Commit | Line | Data |
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5bf74dea | 1 | /* -*-c-*- |
5bf74dea | 2 | * |
3 | * Karatsuba-based squaring algorithm | |
4 | * | |
5 | * (c) 1999 Straylight/Edgeware | |
6 | */ | |
7 | ||
45c0fd36 | 8 | /*----- Licensing notice --------------------------------------------------* |
5bf74dea | 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 | * |
5bf74dea | 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 | * |
5bf74dea | 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 | ||
5bf74dea | 28 | /*----- Header files ------------------------------------------------------*/ |
29 | ||
4468424e | 30 | #include <assert.h> |
5bf74dea | 31 | #include <stdio.h> |
32 | ||
33 | #include "mpx.h" | |
52cdaca9 | 34 | #include "karatsuba.h" |
5bf74dea | 35 | |
36 | /*----- Tweakables --------------------------------------------------------*/ | |
37 | ||
38 | #ifdef TEST_RIG | |
52cdaca9 | 39 | # undef MPK_THRESH |
dd22938e | 40 | # define MPK_THRESH 4 |
5bf74dea | 41 | #endif |
42 | ||
5bf74dea | 43 | /*----- Main code ---------------------------------------------------------*/ |
44 | ||
45 | /* --- @mpx_ksqr@ --- * | |
46 | * | |
47 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer | |
48 | * @const mpw *av, *avl@ = pointer to first argument | |
49 | * @mpw *sv, *svl@ = pointer to scratch workspace | |
50 | * | |
51 | * Returns: --- | |
52 | * | |
53 | * Use: Squares a multiprecision integers using something similar to | |
54 | * Karatsuba's multiplication algorithm. This is rather faster | |
55 | * than traditional long multiplication (e.g., @mpx_umul@) on | |
56 | * large numbers, although more expensive on small ones, and | |
57 | * rather simpler than full-blown Karatsuba multiplication. | |
58 | * | |
dd22938e | 59 | * The destination must be three times as large as the larger |
60 | * argument. The scratch space must be five times as large as | |
61 | * the larger argument. | |
5bf74dea | 62 | */ |
63 | ||
64 | void mpx_ksqr(mpw *dv, mpw *dvl, | |
65 | const mpw *av, const mpw *avl, | |
66 | mpw *sv, mpw *svl) | |
67 | { | |
68 | const mpw *avm; | |
69 | size_t m; | |
70 | ||
71 | /* --- Dispose of easy cases to @mpx_usqr@ --- * | |
72 | * | |
73 | * Karatsuba is only a win on large numbers, because of all the | |
74 | * recursiveness and bookkeeping. The recursive calls make a quick check | |
75 | * to see whether to bottom out to @mpx_usqr@ which should help quite a | |
76 | * lot, but sometimes the only way to know is to make sure... | |
77 | */ | |
78 | ||
79 | MPX_SHRINK(av, avl); | |
80 | ||
52cdaca9 | 81 | if (avl - av <= MPK_THRESH) { |
5bf74dea | 82 | mpx_usqr(dv, dvl, av, avl); |
83 | return; | |
84 | } | |
85 | ||
86 | /* --- How the algorithm works --- * | |
87 | * | |
d2d86297 | 88 | * The identity for squaring is known to all schoolchildren. |
89 | * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now, | |
90 | * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three | |
91 | * squarings. | |
5bf74dea | 92 | */ |
93 | ||
94 | /* --- First things --- * | |
95 | * | |
96 | * Sort out where to break the factor in half. | |
97 | */ | |
98 | ||
99 | m = (avl - av + 1) >> 1; | |
100 | avm = av + m; | |
101 | ||
102 | /* --- Sort out everything --- */ | |
103 | ||
104 | { | |
4468424e | 105 | mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4; |
