@ -66,7 +66,7 @@ } } \maketitle -This text has been placed in the public domain. This text corresponds to the v0.30 release of the +This text has been placed in the public domain. This text corresponds to the v0.35 release of the LibTomMath project. \begin{alltt} @@ -85,66 +85,32 @@ \tableofcontents \listoffigures -\chapter*{Prefaces to the Draft Edition} -I started this text in April 2003 to complement my LibTomMath library. That is, explain how to implement the functions -contained in LibTomMath. The goal is to have a textbook that any Computer Science student can use when implementing their -own multiple precision arithmetic. The plan I wanted to follow was flesh out all the -ideas and concepts I had floating around in my head and then work on it afterwards refining a little bit at a time. Chance -would have it that I ended up with my summer off from Algonquin College and I was given four months solid to work on the -text. - -Choosing to not waste any time I dove right into the project even before my spring semester was finished. I wrote a bit -off and on at first. The moment my exams were finished I jumped into long 12 to 16 hour days. The result after only -a couple of months was a ten chapter, three hundred page draft that I quickly had distributed to anyone who wanted -to read it. I had Jean-Luc Cooke print copies for me and I brought them to Crypto'03 in Santa Barbara. So far I have -managed to grab a certain level of attention having people from around the world ask me for copies of the text was certain -rewarding. - -Now we are past December 2003. By this time I had pictured that I would have at least finished my second draft of the text. -Currently I am far off from this goal. I've done partial re-writes of chapters one, two and three but they are not even -finished yet. I haven't given up on the project, only had some setbacks. First O'Reilly declined to publish the text then -Addison-Wesley and Greg is tried another which I don't know the name of. However, at this point I want to focus my energy -onto finishing the book not securing a contract. - -So why am I writing this text? It seems like a lot of work right? Most certainly it is a lot of work writing a textbook. -Even the simplest introductory material has to be lined with references and figures. A lot of the text has to be re-written -from point form to prose form to ensure an easier read. Why am I doing all this work for free then? Simple. My philosophy -is quite simply ``Open Source. Open Academia. Open Minds'' which means that to achieve a goal of open minds, that is, -people willing to accept new ideas and explore the unknown you have to make available material they can access freely -without hinderance. - -I've been writing free software since I was about sixteen but only recently have I hit upon software that people have come -to depend upon. I started LibTomCrypt in December 2001 and now several major companies use it as integral portions of their -software. Several educational institutions use it as a matter of course and many freelance developers use it as -part of their projects. To further my contributions I started the LibTomMath project in December 2002 aimed at providing -multiple precision arithmetic routines that students could learn from. That is write routines that are not only easy -to understand and follow but provide quite impressive performance considering they are all in standard portable ISO C. - -The second leg of my philosophy is ``Open Academia'' which is where this textbook comes in. In the end, when all is -said and done the text will be useable by educational institutions as a reference on multiple precision arithmetic. - -At this time I feel I should share a little information about myself. The most common question I was asked at -Crypto'03, perhaps just out of professional courtesy, was which school I either taught at or attended. The unfortunate -truth is that I neither teach at or attend a school of academic reputation. I'm currently at Algonquin College which -is what I'd like to call ``somewhat academic but mostly vocational'' college. In otherwords, job training. - -I'm a 21 year old computer science student mostly self-taught in the areas I am aware of (which includes a half-dozen -computer science fields, a few fields of mathematics and some English). I look forward to teaching someday but I am -still far off from that goal. - -Now it would be improper for me to not introduce the rest of the texts co-authors. While they are only contributing -corrections and editorial feedback their support has been tremendously helpful in presenting the concepts laid out -in the text so far. Greg has always been there for me. He has tracked my LibTom projects since their inception and even -sent cheques to help pay tuition from time to time. His background has provided a wonderful source to bounce ideas off -of and improve the quality of my writing. Mads is another fellow who has just ``been there''. I don't even recall what -his interest in the LibTom projects is but I'm definitely glad he has been around. His ability to catch logical errors -in my written English have saved me on several occasions to say the least. - -What to expect next? Well this is still a rough draft. I've only had the chance to update a few chapters. However, I've -been getting the feeling that people are starting to use my text and I owe them some updated material. My current tenative -plan is to edit one chapter every two weeks starting January 4th. It seems insane but my lower course load at college -should provide ample time. By Crypto'04 I plan to have a 2nd draft of the text polished and ready to hand out to as many -people who will take it. +\chapter*{Prefaces} +When I tell people about my LibTom projects and that I release them as public domain they are often puzzled. +They ask why I did it and especially why I continue to work on them for free. The best I can explain it is ``Because I can.'' +Which seems odd and perhaps too terse for adult conversation. I often qualify it with ``I am able, I am willing.'' which +perhaps explains it better. I am the first to admit there is not anything that special with what I have done. Perhaps +others can see that too and then we would have a society to be proud of. My LibTom projects are what I am doing to give +back to society in the form of tools and knowledge that can help others in their endeavours. + +I started writing this book because it was the most logical task to further my goal of open academia. The LibTomMath source +code itself was written to be easy to follow and learn from. There are times, however, where pure C source code does not +explain the algorithms properly. Hence this book. The book literally starts with the foundation of the library and works +itself outwards to the more complicated algorithms. The use of both pseudo--code and verbatim source code provides a duality +of ``theory'' and ``practice'' that the computer science students of the world shall appreciate. I never deviate too far +from relatively straightforward algebra and I hope that this book can be a valuable learning asset. + +This book and indeed much of the LibTom projects would not exist in their current form if it was not for a plethora +of kind people donating their time, resources and kind words to help support my work. Writing a text of significant +length (along with the source code) is a tiresome and lengthy process. Currently the LibTom project is four years old, +comprises of literally thousands of users and over 100,000 lines of source code, TeX and other material. People like Mads and Greg +were there at the beginning to encourage me to work well. It is amazing how timely validation from others can boost morale to +continue the project. Definitely my parents were there for me by providing room and board during the many months of work in 2003. + +To my many friends whom I have met through the years I thank you for the good times and the words of encouragement. I hope I +honour your kind gestures with this project. + +Open Source. Open Academia. Open Minds. \begin{flushright} Tom St Denis \end{flushright} @@ -937,7 +903,7 @@ EXAM,bn_mp_grow.c -A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line @23,if@) checks +A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line @24,alloc@) checks if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count. If the count is not larger than \textbf{alloc} the function skips the re-allocation part thus saving time. @@ -1310,7 +1276,7 @@ With the mp\_int representation of an integer, calculating the absolute value is trivial. The mp\_abs algorithm will compute the absolute value of an mp\_int. -\newpage\begin{figure}[here] +\begin{figure}[here] \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{mp\_abs}. \\ @@ -1335,6 +1301,9 @@ EXAM,bn_mp_abs.c +This fairly trivial algorithm first eliminates non--required duplications (line @27,a != b@) and then sets the +\textbf{sign} flag to \textbf{MP\_ZPOS}. + \subsection{Integer Negation} With the mp\_int representation of an integer, calculating the negation is also trivial. The mp\_neg algorithm will compute the negative of an mp\_int input. @@ -1368,11 +1337,15 @@ EXAM,bn_mp_neg.c +Like mp\_abs() this function avoids non--required duplications (line @21,a != b@) and then sets the sign. We +have to make sure that only non--zero values get a \textbf{sign} of \textbf{MP\_NEG}. If the mp\_int is zero +than the \textbf{sign} is hard--coded to \textbf{MP\_ZPOS}. + \section{Small Constants} \subsection{Setting Small Constants} Often a mp\_int must be set to a relatively small value such as $1$ or $2$. For these cases the mp\_set algorithm is useful. -\begin{figure}[here] +\newpage\begin{figure}[here] \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{mp\_set}. \\ @@ -1397,11 +1370,14 @@ EXAM,bn_mp_set.c -Line @21,mp_zero@ calls mp\_zero() to clear the mp\_int and reset the sign. Line @22,MP_MASK@ copies the digit -into the least significant location. Note the usage of a new constant \textbf{MP\_MASK}. This constant is used to quickly -reduce an integer modulo $\beta$. Since $\beta$ is of the form $2^k$ for any suitable $k$ it suffices to perform a binary AND with -$MP\_MASK = 2^k - 1$ to perform the reduction. Finally line @23,a->used@ will set the \textbf{used} member with respect to the -digit actually set. This function will always make the integer positive. +First we zero (line @21,mp_zero@) the mp\_int to make sure that the other members are initialized for a +small positive constant. mp\_zero() ensures that the \textbf{sign} is positive and the \textbf{used} count +is zero. Next we set the digit and reduce it modulo $\beta$ (line @22,MP_MASK@). After this step we have to +check if the resulting digit is zero or not. If it is not then we set the \textbf{used} count to one, otherwise +to zero. + +We can quickly reduce modulo $\beta$ since it is of the form $2^k$ and a quick binary AND operation with +$2^k - 1$ will perform the same operation. One important limitation of this function is that it will only set one digit. The size of a digit is not fixed, meaning source that uses this function should take that into account. Only trivially small constants can be set using this function. @@ -1503,10 +1479,12 @@ EXAM,bn_mp_cmp_mag.c -The two if statements on lines @24,if@ and @28,if@ compare the number of digits in the two inputs. These two are performed before all of the digits -are compared since it is a very cheap test to perform and can potentially save considerable time. The implementation given is also not valid -without those two statements. $b.alloc$ may be smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the -array of digits. +The two if statements (lines @24,if@ and @28,if@) compare the number of digits in the two inputs. These two are +performed before all of the digits are compared since it is a very cheap test to perform and can potentially save +considerable time. The implementation given is also not valid without those two statements. $b.alloc$ may be +smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the array of digits. + + \subsection{Signed Comparisons} Comparing with sign considerations is also fairly critical in several routines (\textit{division for example}). Based on an unsigned magnitude @@ -1539,9 +1517,9 @@ EXAM,bn_mp_cmp.c -The two if statements on lines @22,if@ and @26,if@ perform the initial sign comparison. If the signs are not the equal then which ever -has the positive sign is larger. At line @30,if@, the inputs are compared based on magnitudes. If the signs were both negative then -the unsigned comparison is performed in the opposite direction (\textit{line @31,mp_cmp_mag@}). Otherwise, the signs are assumed to +The two if statements (lines @22,if@ and @26,if@) perform the initial sign comparison. If the signs are not the equal then which ever +has the positive sign is larger. The inputs are compared (line @30,if@) based on magnitudes. If the signs were both +negative then the unsigned comparison is performed in the opposite direction (line @31,mp_cmp_mag@). Otherwise, the signs are assumed to be both positive and a forward direction unsigned comparison is performed. \section*{Exercises} @@ -1664,19 +1642,21 @@ EXAM,bn_s_mp_add.c -Lines @27,if@ to @35,}@ perform the initial sorting of the inputs and determine the $min$ and $max$ variables. Note that $x$ is a pointer to a -mp\_int assigned to the largest input, in effect it is a local alias. Lines @37,init@ to @42,}@ ensure that the destination is grown to -accomodate the result of the addition. +We first sort (lines @27,if@ to @35,}@) the inputs based on magnitude and determine the $min$ and $max$ variables. +Note that $x$ is a pointer to an mp\_int assigned to the largest input, in effect it is a local alias. Next we +grow the destination (@37,init@ to @42,}@) ensure that it can accomodate the result of the addition. Similar to the implementation of mp\_copy this function uses the braced code and local aliases coding style. The three aliases that are on lines @56,tmpa@, @59,tmpb@ and @62,tmpc@ represent the two inputs and destination variables respectively. These aliases are used to ensure the compiler does not have to dereference $a$, $b$ or $c$ (respectively) to access the digits of the respective mp\_int. -The initial carry $u$ is cleared on line @65,u = 0@, note that $u$ is of type mp\_digit which ensures type compatibility within the -implementation. The initial addition loop begins on line @66,for@ and ends on line @75,}@. Similarly the conditional addition loop -begins on line @81,for@ and ends on line @90,}@. The addition is finished with the final carry being stored in $tmpc$ on line @94,tmpc++@. -Note the ``++'' operator on the same line. After line @94,tmpc++@ $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$. This is useful -for the next loop on lines @97,for@ to @99,}@ which set any old upper digits to zero. +The initial carry $u$ will be cleared (line @65,u = 0@), note that $u$ is of type mp\_digit which ensures type +compatibility within the implementation. The initial addition (line @66,for@ to @75,}@) adds digits from +both inputs until the smallest input runs out of digits. Similarly the conditional addition loop +(line @81,for@ to @90,}@) adds the remaining digits from the larger of the two inputs. The addition is finished +with the final carry being stored in $tmpc$ (line @94,tmpc++@). Note the ``++'' operator within the same expression. +After line @94,tmpc++@, $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$. This is useful +for the next loop (line @97,for@ to @99,}@) which set any old upper digits to zero. \subsection{Low Level Subtraction} The low level unsigned subtraction algorithm is very similar to the low level unsigned addition algorithm. The principle difference is that the @@ -1692,7 +1672,7 @@ mp\_digit (\textit{this implies $2^{\gamma} > \beta$}). For example, the default for LibTomMath is to use a ``unsigned long'' for the mp\_digit ``type'' while $\beta = 2^{28}$. In ISO C an ``unsigned long'' -data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma = 32$. +data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma \ge 32$. \newpage\begin{figure}[!here] \begin{center} @@ -1759,20 +1739,23 @@ EXAM,bn_s_mp_sub.c -Line @24,min@ and @25,max@ perform the initial hardcoded sorting of the inputs. In reality the $min$ and $max$ variables are only aliases and are only -used to make the source code easier to read. Again the pointer alias optimization is used within this algorithm. Lines @42,tmpa@, @43,tmpb@ and @44,tmpc@ initialize the aliases for -$a$, $b$ and $c$ respectively. - -The first subtraction loop occurs on lines @47,u = 0@ through @61,}@. The theory behind the subtraction loop is exactly the same as that for -the addition loop. As remarked earlier there is an implementation reason for using the ``awkward'' method of extracting the carry -(\textit{see line @57, >>@}). The traditional method for extracting the carry would be to shift by $lg(\beta)$ positions and logically AND -the least significant bit. The AND operation is required because all of the bits above the $\lg(\beta)$'th bit will be set to one after a carry -occurs from subtraction. This carry extraction requires two relatively cheap operations to extract the carry. The other method is to simply -shift the most significant bit to the least significant bit thus extracting the carry with a single cheap operation. This optimization only works on -twos compliment machines which is a safe assumption to make. - -If $a$ has a larger magnitude than $b$ an additional loop (\textit{see lines @64,for@ through @73,}@}) is required to propagate the carry through -$a$ and copy the result to $c$. +Like low level addition we ``sort'' the inputs. Except in this case the sorting is hardcoded +(lines @24,min@ and @25,max@). In reality the $min$ and $max$ variables are only aliases and are only +used to make the source code easier to read. Again the pointer alias optimization is used +within this algorithm. The aliases $tmpa$, $tmpb$ and $tmpc$ are initialized +(lines @42,tmpa@, @43,tmpb@ and @44,tmpc@) for $a$, $b$ and $c$ respectively. + +The first subtraction loop (lines @47,u = 0@ through @61,}@) subtract digits from both inputs until the smaller of +the two inputs has been exhausted. As remarked earlier there is an implementation reason for using the ``awkward'' +method of extracting the carry (line @57, >>@). The traditional method for extracting the carry would be to shift +by $lg(\beta)$ positions and logically AND the least significant bit. The AND operation is required because all of +the bits above the $\lg(\beta)$'th bit will be set to one after a carry occurs from subtraction. This carry +extraction requires two relatively cheap operations to extract the carry. The other method is to simply shift the +most significant bit to the least significant bit thus extracting the carry with a single cheap operation. This +optimization only works on twos compliment machines which is a safe assumption to make. + +If $a$ has a larger magnitude than $b$ an additional loop (lines @64,for@ through @73,}@) is required to propagate +the carry through $a$ and copy the result to $c$. \subsection{High Level Addition} Now that both lower level addition and subtraction algorithms have been established an effective high level signed addition algorithm can be @@ -2098,10 +2081,11 @@ EXAM,bn_mp_lshd.c -The if statement on line @24,if@ ensures that the $b$ variable is greater than zero. The \textbf{used} count is incremented by $b$ before -the copy loop begins. This elminates the need for an additional variable in the for loop. The variable $top$ on line @42,top@ is an alias -for the leading digit while $bottom$ on line @45,bottom@ is an alias for the trailing edge. The aliases form a window of exactly $b$ digits -over the input. +The if statement (line @24,if@) ensures that the $b$ variable is greater than zero since we do not interpret negative +shift counts properly. The \textbf{used} count is incremented by $b$ before the copy loop begins. This elminates +the need for an additional variable in the for loop. The variable $top$ (line @42,top@) is an alias +for the leading digit while $bottom$ (line @45,bottom@) is an alias for the trailing edge. The aliases form a +window of exactly $b$ digits over the input. \subsection{Division by $x$} @@ -2151,9 +2135,9 @@ EXAM,bn_mp_rshd.c -The only noteworthy element of this routine is the lack of a return type. - --- Will update later to give it a return type...Tom +The only noteworthy element of this routine is the lack of a return type since it cannot fail. Like mp\_lshd() we +form a sliding window except we copy in the other direction. After the window (line @59,for (;@) we then zero +the upper digits of the input to make sure the result is correct. \section{Powers of Two} @@ -2214,7 +2198,15 @@ EXAM,bn_mp_mul_2d.c -Notes to be revised when code is updated. -- Tom +The shifting is performed in--place which means the first step (line @24,a != c@) is to copy the input to the +destination. We avoid calling mp\_copy() by making sure the mp\_ints are different. The destination then +has to be grown (line @31,grow@) to accomodate the result. + +If the shift count $b$ is larger than $lg(\beta)$ then a call to mp\_lshd() is used to handle all of the multiples +of $lg(\beta)$. Leaving only a remaining shift of $lg(\beta) - 1$ or fewer bits left. Inside the actual shift +loop (lines @45,if@ to @76,}@) we make use of pre--computed values $shift$ and $mask$. These are used to +extract the carry bit(s) to pass into the next iteration of the loop. The $r$ and $rr$ variables form a +chain between consecutive iterations to propagate the carry. \subsection{Division by Power of Two} @@ -2263,7 +2255,8 @@ result of the remainder operation until the end. This allows $d$ and $a$ to represent the same mp\_int without modifying $a$ before the quotient is obtained. -The remainder of the source code is essentially the same as the source code for mp\_mul\_2d. (-- Fix this paragraph up later, Tom). +The remainder of the source code is essentially the same as the source code for mp\_mul\_2d. The only significant difference is +the direction of the shifts. \subsection{Remainder of Division by Power of Two} @@ -2306,7 +2299,13 @@ EXAM,bn_mp_mod_2d.c --- Add comments later, Tom. +We first avoid cases of $b \le 0$ by simply mp\_zero()'ing the destination in such cases. Next if $2^b$ is larger +than the input we just mp\_copy() the input and return right away. After this point we know we must actually +perform some work to produce the remainder. + +Recalling that reducing modulo $2^k$ and a binary ``and'' with $2^k - 1$ are numerically equivalent we can quickly reduce +the number. First we zero any digits above the last digit in $2^b$ (line @41,for@). Next