chiark / gitweb /
math/mpx-mul4-x86-sse2.S: Use `SHUF' instead of hardwired constants.
[catacomb] / math / gfx-kmul.c
CommitLineData
ae747c9b 1/* -*-c-*-
ae747c9b 2 *
3 * Karatsuba's multiplication algorithm on binary polynomials
4 *
5 * (c) 2000 Straylight/Edgeware
6 */
7
45c0fd36 8/*----- Licensing notice --------------------------------------------------*
ae747c9b 9 *
10 * This file is part of Catacomb.
11 *
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
45c0fd36 16 *
ae747c9b 17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
45c0fd36 21 *
ae747c9b 22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
25 * MA 02111-1307, USA.
26 */
27
ae747c9b 28/*----- Header files ------------------------------------------------------*/
29
30#include <assert.h>
31#include <stdio.h>
32
33#include "gfx.h"
34#include "karatsuba.h"
35
36/*----- Tweakables --------------------------------------------------------*/
37
38#ifdef TEST_RIG
39# undef GFK_THRESH
40# define GFK_THRESH 1
41#endif
42
43/*----- Main code ---------------------------------------------------------*/
44
45/* --- @gfx_kmul@ --- *
46 *
47 * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
48 * @const mpw *av, *avl@ = pointer to first argument
49 * @const mpw *bv, *bvl@ = pointer to second argument
50 * @mpw *sv, *svl@ = pointer to scratch workspace
51 *
52 * Returns: ---
53 *
54 * Use: Multiplies two binary polynomials using Karatsuba's
55 * algorithm. This is rather faster than traditional long
56 * multiplication (e.g., @gfx_umul@) on polynomials with large
57 * degree, although more expensive on small ones.
58 *
59 * The destination must be twice as large as the larger
60 * argument. The scratch space must be twice as large as the
61 * larger argument.
62 */
63
64void gfx_kmul(mpw *dv, mpw *dvl,
65 const mpw *av, const mpw *avl,
66 const mpw *bv, const mpw *bvl,
67 mpw *sv, mpw *svl)
68{
69 const mpw *avm, *bvm;
70 size_t m;
71
72 /* --- Dispose of easy cases to @mpx_umul@ --- *
73 *
74 * Karatsuba is only a win on large numbers, because of all the
75 * recursiveness and bookkeeping. The recursive calls make a quick check
76 * to see whether to bottom out to @gfx_umul@ which should help quite a
77 * lot, but sometimes the only way to know is to make sure...
78 */
79
80 MPX_SHRINK(av, avl);
81 MPX_SHRINK(bv, bvl);
82
83 if (avl - av <= GFK_THRESH || bvl - bv <= GFK_THRESH) {
84 gfx_mul(dv, dvl, av, avl, bv, bvl);
85 return;
86 }
87
88 /* --- How the algorithm works --- *
89 *
90 * Let %$A = xb + y$% and %$B = ub + v$%. Then, simply by expanding,
91 * %$AB = x u b^2 + b(x v + y u) + y v$%. That's not helped any, because
92 * I've got four multiplications, each four times easier than the one I
93 * started with. However, note that I can rewrite the coefficient of %$b$%
94 * as %$xv + yu = (x + y)(u + v) - xu - yv$%. The terms %$xu$% and %$yv$%
95 * I've already calculated, and that leaves only one more multiplication to
96 * do. So now I have three multiplications, each four times easier, and
97 * that's a win.
98 */
99
100 /* --- First things --- *
101 *
102 * Sort out where to break the factors in half. I'll choose the midpoint
103 * of the larger one, since this minimizes the amount of work I have to do
104 * most effectively.
