143 lines
3.0 KiB
C
143 lines
3.0 KiB
C
#include <tommath.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
|
|
*/
|
|
|
|
#ifndef NO_FLOATING_POINT
|
|
#include <math.h>
|
|
#endif
|
|
|
|
/* this function is less generic than mp_n_root, simpler and faster */
|
|
int mp_sqrt(mp_int *arg, mp_int *ret)
|
|
{
|
|
int res;
|
|
mp_int t1,t2;
|
|
int i, j, k;
|
|
#ifndef NO_FLOATING_POINT
|
|
volatile double d;
|
|
mp_digit dig;
|
|
#endif
|
|
|
|
/* 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;
|
|
}
|
|
|
|
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. */
|
|
|
|
d = 0.0;
|
|
for (k = arg->used-1; k >= j; --k) {
|
|
d = ldexp(d, DIGIT_BIT) + (double) (arg->dp[k]);
|
|
}
|
|
|
|
/*
|
|
* 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);
|
|
|
|
/* dig is the most significant mp_digit of the square root */
|
|
|
|
dig = (mp_digit) ldexp(d, -DIGIT_BIT);
|
|
|
|
/*
|
|
* 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.
|
|
*/
|
|
|
|
if (dig) {
|
|
t1.used = i+2;
|
|
d -= ldexp((double) dig, DIGIT_BIT);
|
|
if (d >= 1.0) {
|
|
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;
|
|
}
|
|
} 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. */
|
|
|
|
t1.used = i + 2;
|
|
t1.dp[i+1] = (mp_digit) 1;
|
|
t1.dp[i] = (mp_digit) 0;
|
|
|
|
#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) {
|
|
goto E1;
|
|
}
|
|
if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
|
|
goto E1;
|
|
}
|
|
if ((res = 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);
|
|
|
|
E1: mp_clear(&t2);
|
|
E2: mp_clear(&t1);
|
|
return res;
|
|
}
|
|
|
|
#endif
|