we reduce the +leading digit of both (line @45,&=@) and then mp\_clamp(). \section*{Exercises} \begin{tabular}{cl} @@ -2464,33 +2463,46 @@ EXAM,bn_s_mp_mul_digs.c -Lines @31,if@ to @35,}@ determine if the Comba method can be used first. The conditions for using the Comba routine are that min$(a.used, b.used) < \delta$ and -the number of digits of output is less than \textbf{MP\_WARRAY}. This new constant is used to control -the stack usage in the Comba routines. By default it is set to $\delta$ but can be reduced when memory is at a premium. - -Of particular importance is the calculation of the $ix+iy$'th column on lines @64,mp_word@, @65,mp_word@ and @66,mp_word@. Note how all of the -variables are cast to the type \textbf{mp\_word}, which is also the type of variable $\hat r$. That is to ensure that double precision operations -are used instead of single precision. The multiplication on line @65,) * (@ makes use of a specific GCC optimizer behaviour. On the outset it looks like -the compiler will have to use a double precision multiplication to produce the result required. Such an operation would be horribly slow on most -processors and drag this to a crawl. However, GCC is smart enough to realize that double wide output single precision multipliers can be used. For -example, the instruction ``MUL'' on the x86 processor can multiply two 32-bit values and produce a 64-bit result. +First we determine (line @30,if@) if the Comba method can be used first since it's faster. The conditions for +sing the Comba routine are that min$(a.used, b.used) < \delta$ and the number of digits of output is less than +\textbf{MP\_WARRAY}. This new constant is used to control the stack usage in the Comba routines. By default it is +set to $\delta$ but can be reduced when memory is at a premium. + +If we cannot use the Comba method we proceed to setup the baseline routine. We allocate the the destination mp\_int +$t$ (line @36,init@) to the exact size of the output to avoid further re--allocations. At this point we now +begin the $O(n^2)$ loop. + +This implementation of multiplication has the caveat that it can be trimmed to only produce a variable number of +digits as output. In each iteration of the outer loop the $pb$ variable is set (line @48,MIN@) to the maximum +number of inner loop iterations. + +Inside the inner loop we calculate $\hat r$ as the mp\_word product of the two mp\_digits and the addition of the +carry from the previous iteration. A particularly important observation is that most modern optimizing +C compilers (GCC for instance) can recognize that a $N \times N \rightarrow 2N$ multiplication is all that +is required for the product. In x86 terms for example, this means using the MUL instruction. + +Each digit of the product is stored in turn (line @68,tmpt@) and the carry propagated (line @71,>>@) to the +next iteration. \subsection{Faster Multiplication by the ``Comba'' Method} MARK,COMBA -One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be computed and propagated upwards. This -makes the nested loop very sequential and hard to unroll and implement in parallel. The ``Comba'' \cite{COMBA} method is named after little known -(\textit{in cryptographic venues}) Paul G. Comba who described a method of implementing fast multipliers that do not require nested -carry fixup operations. As an interesting aside it seems that Paul Barrett describes a similar technique in -his 1986 paper \cite{BARRETT} written five years before. - -At the heart of the Comba technique is once again the long-hand algorithm. Except in this case a slight twist is placed on how -the columns of the result are produced. In the standard long-hand algorithm rows of products are produced then added together to form the -final result. In the baseline algorithm the columns are added together after each iteration to get the result instantaneously. - -In the Comba algorithm the columns of the result are produced entirely independently of each other. That is at the $O(n^2)$ level a -simple multiplication and addition step is performed. The carries of the columns are propagated after the nested loop to reduce the amount -of work requiored. Succintly the first step of the algorithm is to compute the product vector $\vec x$ as follows. +One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be +computed and propagated upwards. This makes the nested loop very sequential and hard to unroll and implement +in parallel. The ``Comba'' \cite{COMBA} method is named after little known (\textit{in cryptographic venues}) Paul G. +Comba who described a method of implementing fast multipliers that do not require nested carry fixup operations. As an +interesting aside it seems that Paul Barrett describes a similar technique in his 1986 paper \cite{BARRETT} written +five years before. + +At the heart of the Comba technique is once again the long-hand algorithm. Except in this case a slight +twist is placed on how the columns of the result are produced. In the standard long-hand algorithm rows of products +are produced then added together to form the final result. In the baseline algorithm the columns are added together +after each iteration to get the result instantaneously. + +In the Comba algorithm the columns of the result are produced entirely independently of each other. That is at +the $O(n^2)$ level a simple multiplication and addition step is performed. The carries of the columns are propagated +after the nested loop to reduce the amount of work requiored. Succintly the first step of the algorithm is to compute +the product vector $\vec x$ as follows. \begin{equation} \vec x_n = \sum_{i+j = n} a_ib_j, \forall n \in \lbrace 0, 1, 2, \ldots, i + j \rbrace @@ -2584,38 +2596,32 @@ \textbf{Input}. mp\_int $a$, mp\_int $b$ and an integer $digs$ \\ \textbf{Output}. $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\ \hline \\ -Place an array of \textbf{MP\_WARRAY} double precision digits named $\hat W$ on the stack. \\ +Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the stack. \\ 1. If $c.alloc < digs$ then grow $c$ to $digs$ digits. (\textit{mp\_grow}) \\ 2. If step 1 failed return(\textit{MP\_MEM}).\\ \\ -Zero the temporary array $\hat W$. \\ -3. for $n$ from $0$ to $digs - 1$ do \\ -\hspace{3mm}3.1 $\hat W_n \leftarrow 0$ \\ -\\ -Compute the columns. \\ -4. for $ix$ from $0$ to $a.used - 1$ do \\ -\hspace{3mm}4.1 $pb \leftarrow \mbox{min}(b.used, digs - ix)$ \\ -\hspace{3mm}4.2 If $pb < 1$ then goto step 5. \\ -\hspace{3mm}4.3 for $iy$ from $0$ to $pb - 1$ do \\ -\hspace{6mm}4.3.1 $\hat W_{ix+iy} \leftarrow \hat W_{ix+iy} + a_{ix}b_{iy}$ \\ +3. $pa \leftarrow \mbox{MIN}(digs, a.used + b.used)$ \\ \\ -Propagate the carries upwards. \\ -5. $oldused \leftarrow c.used$ \\ -6. $c.used \leftarrow digs$ \\ -7. If $digs > 1$ then do \\ -\hspace{3mm}7.1. for $ix$ from $1$ to $digs - 1$ do \\ -\hspace{6mm}7.1.1 $\hat W_{ix} \leftarrow \hat W_{ix} + \lfloor \hat W_{ix-1} / \beta \rfloor$ \\ -\hspace{6mm}7.1.2 $c_{ix - 1} \leftarrow \hat W_{ix - 1} \mbox{ (mod }\beta\mbox{)}$ \\ -8. else do \\ -\hspace{3mm}8.1 $ix \leftarrow 0$ \\ -9. $c_{ix} \leftarrow \hat W_{ix} \mbox{ (mod }\beta\mbox{)}$ \\ +4. $\_ \hat W \leftarrow 0$ \\ +5. for $ix$ from 0 to $pa - 1$ do \\ +\hspace{3mm}5.1 $ty \leftarrow \mbox{MIN}(b.used - 1, ix)$ \\ +\hspace{3mm}5.2 $tx \leftarrow ix - ty$ \\ +\hspace{3mm}5.3 $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\ +\hspace{3mm}5.4 for $iz$ from 0 to $iy - 1$ do \\ +\hspace{6mm}5.4.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\ +\hspace{3mm}5.5 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\ +\hspace{3mm}5.6 $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\ +6. $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\ \\ -Zero excess digits. \\ -10. If $digs < oldused$ then do \\ -\hspace{3mm}10.1 for $n$ from $digs$ to $oldused - 1$ do \\ -\hspace{6mm}10.1.1 $c_n \leftarrow 0$ \\ -11. Clamp excessive digits of $c$. (\textit{mp\_clamp}) \\ -12. Return(\textit{MP\_OKAY}). \\ +7. $oldused \leftarrow c.used$ \\ +8. $c.used \leftarrow digs$ \\ +9. for $ix$ from $0$ to $pa$ do \\ +\hspace{3mm}9.1 $c_{ix} \leftarrow W_{ix}$ \\ +10. for $ix$ from $pa + 1$ to $oldused - 1$ do \\ +\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\ +\\ +11. Clamp $c$. \\ +12. Return MP\_OKAY. \\ \hline \end{tabular} \end{center} @@ -2625,15 +2631,24 @@ \end{figure} \textbf{Algorithm fast\_s\_mp\_mul\_digs.} -This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision. The algorithm -essentially peforms the same calculation as algorithm s\_mp\_mul\_digs, just much faster. - -The array $\hat W$ is meant to be on the stack when the algorithm is used. The size of the array does not change which is ideal. Note also that -unlike algorithm s\_mp\_mul\_digs no temporary mp\_int is required since the result is calculated directly in $\hat W$. - -The $O(n^2)$ loop on step four is where the Comba method's advantages begin to show through in comparison to the baseline algorithm. The lack of -a carry variable or propagation in this loop allows the loop to be performed with only single precision multiplication and additions. Now that each -iteration of the inner loop can be performed independent of the others the inner loop can be performed with a high level of parallelism. +This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision. + +The outer loop of this algorithm is more complicated than that of the baseline multiplier. This is because on the inside of the +loop we want to produce one column per pass. This allows the accumulator $\_ \hat W$ to be placed in CPU registers and +reduce the memory bandwidth to two \textbf{mp\_digit} reads per iteration. + +The $ty$ variable is set to the minimum count of $ix$ or the number of digits in $b$. That way if $a$ has more digits than +$b$ this will be limited to $b.used - 1$. The $tx$ variable is set to the to the distance past $b.used$ the variable +$ix$ is. This is used for the immediately subsequent statement where we find $iy$. + +The variable $iy$ is the minimum digits we can read from either $a$ or $b$ before running out. Computing one column at a time +means we have to scan one integer upwards and the other downwards. $a$ starts at $tx$ and $b$ starts at $ty$. In each +pass we are producing the $ix$'th output column and we note that $tx + ty = ix$. As we move $tx$ upwards we have to +move $ty$ downards so the equality remains valid. The $iy$ variable is the number of iterations until +$tx \ge a.used$ or $ty < 0$ occurs. + +After every inner pass we store the lower half of the accumulator into $W_{ix}$ and then propagate the carry of the accumulator +into the next round by dividing $\_ \hat W$ by $\beta$. To measure the benefits of the Comba method over the baseline method consider the number of operations that are required. If the cost in terms of time of a multiply and addition is $p$ and the cost of a carry propagation is $q$ then a baseline multiplication would require @@ -2643,20 +2658,20 @@ EXAM,bn_fast_s_mp_mul_digs.c -The memset on line @47,memset@ clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication -implementation a series of aliases (\textit{lines @67, tmpx@, @70, tmpy@ and @75,_W@}) are used to simplify the inner $O(n^2)$ loop. -In this case a new alias $\_\hat W$ has been added which refers to the double precision columns offset by $ix$ in each pass. - -The inner loop on lines @83,for@, @84,mp_word@ and @85,}@ is where the algorithm will spend the majority of the time, which is why it has been -stripped to the bones of any extra baggage\footnote{Hence the pointer aliases.}. On x86 processors the multiplication and additions amount to at the -very least five instructions (\textit{two loads, two additions, one multiply}) while on the ARMv4 processors they amount to only three -(\textit{one load, one store, one multiply-add}). For both of the x86 and ARMv4 processors the GCC compiler performs a good job at unrolling the loop -and scheduling the instructions so there are very few dependency stalls. - -In theory the difference between the baseline and comba algorithms is a mere $O(qn)$ time difference. However, in the $O(n^2)$ nested loop of the -baseline method there are dependency stalls as the algorithm must wait for the multiplier to finish before propagating the carry to the next -digit. As a result fewer of the often multiple execution units\footnote{The AMD Athlon has three execution units and the Intel P4 has four.} can -be simultaneously used. +As per the pseudo--code we first calculate $pa$ (line @47,MIN@) as the number of digits to output. Next we begin the outer loop +to produce the individual columns of the product. We use the two aliases $tmpx$ and $tmpy$ (lines @61,tmpx@, @62,tmpy@) to point +inside the two multiplicands quickly. + +The inner loop (lines @70,for@ to @72,}@) of this implementation is where the tradeoff come into play. Originally this comba +implementation was ``row--major'' which means it adds to each of the columns in each pass. After the outer loop it would then fix +the carries. This was very fast except it had an annoying drawback. You had to read a mp\_word and two mp\_digits and write +one mp\_word per iteration. On processors such as the Athlon XP and P4 this did not matter much since the cache bandwidth +is very high and it can keep the ALU fed with data. It did, however, matter on older and embedded cpus where cache is often +slower and also often doesn't exist. This new algorithm only performs two reads per iteration under the assumption that the +compiler has aliased $\_ \hat W$ to a CPU register. + +After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines @75,W[ix]@, @78,>>@) to forward it as +a carry for the next pass. After the outer loop we use the final carry (line @82,W[ix]@) as the last digit of the product. \subsection{Polynomial Basis Multiplication} To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication. In the following algorithms @@ -2976,13 +2991,26 @@ EXAM,bn_mp_toom_mul.c --- Comments to be added during editing phase. +The first obvious thing to note is that this algorithm is complicated. The complexity is worth it if you are multiplying very +large numbers. For example, a 10,000 digit multiplication takes approximaly 99,282,205 fewer single precision multiplications with +Toom--Cook than a Comba or baseline approach (this is a savings of more than 99$\%$). For most ``crypto'' sized numbers this +algorithm is not practical as Karatsuba has a much lower cutoff point. + +First we split $a$ and $b$ into three roughly equal portions. This has been accomplished (lines @40,mod@ to @69,rshd@) with +combinations of mp\_rshd() and mp\_mod\_2d() function calls. At this point $a = a2 \cdot \beta^2 + a1 \cdot \beta + a0$ and similiarly +for $b$. + +Next we compute the five points $w0, w1, w2, w3$ and $w4$. Recall that $w0$ and $w4$ can be computed directly from the portions so +we get those out of the way first (lines @72,mul@ and @77,mul@). Next we compute $w1, w2$ and $w3$ using Horners method. + +After this point we solve for the actual values of $w1, w2$ and $w3$ by reducing the $5 \times 5$ system which is relatively +straight forward. \subsection{Signed Multiplication} Now that algorithms to handle multiplications of every useful dimensions have been developed, a rather simple finishing touch is required. So far all of the multiplication algorithms have been unsigned multiplications which leaves only a signed multiplication algorithm to be established. -\newpage\begin{figure}[!here] +\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} @@ -3065,7 +3093,7 @@ The baseline squaring algorithm is meant to be a catch-all squaring algorithm. It will handle any of the input sizes that the faster routines will not handle. -\newpage\begin{figure}[!here] +\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} @@ -3121,9 +3149,14 @@ EXAM,bn_s_mp_sqr.c -Inside the outer loop (\textit{see line @32,for@}) the square term is calculated on line @35,r =@. Line @42,>>@ extracts the carry from the square -term. Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized on lines @45,tmpx@ and @48,tmpt@ respectively. The doubling is performed using two -additions (\textit{see line @57,r + r@}) since it is usually faster than shifting,if not at least as fast. +Inside the outer loop (line @32,for@) the square term is calculated on line @35,r =@. The carry (line @42,>>@) has been +extracted from the mp\_word accumulator using a right shift. Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized +(lines @45,tmpx@ and @48,tmpt@) to simplify the inner loop. The doubling is performed using two +additions (line @57,r + r@) since it is usually faster than shifting, if not at least as fast. + +The important observation is that the inner loop does not begin at $iy = 0$ like for multiplication. As such the inner loops +get progressively shorter as the algorithm proceeds. This is what leads to the savings compared to using a multiplication to +square a number. \subsection{Faster Squaring by the ``Comba'' Method} A major drawback to the baseline method is the requirement for single precision shifting inside the $O(n^2)$ nested loop. Squaring has an additional @@ -3135,9 +3168,9 @@ that $2a + 2b + 2c = 2(a + b + c)$. That is the sum of all of the double products is equal to double the sum of all the products. For example, $ab + ba + ac + ca = 2ab + 2ac = 2(ab + ac)$. -However, we cannot simply double all of the columns, since the squares appear only once per row. The most practical solution is to have two mp\_word -arrays. One array will hold the squares and the other array will hold the double products. With both arrays the doubling and carry propagation can be -moved to a $O(n)$ work level outside the $O(n^2)$ level. +However, we cannot simply double all of the columns, since the squares appear only once per row. The most practical solution is to have two +mp\_word arrays. One array will hold the squares and the other array will hold the double products. With both arrays the doubling and +carry propagation can be moved to a $O(n)$ work level outside the $O(n^2)$ level. In this case, we have an even simpler solution in mind. \newpage\begin{figure}[!here] \begin{small} @@ -3147,34 +3180,34 @@ \textbf{Input}. mp\_int $a$ \\ \textbf{Output}. $b \leftarrow a^2$ \\ \hline \\ -Place two arrays of \textbf{MP\_WARRAY} mp\_words named $\hat W$ and $\hat {X}$ on the stack. \\ +Place an array of \textbf{MP\_WARRAY} mp\_digits named $W$ on the stack. \\ 1. If $b.alloc < 2a.used + 1$ then grow $b$ to $2a.used + 1$ digits. (\textit{mp\_grow}). \\ 2. If step 1 failed return(\textit{MP\_MEM}). \\ -3. for $ix$ from $0$ to $2a.used + 1$ do \\ -\hspace{3mm}3.1 $\hat W_{ix} \leftarrow 0$ \\ -\hspace{3mm}3.2 $\hat {X}_{ix} \leftarrow 0$ \\ -4. for $ix$ from $0$ to $a.used - 1$ do \\ -\hspace{3mm}Compute the square.\\ -\hspace{3mm}4.1 $\hat {X}_{ix+ix} \leftarrow \left ( a_{ix} \right )^2$ \\ -\\ -\hspace{3mm}Compute the double products.\\ -\hspace{3mm}4.2 for $iy$ from $ix + 1$ to $a.used - 1$ do \\ -\hspace{6mm}4.2.1 $\hat W_{ix+iy} \leftarrow \hat W_{ix+iy} + a_{ix}a_{iy}$ \\ -5. $oldused \leftarrow b.used$ \\ -6. $b.used \leftarrow 2a.used + 1$ \\ \\ -Double the products and propagate the carries simultaneously. \\ -7. $\hat W_0 \leftarrow 2 \hat W_0 + \hat {X}_0$ \\ -8. for $ix$ from $1$ to $2a.used$ do \\ -\hspace{3mm}8.1 $\hat W_{ix} \leftarrow 2 \hat W_{ix} + \hat {X}_{ix}$ \\ -\hspace{3mm}8.2 $\hat W_{ix} \leftarrow \hat W_{ix} + \lfloor \hat W_{ix - 1} / \beta \rfloor$ \\ -\hspace{3mm}8.3 $b_{ix-1} \leftarrow W_{ix-1} \mbox{ (mod }\beta\mbox{)}$ \\ -9. $b_{2a.used} \leftarrow \hat W_{2a.used} \mbox{ (mod }\beta\mbox{)}$ \\ -10. if $2a.used + 1 < oldused$ then do \\ -\hspace{3mm}10.1 for $ix$ from $2a.used + 1$ to $oldused$ do \\ -\hspace{6mm}10.1.1 $b_{ix} \leftarrow 0$ \\ -11. Clamp excess digits from $b$. (\textit{mp\_clamp}) \\ -12. Return(\textit{MP\_OKAY}). \\ +3. $pa \leftarrow 2 \cdot a.used$ \\ +4. $\hat W1 \leftarrow 0$ \\ +5. for $ix$ from $0$ to $pa - 1$ do \\ +\hspace{3mm}5.1 $\_ \hat W \leftarrow 0$ \\ +\hspace{3mm}5.2 $ty \leftarrow \mbox{MIN}(a.used - 1, ix)$ \\ +\hspace{3mm}5.3 $tx \leftarrow ix - ty$ \\ +\hspace{3mm}5.4 $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\ +\hspace{3mm}5.5 $iy \leftarrow \mbox{MIN}(iy, \lfloor \left (ty - tx + 1 \right )/2 \rfloor)$ \\ +\hspace{3mm}5.6 for $iz$ from $0$ to $iz - 1$ do \\ +\hspace{6mm}5.6.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx + iz}a_{ty - iz}$ \\ +\hspace{3mm}5.7 $\_ \hat W \leftarrow 2 \cdot \_ \hat W + \hat W1$ \\ +\hspace{3mm}5.8 if $ix$ is even then \\ +\hspace{6mm}5.8.1 $\_ \hat W \leftarrow \_ \hat W + \left ( a_{\lfloor ix/2 \rfloor}\right )^2$ \\ +\hspace{3mm}5.9 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\ +\hspace{3mm}5.10 $\hat W1 \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\ +\\ +6. $oldused \leftarrow b.used$ \\ +7. $b.used \leftarrow 2 \cdot a.used$ \\ +8. for $ix$ from $0$ to $pa - 1$ do \\ +\hspace{3mm}8.1 $b_{ix} \leftarrow W_{ix}$ \\ +9. for $ix$ from $pa$ to $oldused - 1$ do \\ +\hspace{3mm}9.1 $b_{ix} \leftarrow 0$ \\ +10. Clamp excess digits from $b$. (\textit{mp\_clamp}) \\ +11. Return(\textit{MP\_OKAY}). \\ \hline \end{tabular} \end{center} @@ -3183,24 +3216,24 @@ \end{figure} \textbf{Algorithm fast\_s\_mp\_sqr.