| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mpx.h,v 1.11 2000/10/08 15:48:35 mdw Exp $ |
| 4 | * |
| 5 | * Low level multiprecision arithmetic |
| 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: mpx.h,v $ |
| 33 | * Revision 1.11 2000/10/08 15:48:35 mdw |
| 34 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
| 35 | * |
| 36 | * Revision 1.10 2000/10/08 12:06:12 mdw |
| 37 | * Provide @mpx_ueq@ for rapidly testing equality of two integers. |
| 38 | * |
| 39 | * Revision 1.9 1999/12/22 15:49:07 mdw |
| 40 | * New function for division by a small integer. |
| 41 | * |
| 42 | * Revision 1.8 1999/12/11 10:57:43 mdw |
| 43 | * Karatsuba squaring algorithm. |
| 44 | * |
| 45 | * Revision 1.7 1999/12/11 01:51:28 mdw |
| 46 | * Change Karatsuba parameters slightly. |
| 47 | * |
| 48 | * Revision 1.6 1999/12/10 23:23:51 mdw |
| 49 | * Karatsuba-Ofman multiplication algorithm. |
| 50 | * |
| 51 | * Revision 1.5 1999/11/20 22:23:27 mdw |
| 52 | * Add function versions of some low-level macros with wider use. |
| 53 | * |
| 54 | * Revision 1.4 1999/11/17 18:04:43 mdw |
| 55 | * Add two's complement support. Fix a bug in MPX_UMLAN. |
| 56 | * |
| 57 | * Revision 1.3 1999/11/13 01:51:29 mdw |
| 58 | * Minor interface changes. Should be stable now. |
| 59 | * |
| 60 | * Revision 1.2 1999/11/11 17:47:55 mdw |
| 61 | * Minor changes for different `mptypes.h' format. |
| 62 | * |
| 63 | * Revision 1.1 1999/09/03 08:41:12 mdw |
| 64 | * Initial import. |
| 65 | * |
| 66 | */ |
| 67 | |
| 68 | #ifndef CATACOMB_MPX_H |
| 69 | #define CATACOMB_MPX_H |
| 70 | |
| 71 | #ifdef __cplusplus |
| 72 | extern "C" { |
| 73 | #endif |
| 74 | |
| 75 | /*----- The idea ----------------------------------------------------------* |
| 76 | * |
| 77 | * This file provides functions and macros which work on vectors of words as |
| 78 | * unsigned multiprecision integers. The interface works in terms of base |
| 79 | * and limit pointers (i.e., a pointer to the start of a vector, and a |
| 80 | * pointer just past its end) rather than base pointer and length, because |
| 81 | * that requires more arithmetic and state to work on. |
| 82 | * |
| 83 | * The interfaces are slightly bizarre in other ways. Try to use the |
| 84 | * higher-level functions where you can: they're rather better designed to |
| 85 | * actually be friendly and useful. |
| 86 | */ |
| 87 | |
| 88 | /*----- Header files ------------------------------------------------------*/ |
| 89 | |
| 90 | #include <string.h> |
| 91 | |
| 92 | #ifndef CATACOMB_MPW_H |
| 93 | # include "mpw.h" |
| 94 | #endif |
| 95 | |
| 96 | /*----- General manipulation ----------------------------------------------*/ |
| 97 | |
| 98 | /* --- @MPX_SHRINK@ --- * |
| 99 | * |
| 100 | * Arguments: @const mpw *v@ = pointer to vector of words |
| 101 | * @const mpw *vl@ = (updated) current limit of vector |
| 102 | * |
| 103 | * Use: Shrinks down the limit of a multiprecision integer vector. |
| 104 | */ |
| 105 | |
| 106 | #define MPX_SHRINK(v, vl) do { \ |
| 107 | const mpw *_vv = (v), *_vvl = (vl); \ |
| 108 | while (_vvl > _vv && !_vvl[-1]) \ |
| 109 | _vvl--; \ |
| 110 | (vl) = (mpw *)_vvl; \ |
| 111 | } while (0) |
| 112 | |
| 113 | /* --- @MPX_BITS@ --- * |
| 114 | * |
| 115 | * Arguments: @unsigned long b@ = result variable |
| 116 | * @const mpw *v@ = pointer to array of words |
