| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: gfx-kmul.c,v 1.4 2004/04/08 01:36:15 mdw Exp $ |
| 4 | * |
| 5 | * Karatsuba's multiplication algorithm on binary polynomials |
| 6 | * |
| 7 | * (c) 2000 Straylight/Edgeware |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 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. |
| 18 | * |
| 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. |
| 23 | * |
| 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 | |
| 30 | /*----- Header files ------------------------------------------------------*/ |
| 31 | |
| 32 | #include <assert.h> |
| 33 | #include <stdio.h> |
| 34 | |
| 35 | #include "gfx.h" |
| 36 | #include "karatsuba.h" |
| 37 | |
| 38 | /*----- Tweakables --------------------------------------------------------*/ |
| 39 | |
| 40 | #ifdef TEST_RIG |
| 41 | # undef GFK_THRESH |
| 42 | # define GFK_THRESH 1 |
| 43 | #endif |
| 44 | |
| 45 | /*----- Main code ---------------------------------------------------------*/ |
| 46 | |
| 47 | /* --- @gfx_kmul@ --- * |
| 48 | * |
| 49 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
| 50 | * @const mpw *av, *avl@ = pointer to first argument |
| 51 | * @const mpw *bv, *bvl@ = pointer to second argument |
| 52 | * @mpw *sv, *svl@ = pointer to scratch workspace |
| 53 | * |
| 54 | * Returns: --- |
| 55 | * |
| 56 | * Use: Multiplies two binary polynomials using Karatsuba's |
| 57 | * algorithm. This is rather faster than traditional long |
| 58 | * multiplication (e.g., @gfx_umul@) on polynomials with large |
| 59 | * degree, although more expensive on small ones. |
| 60 | * |
| 61 | * The destination must be twice as large as the larger |
| 62 | * argument. The scratch space must be twice as large as the |
| 63 | * larger argument. |
| 64 | */ |
| 65 | |
| 66 | void gfx_kmul(mpw *dv, mpw *dvl, |
| 67 | const mpw *av, const mpw *avl, |
| 68 | const mpw *bv, const mpw *bvl, |
| 69 | mpw *sv, mpw *svl) |
| 70 | { |
| 71 | const mpw *avm, *bvm; |
| 72 | size_t m; |
| 73 | |
| 74 | /* --- Dispose of easy cases to @mpx_umul@ --- * |
| 75 | * |
| 76 | * Karatsuba is only a win on large numbers, because of all the |
| 77 | * recursiveness and bookkeeping. The recursive calls make a quick check |
| 78 | * to see whether to bottom out to @gfx_umul@ which should help quite a |
| 79 | * lot, but sometimes the only way to know is to make sure... |
| 80 | */ |
| 81 | |
| 82 | MPX_SHRINK(av, avl); |
| 83 | MPX_SHRINK(bv, bvl); |
| 84 | |
| 85 | if (avl - av <= GFK_THRESH || bvl - bv <= GFK_THRESH) { |
| 86 | gfx_mul(dv, dvl, av, avl, bv, bvl); |
| 87 | return; |
| 88 | } |
| 89 | |
| 90 | /* --- How the algorithm works --- * |
| 91 | * |
| 92 | * Let %$A = xb + y$% and %$B = ub + v$%. Then, simply by expanding, |
| 93 | * %$AB = x u b^2 + b(x v + y u) + y v$%. That's not helped any, because |
| 94 | * I've got four multiplications, each four times easier than the one I |
| 95 | * started with. However, note that I can rewrite the coefficient of %$b$% |
| 96 | * as %$xv + yu = (x + y)(u + v) - xu - yv$%. The terms %$xu$% and %$yv$% |
| 97 | * I've already calculated, and that leaves only one more multiplication to |
| 98 | * do. So now I have three multiplications, each four times easier, and |
| 99 | * that's a win. |
| 100 | */ |
| 101 | |
| 102 | /* --- First things --- * |
| 103 | * |
| 104 | * Sort out where to break the factors in half. I'll choose the midpoint |
| 105 | * of the larger one, since this minimizes the amount of work I have to do |
| 106 | * most effectively. |
| 107 | */ |
| 108 | |
| 109 | if (avl - av > bvl - bv) { |
| 110 | m = (avl - av + 1) >> 1; |
| 111 | avm = av + m; |
| 112 | if (bvl - bv > m) |
| 113 | bvm = bv + m; |
| 114 | else |
| 115 | bvm = bvl; |
| 116 | } else { |
| 117 | m = (bvl - bv + 1) >> 1; |
| 118 | bvm = bv + m; |
