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32
bn_mp_div.c
32
bn_mp_div.c
@ -40,7 +40,7 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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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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@ -50,7 +50,7 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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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_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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@ -87,17 +87,17 @@ LBL_ERR:
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#else
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/* integer signed division.
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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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* 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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* 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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@ -187,7 +187,7 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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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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/* 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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@ -202,10 +202,10 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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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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/* 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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@ -256,10 +256,10 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
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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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/* 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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@ -15,7 +15,7 @@
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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* Extended euclidean algorithm of (a, b) produces
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/* Extended euclidean algorithm of (a, b) produces
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a*u1 + b*u2 = u3
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*/
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int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
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@ -20,37 +20,37 @@ int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
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{
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mp_int q;
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int p, res;
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if ((res = mp_init(&q)) != MP_OKAY) {
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return res;
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}
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p = mp_count_bits(n);
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p = mp_count_bits(n);
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top:
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/* q = a/2**p, a = a mod 2**p */
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if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
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goto ERR;
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}
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if (d != 1) {
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/* q = q * d */
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if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
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if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
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goto ERR;
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}
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}
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/* a = a + q */
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if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
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goto ERR;
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}
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if (mp_cmp_mag(a, n) != MP_LT) {
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if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
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goto ERR;
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}
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goto top;
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}
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ERR:
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mp_clear(&q);
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return res;
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@ -15,7 +15,7 @@
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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* reduces a modulo n where n is of the form 2**p - d
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/* reduces a modulo n where n is of the form 2**p - d
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This differs from reduce_2k since "d" can be larger
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than a single digit.
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*/
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@ -23,35 +23,35 @@ int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
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{
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mp_int q;
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int p, res;
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if ((res = mp_init(&q)) != MP_OKAY) {
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return res;
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}
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p = mp_count_bits(n);
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p = mp_count_bits(n);
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top:
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/* q = a/2**p, a = a mod 2**p */
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if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
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goto ERR;
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}
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/* q = q * d */
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if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
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if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
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goto ERR;
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}
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/* a = a + q */
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if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
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goto ERR;
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}
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if (mp_cmp_mag(a, n) != MP_LT) {
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if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
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goto ERR;
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}
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goto top;
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}
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ERR:
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mp_clear(&q);
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return res;
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@ -15,28 +15,28 @@
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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* multiplication using the Toom-Cook 3-way algorithm
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/* multiplication using the Toom-Cook 3-way algorithm
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*
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* Much more complicated than Karatsuba but has a lower
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* asymptotic running time of O(N**1.464). This algorithm is
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* only particularly useful on VERY large inputs
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* Much more complicated than Karatsuba but has a lower
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* asymptotic running time of O(N**1.464). This algorithm is
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* only particularly useful on VERY large inputs
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* (we're talking 1000s of digits here...).
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*/
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int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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{
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mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
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int res, B;
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/* init temps */
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if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
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&a0, &a1, &a2, &b0, &b1,
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if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
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&a0, &a1, &a2, &b0, &b1,
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&b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
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return res;
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}
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/* B */
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B = MIN(a->used, b->used) / 3;
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/* a = a2 * B**2 + a1 * B + a0 */
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if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
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goto ERR;
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@ -54,7 +54,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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goto ERR;
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}
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mp_rshd(&a2, B*2);
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/* b = b2 * B**2 + b1 * B + b0 */
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if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
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goto ERR;
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@ -70,17 +70,17 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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goto ERR;
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}
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mp_rshd(&b2, B*2);
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/* w0 = a0*b0 */
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if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
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goto ERR;
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}
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/* w4 = a2 * b2 */
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if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
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goto ERR;
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}
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/* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
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if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
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goto ERR;
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@ -94,7 +94,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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@ -107,11 +107,11 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
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if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
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goto ERR;
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@ -125,7 +125,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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@ -138,11 +138,11 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
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if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
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@ -160,19 +160,19 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
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goto ERR;
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}
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/* now solve the matrix
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/* now solve the matrix
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0 0 0 0 1
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1 2 4 8 16
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1 1 1 1 1
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16 8 4 2 1
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1 0 0 0 0
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using 12 subtractions, 4 shifts,
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2 small divisions and 1 small multiplication
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using 12 subtractions, 4 shifts,
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2 small divisions and 1 small multiplication
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*/
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/* r1 - r4 */
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if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
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goto ERR;
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@ -244,7 +244,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
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goto ERR;
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}
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/* at this point shift W[n] by B*n */
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if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
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goto ERR;
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@ -257,8 +257,8 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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}
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if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
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goto ERR;
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}
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}
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if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
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goto ERR;
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}
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@ -270,15 +270,15 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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}
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if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
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goto ERR;
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}
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}
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ERR:
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mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
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&a0, &a1, &a2, &b0, &b1,
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mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
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&a0, &a1, &a2, &b0, &b1,
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&b2, &tmp1, &tmp2, NULL);
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return res;
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}
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}
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#endif
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/* $Source$ */
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