} -This algorithm computes the square of an input using the Comba technique. It is designed to be a replacement for algorithm s\_mp\_sqr when -the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$. - -This routine requires two arrays of mp\_words to be placed on the stack. The first array $\hat W$ will hold the double products and the second -array $\hat X$ will hold the squares. Though only at most $MP\_WARRAY \over 2$ words of $\hat X$ are used, it has proven faster on most -processors to simply make it a full size array. - -The loop on step 3 will zero the two arrays to prepare them for the squaring step. Step 4.1 computes the squares of the product. Note how -it simply assigns the value into the $\hat X$ array. The nested loop on step 4.2 computes the doubles of the products. This loop -computes the sum of the products for each column. They are not doubled until later. - -After the squaring loop, the products stored in $\hat W$ musted be doubled and the carries propagated forwards. It makes sense to do both -operations at the same time. The expression $\hat W_{ix} \leftarrow 2 \hat W_{ix} + \hat {X}_{ix}$ computes the sum of the double product and the -squares in place. +This algorithm computes the square of an input using the Comba technique. It is designed to be a replacement for algorithm +s\_mp\_sqr when the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$. +This algorithm is very similar to the Comba multiplier except with a few key differences we shall make note of. + +First, we have an accumulator and carry variables $\_ \hat W$ and $\hat W1$ respectively. This is because the inner loop +products are to be doubled. If we had added the previous carry in we would be doubling too much. Next we perform an +addition MIN condition on $iy$ (step 5.5) to prevent overlapping digits. For example, $a_3 \cdot a_5$ is equal +$a_5 \cdot a_3$. Whereas in the multiplication case we would have $5 < a.used$ and $3 \ge 0$ is maintained since we double the sum +of the products just outside the inner loop we have to avoid doing this. This is also a good thing since we perform +fewer multiplications and the routine ends up being faster. + +Finally the last difference is the addition of the ``square'' term outside the inner loop (step 5.8). We add in the square +only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rfloor$ position. EXAM,bn_fast_s_mp_sqr.c --- Write something deep and insightful later, Tom. +This implementation is essentially a copy of Comba multiplication with the appropriate changes added to make it faster for +the special case of squaring. \subsection{Polynomial Basis Squaring} The same algorithm that performs optimal polynomial basis multiplication can be used to perform polynomial basis squaring. The minor exception @@ -3312,14 +3345,13 @@ is exactly at the point where Comba squaring can no longer be used (\textit{128 digits}). On slower processors such as the Intel P4 it is actually below the Comba limit (\textit{at 110 digits}). -This routine uses the same error trap coding style as mp\_karatsuba\_sqr. As the temporary variables are initialized errors are redirected to -the error trap higher up. If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and mp\_clears are executed normally. - -\textit{Last paragraph sucks. re-write! -- Tom} +This routine uses the same error trap coding style as mp\_karatsuba\_sqr. As the temporary variables are initialized errors are +redirected to the error trap higher up. If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and +mp\_clears are executed normally. \subsection{Toom-Cook Squaring} The Toom-Cook squaring algorithm mp\_toom\_sqr is heavily based on the algorithm mp\_toom\_mul with the exception that squarings are used -instead of multiplication to find the five relations.. The reader is encouraged to read the description of the latter algorithm and try to +instead of multiplication to find the five relations. The reader is encouraged to read the description of the latter algorithm and try to derive their own Toom-Cook squaring algorithm. \subsection{High Level Squaring} @@ -3362,12 +3394,9 @@ $\left [ 3 \right ] $ & Devise an efficient algorithm for selection of the radix point to handle inputs \\ & that have different number of digits in Karatsuba multiplication. \\ & \\ -$\left [ 3 \right ] $ & In ~SQUARE~ the fact that every column of a squaring is made up \\ +$\left [ 2 \right ] $ & In ~SQUARE~ the fact that every column of a squaring is made up \\ & of double products and at most one square is stated. Prove this statement. \\ & \\ -$\left [ 2 \right ] $ & In the Comba squaring algorithm half of the $\hat X$ variables are not used. \\ - & Revise algorithm fast\_s\_mp\_sqr to shrink the $\hat X$ array. \\ - & \\ $\left [ 3 \right ] $ & Prove the equation for Karatsuba squaring. \\ & \\ $\left [ 1 \right ] $ & Prove that Karatsuba squaring requires $O \left (n^{lg(3)} \right )$ time. \\ @@ -3375,6 +3404,14 @@ $\left [ 2 \right ] $ & Determine the minimal ratio between addition and multiplication clock cycles \\ & required for equation $6.7$ to be true. \\ & \\ +$\left [ 3 \right ] $ & Implement a threaded version of Comba multiplication (and squaring) where you \\ + & compute subsets of the columns in each thread. Determine a cutoff point where \\ + & it is effective and add the logic to mp\_mul() and mp\_sqr(). \\ + &\\ +$\left [ 4 \right ] $ & Same as the previous but also modify the Karatsuba and Toom-Cook. You must \\ + & increase the throughput of mp\_exptmod() for random odd moduli in the range \\ + & $512 \ldots 4096$ bits significantly ($> 2x$) to complete this challenge. \\ + & \\ \end{tabular} \chapter{Modular Reduction} @@ -3394,7 +3431,7 @@ Modular reductions are normally used to create either finite groups, rings or fields. The most common usage for performance driven modular reductions is in modular exponentiation algorithms. That is to compute $d = a^b \mbox{ (mod }c\mbox{)}$ as fast as possible. This operation is used in the RSA and Diffie-Hellman public key algorithms, for example. Modular multiplication and squaring also appears as a fundamental operation in -Elliptic Curve cryptographic algorithms. As will be discussed in the subsequent chapter there exist fast algorithms for computing modular +elliptic curve cryptographic algorithms. As will be discussed in the subsequent chapter there exist fast algorithms for computing modular exponentiations without having to perform (\textit{in this example}) $b - 1$ multiplications. These algorithms will produce partial results in the range $0 \le x < c^2$ which can be taken advantage of to create several efficient algorithms. They have also been used to create redundancy check algorithms known as CRCs, error correction codes such as Reed-Solomon and solve a variety of number theoeretic problems. @@ -3610,7 +3647,7 @@ In order to use algorithm mp\_reduce the value of $\mu$ must be calculated in advance. Ideally this value should be computed once and stored for future use so that the Barrett algorithm can be used without delay. -\begin{figure}[!here] +\newpage\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} @@ -5818,6 +5855,8 @@ defined. The Legendre function computes whether or not an integer $a$ is a quadratic residue modulo an odd prime $p$. Numerically it is equivalent to equation \ref{eqn:legendre}. +\textit{-- Tom, don't be an ass, cite your source here...!} + \begin{equation} a^{(p-1)/2} \equiv \begin{array}{rl} -1 & \mbox{if }a\mbox{ is a quadratic non-residue.} \\
--- a/tommath.tex Sun Dec 19 11:33:56 2004 +0000 +++ b/tommath.tex Fri May 06 08:59:30 2005 +0000 @@ -49,7 +49,7 @@ \begin{document} \frontmatter \pagestyle{empty} -\title{Implementing Multiple Precision Arithmetic \\ ~ \\ Draft Edition } +\title{Multi--Precision Math} \author{\mbox{ %\begin{small} \begin{tabular}{c} @@ -66,7 +66,7 @@ } } \maketitle -This text has been placed in the public domain. This text corresponds to the v0.30 release of the +This text has been placed in the public domain. This text corresponds to the v0.35 release of the LibTomMath project. \begin{alltt} @@ -85,66 +85,32 @@ \tableofcontents \listoffigures -\chapter*{Prefaces to the Draft Edition} -I started this text in April 2003 to complement my LibTomMath library. That is, explain how to implement the functions -contained in LibTomMath. The goal is to have a textbook that any Computer Science student can use when implementing their -own multiple precision arithmetic. The plan I wanted to follow was flesh out all the -ideas and concepts I had floating around in my head and then work on it afterwards refining a little bit at a time. Chance -would have it that I ended up with my summer off from Algonquin College and I was given four months solid to work on the -text. - -Choosing to not waste any time I dove right into the project even before my spring semester was finished. I wrote a bit -off and on at first. The moment my exams were finished I jumped into long 12 to 16 hour days. The result after only -a couple of months was a ten chapter, three hundred page draft that I quickly had distributed to anyone who wanted -to read it. I had Jean-Luc Cooke print copies for me and I brought them to Crypto'03 in Santa Barbara. So far I have -managed to grab a certain level of attention having people from around the world ask me for copies of the text was certain -rewarding. - -Now we are past December 2003. By this time I had pictured that I would have at least finished my second draft of the text. -Currently I am far off from this goal. I've done partial re-writes of chapters one, two and three but they are not even -finished yet. I haven't given up on the project, only had some setbacks. First O'Reilly declined to publish the text then -Addison-Wesley and Greg is tried another which I don't know the name of. However, at this point I want to focus my energy -onto finishing the book not securing a contract. - -So why am I writing this text? It seems like a lot of work right? Most certainly it is a lot of work writing a textbook. -Even the simplest introductory material has to be lined with references and figures. A lot of the text has to be re-written -from point form to prose form to ensure an easier read. Why am I doing all this work for free then? Simple. My philosophy -is quite simply ``Open Source. Open Academia. Open Minds'' which means that to achieve a goal of open minds, that is, -people willing to accept new ideas and explore the unknown you have to make available material they can access freely -without hinderance. - -I've been writing free software since I was about sixteen but only recently have I hit upon software that people have come -to depend upon. I started LibTomCrypt in December 2001 and now several major companies use it as integral portions of their -software. Several educational institutions use it as a matter of course and many freelance developers use it as -part of their projects. To further my contributions I started the LibTomMath project in December 2002 aimed at providing -multiple precision arithmetic routines that students could learn from. That is write routines that are not only easy -to understand and follow but provide quite impressive performance considering they are all in standard portable ISO C. - -The second leg of my philosophy is ``Open Academia'' which is where this textbook comes in. In the end, when all is -said and done the text will be useable by educational institutions as a reference on multiple precision arithmetic. - -At this time I feel I should share a little information about myself. The most common question I was asked at -Crypto'03, perhaps just out of professional courtesy, was which school I either taught at or attended. The unfortunate -truth is that I neither teach at or attend a school of academic reputation. I'm currently at Algonquin College which -is what I'd like to call ``somewhat academic but mostly vocational'' college. In otherwords, job training. - -I'm a 21 year old computer science student mostly self-taught in the areas I am aware of (which includes a half-dozen -computer science fields, a few fields of mathematics and some English). I look forward to teaching someday but I am -still far off from that goal. - -Now it would be improper for me to not introduce the rest of the texts co-authors. While they are only contributing -corrections and editorial feedback their support has been tremendously helpful in presenting the concepts laid out -in the text so far. Greg has always been there for me. He has tracked my LibTom projects since their inception and even -sent cheques to help pay tuition from time to time. His background has provided a wonderful source to bounce ideas off -of and improve the quality of my writing. Mads is another fellow who has just ``been there''. I don't even recall what -his interest in the LibTom projects is but I'm definitely glad he has been around. His ability to catch logical errors -in my written English have saved me on several occasions to say the least. - -What to expect next? Well this is still a rough draft. I've only had the chance to update a few chapters. However, I've -been getting the feeling that people are starting to use my text and I owe them some updated material. My current tenative -plan is to edit one chapter every two weeks starting January 4th. It seems insane but my lower course load at college -should provide ample time. By Crypto'04 I plan to have a 2nd draft of the text polished and ready to hand out to as many -people who will take it. +\chapter*{Prefaces} +When I tell people about my LibTom projects and that I release them as public domain they are often puzzled. +They ask why I did it and especially why I continue to work on them for free. The best I can explain it is ``Because I can.'' +Which seems odd and perhaps too terse for adult conversation. I often qualify it with ``I am able, I am willing.'' which +perhaps explains it better. I am the first to admit there is not anything that special with what I have done. Perhaps +others can see that too and then we would have a society to be proud of. My LibTom projects are what I am doing to give +back to society in the form of tools and knowledge that can help others in their endeavours. + +I started writing this book because it was the most logical task to further my goal of open academia. The LibTomMath source +code itself was written to be easy to follow and learn from. There are times, however, where pure C source code does not +explain the algorithms properly. Hence this book. The book literally starts with the foundation of the library and works +itself outwards to the more complicated algorithms. The use of both pseudo--code and verbatim source code provides a duality +of ``theory'' and ``practice'' that the computer science students of the world shall appreciate. I never deviate too far +from relatively straightforward algebra and I hope that this book can be a valuable learning asset. + +This book and indeed much of the LibTom projects would not exist in their current form if it was not for a plethora +of kind people donating their time, resources and kind words to help support my work. Writing a text of significant +length (along with the source code) is a tiresome and lengthy process. Currently the LibTom project is four years old, +comprises of literally thousands of users and over 100,000 lines of source code, TeX and other material. People like Mads and Greg +were there at the beginning to encourage me to work well. It is amazing how timely validation from others can boost morale to +continue the project. Definitely my parents were there for me by providing room and board during the many months of work in 2003. + +To my many friends whom I have met through the years I thank you for the good times and the words of encouragement. I hope I +honour your kind gestures with this project. + +Open Source. Open Academia. Open Minds. \begin{flushright} Tom St Denis \end{flushright} @@ -1045,7 +1011,7 @@ \end{alltt} \end{small} -A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line 23) checks +A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line 24) checks if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count. If the count is not larger than \textbf{alloc} the function skips the re-allocation part thus saving time. @@ -1590,14 +1556,20 @@ \begin{alltt} 016 017 /* set to zero */ -018 void -019 mp_zero (mp_int * a) -020 \{ -021 a->sign = MP_ZPOS; -022 a->used = 0; -023 memset (a->dp, 0, sizeof (mp_digit) * a->alloc); -024 \} -025 #endif +018 void mp_zero (mp_int * a) +019 \{ +020 int n; +021 mp_digit *tmp; +022 +023 a->sign = MP_ZPOS; +024 a->used = 0; +025 +026 tmp = a->dp; +027 for (n = 0; n < a->alloc; n++) \{ +028 *tmp++ = 0; +029 \} +030 \} +031 #endif \end{alltt} \end{small} @@ -1609,7 +1581,7 @@ With the mp\_int representation of an integer, calculating the absolute value is trivial. The mp\_abs algorithm will compute the absolute value of an mp\_int. -\newpage\begin{figure}[here] +\begin{figure}[here] \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{mp\_abs}. \\ @@ -1662,6 +1634,9 @@ \end{alltt} \end{small} +This fairly trivial algorithm first eliminates non--required duplications (line 27) and then sets the +\textbf{sign} flag to \textbf{MP\_ZPOS}. + \subsection{Integer Negation} With the mp\_int representation of an integer, calculating the negation is also trivial. The mp\_neg algorithm will compute the negative of an mp\_int input. @@ -1702,23 +1677,33 @@ 018 int mp_neg (mp_int * a, mp_int * b) 019 \{ 020 int res; -021 if ((res = mp_copy (a, b)) != MP_OKAY) \{ -022 return res; -023 \} -024 if (mp_iszero(b) != MP_YES) \{ -025 b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; -026 \} -027 return MP_OKAY; -028 \} -029 #endif +021 if (a != b) \{ +022 if ((res = mp_copy (a, b)) != MP_OKAY) \{ +023 return res; +024 \} +025 \} +026 +027 if (mp_iszero(b) != MP_YES) \{ +028 b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS; +029 \} else \{ +030 b->sign = MP_ZPOS; +031 \} +032 +033 return MP_OKAY; +034 \} +035 #endif \end{alltt} \end{small} +Like mp\_abs() this function avoids non--required duplications (line 21) and then sets the sign. We +have to make sure that only non--zero values get a \textbf{sign} of \textbf{MP\_NEG}. If the mp\_int is zero +than the \textbf{sign} is hard--coded to \textbf{MP\_ZPOS}. + \section{Small Constants} \subsection{Setting Small Constants} Often a mp\_int must be set to a relatively small value such as $1$ or $2$. For these cases the mp\_set algorithm is useful. -\begin{figure}[here] +\newpage\begin{figure}[here] \begin{center} \begin{tabular}{l} \hline Algorithm \textbf{mp\_set}. \\ @@ -1757,11 +1742,14 @@ \end{alltt} \end{small} -Line 20 calls mp\_zero() to clear the mp\_int and reset the sign. Line 21 copies the digit -into the least significant location. Note the usage of a new constant \textbf{MP\_MASK}. This constant is used to quickly -reduce an integer modulo $\beta$. Since $\beta$ is of the form $2^k$ for any suitable $k$ it suffices to perform a binary AND with -$MP\_MASK = 2^k - 1$ to perform the reduction. Finally line 22 will set the \textbf{used} member with respect to the -digit actually set. This function will always make the integer positive. +First we zero (line 20) the mp\_int to make sure that the other members are initialized for a +small positive constant. mp\_zero() ensures that the \textbf{sign} is positive and the \textbf{used} count +is zero. Next we set the digit and reduce it modulo $\beta$ (line 21). After this step we have to +check if the resulting digit is zero or not. If it is not then we set the \textbf{used} count to one, otherwise +to zero. + +We can quickly reduce modulo $\beta$ since it is of the form $2^k$ and a quick binary AND operation with +$2^k - 1$ will perform the same operation. One important limitation of this function is that it will only set one digit. The size of a digit is not fixed, meaning source that uses this function should take that into account. Only trivially small constants can be set using this function. @@ -1936,10 +1924,12 @@ \end{alltt} \end{small} -The two if statements on lines 24 and 28 compare the number of digits in the two inputs. These two are performed before all of the digits -are compared since it is a very cheap test to perform and can potentially save considerable time. The implementation given is also not valid -without those two statements. $b.alloc$ may be smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the -array of digits. +The two if statements (lines 24 and 28) compare the number of digits in the two inputs. These two are +performed before all of the digits are compared since it is a very cheap test to perform and can potentially save +considerable time. The implementation given is also not valid without those two statements. $b.alloc$ may be +smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the array of digits. + + \subsection{Signed Comparisons} Comparing with sign considerations is also fairly critical in several routines (\textit{division for example}). Based on an unsigned magnitude @@ -2000,9 +1990,9 @@ \end{alltt} \end{small} -The two if statements on lines 22 and 23 perform the initial sign comparison. If the signs are not the equal then which ever -has the positive sign is larger. At line 31, the inputs are compared based on magnitudes. If the signs were both negative then -the unsigned comparison is performed in the opposite direction (\textit{line 33}). Otherwise, the signs are assumed to +The two if statements (lines 22 and 23) perform the initial sign comparison. If the signs are not the equal then which ever +has the positive sign is larger. The inputs are compared (line 31) based on magnitudes. If the signs were both +negative then the unsigned comparison is performed in the opposite direction (line 33). Otherwise, the signs are assumed to be both positive and a forward direction unsigned comparison is performed. \section*{Exercises} @@ -2218,19 +2208,21 @@ \end{alltt} \end{small} -Lines 27 to 35 perform the initial sorting of the inputs and determine the $min$ and $max$ variables. Note that $x$ is a pointer to a -mp\_int assigned to the largest input, in effect it is a local alias. Lines 37 to 42 ensure that the destination is grown to -accomodate the result of the addition. +We first sort (lines 27 to 35) the inputs based on magnitude and determine the $min$ and $max$ variables. +Note that $x$ is a pointer to an mp\_int assigned to the largest input, in effect it is a local alias. Next we +grow the destination (37 to 42) ensure that it can accomodate the result of the addition. Similar to the implementation of mp\_copy this function uses the braced code and local aliases coding style. The three aliases that are on lines 55, 58 and 61 represent the two inputs and destination variables respectively. These aliases are used to ensure the compiler does not have to dereference $a$, $b$ or $c$ (respectively) to access the digits of the respective mp\_int. -The initial carry $u$ is cleared on line 64, note that $u$ is of type mp\_digit which ensures type compatibility within the -implementation. The initial addition loop begins on line 65 and ends on line 74. Similarly the conditional addition loop -begins on line 80 and ends on line 90. The addition is finished with the final carry being stored in $tmpc$ on line 93. -Note the ``++'' operator on the same line. After line 93 $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$. This is useful -for the next loop on lines 96 to 99 which set any old upper digits to zero. +The initial carry $u$ will be cleared (line 64), note that $u$ is of type mp\_digit which ensures type +compatibility within the implementation. The initial addition (line 65 to 74) adds digits from +both inputs until the smallest input runs out of digits. Similarly the conditional addition loop +(line 80 to 90) adds the remaining digits from the larger of the two inputs. The addition is finished +with the final carry being stored in $tmpc$ (line 93). Note the ``++'' operator within the same expression. +After line 93, $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$. This is useful +for the next loop (line 96 to 99) which set any old upper digits to zero. \subsection{Low Level Subtraction} The low level unsigned subtraction algorithm is very similar to the low level unsigned addition algorithm. The principle difference is that the @@ -2245,7 +2237,7 @@ mp\_digit (\textit{this implies $2^{\gamma} > \beta$}). For example, the default for LibTomMath is to use a ``unsigned long'' for the mp\_digit ``type'' while $\beta = 2^{28}$. In ISO C an ``unsigned long'' -data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma = 32$. +data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma \ge 32$. \newpage\begin{figure}[!here] \begin{center} @@ -2387,20 +2379,23 @@ \end{alltt} \end{small} -Line 24 and 25 perform the initial hardcoded sorting of the inputs. In reality the $min$ and $max$ variables are only aliases and are only -used to make the source code easier to read. Again the pointer alias optimization is used within this algorithm. Lines 41, 42 and 43 initialize the aliases for -$a$, $b$ and $c$ respectively. - -The first subtraction loop occurs on lines 46 through 60. The theory behind the subtraction loop is exactly the same as that for -the addition loop. As remarked earlier there is an implementation reason for using the ``awkward'' method of extracting the carry -(\textit{see line 56}). The traditional method for extracting the carry would be to shift by $lg(\beta)$ positions and logically AND -the least significant bit. The AND operation is required because all of the bits above the $\lg(\beta)$'th bit will be set to one after a carry -occurs from subtraction. This carry extraction requires two relatively cheap operations to extract the carry. The other method is to simply -shift the most significant bit to the least significant bit thus extracting the carry with a single cheap operation. This optimization only works on -twos compliment machines which is a safe assumption to make. - -If $a$ has a larger magnitude than $b$ an additional loop (\textit{see lines 63 through 72}) is required to propagate the carry through -$a$ and copy the result to $c$. +Like low level addition we ``sort'' the inputs. Except in this case the sorting is hardcoded +(lines 24 and 25). In reality the $min$ and $max$ variables are only aliases and are only +used to make the source code easier to read. Again the pointer alias optimization is used +within this algorithm. The aliases $tmpa$, $tmpb$ and $tmpc$ are initialized +(lines 41, 42 and 43) for $a$, $b$ and $c$ respectively. + +The first subtraction loop (lines 46 through 60) subtract digits from both inputs until the smaller of +the two inputs has been exhausted. As remarked earlier there is an implementation reason for using the ``awkward'' +method of extracting the carry (line 56). The traditional method for extracting the carry would be to shift +by $lg(\beta)$ positions and logically AND the least significant bit. The AND operation is required because all of +the bits above the $\lg(\beta)$'th bit will be set to one after a carry occurs from subtraction. This carry +extraction requires two relatively cheap operations to extract the carry. The other method is to simply shift the +most significant bit to the least significant bit thus extracting the carry with a single cheap operation. This +optimization only works on twos compliment machines which is a safe assumption to make. + +If $a$ has a larger magnitude than $b$ an additional loop (lines 63 through 72) is required to propagate +the carry through $a$ and copy the result to $c$. \subsection{High Level Addition} Now that both lower level addition and subtraction algorithms have been established an effective high level signed addition algorithm can be @@ -2985,10 +2980,11 @@ \end{alltt} \end{small} -The if statement on line 23 ensures that the $b$ variable is greater than zero. The \textbf{used} count is incremented by $b$ before -the copy loop begins. This elminates the need for an additional variable in the for loop. The variable $top$ on line 41 is an alias -for the leading digit while $bottom$ on line 44 is an alias for the trailing edge. The aliases form a window of exactly $b$ digits -over the input. +The if statement (line 23) ensures that the $b$ variable is greater than zero since we do not interpret negative +shift counts properly. The \textbf{used} count is incremented by $b$ before the copy loop begins. This elminates +the need for an additional variable in the for loop. The variable $top$ (line 41) is an alias +for the leading digit while $bottom$ (line 44) is an alias for the trailing edge. The aliases form a +window of exactly $b$ digits over the input. \subsection{Division by $x$} @@ -3095,9 +3091,9 @@ \end{alltt} \end{small} -The only noteworthy element of this routine is the lack of a return type. - --- Will update later to give it a return type...Tom +The only noteworthy element of this routine is the lack of a return type since it cannot fail. Like mp\_lshd() we +form a sliding window except we copy in the other direction. After the window (line 59) we then zero +the upper digits of the input to make sure the result is correct. \section{Powers of Two} @@ -3228,7 +3224,15 @@ \end{alltt} \end{small} -Notes to be revised when code is updated. -- Tom +The shifting is performed in--place which means the first step (line 24) is to copy the input to the +destination. We avoid calling mp\_copy() by making sure the mp\_ints are different. The destination then +has to be grown (line 31) to accomodate the result. + +If the shift count $b$ is larger than $lg(\beta)$ then a call to mp\_lshd() is used to handle all of the multiples +of $lg(\beta)$. Leaving only a remaining shift of $lg(\beta) - 1$ or fewer bits left. Inside the actual shift +loop (lines 45 to 76) we make use of pre--computed values $shift$ and $mask$. These are used to +extract the carry bit(s) to pass into the next iteration of the loop. The $r$ and $rr$ variables form a +chain between consecutive iterations to propagate the carry. \subsection{Division by Power of Two} @@ -3361,7 +3365,8 @@ result of the remainder operation until the end. This allows $d$ and $a$ to represent the same mp\_int without modifying $a$ before the quotient is obtained. -The remainder of the source code is essentially the same as the source code for mp\_mul\_2d. (-- Fix this paragraph up later, Tom). +The remainder of the source code is essentially the same as the source code for mp\_mul\_2d. The only significant difference is +the direction of the shifts. \subsection{Remainder of Division by Power of Two} @@ -3420,7 +3425,7 @@ 027 \} 028 029 /* if the modulus is larger than the value than return */ -030 if (b > (int) (a->used * DIGIT_BIT)) \{ +030 if (b >= (int) (a->used * DIGIT_BIT)) \{ 031 res = mp_copy (a, c); 032 return res; 033 \} @@ -3446,7 +3451,13 @@ \end{alltt} \end{small} --- Add comments later, Tom. +We first avoid cases of $b \le 0$ by simply mp\_zero()'ing the destination in such cases. Next if $2^b$ is larger +than the input we just mp\_copy() the input and return right away. After this point we know we must actually +perform some work to produce the remainder. + +Recalling that reducing modulo $2^k$ and a binary ``and'' with $2^k - 1$ are numerically equivalent we can quickly reduce +the number. First we zero any digits above the last digit in $2^b$ (line 41). Next we reduce the +leading digit of both (line 45) and then mp\_clamp(). \section*{Exercises} \begin{tabular}{cl} @@ -3611,101 +3622,113 @@ 018 * HAC pp. 595, Algorithm 14.12 Modified so you can control how 019 * many digits of output are created. 020 */ -021 int -022 s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -023 \{ -024 mp_int t; -025 int res, pa, pb, ix, iy; -026 mp_digit u; -027 mp_word r; -028 mp_digit tmpx, *tmpt, *tmpy; -029 -030 /* can we use the fast multiplier? */ -031 if (((digs) < MP_WARRAY) && -032 MIN (a->used, b->used) < -033 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{ -034 return fast_s_mp_mul_digs (a, b, c, digs); -035 \} -036 -037 if ((res = mp_init_size (&t, digs)) != MP_OKAY) \{ -038 return res; -039 \} -040 t.used = digs; -041 -042 /* compute the digits of the product directly */ -043 pa = a->used; -044 for (ix = 0; ix < pa; ix++) \{ -045 /* set the carry to zero */ -046 u = 0; -047 -048 /* limit ourselves to making digs digits of output */ -049 pb = MIN (b->used, digs - ix); -050 -051 /* setup some aliases */ -052 /* copy of the digit from a used within the nested loop */ -053 tmpx = a->dp[ix]; -054 -055 /* an alias for the destination shifted ix places */ -056 tmpt = t.dp + ix; -057 -058 /* an alias for the digits of b */ -059 tmpy = b->dp; -060 -061 /* compute the columns of the output and propagate the carry */ -062 for (iy = 0; iy < pb; iy++) \{ -063 /* compute the column as a mp_word */ -064 r = ((mp_word)*tmpt) + -065 ((mp_word)tmpx) * ((mp_word)*tmpy++) + -066 ((mp_word) u); -067 -068 /* the new column is the lower part of the result */ -069 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); -070 -071 /* get the carry word from the result */ -072 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); -073 \} -074 /* set carry if it is placed below digs */ -075 if (ix + iy < digs) \{ -076 *tmpt = u; -077 \} -078 \} -079 -080 mp_clamp (&t); -081 mp_exch (&t, c); -082 -083 mp_clear (&t); -084 return MP_OKAY; -085 \} -086 #endif +021 int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +022 \{ +023 mp_int t; +024 int res, pa, pb, ix, iy; +025 mp_digit u; +026 mp_word r; +027 mp_digit tmpx, *tmpt, *tmpy; +028 +029 /* can we use the fast multiplier? */ +030 if (((digs) < MP_WARRAY) && +031 MIN (a->used, b->used) < +032 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{ +033 return fast_s_mp_mul_digs (a, b, c, digs); +034 \} +035 +036 if ((res = mp_init_size (&t, digs)) != MP_OKAY) \{ +037 return res; +038 \} +039 t.used = digs; +040 +041 /* compute the digits of the product directly */ +042 pa = a->used; +043 for (ix = 0; ix < pa; ix++) \{ +044 /* set the carry to zero */ +045 u = 0; +046 +047 /* limit ourselves to making digs digits of output */ +048 pb = MIN (b->used, digs - ix); +049 +050 /* setup some aliases */ +051 /* copy of the digit from a used within the nested loop */ +052 tmpx = a->dp[ix]; +053 +054 /* an alias for the destination shifted ix places */ +055 tmpt = t.dp + ix; +056 +057 /* an alias for the digits of b */ +058 tmpy = b->dp; +059 +060 /* compute the columns of the output and propagate the carry */ +061 for (iy = 0; iy < pb; iy++) \{ +062 /* compute the column as a mp_word */ +063 r = ((mp_word)*tmpt) + +064 ((mp_word)tmpx) * ((mp_word)*tmpy++) + +065 ((mp_word) u); +066 +067 /* the new column is the lower part of the result */ +068 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); +069 +070 /* get the carry word from the result */ +071 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); +072 \} +073 /* set carry if it is placed below digs */ +074 if (ix + iy < digs) \{ +075 *tmpt = u; +076 \} +077 \} +078 +079 mp_clamp (&t); +080 mp_exch (&t, c); +081 +082 mp_clear (&t); +083 return MP_OKAY; +084 \} +085 #endif \end{alltt} \end{small} -Lines 31 to 35 determine if the Comba method can be used first. The conditions for using the Comba routine are that min$(a.used, b.used) < \delta$ and -the number of digits of output is less than \textbf{MP\_WARRAY}. This new constant is used to control -the stack usage in the Comba routines. By default it is set to $\delta$ but can be reduced when memory is at a premium. - -Of particular importance is the calculation of the $ix+iy$'th column on lines 64, 65 and 66. Note how all of the -variables are cast to the type \textbf{mp\_word}, which is also the type of variable $\hat r$. That is to ensure that double precision operations -are used instead of single precision. The multiplication on line 65 makes use of a specific GCC optimizer behaviour. On the outset it looks like -the compiler will have to use a double precision multiplication to produce the result required. Such an operation would be horribly slow on most -processors and drag this to a crawl. However, GCC is smart enough to realize that double wide output single precision multipliers can be used. For -example, the instruction ``MUL'' on the x86 processor can multiply two 32-bit values and produce a 64-bit result. +First we determine (line 30) if the Comba method can be used first since it's faster. The conditions for +sing the Comba routine are that min$(a.used, b.used) < \delta$ and the number of digits of output is less than +\textbf{MP\_WARRAY}. This new constant is used to control the stack usage in the Comba routines. By default it is +set to $\delta$ but can be reduced when memory is at a premium. + +If we cannot use the Comba method we proceed to setup the baseline routine. We allocate the the destination mp\_int +$t$ (line 36) to the exact size of the output to avoid further re--allocations. At this point we now +begin the $O(n^2)$ loop. + +This implementation of multiplication has the caveat that it can be trimmed to only produce a variable number of +digits as output. In each iteration of the outer loop the $pb$ variable is set (line 48) to the maximum +number of inner loop iterations. + +Inside the inner loop we calculate $\hat r$ as the mp\_word product of the two mp\_digits and the addition of the +carry from the previous iteration. A particularly important observation is that most modern optimizing +C compilers (GCC for instance) can recognize that a $N \times N \rightarrow 2N$ multiplication is all that +is required for the product. In x86 terms for example, this means using the MUL instruction. + +Each digit of the product is stored in turn (line 68) and the carry propagated (line 71) to the +next iteration. \subsection{Faster Multiplication by the ``Comba'' Method} -One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be computed and propagated upwards. This -makes the nested loop very sequential and hard to unroll and implement in parallel. The ``Comba'' \cite{COMBA} method is named after little known -(\textit{in cryptographic venues}) Paul G. Comba who described a method of implementing fast multipliers that do not require nested -carry fixup operations. As an interesting aside it seems that Paul Barrett describes a similar technique in -his 1986 paper \cite{BARRETT} written five years before. - -At the heart of the Comba technique is once again the long-hand algorithm. Except in this case a slight twist is placed on how -the columns of the result are produced. In the standard long-hand algorithm rows of products are produced then added together to form the -final result. In the baseline algorithm the columns are added together after each iteration to get the result instantaneously. - -In the Comba algorithm the columns of the result are produced entirely independently of each other. That is at the $O(n^2)$ level a -simple multiplication and addition step is performed. The carries of the columns are propagated after the nested loop to reduce the amount -of work requiored. Succintly the first step of the algorithm is to compute the product vector $\vec x$ as follows. +One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be +computed and propagated upwards. This makes the nested loop very sequential and hard to unroll and implement +in parallel. The ``Comba'' \cite{COMBA} method is named after little known (\textit{in cryptographic venues}) Paul G. +Comba who described a method of implementing fast multipliers that do not require nested carry fixup operations. As an +interesting aside it seems that Paul Barrett describes a similar technique in his 1986 paper \cite{BARRETT} written +five years before. + +At the heart of the Comba technique is once again the long-hand algorithm. Except in this case a slight +twist is placed on how the columns of the result are produced. In the standard long-hand algorithm rows of products +are produced then added together to form the final result. In the baseline algorithm the columns are added together +after each iteration to get the result instantaneously. + +In the Comba algorithm the columns of the result are produced entirely independently of each other. That is at +the $O(n^2)$ level a simple multiplication and addition step is performed. The carries of the columns are propagated +after the nested loop to reduce the amount of work requiored. Succintly the first step of the algorithm is to compute +the product vector $\vec x$ as follows. \begin{equation} \vec x_n = \sum_{i+j = n} a_ib_j, \forall n \in \lbrace 0, 1, 2, \ldots, i + j \rbrace @@ -3799,38 +3822,32 @@ \textbf{Input}. mp\_int $a$, mp\_int $b$ and an integer $digs$ \\ \textbf{Output}. $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\ \hline \\ -Place an array of \textbf{MP\_WARRAY} double precision digits named $\hat W$ on the stack. \\ +Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the stack. \\ 1. If $c.alloc < digs$ then grow $c$ to $digs$ digits. (\textit{mp\_grow}) \\ 2. If step 1 failed return(\textit{MP\_MEM}).\\ \\ -Zero the temporary array $\hat W$. \\ -3. for $n$ from $0$ to $digs - 1$ do \\ -\hspace{3mm}3.1 $\hat W_n \leftarrow 0$ \\ -\\ -Compute the columns. \\ -4. for $ix$ from $0$ to $a.used - 1$ do \\ -\hspace{3mm}4.1 $pb \leftarrow \mbox{min}(b.used, digs - ix)$ \\ -\hspace{3mm}4.2 If $pb < 1$ then goto step 5. \\ -\hspace{3mm}4.3 for $iy$ from $0$ to $pb - 1$ do \\ -\hspace{6mm}4.3.1 $\hat W_{ix+iy} \leftarrow \hat W_{ix+iy} + a_{ix}b_{iy}$ \\ +3. $pa \leftarrow \mbox{MIN}(digs, a.used + b.used)$ \\ \\ -Propagate the carries upwards. \\ -5. $oldused \leftarrow c.used$ \\ -6. $c.used \leftarrow digs$ \\ -7. If $digs > 1$ then do \\ -\hspace{3mm}7.1. for $ix$ from $1$ to $digs - 1$ do \\ -\hspace{6mm}7.1.1 $\hat W_{ix} \leftarrow \hat W_{ix} + \lfloor \hat W_{ix-1} / \beta \rfloor$ \\ -\hspace{6mm}7.1.2 $c_{ix - 1} \leftarrow \hat W_{ix - 1} \mbox{ (mod }\beta\mbox{)}$ \\ -8. else do \\ -\hspace{3mm}8.1 $ix \leftarrow 0$ \\ -9. $c_{ix} \leftarrow \hat W_{ix} \mbox{ (mod }\beta\mbox{)}$ \\ +4. $\_ \hat W \leftarrow 0$ \\ +5. for $ix$ from 0 to $pa - 1$ do \\ +\hspace{3mm}5.1 $ty \leftarrow \mbox{MIN}(b.used - 1, ix)$ \\ +\hspace{3mm}5.2 $tx \leftarrow ix - ty$ \\ +\hspace{3mm}5.3 $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\ +\hspace{3mm}5.4 for $iz$ from 0 to $iy - 1$ do \\ +\hspace{6mm}5.4.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\ +\hspace{3mm}5.5 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\ +\hspace{3mm}5.6 $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\ +6. $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\ \\ -Zero excess digits. \\ -10. If $digs < oldused$ then do \\ -\hspace{3mm}10.1 for $n$ from $digs$ to $oldused - 1$ do \\ -\hspace{6mm}10.1.1 $c_n \leftarrow 0$ \\ -11. Clamp excessive digits of $c$. (\textit{mp\_clamp}) \\ -12. Return(\textit{MP\_OKAY}). \\ +7. $oldused \leftarrow c.used$ \\ +8. $c.used \leftarrow digs$ \\ +9. for $ix$ from $0$ to $pa$ do \\ +\hspace{3mm}9.1 $c_{ix} \leftarrow W_{ix}$ \\ +10. for $ix$ from $pa + 1$ to $oldused - 1$ do \\ +\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\ +\\ +11. Clamp $c$. \\ +12. Return MP\_OKAY. \\ \hline \end{tabular} \end{center} @@ -3840,15 +3857,24 @@ \end{figure} \textbf{Algorithm fast\_s\_mp\_mul\_digs.} -This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision. The algorithm -essentially peforms the same calculation as algorithm s\_mp\_mul\_digs, just much faster. - -The array $\hat W$ is meant to be on the stack when the algorithm is used. The size of the array does not change which is ideal. Note also that -unlike algorithm s\_mp\_mul\_digs no temporary mp\_int is required since the result is calculated directly in $\hat W$. - -The $O(n^2)$ loop on step four is where the Comba method's advantages begin to show through in comparison to the baseline algorithm. The lack of -a carry variable or propagation in this loop allows the loop to be performed with only single precision multiplication and additions. Now that each -iteration of the inner loop can be performed independent of the others the inner loop can be performed with a high level of parallelism. +This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision. + +The outer loop of this algorithm is more complicated than that of the baseline multiplier. This is because on the inside of the +loop we want to produce one column per pass. This allows the accumulator $\_ \hat W$ to be placed in CPU registers and +reduce the memory bandwidth to two \textbf{mp\_digit} reads per iteration. + +The $ty$ variable is set to the minimum count of $ix$ or the number of digits in $b$. That way if $a$ has more digits than +$b$ this will be limited to $b.used - 1$. The $tx$ variable is set to the to the distance past $b.used$ the variable +$ix$ is. This is used for the immediately subsequent statement where we find $iy$. + +The variable $iy$ is the minimum digits we can read from either $a$ or $b$ before running out. Computing one column at a time +means we have to scan one integer upwards and the other downwards. $a$ starts at $tx$ and $b$ starts at $ty$. In each +pass we are producing the $ix$'th output column and we note that $tx + ty = ix$. As we move $tx$ upwards we have to +move $ty$ downards so the equality remains valid. The $iy$ variable is the number of iterations until +$tx \ge a.used$ or $ty < 0$ occurs. + +After every inner pass we store the lower half of the accumulator into $W_{ix}$ and then propagate the carry of the accumulator +into the next round by dividing $\_ \hat W$ by $\beta$. To measure the benefits of the Comba method over the baseline method consider the number of operations that are required. If the cost in terms of time of a multiply and addition is $p$ and the cost of a carry propagation is $q$ then a baseline multiplication would require @@ -3877,94 +3903,95 @@ 030 * Based on Algorithm 14.12 on pp.595 of HAC. 031 * 032 */ -033 int -034 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -035 \{ -036 int olduse, res, pa, ix, iz; -037 mp_digit W[MP_WARRAY]; -038 register mp_word _W; -039 -040 /* grow the destination as required */ -041 if (c->alloc < digs) \{ -042 if ((res = mp_grow (c, digs)) != MP_OKAY) \{ -043 return res; -044 \} -045 \} -046 -047 /* number of output digits to produce */ -048 pa = MIN(digs, a->used + b->used); -049 -050 /* clear the carry */ -051 _W = 0; -052 for (ix = 0; ix <= pa; ix++) \{ -053 int tx, ty; -054 int iy; -055 mp_digit *tmpx, *tmpy; -056 -057 /* get offsets into the two bignums */ -058 ty = MIN(b->used-1, ix); -059 tx = ix - ty; -060 -061 /* setup temp aliases */ -062 tmpx = a->dp + tx; -063 tmpy = b->dp + ty; -064 -065 /* this is the number of times the loop will iterrate, essentially its - -066 while (tx++ < a->used && ty-- >= 0) \{ ... \} -067 */ -068 iy = MIN(a->used-tx, ty+1); -069 -070 /* execute loop */ -071 for (iz = 0; iz < iy; ++iz) \{ -072 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); -073 \} -074 -075 /* store term */ -076 W[ix] = ((mp_digit)_W) & MP_MASK; -077 -078 /* make next carry */ -079 _W = _W >> ((mp_word)DIGIT_BIT); -080 \} -081 -082 /* setup dest */ -083 olduse = c->used; -084 c->used = digs; -085 -086 \{ -087 register mp_digit *tmpc; -088 tmpc = c->dp; -089 for (ix = 0; ix < digs; ix++) \{ -090 /* now extract the previous digit [below the carry] */ -091 *tmpc++ = W[ix]; -092 \} -093 -094 /* clear unused digits [that existed in the old copy of c] */ -095 for (; ix < olduse; ix++) \{ -096 *tmpc++ = 0; -097 \} -098 \} -099 mp_clamp (c); -100 return MP_OKAY; -101 \} -102 #endif +033 int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) +034 \{ +035 int olduse, res, pa, ix, iz; +036 mp_digit W[MP_WARRAY]; +037 register mp_word _W; +038 +039 /* grow the destination as required */ +040 if (c->alloc < digs) \{ +041 if ((res = mp_grow (c, digs)) != MP_OKAY) \{ +042 return res; +043 \} +044 \} +045 +046 /* number of output digits to produce */ +047 pa = MIN(digs, a->used + b->used); +048 +049 /* clear the carry */ +050 _W = 0; +051 for (ix = 0; ix < pa; ix++) \{ +052 int tx, ty; +053 int iy; +054 mp_digit *tmpx, *tmpy; +055 +056 /* get offsets into the two bignums */ +057 ty = MIN(b->used-1, ix); +058 tx = ix - ty; +059 +060 /* setup temp aliases */ +061 tmpx = a->dp + tx; +062 tmpy = b->dp + ty; +063 +064 /* this is the number of times the loop will iterrate, essentially +065 while (tx++ < a->used && ty-- >= 0) \{ ... \} +066 */ +067 iy = MIN(a->used-tx, ty+1); +068 +069 /* execute loop */ +070 for (iz = 0; iz < iy; ++iz) \{ +071 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); +072 \} +073 +074 /* store term */ +075 W[ix] = ((mp_digit)_W) & MP_MASK; +076 +077 /* make next carry */ +078 _W = _W >> ((mp_word)DIGIT_BIT); +079 \} +080 +081 /* store final carry */ +082 W[ix] = (mp_digit)(_W & MP_MASK); +083 +084 /* setup dest */ +085 olduse = c->used; +086 c->used = pa; +087 +088 \{ +089 register mp_digit *tmpc; +090 tmpc = c->dp; +091 for (ix = 0; ix < pa+1; ix++) \{ +092 /* now extract the previous digit [below the carry] */ +093 *tmpc++ = W[ix]; +094 \} +095 +096 /* clear unused digits [that existed in the old copy of c] */ +097 for (; ix < olduse; ix++) \{ +098 *tmpc++ = 0; +099 \} +100 \} +101 mp_clamp (c); +102 return MP_OKAY; +103 \} +104 #endif \end{alltt} \end{small} -The memset on line @47,memset@ clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication -implementation a series of aliases (\textit{lines 62, 63 and 76}) are used to simplify the inner $O(n^2)$ loop. -In this case a new alias $\_\hat W$ has been added which refers to the double precision columns offset by $ix$ in each pass. - -The inner loop on lines 89, 79 and 80 is where the algorithm will spend the majority of the time, which is why it has been -stripped to the bones of any extra baggage\footnote{Hence the pointer aliases.