diff options
Diffstat (limited to 'libtommath/bn_mp_n_root_ex.c')
-rw-r--r-- | libtommath/bn_mp_n_root_ex.c | 129 |
1 files changed, 0 insertions, 129 deletions
diff --git a/libtommath/bn_mp_n_root_ex.c b/libtommath/bn_mp_n_root_ex.c deleted file mode 100644 index 720cb2f..0000000 --- a/libtommath/bn_mp_n_root_ex.c +++ /dev/null @@ -1,129 +0,0 @@ -#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 - * additional optimizations in place. - * - * 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. This is not meant to - * find huge roots [square and cube, etc]. - */ -int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast) -{ - mp_int t1, t2, t3, a_; - int res; - - /* input must be positive if b is even */ - if (((b & 1u) == 0u) && (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 */ - a_ = *a; - a_.sign = MP_ZPOS; - - /* t2 = 2 */ - mp_set(&t2, 2uL); - - 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 - 1u, &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, 1uL, &t1)) != MP_OKAY) { - goto LBL_T3; - } - } else { - break; - } - } - - /* set the result */ - mp_exch(&t1, c); - - /* set the sign of the result */ - c->sign = a->sign; - - res = MP_OKAY; - -LBL_T3: - mp_clear(&t3); -LBL_T2: - mp_clear(&t2); -LBL_T1: - mp_clear(&t1); - return res; -} -#endif - -/* ref: HEAD -> master, tag: v1.1.0 */ -/* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ -/* commit time: 2019-01-28 20:32:32 +0100 */ |