3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
12 * The library is free for all purposes without any express
15 * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
18 #ifdef BN_MP_DIV_SMALL
20 /* slower bit-bang division... also smaller */
21 int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
26 /* is divisor zero ? */
27 if (mp_iszero (b) == 1) {
31 /* if a < b then q=0, r = a */
32 if (mp_cmp_mag (a, b) == MP_LT) {
45 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
51 n = mp_count_bits(a) - mp_count_bits(b);
52 if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
53 ((res = mp_abs(b, &tb)) != MP_OKAY) ||
54 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
55 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
60 if (mp_cmp(&tb, &ta) != MP_GT) {
61 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
62 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
66 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
67 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
72 /* now q == quotient and ta == remainder */
74 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
77 c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
81 d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
84 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
90 /* integer signed division.
91 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
92 * HAC pp.598 Algorithm 14.20
94 * Note that the description in HAC is horribly
95 * incomplete. For example, it doesn't consider
96 * the case where digits are removed from 'x' in
97 * the inner loop. It also doesn't consider the
98 * case that y has fewer than three digits, etc..
100 * The overall algorithm is as described as
101 * 14.20 from HAC but fixed to treat these cases.
103 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
105 mp_int q, x, y, t1, t2;
106 int res, n, t, i, norm, neg;
108 /* is divisor zero ? */
109 if (mp_iszero (b) == 1) {
113 /* if a < b then q=0, r = a */
114 if (mp_cmp_mag (a, b) == MP_LT) {
116 res = mp_copy (a, d);
126 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
129 q.used = a->used + 2;
131 if ((res = mp_init (&t1)) != MP_OKAY) {
135 if ((res = mp_init (&t2)) != MP_OKAY) {
139 if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
143 if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
148 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
149 x.sign = y.sign = MP_ZPOS;
151 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
152 norm = mp_count_bits(&y) % DIGIT_BIT;
153 if (norm < (int)(DIGIT_BIT-1)) {
154 norm = (DIGIT_BIT-1) - norm;
155 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
158 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
165 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
169 /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
170 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
174 while (mp_cmp (&x, &y) != MP_LT) {
176 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
181 /* reset y by shifting it back down */
184 /* step 3. for i from n down to (t + 1) */
185 for (i = n; i >= (t + 1); i--) {
190 /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
191 * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
192 if (x.dp[i] == y.dp[t]) {
193 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
196 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
197 tmp |= ((mp_word) x.dp[i - 1]);
198 tmp /= ((mp_word) y.dp[t]);
199 if (tmp > (mp_word) MP_MASK)
201 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
204 /* while (q{i-t-1} * (yt * b + y{t-1})) >
205 xi * b**2 + xi-1 * b + xi-2
209 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
211 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
215 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
218 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
222 /* find right hand */
223 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
224 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
227 } while (mp_cmp_mag(&t1, &t2) == MP_GT);
229 /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
230 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
234 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
238 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
242 /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
243 if (x.sign == MP_NEG) {
244 if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
247 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
250 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
254 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
258 /* now q is the quotient and x is the remainder
259 * [which we have to normalize]
262 /* get sign before writing to c */
263 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
272 mp_div_2d (&x, norm, &x, NULL);
280 LBL_T2:mp_clear (&t2);
281 LBL_T1:mp_clear (&t1);