| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mp-gcd.c,v 1.2 1999/11/22 20:49:56 mdw Exp $ |
| 4 | * |
| 5 | * Extended GCD calculation |
| 6 | * |
| 7 | * (c) 1999 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 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: mp-gcd.c,v $ |
| 33 | * Revision 1.2 1999/11/22 20:49:56 mdw |
| 34 | * Fix bug which failed to favour `x' when `y' wasn't wanted and the two |
| 35 | * arguments needed swapping. |
| 36 | * |
| 37 | * Revision 1.1 1999/11/17 18:02:16 mdw |
| 38 | * New multiprecision integer arithmetic suite. |
| 39 | * |
| 40 | */ |
| 41 | |
| 42 | /*----- Header files ------------------------------------------------------*/ |
| 43 | |
| 44 | #include "mp.h" |
| 45 | |
| 46 | /*----- Main code ---------------------------------------------------------*/ |
| 47 | |
| 48 | /* --- @mp_gcd@ --- * |
| 49 | * |
| 50 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
| 51 | * @mp *a, *b@ = sources (must be nonzero) |
| 52 | * |
| 53 | * Returns: --- |
| 54 | * |
| 55 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
| 56 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
| 57 | * inverses. Neither @a@ nor @b@ may be zero. Note that, |
| 58 | * unlike @mp_div@ for example, it is not possible to specify |
| 59 | * explicit destinations -- new MPs are always allocated. |
| 60 | */ |
| 61 | |
| 62 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
| 63 | { |
| 64 | mp *X = MP_ONE, *Y = MP_ZERO; |
| 65 | mp *x = MP_ZERO, *y = MP_ONE; |
| 66 | mp *u, *v; |
| 67 | size_t shift = 0; |
| 68 | int ext = xx || yy; |
| 69 | int swap = 0; |
| 70 | |
| 71 | /* --- Ensure that @a@ is larger than @b@ --- */ |
| 72 | |
| 73 | if (MP_CMP(a, <, b)) { |
| 74 | { mp *t = a; a = b; b = t; } |
| 75 | swap = 1; |
| 76 | } |
| 77 | |
| 78 | /* --- Take a reference to the arguments --- */ |
| 79 | |
| 80 | a = MP_COPY(a); |
| 81 | b = MP_COPY(b); |
| 82 | |
| 83 | /* --- Make sure @a@ and @b@ are not both even --- */ |
| 84 | |
| 85 | if (((a->v[0] | b->v[0]) & 1) == 0) { |
| 86 | mpscan asc, bsc; |
| 87 | |
| 88 | /* --- Break off my copies --- */ |
| 89 | |
| 90 | MP_SPLIT(a); |
| 91 | MP_SPLIT(b); |
| 92 | MP_SCAN(&asc, a); |
| 93 | MP_SCAN(&bsc, b); |
| 94 | |
| 95 | /* --- Start scanning --- */ |
| 96 | |
| 97 | for (;;) { |
| 98 | if (!MP_STEP(&asc) || !MP_STEP(&bsc)) |
| 99 | assert(((void)"zero argument passed to mp_gcd", 0)); |
| 100 | if (MP_BIT(&asc) || MP_BIT(&bsc)) |
| 101 | break; |
| 102 | shift++; |
| 103 | } |
| 104 | |
| 105 | /* --- Shift @a@ and @b@ down --- */ |
| 106 | |
| 107 | a = mp_lsr(a, a, shift); |
| 108 | b = mp_lsr(b, b, shift); |
| 109 | } |
| 110 | |
| 111 | /* --- Set up @u@ and @v@ --- */ |
| 112 | |
| 113 | u = MP_COPY(a); |
| 114 | v = MP_COPY(b); |
| 115 | |
| 116 | /* --- Start the main loop --- */ |
| 117 | |
| 118 | for (;;) { |
| 119 | |