| 117 | * @const mpw *vl@ = limit of vector (from @MPX_SHRINK@) |
| 118 | * |
| 119 | * Use: Calculates the number of bits in a multiprecision value. |
| 120 | */ |
| 121 | |
| 122 | #define MPX_BITS(b, v, vl) do { \ |
| 123 | const mpw *_v = (v), *_vl = (vl); \ |
| 124 | MPX_SHRINK(_v, _vl); \ |
| 125 | if (_v == _vl) \ |
| 126 | (b) = 0; \ |
| 127 | else { \ |
| 128 | unsigned long _b = MPW_BITS * (_vl - _v - 1) + 1; \ |
| 129 | mpw _w = _vl[-1]; \ |
| 130 | unsigned _k = MPW_BITS / 2; \ |
| 131 | while (_k) { \ |
| 132 | if (_w >> _k) { \ |
| 133 | _w >>= _k; \ |
| 134 | _b += _k; \ |
| 135 | } \ |
| 136 | _k >>= 1; \ |
| 137 | } \ |
| 138 | (b) = _b; \ |
| 139 | } \ |
| 140 | } while (0) |
| 141 | |
| 142 | /* --- @MPX_OCTETS@ --- * |
| 143 | * |
| 144 | * Arguments: @size_t o@ = result variable |
| 145 | * @const mpw *v, *vl@ = pointer to array of words |
| 146 | * |
| 147 | * Use: Calculates the number of octets in a multiprecision value. |
| 148 | */ |
| 149 | |
| 150 | #define MPX_OCTETS(o, v, vl) do { \ |
| 151 | const mpw *_v = (v), *_vl = (vl); \ |
| 152 | MPX_SHRINK(_v, _vl); \ |
| 153 | if (_v == _vl) \ |
| 154 | (o) = 0; \ |
| 155 | else { \ |
| 156 | size_t _o = (MPW_BITS / 8) * (_vl - _v - 1); \ |
| 157 | mpw _w = _vl[-1]; \ |
| 158 | unsigned _k = MPW_BITS / 2; \ |
| 159 | while (_k >= 8) { \ |
| 160 | if (_w >> _k) { \ |
| 161 | _w >>= _k; \ |
| 162 | _o += _k >> 3; \ |
| 163 | } \ |
| 164 | _k >>= 1; \ |
| 165 | } \ |
| 166 | if (_w) \ |
| 167 | _o++; \ |
| 168 | (o) = _o; \ |
| 169 | } \ |
| 170 | } while (0) |
| 171 | |
| 172 | /* --- @MPX_COPY@ --- * |
| 173 | * |
| 174 | * Arguments: @dv, dvl@ = destination vector base and limit |
| 175 | * @av, avl@ = source vector base and limit |
| 176 | * |
| 177 | * Use: Copies a multiprecision integer. |
| 178 | */ |
| 179 | |
| 180 | #define MPX_COPY(dv, dvl, av, avl) do { \ |
| 181 | mpw *_dv = (dv), *_dvl = (dvl); \ |
| 182 | size_t _dn = _dvl - _dv; \ |
| 183 | const mpw *_av = (av), *_avl = (avl); \ |
| 184 | size_t _an = _avl - _av; \ |
| 185 | if (_av == _dv) { \ |
| 186 | if (_dvl > _avl) \ |
| 187 | memset(_dv, 0, MPWS(_dn - _an)); \ |
| 188 | } else if (_an >= _dn) \ |
| 189 | memmove(_dv, _av, MPWS(_dn)); \ |
| 190 | else { \ |
| 191 | memmove(_dv, _av, MPWS(_an)); \ |
| 192 | memset(_dv + _an, 0, MPWS(_dn - _an)); \ |
| 193 | } \ |
| 194 | } while (0) |
| 195 | |
| 196 | /* --- @MPX_ZERO@ --- * |
| 197 | * |
| 198 | * Arguments: @v, vl@ = base and limit of vector to clear |
| 199 | * |
| 200 | * Use: Zeroes the area between the two vector pointers. |
| 201 | */ |
| 202 | |
| 203 | #define MPX_ZERO(v, vl) do { \ |
| 204 | mpw *_v = (v), *_vl = (vl); \ |
| 205 | if (_v < _vl) \ |
| 206 | memset(_v, 0, MPWS(_vl - _v)); \ |
| 207 | } while (0) |
| 208 | |
| 209 | /*----- Loading and storing -----------------------------------------------*/ |
| 210 | |
| 211 | /* --- @mpx_storel@ --- * |
| 212 | * |
| 213 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 214 | * @void *p@ = pointer to octet array |
| 215 | * @size_t sz@ = size of octet array |
| 216 | * |
| 217 | * Returns: --- |
| 218 | * |
| 219 | * Use: Stores an MP in an octet array, least significant octet |
| 220 | * first. High-end octets are silently discarded if there |
| 221 | * isn't enough space for them. |
| 222 | */ |
| 223 | |
| 224 | extern void mpx_storel(const mpw */*v*/, const mpw */*vl*/, |
| 225 | void */*p*/, size_t /*sz*/); |
