| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Low-level arithmetic on binary polynomials |
| 4 | * |
| 5 | * (c) 2000 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 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. |
| 16 | * |
| 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. |
| 21 | * |
| 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 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include <assert.h> |
| 31 | |
| 32 | #include "mpx.h" |
| 33 | #include "mpscan.h" |
| 34 | |
| 35 | /*----- Main code ---------------------------------------------------------*/ |
| 36 | |
| 37 | /* --- @gfx_add@ --- * |
| 38 | * |
| 39 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 40 | * @const mpw *av, *avl@ = first addend vector base and limit |
| 41 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
| 42 | * |
| 43 | * Returns: --- |
| 44 | * |
| 45 | * Use: Adds two %$\gf{2}$% polynomials. This is the same as |
| 46 | * subtraction. |
| 47 | */ |
| 48 | |
| 49 | void gfx_add(mpw *dv, mpw *dvl, |
| 50 | const mpw *av, const mpw *avl, |
| 51 | const mpw *bv, const mpw *bvl) |
| 52 | { |
| 53 | MPX_SHRINK(av, avl); |
| 54 | MPX_SHRINK(bv, bvl); |
| 55 | |
| 56 | while (av < avl || bv < bvl) { |
| 57 | mpw a, b; |
| 58 | if (dv >= dvl) |
| 59 | return; |
| 60 | a = (av < avl) ? *av++ : 0; |
| 61 | b = (bv < bvl) ? *bv++ : 0; |
| 62 | *dv++ = a ^ b; |
| 63 | } |
| 64 | if (dv < dvl) |
| 65 | MPX_ZERO(dv, dvl); |
| 66 | } |
| 67 | |
| 68 | /* --- @gfx_acc@ --- * |
| 69 | * |
| 70 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 71 | * @const mpw *av, *avl@ = addend vector base and limit |
| 72 | * |
| 73 | * Returns: --- |
| 74 | * |
| 75 | * Use: Adds the addend into the destination. This is considerably |
| 76 | * faster than the three-address add call. |
| 77 | */ |
| 78 | |
| 79 | void gfx_acc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
| 80 | { |
| 81 | size_t dlen, alen; |
| 82 | |
| 83 | MPX_SHRINK(av, avl); |
| 84 | dlen = dvl - dv; |
| 85 | alen = avl - av; |
| 86 | if (dlen < alen) |
| 87 | avl = av + dlen; |
| 88 | while (av < avl) |
| 89 | *dv++ ^= *av++; |
| 90 | } |
| 91 | |
| 92 | /* --- @gfx_accshift@ --- * |
| 93 | * |
| 94 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 95 | * @const mpw *av, *avl@ = addend vector base and limit |
| 96 | * @size_t n@ = number of bits to shift |
| 97 | * |
| 98 | * Returns: --- |
| 99 | * |
| 100 | * Use: Shifts the argument left by %$n$% places and adds it to the |
| 101 | * destination. This is a primitive used by multiplication and |
| 102 | * division. |
| 103 | */ |
| 104 | |
| 105 | void gfx_accshift(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
| 106 | { |
| 107 | size_t c = n / MPW_BITS; |
| 108 | mpw x = 0, y; |
| 109 | size_t dlen, alen; |
| 110 | |
| 111 | /* --- Sort out the shift amounts --- */ |
| 112 | |
| 113 | if (dvl - dv < c) |
| 114 | return; |
| 115 | dv += c; |
| 116 | n %= MPW_BITS; |
| 117 | if (!n) { |
| 118 | gfx_acc(dv, dvl, av, avl); |
| 119 | return; |
| 120 | } |
| 121 | c = MPW_BITS - n; |
| 122 | |
| 123 | /* --- Sort out vector lengths --- */ |
| 124 | |
| 125 | MPX_SHRINK(av, avl); |
| 126 | dlen = dvl - dv; |
| 127 | alen = avl - av; |
| 128 | if (dlen < alen) |
| 129 | avl = av + dlen; |
| 130 | |
| 131 | /* --- Now do the hard work --- */ |
| 132 | |
| 133 | while (av < avl) { |
| 134 | y = *av++; |
| 135 | *dv++ ^= MPW((y << n) | (x >> c)); |
| 136 | x = y; |
| 137 | } |
| 138 | if (dv < dvl) |