| 119 | if (avl - av > m) |
| 120 | avm = av + m; |
| 121 | else |
| 122 | avm = avl; |
| 123 | } |
| 124 | |
| 125 | /* --- Sort out the middle term --- */ |
| 126 | |
| 127 | { |
| 128 | mpw *bsv = sv + m, *ssv = bsv + m; |
| 129 | mpw *rdv = dv + m, *rdvl = rdv + 2 * m; |
| 130 | |
| 131 | assert(rdvl <= dvl); |
| 132 | assert(ssv <= svl); |
| 133 | UXOR2(sv, bsv, av, avm, avm, avl); |
| 134 | UXOR2(bsv, ssv, bv, bvm, bvm, bvl); |
| 135 | if (m > GFK_THRESH) |
| 136 | gfx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl); |
| 137 | else |
| 138 | gfx_mul(rdv, rdvl, sv, bsv, bsv, ssv); |
| 139 | } |
| 140 | |
| 141 | /* --- Sort out the other two terms --- */ |
| 142 | |
| 143 | { |
| 144 | mpw *svm = sv + m, *ssv = svm + m; |
| 145 | mpw *tdv = dv + m; |
| 146 | mpw *rdv = tdv + m; |
| 147 | |
| 148 | if (avl == avm || bvl == bvm) |
| 149 | MPX_ZERO(rdv + m, dvl); |
| 150 | else { |
| 151 | if (m > GFK_THRESH) |
| 152 | gfx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl); |
| 153 | else |
| 154 | gfx_mul(sv, ssv, avm, avl, bvm, bvl); |
| 155 | MPX_COPY(rdv + m, dvl, svm, ssv); |
| 156 | UXOR(rdv, sv, svm); |
| 157 | UXOR(tdv, sv, ssv); |
| 158 | } |
| 159 | |
| 160 | if (m > GFK_THRESH) |
| 161 | gfx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl); |
| 162 | else |
| 163 | gfx_mul(sv, ssv, av, avm, bv, bvm); |
| 164 | MPX_COPY(dv, tdv, sv, svm); |
| 165 | UXOR(tdv, sv, ssv); |
| 166 | UXOR(tdv, svm, ssv); |
| 167 | } |
| 168 | } |
| 169 | |
| 170 | /*----- Test rig ----------------------------------------------------------*/ |
| 171 | |
| 172 | #ifdef TEST_RIG |
| 173 | |
| 174 | #include <mLib/alloc.h> |
| 175 | #include <mLib/testrig.h> |
| 176 | |
| 177 | #define ALLOC(v, vl, sz) do { \ |
| 178 | size_t _sz = (sz); \ |
| 179 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
| 180 | mpw *_vvl = _vv + _sz; \ |
| 181 | (v) = _vv; \ |
| 182 | (vl) = _vvl; \ |
| 183 | } while (0) |
| 184 | |
| 185 | #define LOAD(v, vl, d) do { \ |
| 186 | const dstr *_d = (d); \ |
| 187 | mpw *_v, *_vl; \ |
| 188 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
| 189 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
| 190 | (v) = _v; \ |
| 191 | (vl) = _vl; \ |
| 192 | } while (0) |
| 193 | |
| 194 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
| 195 | |
| 196 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
| 197 | { |
| 198 | fputs(msg, stderr); |
| 199 | MPX_SHRINK(v, vl); |
| 200 | while (v < vl) |
| 201 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
| 202 | fputc('\n', stderr); |
| 203 | } |
| 204 | |
| 205 | static int mul(dstr *v) |
| 206 | { |
| 207 | mpw *a, *al; |
| 208 | mpw *b, *bl; |
| 209 | mpw *c, *cl; |
| 210 | mpw *d, *dl; |
| 211 | mpw *s, *sl; |
| 212 | size_t m; |
| 213 | int ok = 1; |
| 214 | |
| 215 | LOAD(a, al, &v[0]); |
| 216 | LOAD(b, bl, &v[1]); |
| 217 | LOAD(c, cl, &v[2]); |
| 218 | m = MAX(al - a, bl - b) + 1; |
| 219 | ALLOC(d, dl, 2 * m); |
| 220 | ALLOC(s, sl, 2 * m); |
| 221 | |
| 222 | gfx_kmul(d, dl, a, al, b, bl, s, sl); |
| 223 | if (!mpx_ueq(d, dl, c, cl)) { |
| 224 | fprintf(stderr, "\n*** mul failed\n"); |
| 225 | dumpmp(" a", a, al); |
| 226 | dumpmp(" b", b, bl); |
| 227 | dumpmp("expected", c, cl); |
| 228 | dumpmp(" result", d, dl); |
| 229 | ok = 0; |
| 230 | } |
| 231 | |
| 232 | free(a); free(b); free(c); free(d); free(s); |
| 233 | return (ok); |
| 234 | } |
| 235 | |
| 236 | static test_chunk defs[] = { |
| 237 | { "mul", mul, { &type_hex, &type_hex, &type_hex, 0 } }, |
| 238 | { 0, 0, { 0 } } |
| 239 | }; |
| 240 | |
| 241 | int main(int argc, char *argv[]) |
| 242 | { |
| 243 | test_run(argc, argv, defs, SRCDIR"/tests/gfx"); |
| 244 | return (0); |
| 245 | } |
| 246 | |
| 247 | #endif |
| 248 | |
| 249 | /*----- That's all, folks -------------------------------------------------*/ |