131 lines
2.9 KiB
C
131 lines
2.9 KiB
C
#include "tommath_private.h"
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#ifdef BN_MP_N_ROOT_EX_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*/
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/* find the n'th root of an integer
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*
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* Result found such that (c)**b <= a and (c+1)**b > a
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*
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* This algorithm uses Newton's approximation
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* x[i+1] = x[i] - f(x[i])/f'(x[i])
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* which will find the root in log(N) time where
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* each step involves a fair bit. This is not meant to
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* find huge roots [square and cube, etc].
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*/
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int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
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{
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mp_int t1, t2, t3, a_;
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int res;
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/* input must be positive if b is even */
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if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
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return MP_VAL;
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}
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if ((res = mp_init(&t1)) != MP_OKAY) {
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return res;
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}
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if ((res = mp_init(&t2)) != MP_OKAY) {
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goto LBL_T1;
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}
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if ((res = mp_init(&t3)) != MP_OKAY) {
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goto LBL_T2;
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}
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/* if a is negative fudge the sign but keep track */
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a_ = *a;
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a_.sign = MP_ZPOS;
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/* t2 = 2 */
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mp_set(&t2, 2uL);
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do {
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/* t1 = t2 */
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if ((res = mp_copy(&t2, &t1)) != MP_OKAY) {
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goto LBL_T3;
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}
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/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
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/* t3 = t1**(b-1) */
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if ((res = mp_expt_d_ex(&t1, b - 1u, &t3, fast)) != MP_OKAY) {
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goto LBL_T3;
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}
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/* numerator */
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/* t2 = t1**b */
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if ((res = mp_mul(&t3, &t1, &t2)) != MP_OKAY) {
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goto LBL_T3;
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}
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/* t2 = t1**b - a */
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if ((res = mp_sub(&t2, &a_, &t2)) != MP_OKAY) {
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goto LBL_T3;
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}
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/* denominator */
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/* t3 = t1**(b-1) * b */
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if ((res = mp_mul_d(&t3, b, &t3)) != MP_OKAY) {
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goto LBL_T3;
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}
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/* t3 = (t1**b - a)/(b * t1**(b-1)) */
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if ((res = mp_div(&t2, &t3, &t3, NULL)) != MP_OKAY) {
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goto LBL_T3;
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}
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if ((res = mp_sub(&t1, &t3, &t2)) != MP_OKAY) {
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goto LBL_T3;
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}
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} while (mp_cmp(&t1, &t2) != MP_EQ);
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/* result can be off by a few so check */
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for (;;) {
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if ((res = mp_expt_d_ex(&t1, b, &t2, fast)) != MP_OKAY) {
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goto LBL_T3;
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}
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if (mp_cmp(&t2, &a_) == MP_GT) {
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if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) {
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goto LBL_T3;
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}
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} else {
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break;
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}
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}
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/* set the result */
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mp_exch(&t1, c);
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/* set the sign of the result */
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c->sign = a->sign;
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res = MP_OKAY;
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LBL_T3:
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mp_clear(&t3);
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LBL_T2:
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mp_clear(&t2);
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LBL_T1:
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mp_clear(&t1);
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return res;
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}
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#endif
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/* ref: $Format:%D$ */
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/* git commit: $Format:%H$ */
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/* commit time: $Format:%ai$ */
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