ag/cpython-source-deps
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Import Tcl 8.6.10

Browse Source
This commit is contained in:
Steve Dower
2020-09-24 22:53:56 +01:00
parent 0343d03b22
commit 3bb8e3e086
1005 changed files with 593700 additions and 41637 deletions
Download Patch File Download Diff File Expand all files Collapse all files

197
libtommath/bn_mp_sqrt.c
View File

@@ -1,142 +1,139 @@
#include <tommath.h>
#include "tommath_private.h"
#ifdef BN_MP_SQRT_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.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
*/
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */
#ifndef NO_FLOATING_POINT
#include <math.h>
#if (MP_DIGIT_BIT != 28) || (FLT_RADIX != 2) || (DBL_MANT_DIG != 53) || (DBL_MAX_EXP != 1024)
#define NO_FLOATING_POINT
#endif
#endif
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
mp_err mp_sqrt(const mp_int *arg, mp_int *ret)
{
int res;
mp_int t1,t2;
int i, j, k;
mp_err err;
mp_int t1, t2;
#ifndef NO_FLOATING_POINT
volatile double d;
mp_digit dig;
int i, j, k;
volatile double d;
mp_digit dig;
#endif
/* must be positive */
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* must be positive */
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* easy out */
if (mp_iszero(arg) == MP_YES) {
mp_zero(ret);
return MP_OKAY;
}
i = (arg->used / 2) - 1;
j = 2 * i;
if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
/* easy out */
if (MP_IS_ZERO(arg)) {
mp_zero(ret);
return MP_OKAY;
}
for (k = 0; k < i; ++k) {
t1.dp[k] = (mp_digit) 0;
}
#ifndef NO_FLOATING_POINT
/* Estimate the square root using the hardware floating point unit. */
i = (arg->used / 2) - 1;
j = 2 * i;
if ((err = mp_init_size(&t1, i+2)) != MP_OKAY) {
return err;
}
d = 0.0;
for (k = arg->used-1; k >= j; --k) {
d = ldexp(d, DIGIT_BIT) + (double) (arg->dp[k]);
}
if ((err = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
/*
* At this point, d is the nearest floating point number to the most
* significant 1 or 2 mp_digits of arg. Extract its square root.
*/
d = sqrt(d);
for (k = 0; k < i; ++k) {
t1.dp[k] = (mp_digit) 0;
}
/* dig is the most significant mp_digit of the square root */
/* Estimate the square root using the hardware floating point unit. */
dig = (mp_digit) ldexp(d, -DIGIT_BIT);
d = 0.0;
for (k = arg->used-1; k >= j; --k) {
d = ldexp(d, MP_DIGIT_BIT) + (double)(arg->dp[k]);
}
/*
* If the most significant digit is nonzero, find the next digit down
* by subtracting DIGIT_BIT times thie most significant digit.
* Subtract one from the result so that our initial estimate is always
* low.
*/
/*
* At this point, d is the nearest floating point number to the most
* significant 1 or 2 mp_digits of arg. Extract its square root.
*/
if (dig) {
d = sqrt(d);
/* dig is the most significant mp_digit of the square root */
dig = (mp_digit) ldexp(d, -MP_DIGIT_BIT);
/*
* If the most significant digit is nonzero, find the next digit down
* by subtracting MP_DIGIT_BIT times thie most significant digit.
* Subtract one from the result so that our initial estimate is always
* low.
*/
if (dig) {
t1.used = i+2;
d -= ldexp((double) dig, DIGIT_BIT);
d -= ldexp((double) dig, MP_DIGIT_BIT);
if (d >= 1.0) {
t1.dp[i+1] = dig;
t1.dp[i] = ((mp_digit) d) - 1;
t1.dp[i+1] = dig;
t1.dp[i] = ((mp_digit) d) - 1;
} else {
t1.dp[i+1] = dig-1;
t1.dp[i] = MP_DIGIT_MAX;
t1.dp[i+1] = dig-1;
t1.dp[i] = MP_DIGIT_MAX;
}
} else {
} else {
t1.used = i+1;
t1.dp[i] = ((mp_digit) d) - 1;
}
}
#else
/* Estimate the square root as having 1 in the most significant place. */
if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) {
return err;
}
t1.used = i + 2;
t1.dp[i+1] = (mp_digit) 1;
t1.dp[i] = (mp_digit) 0;
if ((err = mp_init(&t2)) != MP_OKAY) {
goto E2;
}
/* First approx. (not very bad for large arg) */
mp_rshd(&t1, t1.used/2);
#endif
/* t1 > 0 */
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
goto E1;
}
/* And now t1 > sqrt(arg) */
do {
if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
/* t1 > 0 */
if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
goto E1;
}
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
}
if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
goto E1;
}
if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
}
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
goto E1;
}
/* t1 >= sqrt(arg) >= t2 at this point */
} while (mp_cmp_mag(&t1,&t2) == MP_GT);
}
/* And now t1 > sqrt(arg) */
do {
if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) {
goto E1;
}
if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) {
goto E1;
}
if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) {
goto E1;
}
/* t1 >= sqrt(arg) >= t2 at this point */
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
mp_exch(&t1,ret);
mp_exch(&t1, ret);
E1: mp_clear(&t2);
E2: mp_clear(&t1);
return res;
E1:
mp_clear(&t2);
E2:
mp_clear(&t1);
return err;
}
#endif