| 226 | |
| 227 | /* --- @mpx_loadl@ --- * |
| 228 | * |
| 229 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 230 | * @const void *p@ = pointer to octet array |
| 231 | * @size_t sz@ = size of octet array |
| 232 | * |
| 233 | * Returns: --- |
| 234 | * |
| 235 | * Use: Loads an MP in an octet array, least significant octet |
| 236 | * first. High-end octets are ignored if there isn't enough |
| 237 | * space for them. |
| 238 | */ |
| 239 | |
| 240 | extern void mpx_loadl(mpw */*v*/, mpw */*vl*/, |
| 241 | const void */*p*/, size_t /*sz*/); |
| 242 | |
| 243 | /* --- @mpx_storeb@ --- * |
| 244 | * |
| 245 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 246 | * @void *p@ = pointer to octet array |
| 247 | * @size_t sz@ = size of octet array |
| 248 | * |
| 249 | * Returns: --- |
| 250 | * |
| 251 | * Use: Stores an MP in an octet array, most significant octet |
| 252 | * first. High-end octets are silently discarded if there |
| 253 | * isn't enough space for them. |
| 254 | */ |
| 255 | |
| 256 | extern void mpx_storeb(const mpw */*v*/, const mpw */*vl*/, |
| 257 | void */*p*/, size_t /*sz*/); |
| 258 | |
| 259 | /* --- @mpx_loadb@ --- * |
| 260 | * |
| 261 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 262 | * @const void *p@ = pointer to octet array |
| 263 | * @size_t sz@ = size of octet array |
| 264 | * |
| 265 | * Returns: --- |
| 266 | * |
| 267 | * Use: Loads an MP in an octet array, most significant octet |
| 268 | * first. High-end octets are ignored if there isn't enough |
| 269 | * space for them. |
| 270 | */ |
| 271 | |
| 272 | extern void mpx_loadb(mpw */*v*/, mpw */*vl*/, |
| 273 | const void */*p*/, size_t /*sz*/); |
| 274 | |
| 275 | /*----- Logical shifting --------------------------------------------------*/ |
| 276 | |
| 277 | /* --- @mpx_lsl@ --- * |
| 278 | * |
| 279 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 280 | * @const mpw *av, *avl@ = source vector base and limit |
| 281 | * @size_t n@ = number of bit positions to shift by |
| 282 | * |
| 283 | * Returns: --- |
| 284 | * |
| 285 | * Use: Performs a logical shift left operation on an integer. |
| 286 | */ |
| 287 | |
| 288 | extern void mpx_lsl(mpw */*dv*/, mpw */*dvl*/, |
| 289 | const mpw */*av*/, const mpw */*avl*/, |
| 290 | size_t /*n*/); |
| 291 | |
| 292 | /* --- @mpx_lsr@ --- * |
| 293 | * |
| 294 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 295 | * @const mpw *av, *avl@ = source vector base and limit |
| 296 | * @size_t n@ = number of bit positions to shift by |
| 297 | * |
| 298 | * Returns: --- |
| 299 | * |
| 300 | * Use: Performs a logical shift right operation on an integer. |
| 301 | */ |
| 302 | |
| 303 | extern void mpx_lsr(mpw */*dv*/, mpw */*dvl*/, |
| 304 | const mpw */*av*/, const mpw */*avl*/, |
| 305 | size_t /*n*/); |
| 306 | |
| 307 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
| 308 | |
| 309 | /* --- @mpx_2c@ --- * |
| 310 | * |
| 311 | * Arguments: @mpw *dv, *dvl@ = destination vector |
| 312 | * @const mpw *v, *vl@ = source vector |
| 313 | * |
| 314 | * Returns: --- |
| 315 | * |
| 316 | * Use: Calculates the two's complement of @v@. |
| 317 | */ |
| 318 | |
| 319 | extern void mpx_2c(mpw */*dv*/, mpw */*dvl*/, |
| 320 | const mpw */*v*/, const mpw */*vl*/); |
| 321 | |
| 322 | /* --- @mpx_ueq@ --- * |
| 323 | * |
| 324 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
