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#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.
*
* The library is free for all purposes without any express
* guarantee it works.
*/
/* 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: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */
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