| 139 | *dv++ ^= x >> c; |
| 140 | } |
| 141 | |
| 142 | /* --- @gfx_mul@ --- * |
| 143 | * |
| 144 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 145 | * @const mpw *av, *avl@ = first argument vector base and limit |
| 146 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 147 | * |
| 148 | * Returns: --- |
| 149 | * |
| 150 | * Use: Does multiplication of polynomials over %$\gf{2}$%. |
| 151 | */ |
| 152 | |
| 153 | void gfx_mul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 154 | const mpw *bv, const mpw *bvl) |
| 155 | { |
| 156 | mpscan sc; |
| 157 | const mpw *v; |
| 158 | mpw *vv; |
| 159 | mpw z; |
| 160 | mpd x, y; |
| 161 | |
| 162 | MPX_SHRINK(av, avl); |
| 163 | MPX_SHRINK(bv, bvl); |
| 164 | MPSCAN_INITX(&sc, av, avl); |
| 165 | MPX_ZERO(dv, dvl); |
| 166 | |
| 167 | while (bv < bvl && dv < dvl) { |
| 168 | x = 0; |
| 169 | for (v = av, vv = dv++; v < avl && vv < dvl; v++) { |
| 170 | z = *bv; y = *v; |
| 171 | while (z) { |
| 172 | if (z & 1u) x ^= y; |
| 173 | z >>= 1; y <<= 1; |
| 174 | } |
| 175 | *vv++ ^= MPW(x); |
| 176 | x >>= MPW_BITS; |
| 177 | } |
| 178 | if (vv < dvl) |
| 179 | *vv++ = MPW(x); |
| 180 | bv++; |
| 181 | } |
| 182 | } |
| 183 | |
| 184 | /* --- @gfx_div@ --- * |
| 185 | * |
| 186 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
| 187 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
| 188 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
| 189 | * |
| 190 | * Returns: --- |
| 191 | * |
| 192 | * Use: Performs division on polynomials over %$\gf{2}$%. |
| 193 | */ |
| 194 | |
| 195 | void gfx_div(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
| 196 | const mpw *dv, const mpw *dvl) |
| 197 | { |
| 198 | size_t dlen, rlen, qlen; |
| 199 | size_t dbits; |
| 200 | mpw *rvv, *rvd; |
| 201 | unsigned rvm, n, qi; |
| 202 | mpw q; |
| 203 | |
| 204 | MPX_SHRINK(rv, rvl); |
| 205 | MPX_SHRINK(dv, dvl); |
| 206 | assert(((void)"division by zero in gfx_div", dv < dvl)); |
| 207 | MPX_BITS(dbits, dv, dvl); |
| 208 | dlen = dvl - dv; |
| 209 | rlen = rvl - rv; |
| 210 | qlen = qvl - qv; |
| 211 | |
| 212 | MPX_ZERO(qv, qvl); |
| 213 | if (dlen > rlen) |
| 214 | return; |
| 215 | rvd = rvl - dlen; |
| 216 | rvv = rvl - 1; |
| 217 | rvm = 1 << (MPW_BITS - 1); |
| 218 | n = MPW_BITS - (dbits % MPW_BITS); |
| 219 | if (n == MPW_BITS) |
| 220 | n = 0; |
| 221 | q = 0; |
| 222 | qi = rvd - rv; |
| 223 | |
| 224 | for (;;) { |
| 225 | q <<= 1; |
| 226 | if (*rvv & rvm) { |
| 227 | q |= 1; |
| 228 | gfx_accshift(rvd, rvl, dv, dvl, n); |
| 229 | } |
| 230 | rvm >>= 1; |
| 231 | if (!rvm) { |
| 232 | rvm = 1 << (MPW_BITS - 1); |
| 233 | rvv--; |
| 234 | } |
| 235 | if (n) |
| 236 | n--; |
| 237 | else { |
| 238 | if (qi < qlen) |
| 239 | qv[qi] = q; |
| 240 | q = 0; |
| 241 | qi--; |
| 242 | if (rvd == rv) |
| 243 | break; |
| 244 | n = MPW_BITS - 1; |
| 245 | rvd--; |
| 246 | } |
| 247 | } |
| 248 | } |
| 249 | |
| 250 | /*----- Test rig ----------------------------------------------------------*/ |
| 251 | |
| 252 | #ifdef TEST_RIG |
| 253 | |
| 254 | #include <mLib/alloc.h> |
| 255 | #include <mLib/dstr.h> |
| 256 | #include <mLib/quis.h> |
| 257 | #include <mLib/testrig.h> |
| 258 | |
| 259 | #define ALLOC(v, vl, sz) do { \ |
| 260 | size_t _sz = (sz); \ |
| 261 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
| 262 | mpw *_vvl = _vv + _sz; \ |
| 263 | (v) = _vv; \ |
| 264 | (vl) = _vvl; \ |
| 265 | } while (0) |
| 266 | |
| 267 | #define LOAD(v, vl, d) do { \ |
