### view libtommath/bn_mp_n_root_ex.c @ 1490:9b87cbe931e3

build: Remove unused constructs: `space' and `AC_PROG_MAKE_SET' The makefile variable `space' is never used. The autoconf output variable `SET_MAKE' is never used, so the autoconf macro `AC_PROG_MAKE_SET' has been removed.
author Michael Witten Mon, 31 Jul 2017 23:55:52 +0000 8bba51a55704 f52919ffd3b1
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line source
```#include <tommath_private.h>
#ifdef BN_MP_N_ROOT_EX_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
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, [email protected], http://libtom.org
*/

/* find the n'th root of an integer
*
* Result found such that (c)**b <= a and (c+1)**b > a
*
* This algorithm uses Newton's approximation
* x[i+1] = x[i] - f(x[i])/f'(x[i])
* which will find the root in log(N) time where
* each step involves a fair bit.  This is not meant to
* find huge roots [square and cube, etc].
*/
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
{
mp_int  t1, t2, t3;
int     res, neg;

/* input must be positive if b is even */
if (((b & 1) == 0) && (a->sign == MP_NEG)) {
return MP_VAL;
}

if ((res = mp_init (&t1)) != MP_OKAY) {
return res;
}

if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}

if ((res = mp_init (&t3)) != MP_OKAY) {
goto LBL_T2;
}

/* if a is negative fudge the sign but keep track */
neg     = a->sign;
a->sign = MP_ZPOS;

/* t2 = 2 */
mp_set (&t2, 2);

do {
/* t1 = t2 */
if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
goto LBL_T3;
}

/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */

/* t3 = t1**(b-1) */
if ((res = mp_expt_d_ex (&t1, b - 1, &t3, fast)) != MP_OKAY) {
goto LBL_T3;
}

/* numerator */
/* t2 = t1**b */
if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
goto LBL_T3;
}

/* t2 = t1**b - a */
if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
goto LBL_T3;
}

/* denominator */
/* t3 = t1**(b-1) * b  */
if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
goto LBL_T3;
}

/* t3 = (t1**b - a)/(b * t1**(b-1)) */
if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
goto LBL_T3;
}

if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
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_ex (&t1, b, &t2, fast)) != MP_OKAY) {
goto LBL_T3;
}

if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
goto LBL_T3;
}
} else {
break;
}
}

/* reset the sign of a first */
a->sign = neg;

/* set the result */
mp_exch (&t1, c);

/* set the sign of the result */
c->sign = neg;

res = MP_OKAY;

LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
return res;
}
#endif

/* ref:         \$Format:%D\$ */
/* git commit:  \$Format:%H\$ */
/* commit time: \$Format:%ai\$ */
```