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5bf74dea | 1 | /* -*-c-*- |
2 | * | |
12ed8a1f | 3 | * $Id$ |
5bf74dea | 4 | * |
5 | * Karatsuba-based squaring algorithm | |
6 | * | |
7 | * (c) 1999 Straylight/Edgeware | |
8 | */ | |
9 | ||
45c0fd36 | 10 | /*----- Licensing notice --------------------------------------------------* |
5bf74dea | 11 | * |
12 | * This file is part of Catacomb. | |
13 | * | |
14 | * Catacomb is free software; you can redistribute it and/or modify | |
15 | * it under the terms of the GNU Library General Public License as | |
16 | * published by the Free Software Foundation; either version 2 of the | |
17 | * License, or (at your option) any later version. | |
45c0fd36 | 18 | * |
5bf74dea | 19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
22 | * GNU Library General Public License for more details. | |
45c0fd36 | 23 | * |
5bf74dea | 24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free | |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, | |
27 | * MA 02111-1307, USA. | |
28 | */ | |
29 | ||
5bf74dea | 30 | /*----- Header files ------------------------------------------------------*/ |
31 | ||
4468424e | 32 | #include <assert.h> |
5bf74dea | 33 | #include <stdio.h> |
34 | ||
35 | #include "mpx.h" | |
52cdaca9 | 36 | #include "karatsuba.h" |
5bf74dea | 37 | |
38 | /*----- Tweakables --------------------------------------------------------*/ | |
39 | ||
40 | #ifdef TEST_RIG | |
52cdaca9 | 41 | # undef MPK_THRESH |
dd22938e | 42 | # define MPK_THRESH 4 |
5bf74dea | 43 | #endif |
44 | ||
5bf74dea | 45 | /*----- Main code ---------------------------------------------------------*/ |
46 | ||
47 | /* --- @mpx_ksqr@ --- * | |
48 | * | |
49 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer | |
50 | * @const mpw *av, *avl@ = pointer to first argument | |
51 | * @mpw *sv, *svl@ = pointer to scratch workspace | |
52 | * | |
53 | * Returns: --- | |
54 | * | |
55 | * Use: Squares a multiprecision integers using something similar to | |
56 | * Karatsuba's multiplication algorithm. This is rather faster | |
57 | * than traditional long multiplication (e.g., @mpx_umul@) on | |
58 | * large numbers, although more expensive on small ones, and | |
59 | * rather simpler than full-blown Karatsuba multiplication. | |
60 | * | |
dd22938e | 61 | * The destination must be three times as large as the larger |
62 | * argument. The scratch space must be five times as large as | |
63 | * the larger argument. | |
5bf74dea | 64 | */ |
65 | ||
66 | void mpx_ksqr(mpw *dv, mpw *dvl, | |
67 | const mpw *av, const mpw *avl, | |
68 | mpw *sv, mpw *svl) | |
69 | { | |
70 | const mpw *avm; | |
71 | size_t m; | |
72 | ||
73 | /* --- Dispose of easy cases to @mpx_usqr@ --- * | |
74 | * | |
75 | * Karatsuba is only a win on large numbers, because of all the | |
76 | * recursiveness and bookkeeping. The recursive calls make a quick check | |
77 | * to see whether to bottom out to @mpx_usqr@ which should help quite a | |
78 | * lot, but sometimes the only way to know is to make sure... | |
79 | */ | |
80 | ||
81 | MPX_SHRINK(av, avl); | |
82 | ||
52cdaca9 | 83 | if (avl - av <= MPK_THRESH) { |
5bf74dea | 84 | mpx_usqr(dv, dvl, av, avl); |
85 | return; | |
86 | } | |
87 | ||
88 | /* --- How the algorithm works --- * | |
89 | * | |
d2d86297 | 90 | * The identity for squaring is known to all schoolchildren. |
91 | * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now, | |
92 | * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three | |
93 | * squarings. | |
5bf74dea | 94 | */ |
95 | ||
96 | /* --- First things --- * | |
97 | * | |
