Mercurial > dropbear
view libtommath/bn_mp_root_u32.c @ 1938:77bc00dcc19f default tip main master
Bump version to 2022.82
author | Matt Johnston <matt@ucc.asn.au> |
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date | Fri, 01 Apr 2022 14:43:27 +0800 |
parents | 1051e4eea25a |
children |
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#include "tommath_private.h" #ifdef BN_MP_ROOT_U32_C /* LibTomMath, multiple-precision integer library -- Tom St Denis */ /* SPDX-License-Identifier: Unlicense */ /* 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. */ mp_err mp_root_u32(const mp_int *a, uint32_t b, mp_int *c) { mp_int t1, t2, t3, a_; mp_ord cmp; int ilog2; mp_err err; /* input must be positive if b is even */ if (((b & 1u) == 0u) && (a->sign == MP_NEG)) { return MP_VAL; } if ((err = mp_init_multi(&t1, &t2, &t3, NULL)) != MP_OKAY) { return err; } /* if a is negative fudge the sign but keep track */ a_ = *a; a_.sign = MP_ZPOS; /* Compute seed: 2^(log_2(n)/b + 2)*/ ilog2 = mp_count_bits(a); /* If "b" is larger than INT_MAX it is also larger than log_2(n) because the bit-length of the "n" is measured with an int and hence the root is always < 2 (two). */ if (b > (uint32_t)(INT_MAX/2)) { mp_set(c, 1uL); c->sign = a->sign; err = MP_OKAY; goto LBL_ERR; } /* "b" is smaller than INT_MAX, we can cast safely */ if (ilog2 < (int)b) { mp_set(c, 1uL); c->sign = a->sign; err = MP_OKAY; goto LBL_ERR; } ilog2 = ilog2 / ((int)b); if (ilog2 == 0) { mp_set(c, 1uL); c->sign = a->sign; err = MP_OKAY; goto LBL_ERR; } /* Start value must be larger than root */ ilog2 += 2; if ((err = mp_2expt(&t2,ilog2)) != MP_OKAY) goto LBL_ERR; do { /* t1 = t2 */ if ((err = mp_copy(&t2, &t1)) != MP_OKAY) goto LBL_ERR; /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */ /* t3 = t1**(b-1) */ if ((err = mp_expt_u32(&t1, b - 1u, &t3)) != MP_OKAY) goto LBL_ERR; /* numerator */ /* t2 = t1**b */ if ((err = mp_mul(&t3, &t1, &t2)) != MP_OKAY) goto LBL_ERR; /* t2 = t1**b - a */ if ((err = mp_sub(&t2, &a_, &t2)) != MP_OKAY) goto LBL_ERR; /* denominator */ /* t3 = t1**(b-1) * b */ if ((err = mp_mul_d(&t3, b, &t3)) != MP_OKAY) goto LBL_ERR; /* t3 = (t1**b - a)/(b * t1**(b-1)) */ if ((err = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) goto LBL_ERR; if ((err = mp_sub(&t1, &t3, &t2)) != MP_OKAY) goto LBL_ERR; /* Number of rounds is at most log_2(root). If it is more it got stuck, so break out of the loop and do the rest manually. */ if (ilog2-- == 0) { break; } } while (mp_cmp(&t1, &t2) != MP_EQ); /* result can be off by a few so check */ /* Loop beneath can overshoot by one if found root is smaller than actual root */ for (;;) { if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; cmp = mp_cmp(&t2, &a_); if (cmp == MP_EQ) { err = MP_OKAY; goto LBL_ERR; } if (cmp == MP_LT) { if ((err = mp_add_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; } else { break; } } /* correct overshoot from above or from recurrence */ for (;;) { if ((err = mp_expt_u32(&t1, b, &t2)) != MP_OKAY) goto LBL_ERR; if (mp_cmp(&t2, &a_) == MP_GT) { if ((err = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) goto LBL_ERR; } else { break; } } /* set the result */ mp_exch(&t1, c); /* set the sign of the result */ c->sign = a->sign; err = MP_OKAY; LBL_ERR: mp_clear_multi(&t1, &t2, &t3, NULL); return err; } #endif