105 */
106
107 if (avl - av > bvl - bv) {
108 m = (avl - av + 1) >> 1;
109 avm = av + m;
110 if (bvl - bv > m)
111 bvm = bv + m;
112 else
113 bvm = bvl;
114 } else {
115 m = (bvl - bv + 1) >> 1;
116 bvm = bv + m;
117 if (avl - av > m)
118 avm = av + m;
119 else
120 avm = avl;
121 }
122
ae747c9b 123 /* --- Sort out the middle term --- */
124
125 {
126 mpw *bsv = sv + m, *ssv = bsv + m;
127 mpw *rdv = dv + m, *rdvl = rdv + 2 * m;
128
432c4e18 129 assert(rdvl <= dvl);
130 assert(ssv <= svl);
ae747c9b 131 UXOR2(sv, bsv, av, avm, avm, avl);
132 UXOR2(bsv, ssv, bv, bvm, bvm, bvl);
133 if (m > GFK_THRESH)
134 gfx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
135 else
136 gfx_mul(rdv, rdvl, sv, bsv, bsv, ssv);
137 }
138
139 /* --- Sort out the other two terms --- */
140
141 {
142 mpw *svm = sv + m, *ssv = svm + m;
143 mpw *tdv = dv + m;
144 mpw *rdv = tdv + m;
145
146 if (avl == avm || bvl == bvm)
147 MPX_ZERO(rdv + m, dvl);
148 else {
149 if (m > GFK_THRESH)
150 gfx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
151 else
152 gfx_mul(sv, ssv, avm, avl, bvm, bvl);
153 MPX_COPY(rdv + m, dvl, svm, ssv);
154 UXOR(rdv, sv, svm);
155 UXOR(tdv, sv, ssv);
156 }
157
158 if (m > GFK_THRESH)
159 gfx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
160 else
161 gfx_mul(sv, ssv, av, avm, bv, bvm);
162 MPX_COPY(dv, tdv, sv, svm);
163 UXOR(tdv, sv, ssv);
164 UXOR(tdv, svm, ssv);
165 }
166}
167
168/*----- Test rig ----------------------------------------------------------*/
169
170#ifdef TEST_RIG
171
172#include <mLib/alloc.h>
173#include <mLib/testrig.h>
174
45c0fd36
MW
175#define ALLOC(v, vl, sz) do { \
176 size_t _sz = (sz); \
177 mpw *_vv = xmalloc(MPWS(_sz)); \
178 mpw *_vvl = _vv + _sz; \
179 (v) = _vv; \
180 (vl) = _vvl; \
ae747c9b 181} while (0)
182
45c0fd36
MW
183#define LOAD(v, vl, d) do { \
184 const dstr *_d = (d); \
185 mpw *_v, *_vl; \
186 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
187 mpx_loadb(_v, _vl, _d->buf, _d->len); \
188 (v) = _v; \
189 (vl) = _vl; \
ae747c9b 190} while (0)
191
192#define MAX(x, y) ((x) > (y) ? (x) : (y))
193
194static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
195{
196 fputs(msg, stderr);
197 MPX_SHRINK(v, vl);
198 while (v < vl)
199 fprintf(stderr, " %08lx", (unsigned long)*--vl);
200 fputc('\n', stderr);
201}
202
203static int mul(dstr *v)
204{
205 mpw *a, *al;
206 mpw *b, *bl;
207 mpw *c, *cl;
208 mpw *d, *dl;
209 mpw *s, *sl;
210 size_t m;
211 int ok = 1;
212
213 LOAD(a, al, &v[0]);
214 LOAD(b, bl, &v[1]);
215 LOAD(c, cl, &v[2]);
216 m = MAX(al - a, bl - b) + 1;
217 ALLOC(d, dl, 2 * m);
218 ALLOC(s, sl, 2 * m);
219
220 gfx_kmul(d, dl, a, al, b, bl, s, sl);
221 if (!mpx_ueq(d, dl, c, cl)) {
222 fprintf(stderr, "\n*** mul failed\n");
45c0fd36
MW
223 dumpmp(" a", a, al);
224 dumpmp(" b", b, bl);
ae747c9b 225 dumpmp("expected", c, cl);
226 dumpmp(" result", d, dl);
227 ok = 0;
228 }
229
12ed8a1f 230 xfree(a); xfree(b); xfree(c); xfree(d); xfree(s);
ae747c9b 231 return (ok);
232}
233
234static test_chunk defs[] = {
235 { "mul", mul, { &type_hex, &type_hex, &type_hex, 0 } },
236 { 0, 0, { 0 } }
237};
238
239int main(int argc, char *argv[])
240{
0f00dc4c 241 test_run(argc, argv, defs, SRCDIR"/t/gfx");
ae747c9b 242 return (0);
243}
244
245#endif
246
247/*----- That's all, folks -------------------------------------------------*/