| 325 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 326 | * |
| 327 | * Returns: Nonzero if the two vectors are equal. |
| 328 | * |
| 329 | * Use: Performs an unsigned integer test for equality. |
| 330 | */ |
| 331 | |
| 332 | extern int mpx_ueq(const mpw */*av*/, const mpw */*avl*/, |
| 333 | const mpw */*bv*/, const mpw */*bvl*/); |
| 334 | |
| 335 | /* --- @mpx_ucmp@ --- * |
| 336 | * |
| 337 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
| 338 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 339 | * |
| 340 | * Returns: Less than, equal to, or greater than zero depending on |
| 341 | * whether @a@ is less than, equal to or greater than @b@, |
| 342 | * respectively. |
| 343 | * |
| 344 | * Use: Performs an unsigned integer comparison. |
| 345 | */ |
| 346 | |
| 347 | #define MPX_UCMP(av, avl, op, dv, dvl) \ |
| 348 | (mpx_ucmp((av), (avl), (dv), (dvl)) op 0) |
| 349 | |
| 350 | extern int mpx_ucmp(const mpw */*av*/, const mpw */*avl*/, |
| 351 | const mpw */*bv*/, const mpw */*bvl*/); |
| 352 | |
| 353 | /* --- @mpx_uadd@ --- * |
| 354 | * |
| 355 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 356 | * @const mpw *av, *avl@ = first addend vector base and limit |
| 357 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
| 358 | * |
| 359 | * Returns: --- |
| 360 | * |
| 361 | * Use: Performs unsigned integer addition. If the result overflows |
| 362 | * the destination vector, high-order bits are discarded. This |
| 363 | * means that two's complement addition happens more or less for |
| 364 | * free, although that's more a side-effect than anything else. |
| 365 | * The result vector may be equal to either or both source |
| 366 | * vectors, but may not otherwise overlap them. |
| 367 | */ |
| 368 | |
| 369 | extern void mpx_uadd(mpw */*dv*/, mpw */*dvl*/, |
| 370 | const mpw */*av*/, const mpw */*avl*/, |
| 371 | const mpw */*bv*/, const mpw */*bvl*/); |
| 372 | |
| 373 | /* --- @mpx_uaddn@ --- * |
| 374 | * |
| 375 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
| 376 | * @mpw n@ = other addend |
| 377 | * |
| 378 | * Returns: --- |
| 379 | * |
| 380 | * Use: Adds a small integer to a multiprecision number. |
| 381 | */ |
| 382 | |
| 383 | #define MPX_UADDN(dv, dvl, n) do { \ |
| 384 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
| 385 | mpw _c = (n); \ |
| 386 | \ |
| 387 | while (_c && _ddv < _ddvl) { \ |
| 388 | mpd _x = (mpd)*_ddv + (mpd)_c; \ |
| 389 | *_ddv++ = MPW(_x); \ |
| 390 | _c = _x >> MPW_BITS; \ |
| 391 | } \ |
| 392 | } while (0) |
| 393 | |
| 394 | extern void mpx_uaddn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
| 395 | |
| 396 | /* --- @mpx_usub@ --- * |
| 397 | * |
| 398 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 399 | * @const mpw *av, *avl@ = first argument vector base and limit |
| 400 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 401 | * |
| 402 | * Returns: --- |
| 403 | * |
| 404 | * Use: Performs unsigned integer subtraction. If the result |
| 405 | * overflows the destination vector, high-order bits are |
| 406 | * discarded. This means that two's complement subtraction |
| 407 | * happens more or less for free, although that's more a side- |
| 408 | * effect than anything else. The result vector may be equal to |
| 409 | * either or both source vectors, but may not otherwise overlap |
| 410 | * them. |
| 411 | */ |
