141 lines
3.0 KiB
C
141 lines
3.0 KiB
C
#include "tommath_private.h"
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#ifdef BN_MP_SQRT_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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#ifndef NO_FLOATING_POINT
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#include <float.h>
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#include <math.h>
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#if (MP_DIGIT_BIT != 28) || (FLT_RADIX != 2) || (DBL_MANT_DIG != 53) || (DBL_MAX_EXP != 1024)
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#define NO_FLOATING_POINT
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#endif
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#endif
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/* this function is less generic than mp_n_root, simpler and faster */
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mp_err mp_sqrt(const mp_int *arg, mp_int *ret)
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{
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mp_err err;
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mp_int t1, t2;
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#ifndef NO_FLOATING_POINT
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int i, j, k;
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volatile double d;
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mp_digit dig;
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#endif
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/* must be positive */
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if (arg->sign == MP_NEG) {
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return MP_VAL;
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}
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/* easy out */
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if (MP_IS_ZERO(arg)) {
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mp_zero(ret);
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return MP_OKAY;
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}
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#ifndef NO_FLOATING_POINT
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i = (arg->used / 2) - 1;
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j = 2 * i;
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if ((err = mp_init_size(&t1, i+2)) != MP_OKAY) {
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return err;
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}
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if ((err = mp_init(&t2)) != MP_OKAY) {
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goto E2;
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}
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for (k = 0; k < i; ++k) {
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t1.dp[k] = (mp_digit) 0;
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}
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/* Estimate the square root using the hardware floating point unit. */
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d = 0.0;
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for (k = arg->used-1; k >= j; --k) {
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d = ldexp(d, MP_DIGIT_BIT) + (double)(arg->dp[k]);
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}
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/*
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* At this point, d is the nearest floating point number to the most
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* significant 1 or 2 mp_digits of arg. Extract its square root.
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*/
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d = sqrt(d);
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/* dig is the most significant mp_digit of the square root */
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dig = (mp_digit) ldexp(d, -MP_DIGIT_BIT);
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/*
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* If the most significant digit is nonzero, find the next digit down
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* by subtracting MP_DIGIT_BIT times thie most significant digit.
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* Subtract one from the result so that our initial estimate is always
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* low.
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*/
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if (dig) {
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t1.used = i+2;
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d -= ldexp((double) dig, MP_DIGIT_BIT);
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if (d >= 1.0) {
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t1.dp[i+1] = dig;
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t1.dp[i] = ((mp_digit) d) - 1;
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} else {
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t1.dp[i+1] = dig-1;
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t1.dp[i] = MP_DIGIT_MAX;
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}
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} else {
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t1.used = i+1;
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t1.dp[i] = ((mp_digit) d) - 1;
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}
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#else
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if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) {
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return err;
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}
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if ((err = mp_init(&t2)) != MP_OKAY) {
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goto E2;
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}
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/* First approx. (not very bad for large arg) */
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mp_rshd(&t1, t1.used/2);
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#endif
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/* t1 > 0 */
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if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
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goto E1;
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}
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if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
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goto E1;
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}
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if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
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goto E1;
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}
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/* And now t1 > sqrt(arg) */
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do {
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if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
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goto E1;
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}
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if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
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goto E1;
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}
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if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
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goto E1;
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}
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/* t1 >= sqrt(arg) >= t2 at this point */
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} while (mp_cmp_mag(&t1, &t2) == MP_GT);
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mp_exch(&t1, ret);
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E1:
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mp_clear(&t2);
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E2:
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mp_clear(&t1);
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return err;
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}
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#endif
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