}. On x86 processors the multiplication and additions amount to at the -very least five instructions (\textit{two loads, two additions, one multiply}) while on the ARMv4 processors they amount to only three -(\textit{one load, one store, one multiply-add}). For both of the x86 and ARMv4 processors the GCC compiler performs a good job at unrolling the loop -and scheduling the instructions so there are very few dependency stalls. - -In theory the difference between the baseline and comba algorithms is a mere $O(qn)$ time difference. However, in the $O(n^2)$ nested loop of the -baseline method there are dependency stalls as the algorithm must wait for the multiplier to finish before propagating the carry to the next -digit. As a result fewer of the often multiple execution units\footnote{The AMD Athlon has three execution units and the Intel P4 has four.} can -be simultaneously used. +As per the pseudo--code we first calculate $pa$ (line 47) as the number of digits to output. Next we begin the outer loop +to produce the individual columns of the product. We use the two aliases $tmpx$ and $tmpy$ (lines 61, 62) to point +inside the two multiplicands quickly. + +The inner loop (lines 70 to 72) of this implementation is where the tradeoff come into play. Originally this comba +implementation was ``row--major'' which means it adds to each of the columns in each pass. After the outer loop it would then fix +the carries. This was very fast except it had an annoying drawback. You had to read a mp\_word and two mp\_digits and write +one mp\_word per iteration. On processors such as the Athlon XP and P4 this did not matter much since the cache bandwidth +is very high and it can keep the ALU fed with data. It did, however, matter on older and embedded cpus where cache is often +slower and also often doesn't exist. This new algorithm only performs two reads per iteration under the assumption that the +compiler has aliased $\_ \hat W$ to a CPU register. + +After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines 75, 78) to forward it as +a carry for the next pass. After the outer loop we use the final carry (line 82) as the last digit of the product. \subsection{Polynomial Basis Multiplication} To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication. In the following algorithms @@ -4441,277 +4468,290 @@ 016 017 /* multiplication using the Toom-Cook 3-way algorithm 018 * -019 * Much more complicated than Karatsuba but has a lower asymptotic running t - ime of -020 * O(N**1.464). This algorithm is only particularly useful on VERY large -021 * inputs (we're talking 1000s of digits here...). -022 */ -023 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) -024 \{ -025 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; -026 int res, B; -027 -028 /* init temps */ -029 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, -030 &a0, &a1, &a2, &b0, &b1, -031 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{ -032 return res; -033 \} -034 -035 /* B */ -036 B = MIN(a->used, b->used) / 3; -037 -038 /* a = a2 * B**2 + a1 * B + a0 */ -039 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{ -040 goto ERR; -041 \} -042 -043 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{ -044 goto ERR; -045 \} -046 mp_rshd(&a1, B); -047 mp_mod_2d(&a1, DIGIT_BIT * B, &a1); -048 -049 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{ -050 goto ERR; -051 \} -052 mp_rshd(&a2, B*2); -053 -054 /* b = b2 * B**2 + b1 * B + b0 */ -055 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{ -056 goto ERR; -057 \} -058 -059 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{ -060 goto ERR; -061 \} -062 mp_rshd(&b1, B); -063 mp_mod_2d(&b1, DIGIT_BIT * B, &b1); -064 -065 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{ -066 goto ERR; -067 \} -068 mp_rshd(&b2, B*2); -069 -070 /* w0 = a0*b0 */ -071 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{ -072 goto ERR; -073 \} -074 -075 /* w4 = a2 * b2 */ -076 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{ -077 goto ERR; -078 \} -079 -080 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ -081 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{ -082 goto ERR; -083 \} -084 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ -085 goto ERR; -086 \} -087 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ -088 goto ERR; -089 \} -090 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{ -091 goto ERR; -092 \} -093 -094 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{ -095 goto ERR; -096 \} -097 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ -098 goto ERR; -099 \} -100 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ -101 goto ERR; -102 \} -103 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{ -104 goto ERR; -105 \} -106 -107 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{ -108 goto ERR; -109 \} -110 -111 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ -112 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{ -113 goto ERR; -114 \} -115 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ -116 goto ERR; -117 \} -118 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ -119 goto ERR; -120 \} -121 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ -122 goto ERR; -123 \} -124 -125 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{ -126 goto ERR; -127 \} -128 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ -129 goto ERR; -130 \} -131 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ -132 goto ERR; -133 \} -134 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ -135 goto ERR; -136 \} -137 -138 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{ -139 goto ERR; -140 \} -141 -142 -143 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ -144 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{ -145 goto ERR; -146 \} -147 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ -148 goto ERR; -149 \} -150 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{ -151 goto ERR; -152 \} -153 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ -154 goto ERR; -155 \} -156 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{ -157 goto ERR; -158 \} -159 -160 /* now solve the matrix -161 -162 0 0 0 0 1 -163 1 2 4 8 16 -164 1 1 1 1 1 -165 16 8 4 2 1 -166 1 0 0 0 0 -167 -168 using 12 subtractions, 4 shifts, -169 2 small divisions and 1 small multiplication -170 */ -171 -172 /* r1 - r4 */ -173 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{ -174 goto ERR; -175 \} -176 /* r3 - r0 */ -177 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{ -178 goto ERR; -179 \} -180 /* r1/2 */ -181 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{ -182 goto ERR; -183 \} -184 /* r3/2 */ -185 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{ -186 goto ERR; -187 \} -188 /* r2 - r0 - r4 */ -189 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{ -190 goto ERR; -191 \} -192 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{ -193 goto ERR; -194 \} -195 /* r1 - r2 */ -196 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ -197 goto ERR; -198 \} -199 /* r3 - r2 */ -200 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ -201 goto ERR; -202 \} -203 /* r1 - 8r0 */ -204 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{ -205 goto ERR; -206 \} -207 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{ -208 goto ERR; -209 \} -210 /* r3 - 8r4 */ -211 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{ -212 goto ERR; -213 \} -214 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{ -215 goto ERR; -216 \} -217 /* 3r2 - r1 - r3 */ -218 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{ -219 goto ERR; -220 \} -221 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{ -222 goto ERR; -223 \} -224 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{ -225 goto ERR; -226 \} -227 /* r1 - r2 */ -228 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ -229 goto ERR; -230 \} -231 /* r3 - r2 */ -232 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ -233 goto ERR; -234 \} -235 /* r1/3 */ -236 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{ -237 goto ERR; -238 \} -239 /* r3/3 */ -240 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{ -241 goto ERR; -242 \} -243 -244 /* at this point shift W[n] by B*n */ -245 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{ -246 goto ERR; -247 \} -248 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{ -249 goto ERR; -250 \} -251 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{ -252 goto ERR; -253 \} -254 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{ -255 goto ERR; -256 \} -257 -258 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{ -259 goto ERR; -260 \} -261 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{ -262 goto ERR; -263 \} -264 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{ -265 goto ERR; -266 \} -267 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{ -268 goto ERR; -269 \} -270 -271 ERR: -272 mp_clear_multi(&w0, &w1, &w2, &w3, &w4, -273 &a0, &a1, &a2, &b0, &b1, -274 &b2, &tmp1, &tmp2, NULL); -275 return res; -276 \} -277 -278 #endif +019 * Much more complicated than Karatsuba but has a lower +020 * asymptotic running time of O(N**1.464). This algorithm is +021 * only particularly useful on VERY large inputs +022 * (we're talking 1000s of digits here...). +023 */ +024 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) +025 \{ +026 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; +027 int res, B; +028 +029 /* init temps */ +030 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, +031 &a0, &a1, &a2, &b0, &b1, +032 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{ +033 return res; +034 \} +035 +036 /* B */ +037 B = MIN(a->used, b->used) / 3; +038 +039 /* a = a2 * B**2 + a1 * B + a0 */ +040 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{ +041 goto ERR; +042 \} +043 +044 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{ +045 goto ERR; +046 \} +047 mp_rshd(&a1, B); +048 mp_mod_2d(&a1, DIGIT_BIT * B, &a1); +049 +050 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{ +051 goto ERR; +052 \} +053 mp_rshd(&a2, B*2); +054 +055 /* b = b2 * B**2 + b1 * B + b0 */ +056 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{ +057 goto ERR; +058 \} +059 +060 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{ +061 goto ERR; +062 \} +063 mp_rshd(&b1, B); +064 mp_mod_2d(&b1, DIGIT_BIT * B, &b1); +065 +066 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{ +067 goto ERR; +068 \} +069 mp_rshd(&b2, B*2); +070 +071 /* w0 = a0*b0 */ +072 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{ +073 goto ERR; +074 \} +075 +076 /* w4 = a2 * b2 */ +077 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{ +078 goto ERR; +079 \} +080 +081 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ +082 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{ +083 goto ERR; +084 \} +085 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ +086 goto ERR; +087 \} +088 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ +089 goto ERR; +090 \} +091 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{ +092 goto ERR; +093 \} +094 +095 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{ +096 goto ERR; +097 \} +098 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ +099 goto ERR; +100 \} +101 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ +102 goto ERR; +103 \} +104 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{ +105 goto ERR; +106 \} +107 +108 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{ +109 goto ERR; +110 \} +111 +112 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ +113 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{ +114 goto ERR; +115 \} +116 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ +117 goto ERR; +118 \} +119 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ +120 goto ERR; +121 \} +122 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ +123 goto ERR; +124 \} +125 +126 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{ +127 goto ERR; +128 \} +129 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ +130 goto ERR; +131 \} +132 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ +133 goto ERR; +134 \} +135 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ +136 goto ERR; +137 \} +138 +139 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{ +140 goto ERR; +141 \} +142 +143 +144 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ +145 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{ +146 goto ERR; +147 \} +148 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ +149 goto ERR; +150 \} +151 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{ +152 goto ERR; +153 \} +154 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ +155 goto ERR; +156 \} +157 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{ +158 goto ERR; +159 \} +160 +161 /* now solve the matrix +162 +163 0 0 0 0 1 +164 1 2 4 8 16 +165 1 1 1 1 1 +166 16 8 4 2 1 +167 1 0 0 0 0 +168 +169 using 12 subtractions, 4 shifts, +170 2 small divisions and 1 small multiplication +171 */ +172 +173 /* r1 - r4 */ +174 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{ +175 goto ERR; +176 \} +177 /* r3 - r0 */ +178 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{ +179 goto ERR; +180 \} +181 /* r1/2 */ +182 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{ +183 goto ERR; +184 \} +185 /* r3/2 */ +186 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{ +187 goto ERR; +188 \} +189 /* r2 - r0 - r4 */ +190 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{ +191 goto ERR; +192 \} +193 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{ +194 goto ERR; +195 \} +196 /* r1 - r2 */ +197 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ +198 goto ERR; +199 \} +200 /* r3 - r2 */ +201 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ +202 goto ERR; +203 \} +204 /* r1 - 8r0 */ +205 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{ +206 goto ERR; +207 \} +208 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{ +209 goto ERR; +210 \} +211 /* r3 - 8r4 */ +212 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{ +213 goto ERR; +214 \} +215 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{ +216 goto ERR; +217 \} +218 /* 3r2 - r1 - r3 */ +219 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{ +220 goto ERR; +221 \} +222 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{ +223 goto ERR; +224 \} +225 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{ +226 goto ERR; +227 \} +228 /* r1 - r2 */ +229 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ +230 goto ERR; +231 \} +232 /* r3 - r2 */ +233 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ +234 goto ERR; +235 \} +236 /* r1/3 */ +237 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{ +238 goto ERR; +239 \} +240 /* r3/3 */ +241 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{ +242 goto ERR; +243 \} +244 +245 /* at this point shift W[n] by B*n */ +246 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{ +247 goto ERR; +248 \} +249 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{ +250 goto ERR; +251 \} +252 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{ +253 goto ERR; +254 \} +255 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{ +256 goto ERR; +257 \} +258 +259 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{ +260 goto ERR; +261 \} +262 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{ +263 goto ERR; +264 \} +265 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{ +266 goto ERR; +267 \} +268 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{ +269 goto ERR; +270 \} +271 +272 ERR: +273 mp_clear_multi(&w0, &w1, &w2, &w3, &w4, +274 &a0, &a1, &a2, &b0, &b1, +275 &b2, &tmp1, &tmp2, NULL); +276 return res; +277 \} +278 +279 #endif \end{alltt} \end{small} --- Comments to be added during editing phase. +The first obvious thing to note is that this algorithm is complicated. The complexity is worth it if you are multiplying very +large numbers. For example, a 10,000 digit multiplication takes approximaly 99,282,205 fewer single precision multiplications with +Toom--Cook than a Comba or baseline approach (this is a savings of more than 99$\%$). For most ``crypto'' sized numbers this +algorithm is not practical as Karatsuba has a much lower cutoff point. + +First we split $a$ and $b$ into three roughly equal portions. This has been accomplished (lines 40 to 69) with +combinations of mp\_rshd() and mp\_mod\_2d() function calls. At this point $a = a2 \cdot \beta^2 + a1 \cdot \beta + a0$ and similiarly +for $b$. + +Next we compute the five points $w0, w1, w2, w3$ and $w4$. Recall that $w0$ and $w4$ can be computed directly from the portions so +we get those out of the way first (lines 72 and 77). Next we compute $w1, w2$ and $w3$ using Horners method. + +After this point we solve for the actual values of $w1, w2$ and $w3$ by reducing the $5 \times 5$ system which is relatively +straight forward. \subsection{Signed Multiplication} Now that algorithms to handle multiplications of every useful dimensions have been developed, a rather simple finishing touch is required. So far all of the multiplication algorithms have been unsigned multiplications which leaves only a signed multiplication algorithm to be established. -\newpage\begin{figure}[!here] +\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} @@ -4844,7 +4884,7 @@ The baseline squaring algorithm is meant to be a catch-all squaring algorithm. It will handle any of the input sizes that the faster routines will not handle. -\newpage\begin{figure}[!here] +\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} @@ -4904,75 +4944,79 @@ \begin{alltt} 016 017 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ -018 int -019 s_mp_sqr (mp_int * a, mp_int * b) -020 \{ -021 mp_int t; -022 int res, ix, iy, pa; -023 mp_word r; -024 mp_digit u, tmpx, *tmpt; -025 -026 pa = a->used; -027 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) \{ -028 return res; -029 \} -030 -031 /* default used is maximum possible size */ -032 t.used = 2*pa + 1; -033 -034 for (ix = 0; ix < pa; ix++) \{ -035 /* first calculate the digit at 2*ix */ -036 /* calculate double precision result */ -037 r = ((mp_word) t.dp[2*ix]) + -038 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]); -039 -040 /* store lower part in result */ -041 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK)); -042 -043 /* get the carry */ -044 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); -045 -046 /* left hand side of A[ix] * A[iy] */ -047 tmpx = a->dp[ix]; -048 -049 /* alias for where to store the results */ -050 tmpt = t.dp + (2*ix + 1); -051 -052 for (iy = ix + 1; iy < pa; iy++) \{ -053 /* first calculate the product */ -054 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]); -055 -056 /* now calculate the double precision result, note we use -057 * addition instead of *2 since it's easier to optimize -058 */ -059 r = ((mp_word) *tmpt) + r + r + ((mp_word) u); -060 -061 /* store lower part */ -062 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); -063 -064 /* get carry */ -065 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); -066 \} -067 /* propagate upwards */ -068 while (u != ((mp_digit) 0)) \{ -069 r = ((mp_word) *tmpt) + ((mp_word) u); -070 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); -071 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); -072 \} -073 \} -074 -075 mp_clamp (&t); -076 mp_exch (&t, b); -077 mp_clear (&t); -078 return MP_OKAY; -079 \} -080 #endif +018 int s_mp_sqr (mp_int * a, mp_int * b) +019 \{ +020 mp_int t; +021 int res, ix, iy, pa; +022 mp_word r; +023 mp_digit u, tmpx, *tmpt; +024 +025 pa = a->used; +026 if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) \{ +027 return res; +028 \} +029 +030 /* default used is maximum possible size */ +031 t.used = 2*pa + 1; +032 +033 for (ix = 0; ix < pa; ix++) \{ +034 /* first calculate the digit at 2*ix */ +035 /* calculate double precision result */ +036 r = ((mp_word) t.dp[2*ix]) + +037 ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]); +038 +039 /* store lower part in result */ +040 t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK)); +041 +042 /* get the carry */ +043 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); +044 +045 /* left hand side of A[ix] * A[iy] */ +046 tmpx = a->dp[ix]; +047 +048 /* alias for where to store the results */ +049 tmpt = t.dp + (2*ix + 1); +050 +051 for (iy = ix + 1; iy < pa; iy++) \{ +052 /* first calculate the product */ +053 r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]); +054 +055 /* now calculate the double precision result, note we use +056 * addition instead of *2 since it's easier to optimize +057 */ +058 r = ((mp_word) *tmpt) + r + r + ((mp_word) u); +059 +060 /* store lower part */ +061 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); +062 +063 /* get carry */ +064 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); +065 \} +066 /* propagate upwards */ +067 while (u != ((mp_digit) 0)) \{ +068 r = ((mp_word) *tmpt) + ((mp_word) u); +069 *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); +070 u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); +071 \} +072 \} +073 +074 mp_clamp (&t); +075 mp_exch (&t, b); +076 mp_clear (&t); +077 return MP_OKAY; +078 \} +079 #endif \end{alltt} \end{small} -Inside the outer loop (\textit{see line 34}) the square term is calculated on line 37. Line 44 extracts the carry from the square -term. Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized on lines 47 and 50 respectively. The doubling is performed using two -additions (\textit{see line 59}) since it is usually faster than shifting,if not at least as fast. +Inside the outer loop (line 33) the square term is calculated on line 36. The carry (line 43) has been +extracted from the mp\_word accumulator using a right shift. Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized +(lines 46 and 49) to simplify the inner loop. The doubling is performed using two +additions (line 58) since it is usually faster than shifting, if not at least as fast. + +The important observation is that the inner loop does not begin at $iy = 0$ like for multiplication. As such the inner loops +get progressively shorter as the algorithm proceeds. This is what leads to the savings compared to using a multiplication to +square a number. \subsection{Faster Squaring by the ``Comba'' Method} A major drawback to the baseline method is the requirement for single precision shifting inside the $O(n^2)$ nested loop. Squaring has an additional @@ -4984,9 +5028,9 @@ that $2a + 2b + 2c = 2(a + b + c)$. That is the sum of all of the double products is equal to double the sum of all the products. For example, $ab + ba + ac + ca = 2ab + 2ac = 2(ab + ac)$. -However, we cannot simply double all of the columns, since the squares appear only once per row. The most practical solution is to have two mp\_word -arrays. One array will hold the squares and the other array will hold the double products. With both arrays the doubling and carry propagation can be -moved to a $O(n)$ work level outside the $O(n^2)$ level. +However, we cannot simply double all of the columns, since the squares appear only once per row. The most practical solution is to have two +mp\_word arrays. One array will hold the squares and the other array will hold the double products. With both arrays the doubling and +carry propagation can be moved to a $O(n)$ work level outside the $O(n^2)$ level. In this case, we have an even simpler solution in mind. \newpage\begin{figure}[!here] \begin{small} @@ -4996,34 +5040,34 @@ \textbf{Input}. mp\_int $a$ \\ \textbf{Output}. $b \leftarrow a^2$ \\ \hline \\ -Place two arrays of \textbf{MP\_WARRAY} mp\_words named $\hat W$ and $\hat {X}$ on the stack. \\ +Place an array of \textbf{MP\_WARRAY} mp\_digits named $W$ on the stack. \\ 1. If $b.alloc < 2a.used + 1$ then grow $b$ to $2a.used + 1$ digits. (\textit{mp\_grow}). \\ 2. If step 1 failed return(\textit{MP\_MEM}). \\ -3. for $ix$ from $0$ to $2a.used + 1$ do \\ -\hspace{3mm}3.1 $\hat W_{ix} \leftarrow 0$ \\ -\hspace{3mm}3.2 $\hat {X}_{ix} \leftarrow 0$ \\ -4. for $ix$ from $0$ to $a.used - 1$ do \\ -\hspace{3mm}Compute the square.\\ -\hspace{3mm}4.1 $\hat {X}_{ix+ix} \leftarrow \left ( a_{ix} \right )^2$ \\ -\\ -\hspace{3mm}Compute the double products.\\ -\hspace{3mm}4.2 for $iy$ from $ix + 1$ to $a.used - 1$ do \\ -\hspace{6mm}4.2.1 $\hat W_{ix+iy} \leftarrow \hat W_{ix+iy} + a_{ix}a_{iy}$ \\ -5. $oldused \leftarrow b.used$ \\ -6. $b.used \leftarrow 2a.used + 1$ \\ \\ -Double the products and propagate the carries simultaneously. \\ -7. $\hat W_0 \leftarrow 2 \hat W_0 + \hat {X}_0$ \\ -8. for $ix$ from $1$ to $2a.used$ do \\ -\hspace{3mm}8.1 $\hat W_{ix} \leftarrow 2 \hat W_{ix} + \hat {X}_{ix}$ \\ -\hspace{3mm}8.2 $\hat W_{ix} \leftarrow \hat W_{ix} + \lfloor \hat W_{ix - 1} / \beta \rfloor$ \\ -\hspace{3mm}8.3 $b_{ix-1} \leftarrow W_{ix-1} \mbox{ (mod }\beta\mbox{)}$ \\ -9. $b_{2a.used} \leftarrow \hat W_{2a.used} \mbox{ (mod }\beta\mbox{)}$ \\ -10. if $2a.used + 1 < oldused$ then do \\ -\hspace{3mm}10.1 for $ix$ from $2a.used + 1$ to $oldused$ do \\ -\hspace{6mm}10.1.1 $b_{ix} \leftarrow 0$ \\ -11. Clamp excess digits from $b$. (\textit{mp\_clamp}) \\ -12. Return(\textit{MP\_OKAY}). \\ +3. $pa \leftarrow 2 \cdot a.used$ \\ +4. $\hat W1 \leftarrow 0$ \\ +5. for $ix$ from $0$ to $pa - 1$ do \\ +\hspace{3mm}5.1 $\_ \hat W \leftarrow 0$ \\ +\hspace{3mm}5.2 $ty \leftarrow \mbox{MIN}(a.used - 1, ix)$ \\ +\hspace{3mm}5.3 $tx \leftarrow ix - ty$ \\ +\hspace{3mm}5.4 $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\ +\hspace{3mm}5.5 $iy \leftarrow \mbox{MIN}(iy, \lfloor \left (ty - tx + 1 \right )/2 \rfloor)$ \\ +\hspace{3mm}5.6 for $iz$ from $0$ to $iz - 1$ do \\ +\hspace{6mm}5.6.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx + iz}a_{ty - iz}$ \\ +\hspace{3mm}5.7 $\_ \hat W \leftarrow 2 \cdot \_ \hat W + \hat W1$ \\ +\hspace{3mm}5.8 if $ix$ is even then \\ +\hspace{6mm}5.8.1 $\_ \hat W \leftarrow \_ \hat W + \left ( a_{\lfloor ix/2 \rfloor}\right )^2$ \\ +\hspace{3mm}5.9 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\ +\hspace{3mm}5.10 $\hat W1 \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\ +\\ +6. $oldused \leftarrow b.used$ \\ +7. $b.used \leftarrow 2 \cdot a.used$ \\ +8. for $ix$ from $0$ to $pa - 1$ do \\ +\hspace{3mm}8.1 $b_{ix} \leftarrow W_{ix}$ \\ +9. for $ix$ from $pa$ to $oldused - 1$ do \\ +\hspace{3mm}9.1 $b_{ix} \leftarrow 0$ \\ +10. Clamp excess digits from $b$. (\textit{mp\_clamp}) \\ +11. Return(\textit{MP\_OKAY}). \\ \hline \end{tabular} \end{center} @@ -5032,146 +5076,123 @@ \end{figure} \textbf{Algorithm fast\_s\_mp\_sqr.} -This algorithm computes the square of an input using the Comba technique. It is designed to be a replacement for algorithm s\_mp\_sqr when -the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$. - -This routine requires two arrays of mp\_words to be placed on the stack. The first array $\hat W$ will hold the double products and the second -array $\hat X$ will hold the squares. Though only at most $MP\_WARRAY \over 2$ words of $\hat X$ are used, it has proven faster on most -processors to simply make it a full size array. - -The loop on step 3 will zero the two arrays to prepare them for the squaring step. Step 4.1 computes the squares of the product. Note how -it simply assigns the value into the $\hat X$ array. The nested loop on step 4.2 computes the doubles of the products. This loop -computes the sum of the products for each column. They are not doubled until later. - -After the squaring loop, the products stored in $\hat W$ musted be doubled and the carries propagated forwards. It makes sense to do both -operations at the same time. The expression $\hat W_{ix} \leftarrow 2 \hat W_{ix} + \hat {X}_{ix}$ computes the sum of the double product and the -squares in place. +This algorithm computes the square of an input using the Comba technique. It is designed to be a replacement for algorithm +s\_mp\_sqr when the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$. +This algorithm is very similar to the Comba multiplier except with a few key differences we shall make note of. + +First, we have an accumulator and carry variables $\_ \hat W$ and $\hat W1$ respectively. This is because the inner loop +products are to be doubled. If we had added the previous carry in we would be doubling too much. Next we perform an +addition MIN condition on $iy$ (step 5.5) to prevent overlapping digits. For example, $a_3 \cdot a_5$ is equal +$a_5 \cdot a_3$. Whereas in the multiplication case we would have $5 < a.used$ and $3 \ge 0$ is maintained since we double the sum +of the products just outside the inner loop we have to avoid doing this. This is also a good thing since we perform +fewer multiplications and the routine ends up being faster. + +Finally the last difference is the addition of the ``square'' term outside the inner loop (step 5.8). We add in the square +only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rfloor$ position. \vspace{+3mm}\begin{small} \hspace{-5.1mm}{\bf File}: bn\_fast\_s\_mp\_sqr.c \vspace{-3mm} \begin{alltt} 016 -017 /* fast squaring -018 * -019 * This is the comba method where the columns of the product -020 * are computed first then the carries are computed. This -021 * has the effect of making a very simple inner loop that -022 * is executed the most -023 * -024 * W2 represents the outer products and W the inner. -025 * -026 * A further optimizations is made because the inner -027 * products are of the form "A * B * 2". The *2 part does -028 * not need to be computed until the end which is good -029 * because 64-bit shifts are slow! -030 * -031 * Based on Algorithm 14.16 on pp.597 of HAC. -032 * -033 */ -034 /* the jist of squaring... -035 -036 you do like mult except the offset of the tmpx [one that starts closer to ze - ro] -037 can't equal the offset of tmpy. So basically you set up iy like before then - you min it with -038 (ty-tx) so that it never happens. You double all those you add in the inner - loop -039 -040 After that loop you do the squares and add them in. -041 -042 Remove W2 and don't memset W -043 -044 */ -045 -046 int fast_s_mp_sqr (mp_int * a, mp_int * b) -047 \{ -048 int olduse, res, pa, ix, iz; -049 mp_digit W[MP_WARRAY], *tmpx; -050 mp_word W1; -051 -052 /* grow the destination as required */ -053 pa = a->used + a->used; -054 if (b->alloc < pa) \{ -055 if ((res = mp_grow (b, pa)) != MP_OKAY) \{ -056 return res; -057 \} -058 \} -059 -060 /* number of output digits to produce */ -061 W1 = 0; -062 for (ix = 0; ix <= pa; ix++) \{ -063 int tx, ty, iy; -064 mp_word _W; -065 mp_digit *tmpy; -066 -067 /* clear counter */ -068 _W = 0; +017 /* the jist of squaring... +018 * you do like mult except the offset of the tmpx [one that +019 * starts closer to zero] can't equal the offset of tmpy. +020 * So basically you set up iy like before then you min it with +021 * (ty-tx) so that it never happens. You double all those +022 * you add in the inner loop +023 +024 After that loop you do the squares and add them in. +025 */ +026 +027 int fast_s_mp_sqr (mp_int * a, mp_int * b) +028 \{ +029 int olduse, res, pa, ix, iz; +030 mp_digit W[MP_WARRAY], *tmpx; +031 mp_word W1; +032 +033 /* grow the destination as required */ +034 pa = a->used + a->used; +035 if (b->alloc < pa) \{ +036 if ((res = mp_grow (b, pa)) != MP_OKAY) \{ +037 return res; +038 \} +039 \} +040 +041 /* number of output digits to produce */ +042 W1 = 0; +043 for (ix = 0; ix < pa; ix++) \{ +044 int tx, ty, iy; +045 mp_word _W; +046 mp_digit *tmpy; +047 +048 /* clear counter */ +049 _W = 0; +050 +051 /* get offsets into the two bignums */ +052 ty = MIN(a->used-1, ix); +053 tx = ix - ty; +054 +055 /* setup temp aliases */ +056 tmpx = a->dp + tx; +057 tmpy = a->dp + ty; +058 +059 /* this is the number of times the loop will iterrate, essentially +060 while (tx++ < a->used && ty-- >= 0) \{ ... \} +061 */ +062 iy = MIN(a->used-tx, ty+1); +063 +064 /* now for squaring tx can never equal ty +065 * we halve the distance since they approach at a rate of 2x +066 * and we have to round because odd cases need to be executed +067 */ +068 iy = MIN(iy, (ty-tx+1)>>1); 069 -070 /* get offsets into the two bignums */ -071 ty = MIN(a->used-1, ix); -072 tx = ix - ty; -073 -074 /* setup temp aliases */ -075 tmpx = a->dp + tx; -076 tmpy = a->dp + ty; +070 /* execute loop */ +071 for (iz = 0; iz < iy; iz++) \{ +072 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); +073 \} +074 +075 /* double the inner product and add carry */ +076 _W = _W + _W + W1; 077 -078 /* this is the number of times the loop will iterrate, essentially its - -079 while (tx++ < a->used && ty-- >= 0) \{ ... \} -080 */ -081 iy = MIN(a->used-tx, ty+1); +078 /* even columns have the square term in them */ +079 if ((ix&1) == 0) \{ +080 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); +081 \} 082 -083 /* now for squaring tx can never equal ty -084 * we halve the distance since they approach at a rate of 2x -085 * and we have to round because odd cases need to be executed -086 */ -087 iy = MIN(iy, (ty-tx+1)>>1); -088 -089 /* execute loop */ -090 for (iz = 0; iz < iy; iz++) \{ -091 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); -092 \} +083 /* store it */ +084 W[ix] = (mp_digit)(_W & MP_MASK); +085 +086 /* make next carry */ +087 W1 = _W >> ((mp_word)DIGIT_BIT); +088 \} +089 +090 /* setup dest */ +091 olduse = b->used; +092 b->used = a->used+a->used; 093 -094 /* double the inner product and add carry */ -095 _W = _W + _W + W1; -096 -097 /* even columns have the square term in them */ -098 if ((ix&1) == 0) \{ -099 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); -100 \} -101 -102 /* store it */ -103 W[ix] = _W; -104 -105 /* make next carry */ -106 W1 = _W >> ((mp_word)DIGIT_BIT); -107 \} -108 -109 /* setup dest */ -110 olduse = b->used; -111 b->used = a->used+a->used; -112 -113 \{ -114 mp_digit *tmpb; -115 tmpb = b->dp; -116 for (ix = 0; ix < pa; ix++) \{ -117 *tmpb++ = W[ix] & MP_MASK; -118 \} -119 -120 /* clear unused digits [that existed in the old copy of c] */ -121 for (; ix < olduse; ix++) \{ -122 *tmpb++ = 0; -123 \} -124 \} -125 mp_clamp (b); -126 return MP_OKAY; -127 \} -128 #endif +094 \{ +095 mp_digit *tmpb; +096 tmpb = b->dp; +097 for (ix = 0; ix < pa; ix++) \{ +098 *tmpb++ = W[ix] & MP_MASK; +099 \} +100 +101 /* clear unused digits [that existed in the old copy of c] */ +102 for (; ix < olduse; ix++) \{ +103 *tmpb++ = 0; +104 \} +105 \} +106 mp_clamp (b); +107 return MP_OKAY; +108 \} +109 #endif \end{alltt} \end{small} --- Write something deep and insightful later, Tom. +This implementation is essentially a copy of Comba multiplication with the appropriate changes added to make it faster for +the special case of squaring. \subsection{Polynomial Basis Squaring} The same algorithm that performs optimal polynomial basis multiplication can be used to perform polynomial basis squaring. The minor exception @@ -5389,14 +5410,13 @@ is exactly at the point where Comba squaring can no longer be used (\textit{128 digits}). On slower processors such as the Intel P4 it is actually below the Comba limit (\textit{at 110 digits}). -This routine uses the same error trap coding style as mp\_karatsuba\_sqr. As the temporary variables are initialized errors are redirected to -the error trap higher up. If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and mp\_clears are executed normally. - -\textit{Last paragraph sucks. re-write! -- Tom} +This routine uses the same error trap coding style as mp\_karatsuba\_sqr. As the temporary variables are initialized errors are +redirected to the error trap higher up. If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and +mp\_clears are executed normally. \subsection{Toom-Cook Squaring} The Toom-Cook squaring algorithm mp\_toom\_sqr is heavily based on the algorithm mp\_toom\_mul with the exception that squarings are used -instead of multiplication to find the five relations.. The reader is encouraged to read the description of the latter algorithm and try to +instead of multiplication to find the five relations. The reader is encouraged to read the description of the latter algorithm and try to derive their own Toom-Cook squaring algorithm. \subsection{High Level Squaring} @@ -5482,12 +5502,9 @@ $\left [ 3 \right ] $ & Devise an efficient algorithm for selection of the radix point to handle inputs \\ & that have different number of digits in Karatsuba multiplication. \\ & \\ -$\left [ 3 \right ] $ & In section 5.3 the fact that every column of a squaring is made up \\ +$\left [ 2 \right ] $ & In section 5.3 the fact that every column of a squaring is made up \\ & of double products and at most one square is stated. Prove this statement. \\ & \\ -$\left [ 2 \right ] $ & In the Comba squaring algorithm half of the $\hat X$ variables are not used. \\ - & Revise algorithm fast\_s\_mp\_sqr to shrink the $\hat X$ array. \\ - & \\ $\left [ 3 \right ] $ & Prove the equation for Karatsuba squaring. \\ & \\ $\left [ 1 \right ] $ & Prove that Karatsuba squaring requires $O \left (n^{lg(3)} \right )$ time. \\ @@ -5495,6 +5512,14 @@ $\left [ 2 \right ] $ & Determine the minimal ratio between addition and multiplication clock cycles \\ & required for equation $6.7$ to be true. \\ & \\ +$\left [ 3 \right ] $ & Implement a threaded version of Comba multiplication (and squaring) where you \\ + & compute subsets of the columns in each thread. Determine a cutoff point where \\ + & it is effective and add the logic to mp\_mul() and mp\_sqr(). \\ + &\\ +$\left [ 4 \right ] $ & Same as the previous but also modify the Karatsuba and Toom-Cook. You must \\ + & increase the throughput of mp\_exptmod() for random odd moduli in the range \\ + & $512 \ldots 4096$ bits significantly ($> 2x$) to complete this challenge. \\ + & \\ \end{tabular} \chapter{Modular Reduction} @@ -5513,7 +5538,7 @@ Modular reductions are normally used to create either finite groups, rings or fields. The most common usage for performance driven modular reductions is in modular exponentiation algorithms. That is to compute $d = a^b \mbox{ (mod }c\mbox{)}$ as fast as possible. This operation is used in the RSA and Diffie-Hellman public key algorithms, for example. Modular multiplication and squaring also appears as a fundamental operation in -Elliptic Curve cryptographic algorithms. As will be discussed in the subsequent chapter there exist fast algorithms for computing modular +elliptic curve cryptographic algorithms. As will be discussed in the subsequent chapter there exist fast algorithms for computing modular exponentiations without having to perform (\textit{in this example}) $b - 1$ multiplications. These algorithms will produce partial results in the range $0 \le x < c^2$ which can be taken advantage of to create several efficient algorithms. They have also been used to create redundancy check algorithms known as CRCs, error correction codes such as Reed-Solomon and solve a variety of number theoeretic problems. @@ -5727,95 +5752,94 @@ 018 * precomputed via mp_reduce_setup. 019 * From HAC pp.604 Algorithm 14.42 020 */ -021 int -022 mp_reduce (mp_int * x, mp_int * m, mp_int * mu) -023 \{ -024 mp_int q; -025 int res, um = m->used; -026 -027 /* q = x */ -028 if ((res = mp_init_copy (&q, x)) != MP_OKAY) \{ -029 return res; -030 \} -031 -032 /* q1 = x / b**(k-1) */ -033 mp_rshd (&q, um - 1); -034 -035 /* according to HAC this optimization is ok */ -036 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) \{ -037 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) \{ -038 goto CLEANUP; -039 \} -040 \} else \{ -041 #ifdef BN_S_MP_MUL_HIGH_DIGS_C -042 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{ -043 goto CLEANUP; -044 \} -045 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) -046 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{ -047 goto CLEANUP; -048 \} -049 #else -050 \{ -051 res = MP_VAL; -052 goto CLEANUP; -053 \} -054 #endif -055 \} -056 -057 /* q3 = q2 / b**(k+1) */ -058 mp_rshd (&q, um + 1); -059 -060 /* x = x mod b**(k+1), quick (no division) */ -061 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{ -062 goto CLEANUP; -063 \} -064 -065 /* q = q * m mod b**(k+1), quick (no division) */ -066 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{ -067 goto CLEANUP; -068 \} -069 -070 /* x = x - q */ -071 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{ -072 goto CLEANUP; -073 \} -074 -075 /* If x < 0, add b**(k+1) to it */ -076 if (mp_cmp_d (x, 0) == MP_LT) \{ -077 mp_set (&q, 1); -078 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) -079 goto CLEANUP; -080 if ((res = mp_add (x, &q, x)) != MP_OKAY) -081 goto CLEANUP; -082 \} -083 -084 /* Back off if it's too big */ -085 while (mp_cmp (x, m) != MP_LT) \{ -086 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{ -087 goto CLEANUP; -088 \} -089 \} -090 -091 CLEANUP: -092 mp_clear (&q); -093 -094 return res; -095 \} -096 #endif +021 int mp_reduce (mp_int * x, mp_int * m, mp_int * mu) +022 \{ +023 mp_int q; +024 int res, um = m->used; +025 +026 /* q = x */ +027 if ((res = mp_init_copy (&q, x)) != MP_OKAY) \{ +028 return res; +029 \} +030 +031 /* q1 = x / b**(k-1) */ +032 mp_rshd (&q, um - 1); +033 +034 /* according to HAC this optimization is ok */ +035 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) \{ +036 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) \{ +037 goto CLEANUP; +038 \} +039 \} else \{ +040 #ifdef BN_S_MP_MUL_HIGH_DIGS_C +041 if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) \{ +042 goto CLEANUP; +043 \} +044 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) +045 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) \{ +046 goto CLEANUP; +047 \} +048 #else +049 \{ +050 res = MP_VAL; +051 goto CLEANUP; +052 \} +053 #endif +054 \} +055 +056 /* q3 = q2 / b**(k+1) */ +057 mp_rshd (&q, um + 1); +058 +059 /* x = x mod b**(k+1), quick (no division) */ +060 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{ +061 goto CLEANUP; +062 \} +063 +064 /* q = q * m mod b**(k+1), quick (no division) */ +065 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{ +066 goto CLEANUP; +067 \} +068 +069 /* x = x - q */ +070 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{ +071 goto CLEANUP; +072 \} +073 +074 /* If x < 0, add b**(k+1) to it */ +075 if (mp_cmp_d (x, 0) == MP_LT) \{ +076 mp_set (&q, 1); +077 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) +078 goto CLEANUP; +079 if ((res = mp_add (x, &q, x)) != MP_OKAY) +080 goto CLEANUP; +081 \} +082 +083 /* Back off if it's too big */ +084 while (mp_cmp (x, m) != MP_LT) \{ +085 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{ +086 goto CLEANUP; +087 \} +088 \} +089 +090 CLEANUP: +091 mp_clear (&q); +092 +093 return res; +094 \} +095 #endif \end{alltt} \end{small} The first multiplication that determines the quotient can be performed by only producing the digits from $m - 1$ and up. This essentially halves the number of single precision multiplications required. However, the optimization is only safe if $\beta$ is much larger than the number of digits -in the modulus. In the