293 lines
6.9 KiB
C
293 lines
6.9 KiB
C
#include <tommath.h>
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#ifdef BN_MP_DIV_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
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*/
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#ifdef BN_MP_DIV_SMALL
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/* slower bit-bang division... also smaller */
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int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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{
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mp_int ta, tb, tq, q;
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int res, n, n2;
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/* is divisor zero ? */
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if (mp_iszero (b) == 1) {
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return MP_VAL;
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}
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/* if a < b then q=0, r = a */
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if (mp_cmp_mag (a, b) == MP_LT) {
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if (d != NULL) {
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res = mp_copy (a, d);
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} else {
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res = MP_OKAY;
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}
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if (c != NULL) {
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mp_zero (c);
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}
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return res;
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}
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/* init our temps */
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if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
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return res;
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}
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mp_set(&tq, 1);
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n = mp_count_bits(a) - mp_count_bits(b);
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if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
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((res = mp_abs(b, &tb)) != MP_OKAY) ||
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((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
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((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
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goto LBL_ERR;
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}
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while (n-- >= 0) {
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if (mp_cmp(&tb, &ta) != MP_GT) {
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if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
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((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
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goto LBL_ERR;
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}
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}
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if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
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((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
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goto LBL_ERR;
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}
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}
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/* now q == quotient and ta == remainder */
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n = a->sign;
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n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
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if (c != NULL) {
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mp_exch(c, &q);
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c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
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}
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if (d != NULL) {
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mp_exch(d, &ta);
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d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
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}
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LBL_ERR:
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mp_clear_multi(&ta, &tb, &tq, &q, NULL);
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return res;
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}
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#else
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/* integer signed division.
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* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
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* HAC pp.598 Algorithm 14.20
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*
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* Note that the description in HAC is horribly
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* incomplete. For example, it doesn't consider
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* the case where digits are removed from 'x' in
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* the inner loop. It also doesn't consider the
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* case that y has fewer than three digits, etc..
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*
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* The overall algorithm is as described as
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* 14.20 from HAC but fixed to treat these cases.
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*/
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int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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{
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mp_int q, x, y, t1, t2;
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int res, n, t, i, norm, neg;
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/* is divisor zero ? */
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if (mp_iszero (b) == 1) {
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return MP_VAL;
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}
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/* if a < b then q=0, r = a */
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if (mp_cmp_mag (a, b) == MP_LT) {
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if (d != NULL) {
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res = mp_copy (a, d);
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} else {
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res = MP_OKAY;
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}
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if (c != NULL) {
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mp_zero (c);
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}
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return res;
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}
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if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
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return res;
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}
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q.used = a->used + 2;
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if ((res = mp_init (&t1)) != MP_OKAY) {
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goto LBL_Q;
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}
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if ((res = mp_init (&t2)) != MP_OKAY) {
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goto LBL_T1;
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}
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if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
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goto LBL_T2;
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}
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if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
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goto LBL_X;
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}
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/* fix the sign */
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neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
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x.sign = y.sign = MP_ZPOS;
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/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
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norm = mp_count_bits(&y) % DIGIT_BIT;
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if (norm < (int)(DIGIT_BIT-1)) {
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norm = (DIGIT_BIT-1) - norm;
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if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
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goto LBL_Y;
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}
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if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
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goto LBL_Y;
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}
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} else {
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norm = 0;
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}
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/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
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n = x.used - 1;
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t = y.used - 1;
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/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
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if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
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goto LBL_Y;
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}
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while (mp_cmp (&x, &y) != MP_LT) {
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++(q.dp[n - t]);
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if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
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goto LBL_Y;
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}
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}
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/* reset y by shifting it back down */
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mp_rshd (&y, n - t);
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/* step 3. for i from n down to (t + 1) */
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for (i = n; i >= (t + 1); i--) {
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if (i > x.used) {
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continue;
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}
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/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
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* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
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if (x.dp[i] == y.dp[t]) {
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q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
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} else {
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mp_word tmp;
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tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
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tmp |= ((mp_word) x.dp[i - 1]);
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tmp /= ((mp_word) y.dp[t]);
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if (tmp > (mp_word) MP_MASK)
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tmp = MP_MASK;
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q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
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}
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/* while (q{i-t-1} * (yt * b + y{t-1})) >
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xi * b**2 + xi-1 * b + xi-2
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do q{i-t-1} -= 1;
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*/
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q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
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do {
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q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
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/* find left hand */
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mp_zero (&t1);
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t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
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t1.dp[1] = y.dp[t];
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t1.used = 2;
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if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
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goto LBL_Y;
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}
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/* find right hand */
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t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
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t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
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t2.dp[2] = x.dp[i];
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t2.used = 3;
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} while (mp_cmp_mag(&t1, &t2) == MP_GT);
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/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
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if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
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goto LBL_Y;
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}
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if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
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goto LBL_Y;
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}
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if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
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goto LBL_Y;
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}
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/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
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if (x.sign == MP_NEG) {
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if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
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goto LBL_Y;
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}
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if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
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goto LBL_Y;
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}
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if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
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goto LBL_Y;
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}
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q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
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}
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}
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/* now q is the quotient and x is the remainder
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* [which we have to normalize]
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*/
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/* get sign before writing to c */
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x.sign = x.used == 0 ? MP_ZPOS : a->sign;
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if (c != NULL) {
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mp_clamp (&q);
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mp_exch (&q, c);
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c->sign = neg;
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}
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if (d != NULL) {
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mp_div_2d (&x, norm, &x, NULL);
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mp_exch (&x, d);
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}
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res = MP_OKAY;
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LBL_Y:mp_clear (&y);
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LBL_X:mp_clear (&x);
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LBL_T2:mp_clear (&t2);
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LBL_T1:mp_clear (&t1);
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LBL_Q:mp_clear (&q);
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return res;
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}
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#endif
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#endif
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/* $Source: /cvs/libtom/libtommath/bn_mp_div.c,v $ */
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/* $Revision: 1.4 $ */
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/* $Date: 2006/12/28 01:25:13 $ */
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