| 412 | |
| 413 | extern void mpx_usub(mpw */*dv*/, mpw */*dvl*/, |
| 414 | const mpw */*av*/, const mpw */*avl*/, |
| 415 | const mpw */*bv*/, const mpw */*bvl*/); |
| 416 | |
| 417 | /* --- @mpx_usubn@ --- * |
| 418 | * |
| 419 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
| 420 | * @n@ = subtrahend |
| 421 | * |
| 422 | * Returns: --- |
| 423 | * |
| 424 | * Use: Subtracts a small integer from a multiprecision number. |
| 425 | */ |
| 426 | |
| 427 | #define MPX_USUBN(dv, dvl, n) do { \ |
| 428 | mpw *_ddv = (dv), *_ddvl = (dvl); \ |
| 429 | mpw _c = (n); \ |
| 430 | \ |
| 431 | while (_ddv < _ddvl) { \ |
| 432 | mpd _x = (mpd)*_ddv - (mpd)_c; \ |
| 433 | *_ddv++ = MPW(_x); \ |
| 434 | if (_x >> MPW_BITS) \ |
| 435 | _c = 1; \ |
| 436 | else \ |
| 437 | break; \ |
| 438 | } \ |
| 439 | } while (0) |
| 440 | |
| 441 | extern void mpx_usubn(mpw */*dv*/, mpw */*dvl*/, mpw /*n*/); |
| 442 | |
| 443 | /* --- @mpx_umul@ --- * |
| 444 | * |
| 445 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 446 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 447 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
| 448 | * |
| 449 | * Returns: --- |
| 450 | * |
| 451 | * Use: Performs unsigned integer multiplication. If the result |
| 452 | * overflows the desination vector, high-order bits are |
| 453 | * discarded. The result vector may not overlap the argument |
| 454 | * vectors in any way. |
| 455 | */ |
| 456 | |
| 457 | extern void mpx_umul(mpw */*dv*/, mpw */*dvl*/, |
| 458 | const mpw */*av*/, const mpw */*avl*/, |
| 459 | const mpw */*bv*/, const mpw */*bvl*/); |
| 460 | |
| 461 | /* --- @mpx_umuln@ --- * |
| 462 | * |
| 463 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 464 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 465 | * @mpw m@ = multiplier |
| 466 | * |
| 467 | * Returns: --- |
| 468 | * |
| 469 | * Use: Multiplies a multiprecision integer by a single-word value. |
| 470 | * The destination and source may be equal. The destination |
| 471 | * is completely cleared after use. |
| 472 | */ |
| 473 | |
| 474 | #define MPX_UMULN(dv, dvl, av, avl, m) do { \ |
| 475 | mpw *_dv = (dv), *_dvl = (dvl); \ |
| 476 | const mpw *_av = (av), *_avl = (avl); \ |
| 477 | mpw _c = 0; \ |
| 478 | mpd _m = (m); \ |
| 479 | \ |
| 480 | while (_av < _avl) { \ |
| 481 | mpd _x; \ |
| 482 | if (_dv >= _dvl) \ |
| 483 | break; \ |
| 484 | _x = (mpd)_m * (mpd)*_av++ + _c; \ |
| 485 | *_dv++ = MPW(_x); \ |
| 486 | _c = _x >> MPW_BITS; \ |
| 487 | } \ |
| 488 | if (_dv < _dvl) { \ |
| 489 | *_dv++ = MPW(_c); \ |
| 490 | MPX_ZERO(_dv, _dvl); \ |
| 491 | } \ |
| 492 | } while (0) |
| 493 | |
| 494 | extern void mpx_umuln(mpw */*dv*/, mpw */*dvl*/, |
| 495 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
| 496 | |
| 497 | /* --- @mpx_umlan@ --- * |
| 498 | * |
| 499 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
| 500 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 501 | * @mpw m@ = multiplier |
| 502 | * |
| 503 | * Returns: --- |
| 504 | * |
| 505 | * Use: Multiplies a multiprecision integer by a single-word value |
| 506 | * and adds the result to an accumulator. |
| 507 | */ |
| 508 | |
| 509 | #define MPX_UMLAN(dv, dvl, av, avl, m) do { \ |
| 510 | mpw *_dv = (dv), *_dvl = (dvl); \ |
| 511 | const mpw *_av = (av), *_avl = (avl); \ |
| 512 | mpw _cc = 0; \ |
| 513 | mpd _m = (m); \ |
| 514 | \ |
