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, tomstdenis@gmail.com, http://libtom.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 */
47int 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 (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
127    goto X1Y1;          /* t1 = x1 - x0 */
128  if (s_mp_add (&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
133  /* add x0y0 */
134  if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
135    goto X1Y1;          /* t2 = x0y0 + x1y1 */
136  if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
137    goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
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
153X1Y1:mp_clear (&x1y1);
154X0Y0:mp_clear (&x0y0);
155T1:mp_clear (&t1);
156Y1:mp_clear (&y1);
157Y0:mp_clear (&y0);
158X1:mp_clear (&x1);
159X0:mp_clear (&x0);
160ERR:
161  return err;
162}
163#endif
164
165/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */
166/* $Revision: 1.6 $ */
167/* $Date: 2006/12/28 01:25:13 $ */
168