5bf74dea | 106 | mpw *tdv = dv + m; |
107 | mpw *rdv = tdv + m; | |
108 | ||
dd22938e | 109 | assert(rdv + m + 4 < dvl); |
110 | assert(ssv < svl); | |
d2d86297 | 111 | UADD2(sv, svm, av, avm, avm, avl); |
52cdaca9 | 112 | if (m > MPK_THRESH) |
d2d86297 | 113 | mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl); |
5bf74dea | 114 | else |
d2d86297 | 115 | mpx_usqr(tdv, rdv + m + 4, sv, svm + 1); |
5bf74dea | 116 | |
52cdaca9 | 117 | if (m > MPK_THRESH) |
5bf74dea | 118 | mpx_ksqr(sv, ssv, avm, avl, ssv, svl); |
119 | else | |
120 | mpx_usqr(sv, ssv, avm, avl); | |
4468424e | 121 | MPX_COPY(rdv + m + 1, dvl, svm + 1, svn); |
122 | UADD(rdv, sv, svm + 1); | |
d2d86297 | 123 | USUB(tdv, sv, svn); |
45c0fd36 | 124 | |
52cdaca9 | 125 | if (m > MPK_THRESH) |
5bf74dea | 126 | mpx_ksqr(sv, ssv, av, avm, ssv, svl); |
127 | else | |
128 | mpx_usqr(sv, ssv, av, avm); | |
4468424e | 129 | MPX_COPY(dv, tdv, sv, svm); |
130 | UADD(tdv, svm, svn); | |
d2d86297 | 131 | USUB(tdv, sv, svn); |
5bf74dea | 132 | } |
133 | } | |
134 | ||
135 | /*----- Test rig ----------------------------------------------------------*/ | |
136 | ||
137 | #ifdef TEST_RIG | |
138 | ||
139 | #include <mLib/alloc.h> | |
140 | #include <mLib/testrig.h> | |
141 | ||
45c0fd36 MW |
142 | #define ALLOC(v, vl, sz) do { \ |
143 | size_t _sz = (sz); \ | |
144 | mpw *_vv = xmalloc(MPWS(_sz)); \ | |
145 | mpw *_vvl = _vv + _sz; \ | |
146 | (v) = _vv; \ | |
147 | (vl) = _vvl; \ | |
5bf74dea | 148 | } while (0) |
149 | ||
45c0fd36 MW |
150 | #define LOAD(v, vl, d) do { \ |
151 | const dstr *_d = (d); \ | |
152 | mpw *_v, *_vl; \ | |
153 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ | |
154 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ | |
155 | (v) = _v; \ | |
156 | (vl) = _vl; \ | |
5bf74dea | 157 | } while (0) |
158 | ||
159 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) | |
160 | ||
161 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) | |
162 | { | |
163 | fputs(msg, stderr); | |
164 | MPX_SHRINK(v, vl); | |
165 | while (v < vl) | |
166 | fprintf(stderr, " %08lx", (unsigned long)*--vl); | |
167 | fputc('\n', stderr); | |
168 | } | |
169 | ||
170 | static int usqr(dstr *v) | |
171 | { | |
172 | mpw *a, *al; | |
173 | mpw *c, *cl; | |
174 | mpw *d, *dl; | |
175 | mpw *s, *sl; | |
176 | size_t m; | |
177 | int ok = 1; | |
178 | ||
179 | LOAD(a, al, &v[0]); | |
180 | LOAD(c, cl, &v[1]); | |
181 | m = al - a + 1; | |
dd22938e | 182 | ALLOC(d, dl, 3 * m); |
183 | ALLOC(s, sl, 5 * m); | |
5bf74dea | 184 | |
185 | mpx_ksqr(d, dl, a, al, s, sl); | |
c9060100 | 186 | if (!mpx_ueq(d, dl, c, cl)) { |
5bf74dea | 187 | fprintf(stderr, "\n*** usqr failed\n"); |
45c0fd36 | 188 | dumpmp(" a", a, al); |
5bf74dea | 189 | dumpmp("expected", c, cl); |
190 | dumpmp(" result", d, dl); | |
191 | ok = 0; | |
192 | } | |
193 | ||
12ed8a1f | 194 | xfree(a); xfree(c); xfree(d); xfree(s); |
5bf74dea | 195 | return (ok); |
196 | } | |
197 | ||
198 | static test_chunk defs[] = { | |
199 | { "usqr", usqr, { &type_hex, &type_hex, 0 } }, | |
200 | { 0, 0, { 0 } } | |
201 | }; | |
202 | ||
203 | int main(int argc, char *argv[]) | |
204 | { | |
0f00dc4c | 205 | test_run(argc, argv, defs, SRCDIR"/t/mpx"); |
5bf74dea | 206 | return (0); |
207 | } | |
208 | ||
209 | #endif | |
210 | ||
211 | /*----- That's all, folks -------------------------------------------------*/ |