### comparison libtommath/bn_mp_karatsuba_mul.c @ 284:eed26cff980b

author Matt Johnston Wed, 08 Mar 2006 13:23:49 +0000 5ff8218bcee9
comparison
equal inserted replaced
283:bd240aa12ba7 284:eed26cff980b
1 #include <tommath.h>
2 #ifdef BN_MP_KARATSUBA_MUL_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
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.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, [email protected], http://math.libtomcrypt.org
16 */
17
18 /* c = |a| * |b| using Karatsuba Multiplication using
19 * three half size multiplications
20 *
21 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
22 * let n represent half of the number of digits in
23 * the min(a,b)
24 *
25 * a = a1 * B**n + a0
26 * b = b1 * B**n + b0
27 *
28 * Then, a * b =>
29 a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
30 *
31 * Note that a1b1 and a0b0 are used twice and only need to be
32 * computed once. So in total three half size (half # of
33 * digit) multiplications are performed, a0b0, a1b1 and
34 * (a1-b1)(a0-b0)
35 *
36 * Note that a multiplication of half the digits requires
37 * 1/4th the number of single precision multiplications so in
38 * total after one call 25% of the single precision multiplications
39 * are saved. Note also that the call to mp_mul can end up back
40 * in this function if the a0, a1, b0, or b1 are above the threshold.
41 * This is known as divide-and-conquer and leads to the famous
42 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
43 * the standard O(N**2) that the baseline/comba methods use.
44 * Generally though the overhead of this method doesn't pay off
45 * until a certain size (N ~ 80) is reached.
46 */
47 int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
48 {
49 mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
50 int B, err;
51
52 /* default the return code to an error */
53 err = MP_MEM;
54
55 /* min # of digits */
56 B = MIN (a->used, b->used);
57
58 /* now divide in two */
59 B = B >> 1;
60
61 /* init copy all the temps */
62 if (mp_init_size (&x0, B) != MP_OKAY)
63 goto ERR;
64 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
65 goto X0;
66 if (mp_init_size (&y0, B) != MP_OKAY)
67 goto X1;
68 if (mp_init_size (&y1, b->used - B) != MP_OKAY)
69 goto Y0;
70
71 /* init temps */
72 if (mp_init_size (&t1, B * 2) != MP_OKAY)
73 goto Y1;
74 if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
75 goto T1;
76 if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
77 goto X0Y0;
78
79 /* now shift the digits */
80 x0.used = y0.used = B;
81 x1.used = a->used - B;
82 y1.used = b->used - B;
83
84 {
85 register int x;
86 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
87
88 /* we copy the digits directly instead of using higher level functions
89 * since we also need to shift the digits
90 */
91 tmpa = a->dp;
92 tmpb = b->dp;
93
94 tmpx = x0.dp;
95 tmpy = y0.dp;
96 for (x = 0; x < B; x++) {
97 *tmpx++ = *tmpa++;
98 *tmpy++ = *tmpb++;
99 }
100
101 tmpx = x1.dp;
102 for (x = B; x < a->used; x++) {
103 *tmpx++ = *tmpa++;
104 }
105
106 tmpy = y1.dp;
107 for (x = B; x < b->used; x++) {
108 *tmpy++ = *tmpb++;
109 }
110 }
111
112 /* only need to clamp the lower words since by definition the
113 * upper words x1/y1 must have a known number of digits
114 */
115 mp_clamp (&x0);
116 mp_clamp (&y0);
117
118 /* now calc the products x0y0 and x1y1 */
119 /* after this x0 is no longer required, free temp [x0==t2]! */
120 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
121 goto X1Y1; /* x0y0 = x0*y0 */
122 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
123 goto X1Y1; /* x1y1 = x1*y1 */
124
125 /* now calc x1-x0 and y1-y0 */
126 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
127 goto X1Y1; /* t1 = x1 - x0 */
128 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
129 goto X1Y1; /* t2 = y1 - y0 */
130 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
131 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
132
134 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
135 goto X1Y1; /* t2 = x0y0 + x1y1 */
136 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
137 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
138
139 /* shift by B */
140 if (mp_lshd (&t1, B) != MP_OKAY)
141 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
142 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
143 goto X1Y1; /* x1y1 = x1y1 << 2*B */
144
145 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
146 goto X1Y1; /* t1 = x0y0 + t1 */
147 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
148 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
149
150 /* Algorithm succeeded set the return code to MP_OKAY */
151 err = MP_OKAY;
152
153 X1Y1:mp_clear (&x1y1);
154 X0Y0:mp_clear (&x0y0);
155 T1:mp_clear (&t1);
156 Y1:mp_clear (&y1);
157 Y0:mp_clear (&y0);
158 X1:mp_clear (&x1);
159 X0:mp_clear (&x0);
160 ERR:
161 return err;
162 }
163 #endif