Line data Source code
1 : #include "tommath_private.h"
2 : #ifdef BN_S_MP_KARATSUBA_MUL_C
3 : /* LibTomMath, multiple-precision integer library -- Tom St Denis */
4 : /* SPDX-License-Identifier: Unlicense */
5 :
6 : /* c = |a| * |b| using Karatsuba Multiplication using
7 : * three half size multiplications
8 : *
9 : * Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
10 : * let n represent half of the number of digits in
11 : * the min(a,b)
12 : *
13 : * a = a1 * B**n + a0
14 : * b = b1 * B**n + b0
15 : *
16 : * Then, a * b =>
17 : a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
18 : *
19 : * Note that a1b1 and a0b0 are used twice and only need to be
20 : * computed once. So in total three half size (half # of
21 : * digit) multiplications are performed, a0b0, a1b1 and
22 : * (a1+b1)(a0+b0)
23 : *
24 : * Note that a multiplication of half the digits requires
25 : * 1/4th the number of single precision multiplications so in
26 : * total after one call 25% of the single precision multiplications
27 : * are saved. Note also that the call to mp_mul can end up back
28 : * in this function if the a0, a1, b0, or b1 are above the threshold.
29 : * This is known as divide-and-conquer and leads to the famous
30 : * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
31 : * the standard O(N**2) that the baseline/comba methods use.
32 : * Generally though the overhead of this method doesn't pay off
33 : * until a certain size (N ~ 80) is reached.
34 : */
35 906 : mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
36 : {
37 0 : mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
38 0 : int B;
39 906 : mp_err err = MP_MEM; /* default the return code to an error */
40 :
41 : /* min # of digits */
42 906 : B = MP_MIN(a->used, b->used);
43 :
44 : /* now divide in two */
45 906 : B = B >> 1;
46 :
47 : /* init copy all the temps */
48 906 : if (mp_init_size(&x0, B) != MP_OKAY) {
49 0 : goto LBL_ERR;
50 : }
51 906 : if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
52 0 : goto X0;
53 : }
54 906 : if (mp_init_size(&y0, B) != MP_OKAY) {
55 0 : goto X1;
56 : }
57 906 : if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
58 0 : goto Y0;
59 : }
60 :
61 : /* init temps */
62 906 : if (mp_init_size(&t1, B * 2) != MP_OKAY) {
63 0 : goto Y1;
64 : }
65 906 : if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
66 0 : goto T1;
67 : }
68 906 : if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
69 0 : goto X0Y0;
70 : }
71 :
72 : /* now shift the digits */
73 906 : x0.used = y0.used = B;
74 906 : x1.used = a->used - B;
75 906 : y1.used = b->used - B;
76 :
77 : {
78 0 : int x;
79 0 : mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
80 :
81 : /* we copy the digits directly instead of using higher level functions
82 : * since we also need to shift the digits
83 : */
84 906 : tmpa = a->dp;
85 906 : tmpb = b->dp;
86 :
87 906 : tmpx = x0.dp;
88 906 : tmpy = y0.dp;
89 62514 : for (x = 0; x < B; x++) {
90 61608 : *tmpx++ = *tmpa++;
91 61608 : *tmpy++ = *tmpb++;
92 : }
93 :
94 906 : tmpx = x1.dp;
95 63420 : for (x = B; x < a->used; x++) {
96 62514 : *tmpx++ = *tmpa++;
97 : }
98 :
99 906 : tmpy = y1.dp;
100 63420 : for (x = B; x < b->used; x++) {
101 62514 : *tmpy++ = *tmpb++;
102 : }
103 : }
104 :
105 : /* only need to clamp the lower words since by definition the
106 : * upper words x1/y1 must have a known number of digits
107 : */
108 906 : mp_clamp(&x0);
109 906 : mp_clamp(&y0);
110 :
111 : /* now calc the products x0y0 and x1y1 */
112 : /* after this x0 is no longer required, free temp [x0==t2]! */
113 906 : if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) {
114 0 : goto X1Y1; /* x0y0 = x0*y0 */
115 : }
116 906 : if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) {
117 0 : goto X1Y1; /* x1y1 = x1*y1 */
118 : }
119 :
120 : /* now calc x1+x0 and y1+y0 */
121 906 : if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) {
122 0 : goto X1Y1; /* t1 = x1 - x0 */
123 : }
124 906 : if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) {
125 0 : goto X1Y1; /* t2 = y1 - y0 */
126 : }
127 906 : if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
128 0 : goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
129 : }
130 :
131 : /* add x0y0 */
132 906 : if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
133 0 : goto X1Y1; /* t2 = x0y0 + x1y1 */
134 : }
135 906 : if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
136 0 : goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
137 : }
138 :
139 : /* shift by B */
140 906 : if (mp_lshd(&t1, B) != MP_OKAY) {
141 0 : goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
142 : }
143 906 : if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
144 0 : goto X1Y1; /* x1y1 = x1y1 << 2*B */
145 : }
146 :
147 906 : if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
148 0 : goto X1Y1; /* t1 = x0y0 + t1 */
149 : }
150 906 : if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
151 0 : goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
152 : }
153 :
154 : /* Algorithm succeeded set the return code to MP_OKAY */
155 906 : err = MP_OKAY;
156 :
157 906 : X1Y1:
158 906 : mp_clear(&x1y1);
159 906 : X0Y0:
160 906 : mp_clear(&x0y0);
161 906 : T1:
162 906 : mp_clear(&t1);
163 906 : Y1:
164 906 : mp_clear(&y1);
165 906 : Y0:
166 906 : mp_clear(&y0);
167 906 : X1:
168 906 : mp_clear(&x1);
169 906 : X0:
170 906 : mp_clear(&x0);
171 906 : LBL_ERR:
172 906 : return err;
173 : }
174 : #endif
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