| 120 | /* --- While @u@ is even --- */ |
| 121 | |
| 122 | { |
| 123 | mpscan sc, xsc, ysc; |
| 124 | size_t n = 0, nn = 0; |
| 125 | |
| 126 | MP_SCAN(&sc, u); |
| 127 | MP_SCAN(&xsc, X); MP_SCAN(&ysc, Y); |
| 128 | for (;;) { |
| 129 | MP_STEP(&sc); |
| 130 | MP_STEP(&xsc); MP_STEP(&ysc); |
| 131 | if (MP_BIT(&sc)) |
| 132 | break; |
| 133 | if (ext && (MP_BIT(&xsc) | MP_BIT(&ysc))) { |
| 134 | if (n) { |
| 135 | X = mp_lsr(X, X, n); |
| 136 | Y = mp_lsr(Y, Y, n); |
| 137 | n = 0; |
| 138 | } |
| 139 | X = mp_add(X, X, b); |
| 140 | Y = mp_sub(Y, Y, a); |
| 141 | MP_SCAN(&xsc, X); |
| 142 | MP_SCAN(&ysc, Y); |
| 143 | MP_STEP(&xsc); MP_STEP(&ysc); |
| 144 | } |
| 145 | n++; nn++; |
| 146 | } |
| 147 | |
| 148 | if (nn) { |
| 149 | u = mp_lsr(u, u, nn); |
| 150 | if (ext && n) { |
| 151 | X = mp_lsr(X, X, n); |
| 152 | Y = mp_lsr(Y, Y, n); |
| 153 | } |
| 154 | } |
| 155 | } |
| 156 | |
| 157 | /* --- While @v@ is even --- */ |
| 158 | |
| 159 | { |
| 160 | mpscan sc, xsc, ysc; |
| 161 | size_t n = 0, nn = 0; |
| 162 | |
| 163 | MP_SCAN(&sc, v); |
| 164 | MP_SCAN(&xsc, x); MP_SCAN(&ysc, y); |
| 165 | for (;;) { |
| 166 | MP_STEP(&sc); |
| 167 | MP_STEP(&xsc); MP_STEP(&ysc); |
| 168 | if (MP_BIT(&sc)) |
| 169 | break; |
| 170 | if (ext && (MP_BIT(&xsc) | MP_BIT(&ysc))) { |
| 171 | if (n) { |
| 172 | x = mp_lsr(x, x, n); |
| 173 | y = mp_lsr(y, y, n); |
| 174 | n = 0; |
| 175 | } |
| 176 | x = mp_add(x, x, b); |
| 177 | y = mp_sub(y, y, a); |
| 178 | MP_SCAN(&xsc, x); |
| 179 | MP_SCAN(&ysc, y); |
| 180 | MP_STEP(&xsc); MP_STEP(&ysc); |
| 181 | } |
| 182 | n++; nn++; |
| 183 | } |
| 184 | |
| 185 | if (nn) { |
| 186 | v = mp_lsr(v, v, nn); |
| 187 | if (ext && n) { |
| 188 | x = mp_lsr(x, x, n); |
| 189 | y = mp_lsr(y, y, n); |
| 190 | } |
| 191 | } |
| 192 | } |
| 193 | |
| 194 | /* --- End-of-loop fiddling --- */ |
| 195 | |
| 196 | if (MP_CMP(u, >=, v)) { |
| 197 | u = mp_sub(u, u, v); |
| 198 | if (ext) { |
| 199 | X = mp_sub(X, X, x); |
| 200 | Y = mp_sub(Y, Y, y); |
| 201 | } |
| 202 | } else { |
| 203 | v = mp_sub(v, v, u); |
| 204 | if (ext) { |
| 205 | x = mp_sub(x, x, X); |
| 206 | y = mp_sub(y, y, Y); |
| 207 | } |
| 208 | } |
| 209 | |
| 210 | if (MP_CMP(u, ==, MP_ZERO)) |
| 211 | break; |
| 212 | } |
| 213 | |
| 214 | /* --- Write the results out --- */ |
| 215 | |
| 216 | if (gcd) |
| 217 | *gcd = mp_lsl(v, v, shift); |
| 218 | else |
| 219 | MP_DROP(v); |
| 220 | |
| 221 | /* --- Perform a little normalization --- * |
| 222 | * |
| 223 | * Ensure that the coefficient returned is positive, if there is only one. |
| 224 | * If there are two, favour @y@. |
| 225 | */ |
| 226 | |
| 227 | if (ext) { |
| 228 | if (swap) { |
| 229 | mp *t = x; x = y; y = t; |
| 230 | t = a; a = b; b = t; |
| 231 | } |
| 232 | if (yy) { |
| 233 | if (y->f & MP_NEG) { |
| 234 | y = mp_add(y, y, a); |
| 235 | x = mp_sub(x, x, b); |
| 236 | } |
