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comparison bn_mp_karatsuba_mul.c @ 1:22d5cf7d4b1a libtommath

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Renaming branch
author Matt Johnston <matt@ucc.asn.au>
date Mon, 31 May 2004 18:23:46 +0000
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-1:000000000000 1:22d5cf7d4b1a
1 /* LibTomMath, multiple-precision integer library -- Tom St Denis
2 *
3 * LibTomMath is a library that provides multiple-precision
4 * integer arithmetic as well as number theoretic functionality.
5 *
6 * The library was designed directly after the MPI library by
7 * Michael Fromberger but has been written from scratch with
8 * additional optimizations in place.
9 *
10 * The library is free for all purposes without any express
11 * guarantee it works.
12 *
13 * Tom St Denis, [email protected], http://math.libtomcrypt.org
14 */
15 #include <tommath.h>
16
17 /* c = |a| * |b| using Karatsuba Multiplication using
18 * three half size multiplications
19 *
20 * Let B represent the radix [e.g. 2**DIGIT_BIT] and
21 * let n represent half of the number of digits in
22 * the min(a,b)
23 *
24 * a = a1 * B**n + a0
25 * b = b1 * B**n + b0
26 *
27 * Then, a * b =>
28 a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
29 *
30 * Note that a1b1 and a0b0 are used twice and only need to be
31 * computed once. So in total three half size (half # of
32 * digit) multiplications are performed, a0b0, a1b1 and
33 * (a1-b1)(a0-b0)
34 *
35 * Note that a multiplication of half the digits requires
36 * 1/4th the number of single precision multiplications so in
37 * total after one call 25% of the single precision multiplications
38 * are saved. Note also that the call to mp_mul can end up back
39 * in this function if the a0, a1, b0, or b1 are above the threshold.
40 * This is known as divide-and-conquer and leads to the famous
41 * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
42 * the standard O(N**2) that the baseline/comba methods use.
43 * Generally though the overhead of this method doesn't pay off
44 * until a certain size (N ~ 80) is reached.
45 */
46 int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
47 {
48 mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
49 int B, err;
50
51 /* default the return code to an error */
52 err = MP_MEM;
53
54 /* min # of digits */
55 B = MIN (a->used, b->used);
56
57 /* now divide in two */
58 B = B >> 1;
59
60 /* init copy all the temps */
61 if (mp_init_size (&x0, B) != MP_OKAY)
62 goto ERR;
63 if (mp_init_size (&x1, a->used - B) != MP_OKAY)
64 goto X0;
65 if (mp_init_size (&y0, B) != MP_OKAY)
66 goto X1;
67 if (mp_init_size (&y1, b->used - B) != MP_OKAY)
68 goto Y0;
69
70 /* init temps */
71 if (mp_init_size (&t1, B * 2) != MP_OKAY)
72 goto Y1;
73 if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
74 goto T1;
75 if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
76 goto X0Y0;
77
78 /* now shift the digits */
79 x0.sign = x1.sign = a->sign;
80 y0.sign = y1.sign = b->sign;
81
82 x0.used = y0.used = B;
83 x1.used = a->used - B;
84 y1.used = b->used - B;
85
86 {
87 register int x;
88 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
89
90 /* we copy the digits directly instead of using higher level functions
91 * since we also need to shift the digits
92 */
93 tmpa = a->dp;
94 tmpb = b->dp;
95
96 tmpx = x0.dp;
97 tmpy = y0.dp;
98 for (x = 0; x < B; x++) {
99 *tmpx++ = *tmpa++;
100 *tmpy++ = *tmpb++;
101 }
102
103 tmpx = x1.dp;
104 for (x = B; x < a->used; x++) {
105 *tmpx++ = *tmpa++;
106 }
107
108 tmpy = y1.dp;
109 for (x = B; x < b->used; x++) {
110 *tmpy++ = *tmpb++;
111 }
112 }
113
114 /* only need to clamp the lower words since by definition the
115 * upper words x1/y1 must have a known number of digits
116 */
117 mp_clamp (&x0);
118 mp_clamp (&y0);
119
120 /* now calc the products x0y0 and x1y1 */
121 /* after this x0 is no longer required, free temp [x0==t2]! */
122 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
123 goto X1Y1; /* x0y0 = x0*y0 */
124 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
125 goto X1Y1; /* x1y1 = x1*y1 */
126
127 /* now calc x1-x0 and y1-y0 */
128 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
129 goto X1Y1; /* t1 = x1 - x0 */
130 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
131 goto X1Y1; /* t2 = y1 - y0 */
132 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
133 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
134
135 /* add x0y0 */
136 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
137 goto X1Y1; /* t2 = x0y0 + x1y1 */
138 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
139 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
140
141 /* shift by B */
142 if (mp_lshd (&t1, B) != MP_OKAY)
143 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
144 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
145 goto X1Y1; /* x1y1 = x1y1 << 2*B */
146
147 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
148 goto X1Y1; /* t1 = x0y0 + t1 */
149 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
150 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
151
152 /* Algorithm succeeded set the return code to MP_OKAY */
153 err = MP_OKAY;
154
155 X1Y1:mp_clear (&x1y1);
156 X0Y0:mp_clear (&x0y0);
157 T1:mp_clear (&t1);
158 Y1:mp_clear (&y1);
159 Y0:mp_clear (&y0);
160 X1:mp_clear (&x1);
161 X0:mp_clear (&x0);
162 ERR:
163 return err;
164 }