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tommath/bn_mp_div.c

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7.2 KiB
C
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#include "tommath_private.h"
#ifdef BN_MP_DIV_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.
*
* SPDX-License-Identifier: Unlicense
*/
#ifdef BN_MP_DIV_SMALL
/* slower bit-bang division... also smaller */
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
mp_int ta, tb, tq, q;
int res, n, n2;
/* is divisor zero ? */
if (mp_iszero(b) == MP_YES) {
return MP_VAL;
}
/* if a < b then q=0, r = a */
if (mp_cmp_mag(a, b) == MP_LT) {
if (d != NULL) {
res = mp_copy(a, d);
} else {
res = MP_OKAY;
}
if (c != NULL) {
mp_zero(c);
}
return res;
}
/* init our temps */
if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
return res;
}
mp_set(&tq, 1uL);
n = mp_count_bits(a) - mp_count_bits(b);
if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
((res = mp_abs(b, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
goto LBL_ERR;
}
while (n-- >= 0) {
if (mp_cmp(&tb, &ta) != MP_GT) {
if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
goto LBL_ERR;
}
}
if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
goto LBL_ERR;
}
}
/* now q == quotient and ta == remainder */
n = a->sign;
n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
if (c != NULL) {
mp_exch(c, &q);
c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
}
if (d != NULL) {
mp_exch(d, &ta);
d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
}
LBL_ERR:
mp_clear_multi(&ta, &tb, &tq, &q, NULL);
return res;
}
#else
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
* HAC pp.598 Algorithm 14.20
*
* Note that the description in HAC is horribly
* incomplete. For example, it doesn't consider
* the case where digits are removed from 'x' in
* the inner loop. It also doesn't consider the
* case that y has fewer than three digits, etc..
*
* The overall algorithm is as described as
* 14.20 from HAC but fixed to treat these cases.
*/
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
/* is divisor zero ? */
if (mp_iszero(b) == MP_YES) {
return MP_VAL;
}
/* if a < b then q=0, r = a */
if (mp_cmp_mag(a, b) == MP_LT) {
if (d != NULL) {
res = mp_copy(a, d);
} else {
res = MP_OKAY;
}
if (c != NULL) {
mp_zero(c);
}
return res;
}
if ((res = mp_init_size(&q, a->used + 2)) != MP_OKAY) {
return res;
}
q.used = a->used + 2;
if ((res = mp_init(&t1)) != MP_OKAY) {
goto LBL_Q;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init_copy(&x, a)) != MP_OKAY) {
goto LBL_T2;
}
if ((res = mp_init_copy(&y, b)) != MP_OKAY) {
goto LBL_X;
}
/* fix the sign */
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
x.sign = y.sign = MP_ZPOS;
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = mp_count_bits(&y) % DIGIT_BIT;
if (norm < (DIGIT_BIT - 1)) {
norm = (DIGIT_BIT - 1) - norm;
if ((res = mp_mul_2d(&x, norm, &x)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_mul_2d(&y, norm, &y)) != MP_OKAY) {
goto LBL_Y;
}
} else {
norm = 0;
}
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
n = x.used - 1;
t = y.used - 1;
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
if ((res = mp_lshd(&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
goto LBL_Y;
}
while (mp_cmp(&x, &y) != MP_LT) {
++(q.dp[n - t]);
if ((res = mp_sub(&x, &y, &x)) != MP_OKAY) {
goto LBL_Y;
}
}
/* reset y by shifting it back down */
mp_rshd(&y, n - t);
/* step 3. for i from n down to (t + 1) */
for (i = n; i >= (t + 1); i--) {
if (i > x.used) {
continue;
}
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[(i - t) - 1] = ((mp_digit)1 << (mp_digit)DIGIT_BIT) - (mp_digit)1;
} else {
mp_word tmp;
tmp = (mp_word)x.dp[i] << (mp_word)DIGIT_BIT;
tmp |= (mp_word)x.dp[i - 1];
tmp /= (mp_word)y.dp[t];
if (tmp > (mp_word)MP_MASK) {
tmp = MP_MASK;
}
q.dp[(i - t) - 1] = (mp_digit)(tmp & (mp_word)MP_MASK);
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
do q{i-t-1} -= 1;
*/
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1uL) & (mp_digit)MP_MASK;
do {
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK;
/* find left hand */
mp_zero(&t1);
t1.dp[0] = ((t - 1) < 0) ? 0u : y.dp[t - 1];
t1.dp[1] = y.dp[t];
t1.used = 2;
if ((res = mp_mul_d(&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
goto LBL_Y;
}
/* find right hand */
t2.dp[0] = ((i - 2) < 0) ? 0u : x.dp[i - 2];
t2.dp[1] = ((i - 1) < 0) ? 0u : x.dp[i - 1];
t2.dp[2] = x.dp[i];
t2.used = 3;
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
if ((res = mp_mul_d(&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_sub(&x, &t1, &x)) != MP_OKAY) {
goto LBL_Y;
}
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == MP_NEG) {
if ((res = mp_copy(&y, &t1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_lshd(&t1, (i - t) - 1)) != MP_OKAY) {
goto LBL_Y;
}
if ((res = mp_add(&x, &t1, &x)) != MP_OKAY) {
goto LBL_Y;
}
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & MP_MASK;
}
}
/* now q is the quotient and x is the remainder
* [which we have to normalize]
*/
/* get sign before writing to c */
x.sign = (x.used == 0) ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
c->sign = neg;
}
if (d != NULL) {
if ((res = mp_div_2d(&x, norm, &x, NULL)) != MP_OKAY) {
goto LBL_Y;
}
mp_exch(&x, d);
}
res = MP_OKAY;
LBL_Y:
mp_clear(&y);
LBL_X:
mp_clear(&x);
LBL_T2:
mp_clear(&t2);
LBL_T1:
mp_clear(&t1);
LBL_Q:
mp_clear(&q);
return res;
}
#endif
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */
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