source code this is evaluated on lines 36 to 44 where algorithm s\_mp\_mul\_high\_digs is used when it is +in the modulus. In the source code this is evaluated on lines 36 to 43 where algorithm s\_mp\_mul\_high\_digs is used when it is safe to do so. \subsection{The Barrett Setup Algorithm} In order to use algorithm mp\_reduce the value of $\mu$ must be calculated in advance. Ideally this value should be computed once and stored for future use so that the Barrett algorithm can be used without delay. -\begin{figure}[!here] +\newpage\begin{figure}[!here] \begin{small} \begin{center} \begin{tabular}{l} @@ -6311,161 +6335,160 @@ 022 * 023 * Based on Algorithm 14.32 on pp.601 of HAC. 024 */ -025 int -026 fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) -027 \{ -028 int ix, res, olduse; -029 mp_word W[MP_WARRAY]; -030 -031 /* get old used count */ -032 olduse = x->used; -033 -034 /* grow a as required */ -035 if (x->alloc < n->used + 1) \{ -036 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) \{ -037 return res; -038 \} -039 \} -040 -041 /* first we have to get the digits of the input into -042 * an array of double precision words W[...] -043 */ -044 \{ -045 register mp_word *_W; -046 register mp_digit *tmpx; -047 -048 /* alias for the W[] array */ -049 _W = W; -050 -051 /* alias for the digits of x*/ -052 tmpx = x->dp; -053 -054 /* copy the digits of a into W[0..a->used-1] */ -055 for (ix = 0; ix < x->used; ix++) \{ -056 *_W++ = *tmpx++; -057 \} -058 -059 /* zero the high words of W[a->used..m->used*2] */ -060 for (; ix < n->used * 2 + 1; ix++) \{ -061 *_W++ = 0; -062 \} -063 \} -064 -065 /* now we proceed to zero successive digits -066 * from the least significant upwards -067 */ -068 for (ix = 0; ix < n->used; ix++) \{ -069 /* mu = ai * m' mod b -070 * -071 * We avoid a double precision multiplication (which isn't required) -072 * by casting the value down to a mp_digit. Note this requires -073 * that W[ix-1] have the carry cleared (see after the inner loop) -074 */ -075 register mp_digit mu; -076 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); -077 -078 /* a = a + mu * m * b**i -079 * -080 * This is computed in place and on the fly. The multiplication -081 * by b**i is handled by offseting which columns the results -082 * are added to. -083 * -084 * Note the comba method normally doesn't handle carries in the -085 * inner loop In this case we fix the carry from the previous -086 * column since the Montgomery reduction requires digits of the -087 * result (so far) [see above] to work. This is -088 * handled by fixing up one carry after the inner loop. The -089 * carry fixups are done in order so after these loops the -090 * first m->used words of W[] have the carries fixed -091 */ -092 \{ -093 register int iy; -094 register mp_digit *tmpn; -095 register mp_word *_W; -096 -097 /* alias for the digits of the modulus */ -098 tmpn = n->dp; -099 -100 /* Alias for the columns set by an offset of ix */ -101 _W = W + ix; -102 -103 /* inner loop */ -104 for (iy = 0; iy < n->used; iy++) \{ -105 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); -106 \} -107 \} -108 -109 /* now fix carry for next digit, W[ix+1] */ -110 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); -111 \} -112 -113 /* now we have to propagate the carries and -114 * shift the words downward [all those least -115 * significant digits we zeroed]. -116 */ -117 \{ -118 register mp_digit *tmpx; -119 register mp_word *_W, *_W1; -120 -121 /* nox fix rest of carries */ -122 -123 /* alias for current word */ -124 _W1 = W + ix; -125 -126 /* alias for next word, where the carry goes */ -127 _W = W + ++ix; -128 -129 for (; ix <= n->used * 2 + 1; ix++) \{ -130 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); -131 \} -132 -133 /* copy out, A = A/b**n -134 * -135 * The result is A/b**n but instead of converting from an -136 * array of mp_word to mp_digit than calling mp_rshd -137 * we just copy them in the right order -138 */ -139 -140 /* alias for destination word */ -141 tmpx = x->dp; -142 -143 /* alias for shifted double precision result */ -144 _W = W + n->used; -145 -146 for (ix = 0; ix < n->used + 1; ix++) \{ -147 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); -148 \} -149 -150 /* zero oldused digits, if the input a was larger than -151 * m->used+1 we'll have to clear the digits -152 */ -153 for (; ix < olduse; ix++) \{ -154 *tmpx++ = 0; -155 \} -156 \} -157 -158 /* set the max used and clamp */ -159 x->used = n->used + 1; -160 mp_clamp (x); -161 -162 /* if A >= m then A = A - m */ -163 if (mp_cmp_mag (x, n) != MP_LT) \{ -164 return s_mp_sub (x, n, x); -165 \} -166 return MP_OKAY; -167 \} -168 #endif +025 int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) +026 \{ +027 int ix, res, olduse; +028 mp_word W[MP_WARRAY]; +029 +030 /* get old used count */ +031 olduse = x->used; +032 +033 /* grow a as required */ +034 if (x->alloc < n->used + 1) \{ +035 if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) \{ +036 return res; +037 \} +038 \} +039 +040 /* first we have to get the digits of the input into +041 * an array of double precision words W[...] +042 */ +043 \{ +044 register mp_word *_W; +045 register mp_digit *tmpx; +046 +047 /* alias for the W[] array */ +048 _W = W; +049 +050 /* alias for the digits of x*/ +051 tmpx = x->dp; +052 +053 /* copy the digits of a into W[0..a->used-1] */ +054 for (ix = 0; ix < x->used; ix++) \{ +055 *_W++ = *tmpx++; +056 \} +057 +058 /* zero the high words of W[a->used..m->used*2] */ +059 for (; ix < n->used * 2 + 1; ix++) \{ +060 *_W++ = 0; +061 \} +062 \} +063 +064 /* now we proceed to zero successive digits +065 * from the least significant upwards +066 */ +067 for (ix = 0; ix < n->used; ix++) \{ +068 /* mu = ai * m' mod b +069 * +070 * We avoid a double precision multiplication (which isn't required) +071 * by casting the value down to a mp_digit. Note this requires +072 * that W[ix-1] have the carry cleared (see after the inner loop) +073 */ +074 register mp_digit mu; +075 mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); +076 +077 /* a = a + mu * m * b**i +078 * +079 * This is computed in place and on the fly. The multiplication +080 * by b**i is handled by offseting which columns the results +081 * are added to. +082 * +083 * Note the comba method normally doesn't handle carries in the +084 * inner loop In this case we fix the carry from the previous +085 * column since the Montgomery reduction requires digits of the +086 * result (so far) [see above] to work. This is +087 * handled by fixing up one carry after the inner loop. The +088 * carry fixups are done in order so after these loops the +089 * first m->used words of W[] have the carries fixed +090 */ +091 \{ +092 register int iy; +093 register mp_digit *tmpn; +094 register mp_word *_W; +095 +096 /* alias for the digits of the modulus */ +097 tmpn = n->dp; +098 +099 /* Alias for the columns set by an offset of ix */ +100 _W = W + ix; +101 +102 /* inner loop */ +103 for (iy = 0; iy < n->used; iy++) \{ +104 *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); +105 \} +106 \} +107 +108 /* now fix carry for next digit, W[ix+1] */ +109 W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); +110 \} +111 +112 /* now we have to propagate the carries and +113 * shift the words downward [all those least +114 * significant digits we zeroed]. +115 */ +116 \{ +117 register mp_digit *tmpx; +118 register mp_word *_W, *_W1; +119 +120 /* nox fix rest of carries */ +121 +122 /* alias for current word */ +123 _W1 = W + ix; +124 +125 /* alias for next word, where the carry goes */ +126 _W = W + ++ix; +127 +128 for (; ix <= n->used * 2 + 1; ix++) \{ +129 *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); +130 \} +131 +132 /* copy out, A = A/b**n +133 * +134 * The result is A/b**n but instead of converting from an +135 * array of mp_word to mp_digit than calling mp_rshd +136 * we just copy them in the right order +137 */ +138 +139 /* alias for destination word */ +140 tmpx = x->dp; +141 +142 /* alias for shifted double precision result */ +143 _W = W + n->used; +144 +145 for (ix = 0; ix < n->used + 1; ix++) \{ +146 *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); +147 \} +148 +149 /* zero oldused digits, if the input a was larger than +150 * m->used+1 we'll have to clear the digits +151 */ +152 for (; ix < olduse; ix++) \{ +153 *tmpx++ = 0; +154 \} +155 \} +156 +157 /* set the max used and clamp */ +158 x->used = n->used + 1; +159 mp_clamp (x); +160 +161 /* if A >= m then A = A - m */ +162 if (mp_cmp_mag (x, n) != MP_LT) \{ +163 return s_mp_sub (x, n, x); +164 \} +165 return MP_OKAY; +166 \} +167 #endif \end{alltt} \end{small} -The $\hat W$ array is first filled with digits of $x$ on line 48 then the rest of the digits are zeroed on line 55. Both loops share +The $\hat W$ array is first filled with digits of $x$ on line 50 then the rest of the digits are zeroed on line 54. Both loops share the same alias variables to make the code easier to read. The value of $\mu$ is calculated in an interesting fashion. First the value $\hat W_{ix}$ is reduced modulo $\beta$ and cast to a mp\_digit. This -forces the compiler to use a single precision multiplication and prevents any concerns about loss of precision. Line 110 fixes the carry +forces the compiler to use a single precision multiplication and prevents any concerns about loss of precision. Line 109 fixes the carry for the next iteration of the loop by propagating the carry from $\hat W_{ix}$ to $\hat W_{ix+1}$. -The for loop on line 109 propagates the rest of the carries upwards through the columns. The for loop on line 126 reduces the columns +The for loop on line 108 propagates the rest of the carries upwards through the columns. The for loop on line 125 reduces the columns modulo $\beta$ and shifts them $k$ places at the same time. The alias $\_ \hat W$ actually refers to the array $\hat W$ starting at the $n.used$'th digit, that is $\_ \hat W_{t} = \hat W_{n.used + t}$. @@ -6739,7 +6762,7 @@ 019 * Based on algorithm from the paper 020 * 021 * "Generating Efficient Primes for Discrete Log Cryptosystems" -022 * Chae Hoon Lim, Pil Loong Lee, +022 * Chae Hoon Lim, Pil Joong Lee, 023 * POSTECH Information Research Laboratories 024 * 025 * The modulus must be of a special format [see manual] @@ -6965,51 +6988,50 @@ \begin{alltt} 016 017 /* reduces a modulo n where n is of the form 2**p - d */ -018 int -019 mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) -020 \{ -021 mp_int q; -022 int p, res; -023 -024 if ((res = mp_init(&q)) != MP_OKAY) \{ -025 return res; -026 \} -027 -028 p = mp_count_bits(n); -029 top: -030 /* q = a/2**p, a = a mod 2**p */ -031 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) \{ -032 goto ERR; -033 \} -034 -035 if (d != 1) \{ -036 /* q = q * d */ -037 if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) \{ -038 goto ERR; -039 \} -040 \} -041 -042 /* a = a + q */ -043 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) \{ -044 goto ERR; -045 \} -046 -047 if (mp_cmp_mag(a, n) != MP_LT) \{ -048 s_mp_sub(a, n, a); -049 goto top; -050 \} -051 -052 ERR: -053 mp_clear(&q); -054 return res; -055 \} -056 -057 #endif +018 int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) +019 \{ +020 mp_int q; +021 int p, res; +022 +023 if ((res = mp_init(&q)) != MP_OKAY) \{ +024 return res; +025 \} +026 +027 p = mp_count_bits(n); +028 top: +029 /* q = a/2**p, a = a mod 2**p */ +030 if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) \{ +031 goto ERR; +032 \} +033 +034 if (d != 1) \{ +035 /* q = q * d */ +036 if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) \{ +037 goto ERR; +038 \} +039 \} +040 +041 /* a = a + q */ +042 if ((res = s_mp_add(a, &q, a)) != MP_OKAY) \{ +043 goto ERR; +044 \} +045 +046 if (mp_cmp_mag(a, n) != MP_LT) \{ +047 s_mp_sub(a, n, a); +048 goto top; +049 \} +050 +051 ERR: +052 mp_clear(&q); +053 return res; +054 \} +055 +056 #endif \end{alltt} \end{small} The algorithm mp\_count\_bits calculates the number of bits in an mp\_int which is used to find the initial value of $p$. The call to mp\_div\_2d -on line 31 calculates both the quotient $q$ and the remainder $a$ required. By doing both in a single function call the code size +on line 30 calculates both the quotient $q$ and the remainder $a$ required. By doing both in a single function call the code size is kept fairly small. The multiplication by $k$ is only performed if $k > 1$. This allows reductions modulo $2^p - 1$ to be performed without any multiplications. @@ -7049,32 +7071,31 @@ \begin{alltt} 016 017 /* determines the setup value */ -018 int -019 mp_reduce_2k_setup(mp_int *a, mp_digit *d) -020 \{ -021 int res, p; -022 mp_int tmp; -023 -024 if ((res = mp_init(&tmp)) != MP_OKAY) \{ -025 return res; -026 \} -027 -028 p = mp_count_bits(a); -029 if ((res = mp_2expt(&tmp, p)) != MP_OKAY) \{ -030 mp_clear(&tmp); -031 return res; -032 \} -033 -034 if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) \{ -035 mp_clear(&tmp); -036 return res; -037 \} -038 -039 *d = tmp.dp[0]; -040 mp_clear(&tmp); -041 return MP_OKAY; -042 \} -043 #endif +018 int mp_reduce_2k_setup(mp_int *a, mp_digit *d) +019 \{ +020 int res, p; +021 mp_int tmp; +022 +023 if ((res = mp_init(&tmp)) != MP_OKAY) \{ +024 return res; +025 \} +026 +027 p = mp_count_bits(a); +028 if ((res = mp_2expt(&tmp, p)) != MP_OKAY) \{ +029 mp_clear(&tmp); +030 return res; +031 \} +032 +033 if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) \{ +034 mp_clear(&tmp); +035 return res; +036 \} +037 +038 *d = tmp.dp[0]; +039 mp_clear(&tmp); +040 return MP_OKAY; +041 \} +042 #endif \end{alltt} \end{small} @@ -7127,9 +7148,9 @@ 021 mp_digit iz; 022 023 if (a->used == 0) \{ -024 return 0; +024 return MP_NO; 025 \} else if (a->used == 1) \{ -026 return 1; +026 return MP_YES; 027 \} else if (a->used > 1) \{ 028 iy = mp_count_bits(a); 029 iz = 1; @@ -7138,7 +7159,7 @@ 032 /* Test every bit from the second digit up, must be 1 */ 033 for (ix = DIGIT_BIT; ix < iy; ix++) \{ 034 if ((a->dp[iw] & iz) == 0) \{ -035 return 0; +035 return MP_NO; 036 \} 037 iz <<= 1; 038 if (iz > (mp_digit)MP_MASK) \{ @@ -7147,7 +7168,7 @@ 041 \} 042 \} 043 \} -044 return 1; +044 return MP_YES; 045 \} 046 047 #endif @@ -7594,43 +7615,51 @@ 060 return err; 061 #else 062 /* no invmod */ -063 return MP_VAL +063 return MP_VAL; 064 #endif 065 \} 066 -067 #ifdef BN_MP_DR_IS_MODULUS_C -068 /* is it a DR modulus? */ -069 dr = mp_dr_is_modulus(P); -070 #else -071 dr = 0; +067 /* modified diminished radix reduction */ +068 #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) +069 if (mp_reduce_is_2k_l(P) == MP_YES) \{ +070 return s_mp_exptmod(G, X, P, Y, 1); +071 \} 072 #endif 073 -074 #ifdef BN_MP_REDUCE_IS_2K_C -075 /* if not, is it a uDR modulus? */ -076 if (dr == 0) \{ -077 dr = mp_reduce_is_2k(P) << 1; -078 \} -079 #endif -080 -081 /* if the modulus is odd or dr != 0 use the fast method */ -082 #ifdef BN_MP_EXPTMOD_FAST_C -083 if (mp_isodd (P) == 1 || dr != 0) \{ -084 return mp_exptmod_fast (G, X, P, Y, dr); -085 \} else \{ -086 #endif -087 #ifdef BN_S_MP_EXPTMOD_C -088 /* otherwise use the generic Barrett reduction technique */ -089 return s_mp_exptmod (G, X, P, Y); -090 #else -091 /* no exptmod for evens */ -092 return MP_VAL; -093 #endif -094 #ifdef BN_MP_EXPTMOD_FAST_C -095 \} -096 #endif -097 \} -098 -099 #endif +074 #ifdef BN_MP_DR_IS_MODULUS_C +075 /* is it a DR modulus? */ +076 dr = mp_dr_is_modulus(P); +077 #else +078 /* default to no */ +079 dr = 0; +080 #endif +081 +082 #ifdef BN_MP_REDUCE_IS_2K_C +083 /* if not, is it a unrestricted DR modulus? */ +084 if (dr == 0) \{ +085 dr = mp_reduce_is_2k(P) << 1; +086 \} +087 #endif +088 +089 /* if the modulus is odd or dr != 0 use the montgomery method */ +090 #ifdef BN_MP_EXPTMOD_FAST_C +091 if (mp_isodd (P) == 1 || dr != 0) \{ +092 return mp_exptmod_fast (G, X, P, Y, dr); +093 \} else \{ +094 #endif +095 #ifdef BN_S_MP_EXPTMOD_C +096 /* otherwise use the generic Barrett reduction technique */ +097 return s_mp_exptmod (G, X, P, Y, 0); +098 #else +099 /* no exptmod for evens */ +100 return MP_VAL; +101 #endif +102 #ifdef BN_MP_EXPTMOD_FAST_C +103 \} +104 #endif +105 \} +106 +107 #endif \end{alltt} \end{small} @@ -7639,8 +7668,8 @@ the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$. The algorithm will recuse with these new values with a positive exponent. -If the exponent is positive the algorithm resumes the exponentiation. Line 69 determines if the modulus is of the restricted Diminished Radix -form. If it is not line 77 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one +If the exponent is positive the algorithm resumes the exponentiation. Line 76 determines if the modulus is of the restricted Diminished Radix +form. If it is not line 69 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one of three values. \begin{enumerate} @@ -7649,7 +7678,7 @@ \item $dr = 2$ means that the modulus is of unrestricted Diminished Radix form. \end{enumerate} -Line 67 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise, +Line 69 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise, the slower s\_mp\_exptmod algorithm is used which uses Barrett reduction. \subsection{Barrett Modular Exponentiation} @@ -7817,230 +7846,244 @@ 020 #define TAB_SIZE 256 021 #endif 022 -023 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y) +023 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmod + e) 024 \{ 025 mp_int M[TAB_SIZE], res, mu; 026 mp_digit buf; 027 int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; -028 -029 /* find window size */ -030 x = mp_count_bits (X); -031 if (x <= 7) \{ -032 winsize = 2; -033 \} else if (x <= 36) \{ -034 winsize = 3; -035 \} else if (x <= 140) \{ -036 winsize = 4; -037 \} else if (x <= 450) \{ -038 winsize = 5; -039 \} else if (x <= 1303) \{ -040 winsize = 6; -041 \} else if (x <= 3529) \{ -042 winsize = 7; -043 \} else \{ -044 winsize = 8; -045 \} -046 -047 #ifdef MP_LOW_MEM -048 if (winsize > 5) \{ -049 winsize = 5; -050 \} -051 #endif -052 -053 /* init M array */ -054 /* init first cell */ -055 if ((err = mp_init(&M[1])) != MP_OKAY) \{ -056 return err; -057 \} -058 -059 /* now init the second half of the array */ -060 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ -061 if ((err = mp_init(&M[x])) != MP_OKAY) \{ -062 for (y = 1<<(winsize-1); y < x; y++) \{ -063 mp_clear (&M[y]); -064 \} -065 mp_clear(&M[1]); -066 return err; -067 \} -068 \} -069 -070 /* create mu, used for Barrett reduction */ -071 if ((err = mp_init (&mu)) != MP_OKAY) \{ -072 goto __M; -073 \} -074 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{ -075 goto __MU; -076 \} -077 -078 /* create M table -079 * -080 * The M table contains powers of the base, -081 * e.g. M[x] = G**x mod P -082 * -083 * The first half of the table is not -084 * computed though accept for M[0] and M[1] -085 */ -086 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{ -087 goto __MU; -088 \} -089 -090 /* compute the value at M[1<<(winsize-1)] by squaring -091 * M[1] (winsize-1) times -092 */ -093 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{ -094 goto __MU; -095 \} -096 -097 for (x = 0; x < (winsize - 1); x++) \{ -098 if ((err = mp_sqr (&M[1 << (winsize - 1)], -099 &M[1 << (winsize - 1)])) != MP_OKAY) \{ -100 goto __MU; -101 \} -102 if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{ -103 goto __MU; -104 \} +028 int (*redux)(mp_int*,mp_int*,mp_int*); +029 +030 /* find window size */ +031 x = mp_count_bits (X); +032 if (x <= 7) \{ +033 winsize = 2; +034 \} else if (x <= 36) \{ +035 winsize = 3; +036 \} else if (x <= 140) \{ +037 winsize = 4; +038 \} else if (x <= 450) \{ +039 winsize = 5; +040 \} else if (x <= 1303) \{ +041 winsize = 6; +042 \} else if (x <= 3529) \{ +043 winsize = 7; +044 \} else \{ +045 winsize = 8; +046 \} +047 +048 #ifdef MP_LOW_MEM +049 if (winsize > 5) \{ +050 winsize = 5; +051 \} +052 #endif +053 +054 /* init M array */ +055 /* init first cell */ +056 if ((err = mp_init(&M[1])) != MP_OKAY) \{ +057 return err; +058 \} +059 +060 /* now init the second half of the array */ +061 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ +062 if ((err = mp_init(&M[x])) != MP_OKAY) \{ +063 for (y = 1<<(winsize-1); y < x; y++) \{ +064 mp_clear (&M[y]); +065 \} +066 mp_clear(&M[1]); +067 return err; +068 \} +069 \} +070 +071 /* create mu, used for Barrett reduction */ +072 if ((err = mp_init (&mu)) != MP_OKAY) \{ +073 goto LBL_M; +074 \} +075 +076 if (redmode == 0) \{ +077 if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{ +078 goto LBL_MU; +079 \} +080 redux = mp_reduce; +081 \} else \{ +082 if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) \{ +083 goto LBL_MU; +084 \} +085 redux = mp_reduce_2k_l; +086 \} +087 +088 /* create M table +089 * +090 * The M table contains powers of the base, +091 * e.g. M[x] = G**x mod P +092 * +093 * The first half of the table is not +094 * computed though accept for M[0] and M[1] +095 */ +096 if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{ +097 goto LBL_MU; +098 \} +099 +100 /* compute the value at M[1<<(winsize-1)] by squaring +101 * M[1] (winsize-1) times +102 */ +103 if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{ +104 goto LBL_MU; 105 \} 106 -107 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) -108 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) -109 */ -110 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{ -111 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{ -112 goto __MU; -113 \} -114 if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) \{ -115 goto __MU; -116 \} -117 \} -118 -119 /* setup result */ -120 if ((err = mp_init (&res)) != MP_OKAY) \{ -121 goto __MU; -122 \} -123 mp_set (&res, 1); -124 -125 /* set initial mode and bit cnt */ -126 mode = 0; -127 bitcnt = 1; -128 buf = 0; -129 digidx = X->used - 1; -130 bitcpy = 0; -131 bitbuf = 0; -132 -133 for (;;) \{ -134 /* grab next digit as required */ -135 if (--bitcnt == 0) \{ -136 /* if digidx == -1 we are out of digits */ -137 if (digidx == -1) \{ -138 break; -139 \} -140 /* read next digit and reset the bitcnt */ -141 buf = X->dp[digidx--]; -142 bitcnt = (int) DIGIT_BIT; -143 \} -144 -145 /* grab the next msb from the exponent */ -146 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; -147 buf <<= (mp_digit)1; -148 -149 /* if the bit is zero and mode == 0 then we ignore it -150 * These represent the leading zero bits before the first 1 bit -151 * in the exponent. Technically this opt is not required but it -152 * does lower the # of trivial squaring/reductions used -153 */ -154 if (mode == 0 && y == 0) \{ -155 continue; +107 for (x = 0; x < (winsize - 1); x++) \{ +108 /* square it */ +109 if ((err = mp_sqr (&M[1 << (winsize - 1)], +110 &M[1 << (winsize - 1)])) != MP_OKAY) \{ +111 goto LBL_MU; +112 \} +113 +114 /* reduce modulo P */ +115 if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{ +116 goto LBL_MU; +117 \} +118 \} +119 +120 /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) +121 * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) +122 */ +123 for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{ +124 if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{ +125 goto LBL_MU; +126 \} +127 if ((err = redux (&M[x], P, &mu)) != MP_OKAY) \{ +128 goto LBL_MU; +129 \} +130 \} +131 +132 /* setup result */ +133 if ((err = mp_init (&res)) != MP_OKAY) \{ +134 goto LBL_MU; +135 \} +136 mp_set (&res, 1); +137 +138 /* set initial mode and bit cnt */ +139 mode = 0; +140 bitcnt = 1; +141 buf = 0; +142 digidx = X->used - 1; +143 bitcpy = 0; +144 bitbuf = 0; +145 +146 for (;;) \{ +147 /* grab next digit as required */ +148 if (--bitcnt == 0) \{ +149 /* if digidx == -1 we are out of digits */ +150 if (digidx == -1) \{ +151 break; +152 \} +153 /* read next digit and reset the bitcnt */ +154 buf = X->dp[digidx--]; +155 bitcnt = (int) DIGIT_BIT; 156 \} 157 -158 /* if the bit is zero and mode == 1 then we square */ -159 if (mode == 1 && y == 0) \{ -160 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ -161 goto __RES; -162 \} -163 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{ -164 goto __RES; -165 \} -166 continue; -167 \} -168 -169 /* else we add it to the window */ -170 bitbuf |= (y << (winsize - ++bitcpy)); -171 mode = 2; -172 -173 if (bitcpy == winsize) \{ -174 /* ok window is filled so square as required and multiply */ -175 /* square first */ -176 for (x = 0; x < winsize; x++) \{ -177 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ -178 goto __RES; -179 \} -180 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{ -181 goto __RES; -182 \} -183 \} -184 -185 /* then multiply */ -186 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{ -187 goto __RES; -188 \} -189 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{ -190 goto __RES; -191 \} -192 -193 /* empty window and reset */ -194 bitcpy = 0; -195 bitbuf = 0; -196 mode = 1; -197 \} -198 \} -199 -200 /* if bits remain then square/multiply */ -201 if (mode == 2 && bitcpy > 0) \{ -202 /* square then multiply if the bit is set */ -203 for (x = 0; x < bitcpy; x++) \{ -204 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ -205 goto __RES; -206 \} -207 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{ -208 goto __RES; -209 \} -210 -211 bitbuf <<= 1; -212 if ((bitbuf & (1 << winsize)) != 0) \{ -213 /* then multiply */ -214 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{ -215 goto __RES; -216 \} -217 if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) \{ -218 goto __RES; -219 \} -220 \} -221 \} -222 \} +158 /* grab the next msb from the exponent */ +159 y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; +160 buf <<= (mp_digit)1; +161 +162 /* if the bit is zero and mode == 0 then we ignore it +163 * These represent the leading zero bits before the first 1 bit +164 * in the exponent. Technically this opt is not required but it +165 * does lower the # of trivial squaring/reductions used +166 */ +167 if (mode == 0 && y == 0) \{ +168 continue; +169 \} +170 +171 /* if the bit is zero and mode == 1 then we square */ +172 if (mode == 1 && y == 0) \{ +173 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ +174 goto LBL_RES; +175 \} +176 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +177 goto LBL_RES; +178 \} +179 continue; +180 \} +181 +182 /* else we add it to the window */ +183 bitbuf |= (y << (winsize - ++bitcpy)); +184 mode = 2; +185 +186 if (bitcpy == winsize) \{ +187 /* ok window is filled so square as required and multiply */ +188 /* square first */ +189 for (x = 0; x < winsize; x++) \{ +190 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ +191 goto LBL_RES; +192 \} +193 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +194 goto LBL_RES; +195 \} +196 \} +197 +198 /* then multiply */ +199 if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{ +200 goto LBL_RES; +201 \} +202 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +203 goto LBL_RES; +204 \} +205 +206 /* empty window and reset */ +207 bitcpy = 0; +208 bitbuf = 0; +209 mode = 1; +210 \} +211 \} +212 +213 /* if bits remain then square/multiply */ +214 if (mode == 2 && bitcpy > 0) \{ +215 /* square then multiply if the bit is set */ +216 for (x = 0; x < bitcpy; x++) \{ +217 if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{ +218 goto LBL_RES; +219 \} +220 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +221 goto LBL_RES; +222 \} 223 -224 mp_exch (&res, Y); -225 err = MP_OKAY; -226 __RES:mp_clear (&res); -227 __MU:mp_clear (&mu); -228 __M: -229 mp_clear(&M[1]); -230 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ -231 mp_clear (&M[x]); -232 \} -233 return err; -234 \} -235 #endif +224 bitbuf <<= 1; +225 if ((bitbuf & (1 << winsize)) != 0) \{ +226 /* then multiply */ +227 if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{ +228 goto LBL_RES; +229 \} +230 if ((err = redux (&res, P, &mu)) != MP_OKAY) \{ +231 goto LBL_RES; +232 \} +233 \} +234 \} +235 \} +236 +237 mp_exch (&res, Y); +238 err = MP_OKAY; +239 LBL_RES:mp_clear (&res); +240 LBL_MU:mp_clear (&mu); +241 LBL_M: +242 mp_clear(&M[1]); +243 for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{ +244 mp_clear (&M[x]); +245 \} +246 return err; +247 \} +248 #endif \end{alltt} \end{small} -Lines 31 through 41 determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted +Lines 21 through 40 determine the optimal window size based on the length of the exponent in bits. The window divisions are sorted from smallest to greatest so that in each \textbf{if} statement only one condition must be tested. For example, by the \textbf{if} statement -on line 33 the value of $x$ is already known to be greater than $140$. - -The conditional piece of code beginning on line 47 allows the window size to be restricted to five bits. This logic is used to ensure +on line 32 the value of $x$ is already known to be greater than $140$. + +The conditional piece of code beginning on line 48 allows the window size to be restricted to five bits. This logic is used to ensure the table of precomputed powers of $G$ remains relatively small. -The for loop on line 60 initializes the $M$ array while lines 61 and 74 compute the value of $\mu$ required for +The for loop on line 61 initializes the $M$ array while lines 62 and 77 compute the value of $\mu$ required for Barrett reduction. -- More later. @@ -8386,23 +8429,23 @@ 048 049 mp_set(&tq, 1); 050 n = mp_count_bits(a) - mp_count_bits(b); -051 if (((res = mp_copy(a, &ta)) != MP_OKAY) || -052 ((res = mp_copy(b, &tb)) != MP_OKAY) || +051 if (((res = mp_abs(a, &ta)) != MP_OKAY) || +052 ((res = mp_abs(b, &tb)) != MP_OKAY) || 053 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || 054 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) \{ -055 goto __ERR; +055 goto LBL_ERR; 056 \} 057 058 while (n-- >= 0) \{ 059 if (mp_cmp(&tb, &ta) != MP_GT) \{ 060 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || 061 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) \{ -062 goto __ERR; +062 goto LBL_ERR; 063 \} 064 \} 065 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || 066 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) \{ -067 goto __ERR; +067 goto LBL_ERR; 068 \} 069 \} 070 @@ -8411,13 +8454,13 @@ 073 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); 074 if (c != NULL) \{ 075 mp_exch(c, &q); -076 c->sign = n2; +076 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2; 077 \} 078 if (d != NULL) \{ 079 mp_exch(d, &ta); -080 d->sign = n; +080 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n; 081 \} -082 __ERR: +082 LBL_ERR: 083 mp_clear_multi(&ta, &tb, &tq, &q, NULL); 084 return res; 085 \} @@ -8466,19 +8509,19 @@ 128 q.used = a->used + 2; 129 130 if ((res = mp_init (&t1)) != MP_OKAY) \{ -131 goto __Q; +131 goto LBL_Q; 132 \} 133 134 if ((res = mp_init (&t2)) != MP_OKAY) \{ -135 goto __T1; +135 goto LBL_T1; 136 \} 137 138 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{ -139 goto __T2; +139 goto LBL_T2; 140 \} 141 142 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{ -143 goto __X; +143 goto LBL_X; 144 \} 145 146 /* fix the sign */ @@ -8490,10 +8533,10 @@ 152 if (norm < (int)(DIGIT_BIT-1)) \{ 153 norm = (DIGIT_BIT-1) - norm; 154 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{ -155 goto __Y; +155 goto LBL_Y; 156 \} 157 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{ -158 goto __Y; +158 goto LBL_Y; 159 \} 160 \} else \{ 161 norm = 0; @@ -8505,13 +8548,13 @@ 167 168 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */ 169 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */ -170 goto __Y; +170 goto LBL_Y; 171 \} 172 173 while (mp_cmp (&x, &y) != MP_LT) \{ 174 ++(q.dp[n - t]); 175 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{ -176 goto __Y; +176 goto LBL_Y; 177 \} 178 \} 179 @@ -8553,7 +8596,7 @@ 215 t1.dp[1] = y.dp[t]; 216 t1.used = 2; 217 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{ -218 goto __Y; +218 goto LBL_Y; 219 \} 220 221 /* find right hand */ @@ -8565,27 +8608,27 @@ 227 228 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */ 229 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{ -230 goto __Y; +230 goto LBL_Y; 231 \} 232 233 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{ -234 goto __Y; +234 goto LBL_Y; 235 \} 236 237 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{ -238 goto __Y; +238 goto LBL_Y; 239 \} 240 241 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */ 242 if (x.sign == MP_NEG) \{ 243 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{ -244 goto __Y; +244 goto LBL_Y; 245 \} 246 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{ -247 goto __Y; +247 goto LBL_Y; 248 \} 249 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{ -250 goto __Y; +250 goto LBL_Y; 251 \} 252 253 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; @@ -8612,11 +8655,11 @@ 274 275 res = MP_OKAY; 276 -277 __Y:mp_clear (&y); -278 __X:mp_clear (&x); -279 __T2:mp_clear (&t2); -280 __T1:mp_clear (&t1); -281 __Q:mp_clear (&q); +277 LBL_Y:mp_clear (&y); +278 LBL_X:mp_clear (&x); +279 LBL_T2:mp_clear (&t2); +280 LBL_T1:mp_clear (&t1); +281 LBL_Q:mp_clear (&q); 282 return res; 283 \} 284 @@ -8870,21 +8913,22 @@ 056 u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); 057 \} 058 -059 /* store final carry [if any] */ +059 /* store final carry [if any] and increment ix offset */ 060 *tmpc++ = u; -061 -062 /* now zero digits above the top */ -063 while (ix++ < olduse) \{ -064 *tmpc++ = 0; -065 \} -066 -067 /* set used count */ -068 c->used = a->used + 1; -069 mp_clamp(c); -070 -071 return MP_OKAY; -072 \} -073 #endif +061 ++ix; +062 +063 /* now zero digits above the top */ +064 while (ix++ < olduse) \{ +065 *tmpc++ = 0; +066 \} +067 +068 /* set used count */ +069 c->used = a->used + 1; +070 mp_clamp(c); +071 +072 return MP_OKAY; +073 \} +074 #endif \end{alltt} \end{small} @@ -9130,11 +9174,11 @@ 039 \} 040 041 if ((res = mp_init (&t2)) != MP_OKAY) \{ -042 goto __T1; +042 goto LBL_T1; 043 \} 044 045 if ((res = mp_init (&t3)) != MP_OKAY) \{ -046 goto __T2; +046 goto LBL_T2; 047 \} 048 049 /* if a is negative fudge the sign but keep track */ @@ -9147,52 +9191,52 @@ 056 do \{ 057 /* t1 = t2 */ 058 if ((res = mp_copy (&t2, &t1)) != MP_OKAY) \{ -059 goto __T3; +059 goto LBL_T3; 060 \} 061 062 /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ 063 064 /* t3 = t1**(b-1) */ 065 if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) \{ -066 goto __T3; +066 goto LBL_T3; 067 \} 068 069 /* numerator */ 070 /* t2 = t1**b */ 071 if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) \{ -072 goto __T3; +072 goto LBL_T3; 073 \} 074 075 /* t2 = t1**b - a */ 076 if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) \{ -077 goto __T3; +077 goto LBL_T3; 078 \} 079 080 /* denominator */ 081 /* t3 = t1**(b-1) * b */ 082 if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) \{ -083 goto __T3; +083 goto LBL_T3; 084 \} 085 086 /* t3 = (t1**b - a)/(b * t1**(b-1)) */ 087 if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) \{ -088 goto __T3; +088 goto LBL_T3; 089 \} 090 091 if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) \{ -092 goto __T3; +092 goto LBL_T3; 093 \} 094 \} while (mp_cmp (&t1, &t2) != MP_EQ); 095 096 /* result can be off by a few so check */ 097 for (;;) \{ 098 if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) \{ -099 goto __T3; +099 goto LBL_T3; 100 \} 101 102 if (mp_cmp (&t2, a) == MP_GT) \{ 103 if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) \{ -104 goto __T3; +104 goto LBL_T3; 105 \} 106 \} else \{ 107 break; @@ -9210,9 +9254,9 @@ 119 120 res = MP_OKAY; 121 -122 __T3:mp_clear (&t3); -123 __T2:mp_clear (&t2); -124 __T1:mp_clear (&t1); +122 LBL_T3:mp_clear (&t3); +123 LBL_T2:mp_clear (&t2); +124 LBL_T1:mp_clear (&t1); 125 return res; 126 \} 127 #endif @@ -9272,14 +9316,14 @@ 028 029 /* first place a random non-zero digit */ 030 do \{ -031 d = ((mp_digit) abs (rand ())); +031 d = ((mp_digit) abs (rand ())) & MP_MASK; 032 \} while (d == 0); 033 034 if ((res = mp_add_d (a, d, a)) != MP_OKAY) \{ 035 return res; 036 \} 037 -038 while (digits-- > 0) \{ +038 while (--digits > 0) \{ 039 if ((res = mp_lshd (a, 1)) != MP_OKAY) \{ 040 return res; 041 \} @@ -9376,7 +9420,7 @@ \begin{alltt} 016 017 /* read a string [ASCII] in a given radix */ -018 int mp_read_radix (mp_int * a, char *str, int radix) +018 int mp_read_radix (mp_int * a, const char *str, int radix) 019 \{ 020 int y, res, neg; 021 char ch; @@ -9771,7 +9815,7 @@ 042 \} 043 044 if ((res = mp_init_copy (&v, b)) != MP_OKAY) \{ -045 goto __U; +045 goto LBL_U; 046 \} 047 048 /* must be positive for the remainder of the algorithm */ @@ -9785,24 +9829,24 @@ 056 if (k > 0) \{ 057 /* divide the power of two out */ 058 if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) \{ -059 goto __V; +059 goto LBL_V; 060 \} 061 062 if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) \{ -063 goto __V; +063 goto LBL_V; 064 \} 065 \} 066 067 /* divide any remaining factors of two out */ 068 if (u_lsb != k) \{ 069 if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) \{ -070 goto __V; +070 goto LBL_V; 071 \} 072 \} 073 074 if (v_lsb != k) \{ 075 if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) \{ -076 goto __V; +076 goto LBL_V; 077 \} 078 \} 079 @@ -9815,23 +9859,23 @@ 086 087 /* subtract smallest from largest */ 088 if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) \{ -089 goto __V; +089 goto LBL_V; 090 \} 091 092 /* Divide out all factors of two */ 093 if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) \{ -094 goto __V; +094 goto LBL_V; 095 \} 096 \} 097 098 /* multiply by 2**k which we divided out at the beginning */ 099 if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) \{ -100 goto __V; +100 goto LBL_V; 101 \} 102 c->sign = MP_ZPOS; 103 res = MP_OKAY; -104 __V:mp_clear (&u); -105 __U:mp_clear (&v); +104 LBL_V:mp_clear (&u); +105 LBL_U:mp_clear (&v); 106 return res; 107 \} 108 #endif @@ -9904,20 +9948,20 @@ 027 028 /* t1 = get the GCD of the two inputs */ 029 if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) \{ -030 goto __T; +030 goto LBL_T; 031 \} 032 033 /* divide the smallest by the GCD */ 034 if (mp_cmp_mag(a, b) == MP_LT) \{ 035 /* store quotient in t2 such that t2 * b is the LCM */ 036 if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) \{ -037 goto __T; +037 goto LBL_T; 038 \} 039 res = mp_mul(b, &t2, c); 040 \} else \{ 041 /* store quotient in t2 such that t2 * a is the LCM */ 042 if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) \{ -043 goto __T; +043 goto LBL_T; 044 \} 045 res = mp_mul(a, &t2, c); 046 \} @@ -9925,7 +9969,7 @@ 048 /* fix the sign to positive */ 049 c->sign = MP_ZPOS; 050 -051 __T: +051 LBL_T: 052 mp_clear_multi (&t1, &t2, NULL); 053 return res; 054 \} @@ -9938,6 +9982,8 @@ defined. The Legendre function computes whether or not an integer $a$ is a quadratic residue modulo an odd prime $p$. Numerically it is equivalent to equation \ref{eqn:legendre}. +\textit{-- Tom, don't be an ass, cite your source here...!} + \begin{equation} a^{(p-1)/2} \equiv \begin{array}{rl} -1 & \mbox{if }a\mbox{ is a quadratic non-residue.} \\ @@ -10123,13 +10169,13 @@ 049 \} 050 051 if ((res = mp_init (&p1)) != MP_OKAY) \{ -052 goto __A1; +052 goto LBL_A1; 053 \} 054 055 /* divide out larger power of two */ 056 k = mp_cnt_lsb(&a1); 057 if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) \{ -058 goto __P1; +058 goto LBL_P1; 059 \} 060 061 /* step 4. if e is even set s=1 */ @@ -10157,18 +10203,18 @@ 083 \} else \{ 084 /* n1 = n mod a1 */ 085 if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) \{ -086 goto __P1; +086 goto LBL_P1; 087 \} 088 if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) \{ -089 goto __P1; +089 goto LBL_P1; 090 \} 091 *c = s * r; 092 \} 093 094 /* done */ 095 res = MP_OKAY; -096 __P1:mp_clear (&p1); -097 __A1:mp_clear (&a1); +096 LBL_P1:mp_clear (&p1); +097 LBL_A1:mp_clear (&a1); 098 return res; 099 \} 100 #endif @@ -10406,8 +10452,8 @@ 028 *result = MP_NO; 029 030 for (ix = 0; ix < PRIME_SIZE; ix++) \{ -031 /* what is a mod __prime_tab[ix] */ -032 if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) \{ +031 /* what is a mod LBL_prime_tab[ix] */ +032 if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) \{ 033 return err; 034 \} 035 @@ -10431,7 +10477,7 @@ \hspace{-5.1mm}{\bf File}: bn\_prime\_tab.c \vspace{-3mm} \begin{alltt} -016 const mp_digit __prime_tab[] = \{ +016 const mp_digit ltm_prime_tab[] = \{ 017 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 018 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 019 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, @@ -10547,7 +10593,7 @@ 042 043 /* compute t = b**a mod a */ 044 if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) \{ -045 goto __T; +045 goto LBL_T; 046 \} 047 048 /* is it equal to b? */ @@ -10556,7 +10602,7 @@ 051 \} 052 053 err = MP_OKAY; -054 __T:mp_clear (&t); +054 LBL_T:mp_clear (&t); 055 return err; 056 \} 057 #endif @@ -10638,12 +10684,12 @@ 039 return err; 040 \} 041 if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) \{ -042 goto __N1; +042 goto LBL_N1; 043 \} 044 045 /* set 2**s * r = n1 */ 046 if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) \{ -047 goto __N1; +047 goto LBL_N1; 048 \} 049 050 /* count the number of least significant bits @@ -10653,15 +10699,15 @@ 054 055 /* now divide n - 1 by 2**s */ 056 if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) \{ -057 goto __R; +057 goto LBL_R; 058 \} 059 060 /* compute y = b**r mod a */ 061 if ((err = mp_init (&y)) != MP_OKAY) \{ -062 goto __R; +062 goto LBL_R; 063 \} 064 if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) \{ -065 goto __Y; +065 goto LBL_Y; 066 \} 067 068 /* if y != 1 and y != n1 do */ @@ -10670,12 +10716,12 @@ 071 /* while j <= s-1 and y != n1 */ 072 while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) \{ 073 if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) \{ -074 goto __Y; +074 goto LBL_Y; 075 \} 076 077 /* if y == 1 then composite */ 078 if (mp_cmp_d (&y, 1) == MP_EQ) \{ -079 goto __Y; +079 goto LBL_Y; 080 \} 081 082 ++j; @@ -10683,15 +10729,15 @@ 084 085 /* if y != n1 then composite */ 086 if (mp_cmp (&y, &n1) != MP_EQ) \{ -087 goto __Y; +087 goto LBL_Y; 088 \} 089 \} 090 091 /* probably prime now */ 092 *result = MP_YES; -093 __Y:mp_clear (&y); -094 __R:mp_clear (&r); -095 __N1:mp_clear (&n1); +093 LBL_Y:mp_clear (&y); +094 LBL_R:mp_clear (&r); +095 LBL_N1:mp_clear (&n1); 096 return err; 097 \} 098 #endif
--- a/tommath_class.h Sun Dec 19 11:33:56 2004 +0000 +++ b/tommath_class.h Fri May 06 08:59:30 2005 +0000 @@ -90,8 +90,11 @@ #define BN_MP_READ_UNSIGNED_BIN_C #define BN_MP_REDUCE_C #define BN_MP_REDUCE_2K_C +#define BN_MP_REDUCE_2K_L_C #define BN_MP_REDUCE_2K_SETUP_C +#define BN_MP_REDUCE_2K_SETUP_L_C #define BN_MP_REDUCE_IS_2K_C +#define BN_MP_REDUCE_IS_2K_L_C #define BN_MP_REDUCE_SETUP_C #define BN_MP_RSHD_C #define BN_MP_SET_C @@ -105,7 +108,9 @@ #define BN_MP_SUB_D_C #define BN_MP_SUBMOD_C #define BN_MP_TO_SIGNED_BIN_C +#define BN_MP_TO_SIGNED_BIN_N_C #define BN_MP_TO_UNSIGNED_BIN_C +#define BN_MP_TO_UNSIGNED_BIN_N_C #define BN_MP_TOOM_MUL_C #define BN_MP_TOOM_SQR_C #define BN_MP_TORADIX_C @@ -132,7 +137,7 @@ #define BN_MP_ISEVEN_C #define BN_MP_INIT_MULTI_C #define BN_MP_COPY_C - #define BN_MP_ABS_C + #define BN_MP_MOD_C #define BN_MP_SET_C #define BN_MP_DIV_2_C #define BN_MP_ISODD_C @@ -242,6 +247,7 @@ #define BN_MP_INIT_MULTI_C #define BN_MP_SET_C #define BN_MP_COUNT_BITS_C + #define BN_MP_ABS_C #define BN_MP_MUL_2D_C #define BN_MP_CMP_C #define BN_MP_SUB_C @@ -323,11 +329,12 @@ #define BN_MP_CLEAR_C #define BN_MP_ABS_C #define BN_MP_CLEAR_MULTI_C + #define BN_MP_REDUCE_IS_2K_L_C + #define BN_S_MP_EXPTMOD_C #define BN_MP_DR_IS_MODULUS_C #define BN_MP_REDUCE_IS_2K_C #define BN_MP_ISODD_C #define BN_MP_EXPTMOD_FAST_C - #define BN_S_MP_EXPTMOD_C #endif #if defined(BN_MP_EXPTMOD_FAST_C) @@ -359,6 +366,7 @@ #define BN_MP_DIV_C #define BN_MP_MUL_C #define BN_MP_SUB_C + #define BN_MP_NEG_C #define BN_MP_EXCH_C #define BN_MP_CLEAR_MULTI_C #endif @@ -433,6 +441,7 @@ #if defined(BN_MP_INVMOD_SLOW_C) #define BN_MP_ISZERO_C #define BN_MP_INIT_MULTI_C + #define BN_MP_MOD_C #define BN_MP_COPY_C #define BN_MP_ISEVEN_C #define BN_MP_SET_C @@ -724,6 +733,17 @@ #define BN_MP_CLEAR_C #endif +#if defined(BN_MP_REDUCE_2K_L_C) + #define BN_MP_INIT_C + #define BN_MP_COUNT_BITS_C + #define BN_MP_DIV_2D_C + #define BN_MP_MUL_C + #define BN_S_MP_ADD_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C + #define BN_MP_CLEAR_C +#endif + #if defined(BN_MP_REDUCE_2K_SETUP_C) #define BN_MP_INIT_C #define BN_MP_COUNT_BITS_C @@ -732,11 +752,22 @@ #define BN_S_MP_SUB_C #endif +#if defined(BN_MP_REDUCE_2K_SETUP_L_C) + #define BN_MP_INIT_C + #define BN_MP_2EXPT_C + #define BN_MP_COUNT_BITS_C + #define BN_S_MP_SUB_C + #define BN_MP_CLEAR_C +#endif + #if defined(BN_MP_REDUCE_IS_2K_C) #define BN_MP_REDUCE_2K_C #define BN_MP_COUNT_BITS_C #endif +#if defined(BN_MP_REDUCE_IS_2K_L_C) +#endif + #if defined(BN_MP_REDUCE_SETUP_C) #define BN_MP_2EXPT_C #define BN_MP_DIV_C @@ -814,6 +845,11 @@ #define BN_MP_TO_UNSIGNED_BIN_C #endif +#if defined(BN_MP_TO_SIGNED_BIN_N_C) + #define BN_MP_SIGNED_BIN_SIZE_C + #define BN_MP_TO_SIGNED_BIN_C +#endif + #if defined(BN_MP_TO_UNSIGNED_BIN_C) #define BN_MP_INIT_COPY_C #define BN_MP_ISZERO_C @@ -821,6 +857,11 @@ #define BN_MP_CLEAR_C #endif +#if defined(BN_MP_TO_UNSIGNED_BIN_N_C) + #define BN_MP_UNSIGNED_BIN_SIZE_C + #define BN_MP_TO_UNSIGNED_BIN_C +#endif + #if defined(BN_MP_TOOM_MUL_C) #define BN_MP_INIT_MULTI_C #define BN_MP_MOD_2D_C @@ -901,10 +942,12 @@ #define BN_MP_INIT_C #define BN_MP_CLEAR_C #define BN_MP_REDUCE_SETUP_C + #define BN_MP_REDUCE_C + #define BN_MP_REDUCE_2K_SETUP_L_C + #define BN_MP_REDUCE_2K_L_C #define BN_MP_MOD_C #define BN_MP_COPY_C #define BN_MP_SQR_C - #define BN_MP_REDUCE_C #define BN_MP_MUL_C #define BN_MP_SET_C #define BN_MP_EXCH_C