| 268 | const dstr *_d = (d); \ |
| 269 | mpw *_v, *_vl; \ |
| 270 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
| 271 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
| 272 | (v) = _v; \ |
| 273 | (vl) = _vl; \ |
| 274 | } while (0) |
| 275 | |
| 276 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
| 277 | |
| 278 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
| 279 | { |
| 280 | fputs(msg, stderr); |
| 281 | MPX_SHRINK(v, vl); |
| 282 | while (v < vl) |
| 283 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
| 284 | fputc('\n', stderr); |
| 285 | } |
| 286 | |
| 287 | static int vadd(dstr *v) |
| 288 | { |
| 289 | mpw *a, *al; |
| 290 | mpw *b, *bl; |
| 291 | mpw *c, *cl; |
| 292 | mpw *d, *dl; |
| 293 | int ok = 1; |
| 294 | |
| 295 | LOAD(a, al, &v[0]); |
| 296 | LOAD(b, bl, &v[1]); |
| 297 | LOAD(c, cl, &v[2]); |
| 298 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); |
| 299 | |
| 300 | gfx_add(d, dl, a, al, b, bl); |
| 301 | if (!mpx_ueq(d, dl, c, cl)) { |
| 302 | fprintf(stderr, "\n*** vadd failed\n"); |
| 303 | dumpmp(" a", a, al); |
| 304 | dumpmp(" b", b, bl); |
| 305 | dumpmp("expected", c, cl); |
| 306 | dumpmp(" result", d, dl); |
| 307 | ok = 0; |
| 308 | } |
| 309 | |
| 310 | xfree(a); xfree(b); xfree(c); xfree(d); |
| 311 | return (ok); |
| 312 | } |
| 313 | |
| 314 | static int vmul(dstr *v) |
| 315 | { |
| 316 | mpw *a, *al; |
| 317 | mpw *b, *bl; |
| 318 | mpw *c, *cl; |
| 319 | mpw *d, *dl; |
| 320 | int ok = 1; |
| 321 | |
| 322 | LOAD(a, al, &v[0]); |
| 323 | LOAD(b, bl, &v[1]); |
| 324 | LOAD(c, cl, &v[2]); |
| 325 | ALLOC(d, dl, (al - a) + (bl - b)); |
| 326 | |
| 327 | gfx_mul(d, dl, a, al, b, bl); |
| 328 | if (!mpx_ueq(d, dl, c, cl)) { |
| 329 | fprintf(stderr, "\n*** vmul failed\n"); |
| 330 | dumpmp(" a", a, al); |
| 331 | dumpmp(" b", b, bl); |
| 332 | dumpmp("expected", c, cl); |
| 333 | dumpmp(" result", d, dl); |
| 334 | ok = 0; |
| 335 | } |
| 336 | |
| 337 | xfree(a); xfree(b); xfree(c); xfree(d); |
| 338 | return (ok); |
| 339 | } |
| 340 | |
| 341 | static int vdiv(dstr *v) |
| 342 | { |
| 343 | mpw *a, *al; |
| 344 | mpw *b, *bl; |
| 345 | mpw *q, *ql; |
| 346 | mpw *r, *rl; |
| 347 | mpw *qq, *qql; |
| 348 | int ok = 1; |
| 349 | |
| 350 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); |
| 351 | LOAD(b, bl, &v[1]); |
| 352 | LOAD(q, ql, &v[2]); |
| 353 | LOAD(r, rl, &v[3]); |
| 354 | ALLOC(qq, qql, al - a); |
| 355 | |
| 356 | gfx_div(qq, qql, a, al, b, bl); |
| 357 | if (!mpx_ueq(qq, qql, q, ql) || |
| 358 | !mpx_ueq(a, al, r, rl)) { |
| 359 | fprintf(stderr, "\n*** vdiv failed\n"); |
| 360 | dumpmp(" divisor", b, bl); |
| 361 | dumpmp("expect r", r, rl); |
| 362 | dumpmp("result r", a, al); |
| 363 | dumpmp("expect q", q, ql); |
| 364 | dumpmp("result q", qq, qql); |
| 365 | ok = 0; |
| 366 | } |
| 367 | |
| 368 | xfree(a); xfree(b); xfree(r); xfree(q); xfree(qq); |
| 369 | return (ok); |
| 370 | } |
| 371 | |
| 372 | static test_chunk defs[] = { |
| 373 | { "add", vadd, { &type_hex, &type_hex, &type_hex, 0 } }, |
| 374 | { "mul", vmul, { &type_hex, &type_hex, &type_hex, 0 } }, |
| 375 | { "div", vdiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, |
| 376 | { 0, 0, { 0 } } |
| 377 | }; |
| 378 | |
| 379 | int main(int argc, char *argv[]) |
| 380 | { |
| 381 | test_run(argc, argv, defs, SRCDIR"/t/gfx"); |
| 382 | return (0); |
| 383 | } |
| 384 | |
| 385 | #endif |
| 386 | |
| 387 | /*----- That's all, folks -------------------------------------------------*/ |