98 | * Sort out where to break the factor in half. | |
99 | */ | |
100 | ||
101 | m = (avl - av + 1) >> 1; | |
102 | avm = av + m; | |
103 | ||
104 | /* --- Sort out everything --- */ | |
105 | ||
106 | { | |
4468424e | 107 | mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4; |
5bf74dea | 108 | mpw *tdv = dv + m; |
109 | mpw *rdv = tdv + m; | |
110 | ||
dd22938e | 111 | assert(rdv + m + 4 < dvl); |
112 | assert(ssv < svl); | |
d2d86297 | 113 | UADD2(sv, svm, av, avm, avm, avl); |
52cdaca9 | 114 | if (m > MPK_THRESH) |
d2d86297 | 115 | mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl); |
5bf74dea | 116 | else |
d2d86297 | 117 | mpx_usqr(tdv, rdv + m + 4, sv, svm + 1); |
5bf74dea | 118 | |
52cdaca9 | 119 | if (m > MPK_THRESH) |
5bf74dea | 120 | mpx_ksqr(sv, ssv, avm, avl, ssv, svl); |
121 | else | |
122 | mpx_usqr(sv, ssv, avm, avl); | |
4468424e | 123 | MPX_COPY(rdv + m + 1, dvl, svm + 1, svn); |
124 | UADD(rdv, sv, svm + 1); | |
d2d86297 | 125 | USUB(tdv, sv, svn); |
45c0fd36 | 126 | |
52cdaca9 | 127 | if (m > MPK_THRESH) |
5bf74dea | 128 | mpx_ksqr(sv, ssv, av, avm, ssv, svl); |
129 | else | |
130 | mpx_usqr(sv, ssv, av, avm); | |
4468424e | 131 | MPX_COPY(dv, tdv, sv, svm); |
132 | UADD(tdv, svm, svn); | |
d2d86297 | 133 | USUB(tdv, sv, svn); |
5bf74dea | 134 | } |
135 | } | |
136 | ||
137 | /*----- Test rig ----------------------------------------------------------*/ | |
138 | ||
139 | #ifdef TEST_RIG | |
140 | ||
141 | #include <mLib/alloc.h> | |
142 | #include <mLib/testrig.h> | |
143 | ||
45c0fd36 MW |
144 | #define ALLOC(v, vl, sz) do { \ |
145 | size_t _sz = (sz); \ | |
146 | mpw *_vv = xmalloc(MPWS(_sz)); \ | |
147 | mpw *_vvl = _vv + _sz; \ | |
148 | (v) = _vv; \ | |
149 | (vl) = _vvl; \ | |
5bf74dea | 150 | } while (0) |
151 | ||
45c0fd36 MW |
152 | #define LOAD(v, vl, d) do { \ |
153 | const dstr *_d = (d); \ | |
154 | mpw *_v, *_vl; \ | |
155 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ | |
156 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ | |
157 | (v) = _v; \ | |
158 | (vl) = _vl; \ | |
5bf74dea | 159 | } while (0) |
160 | ||
161 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) | |
162 | ||
163 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) | |
164 | { | |
165 | fputs(msg, stderr); | |
166 | MPX_SHRINK(v, vl); | |
167 | while (v < vl) | |
168 | fprintf(stderr, " %08lx", (unsigned long)*--vl); | |
169 | fputc('\n', stderr); | |
170 | } | |
171 | ||
172 | static int usqr(dstr *v) | |
173 | { | |
174 | mpw *a, *al; | |
175 | mpw *c, *cl; | |
176 | mpw *d, *dl; | |
177 | mpw *s, *sl; | |
178 | size_t m; | |
179 | int ok = 1; | |
180 | ||
181 | LOAD(a, al, &v[0]); | |
182 | LOAD(c, cl, &v[1]); | |
183 | m = al - a + 1; | |
dd22938e | 184 | ALLOC(d, dl, 3 * m); |
185 | ALLOC(s, sl, 5 * m); | |
5bf74dea | 186 | |
187 | mpx_ksqr(d, dl, a, al, s, sl); | |
c9060100 | 188 | if (!mpx_ueq(d, dl, c, cl)) { |
5bf74dea | 189 | fprintf(stderr, "\n*** usqr failed\n"); |
45c0fd36 | 190 | dumpmp(" a", a, al); |
5bf74dea | 191 | dumpmp("expected", c, cl); |
192 | dumpmp(" result", d, dl); | |
193 | ok = 0; | |
194 | } | |
195 | ||
12ed8a1f | 196 | xfree(a); xfree(c); xfree(d); xfree(s); |
5bf74dea | 197 | return (ok); |
198 | } | |
199 | ||
200 | static test_chunk defs[] = { | |
201 | { "usqr", usqr, { &type_hex, &type_hex, 0 } }, | |
202 | { 0, 0, { 0 } } | |
203 | }; | |
204 | ||
205 | int main(int argc, char *argv[]) | |
206 | { | |
207 | test_run(argc, argv, defs, SRCDIR"/tests/mpx"); | |
208 | return (0); | |
209 | } | |
210 | ||
211 | #endif | |
212 | ||
213 | /*----- That's all, folks -------------------------------------------------*/ |