| 237 | } else if (x->f & MP_NEG) |
| 238 | x = mp_add(x, x, b); |
| 239 | |
| 240 | if (xx) *xx = x; else MP_DROP(x); |
| 241 | if (yy) *yy = y; else MP_DROP(y); |
| 242 | } |
| 243 | |
| 244 | MP_DROP(u); |
| 245 | MP_DROP(X); MP_DROP(Y); |
| 246 | MP_DROP(a); MP_DROP(b); |
| 247 | } |
| 248 | |
| 249 | /*----- Test rig ----------------------------------------------------------*/ |
| 250 | |
| 251 | #ifdef TEST_RIG |
| 252 | |
| 253 | static int gcd(dstr *v) |
| 254 | { |
| 255 | int ok = 1; |
| 256 | mp *a = *(mp **)v[0].buf; |
| 257 | mp *b = *(mp **)v[1].buf; |
| 258 | mp *g = *(mp **)v[2].buf; |
| 259 | mp *x = *(mp **)v[3].buf; |
| 260 | mp *y = *(mp **)v[4].buf; |
| 261 | |
| 262 | mp *gg, *xx, *yy; |
| 263 | mp_gcd(&gg, &xx, &yy, a, b); |
| 264 | if (MP_CMP(x, !=, xx)) { |
| 265 | fputs("\n*** mp_gcd(x) failed", stderr); |
| 266 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
| 267 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
| 268 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); |
| 269 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); |
| 270 | fputc('\n', stderr); |
| 271 | ok = 0; |
| 272 | } |
| 273 | if (MP_CMP(y, !=, yy)) { |
| 274 | fputs("\n*** mp_gcd(y) failed", stderr); |
| 275 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
| 276 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
| 277 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); |
| 278 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); |
| 279 | fputc('\n', stderr); |
| 280 | ok = 0; |
| 281 | } |
| 282 | |
| 283 | if (!ok) { |
| 284 | mp *ax = mp_mul(MP_NEW, a, xx); |
| 285 | mp *by = mp_mul(MP_NEW, b, yy); |
| 286 | ax = mp_add(ax, ax, by); |
| 287 | if (MP_CMP(ax, ==, gg)) |
| 288 | fputs("\n*** (Alternative result found.)\n", stderr); |
| 289 | MP_DROP(ax); |
| 290 | MP_DROP(by); |
| 291 | } |
| 292 | |
| 293 | if (MP_CMP(g, !=, gg)) { |
| 294 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
| 295 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
| 296 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
| 297 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); |
| 298 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); |
| 299 | fputc('\n', stderr); |
| 300 | ok = 0; |
| 301 | } |
| 302 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
| 303 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
| 304 | return (ok); |
| 305 | } |
| 306 | |
| 307 | static test_chunk tests[] = { |
| 308 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
| 309 | { 0, 0, { 0 } } |
| 310 | }; |
| 311 | |
| 312 | int main(int argc, char *argv[]) |
| 313 | { |
| 314 | sub_init(); |
| 315 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
| 316 | return (0); |
| 317 | } |
| 318 | |
| 319 | #endif |
| 320 | |
| 321 | /*----- That's all, folks -------------------------------------------------*/ |