| 515 | while (_dv < _dvl && _av < _avl) { \ |
| 516 | mpd _x; \ |
| 517 | _x = (mpd)*_dv + (mpd)_m * (mpd)*_av++ + _cc; \ |
| 518 | *_dv++ = MPW(_x); \ |
| 519 | _cc = _x >> MPW_BITS; \ |
| 520 | } \ |
| 521 | MPX_UADDN(_dv, _dvl, _cc); \ |
| 522 | } while (0) |
| 523 | |
| 524 | extern void mpx_umlan(mpw */*dv*/, mpw */*dvl*/, |
| 525 | const mpw */*av*/, const mpw */*avl*/, mpw m); |
| 526 | |
| 527 | /* --- @mpx_usqr@ --- * |
| 528 | * |
| 529 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 530 | * @const mpw *av, *av@ = source vector base and limit |
| 531 | * |
| 532 | * Returns: --- |
| 533 | * |
| 534 | * Use: Performs unsigned integer squaring. The result vector must |
| 535 | * not overlap the source vector in any way. |
| 536 | */ |
| 537 | |
| 538 | extern void mpx_usqr(mpw */*dv*/, mpw */*dvl*/, |
| 539 | const mpw */*av*/, const mpw */*avl*/); |
| 540 | |
| 541 | /* --- @mpx_udiv@ --- * |
| 542 | * |
| 543 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
| 544 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
| 545 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
| 546 | * @mpw *sv, *svl@ = scratch workspace |
| 547 | * |
| 548 | * Returns: --- |
| 549 | * |
| 550 | * Use: Performs unsigned integer division. If the result overflows |
| 551 | * the quotient vector, high-order bits are discarded. (Clearly |
| 552 | * the remainder vector can't overflow.) The various vectors |
| 553 | * may not overlap in any way. Yes, I know it's a bit odd |
| 554 | * requiring the dividend to be in the result position but it |
| 555 | * does make some sense really. The remainder must have |
| 556 | * headroom for at least two extra words. The scratch space |
| 557 | * must be at least one word larger than the divisor. |
| 558 | */ |
| 559 | |
| 560 | extern void mpx_udiv(mpw */*qv*/, mpw */*qvl*/, mpw */*rv*/, mpw */*rvl*/, |
| 561 | const mpw */*dv*/, const mpw */*dvl*/, |
| 562 | mpw */*sv*/, mpw */*svl*/); |
| 563 | |
| 564 | /* --- @mpx_udivn@ --- * |
| 565 | * |
| 566 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap |
| 567 | * dividend) |
| 568 | * @const mpw *rv, *rvl@ = dividend |
| 569 | * @mpw d@ = single-precision divisor |
| 570 | * |
| 571 | * Returns: Remainder after divison. |
| 572 | * |
| 573 | * Use: Performs a single-precision division operation. |
| 574 | */ |
| 575 | |
| 576 | extern mpw mpx_udivn(mpw */*qv*/, mpw */*qvl*/, |
| 577 | const mpw */*rv*/, const mpw */*rvl*/, mpw /*d*/); |
| 578 | |
| 579 | /*----- Karatsuba multiplication algorithms -------------------------------*/ |
| 580 | |
| 581 | /* --- @MPK_THRESH@ --- * |
| 582 | * |
| 583 | * This is the limiting length for using Karatsuba algorithms. It's best to |
| 584 | * use the simpler classical multiplication method on numbers smaller than |
| 585 | * this. |
| 586 | */ |
| 587 | |
| 588 | #define MPK_THRESH 16 |
| 589 | |
| 590 | /* --- @MPK_SLOP@ --- * |
| 591 | * |
| 592 | * The extra number of words required as scratch space by the Karatsuba |
| 593 | * routines. This is a (generous) guess, since the actual amount of space |
| 594 | * required is proportional to the recursion depth. |
| 595 | */ |
| 596 | |
| 597 | #define MPK_SLOP 64 |
| 598 | |
| 599 | /* --- @mpx_kmul@ --- * |
| 600 | * |
| 601 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
| 602 | * @const mpw *av, *avl@ = pointer to first argument |
| 603 | * @const mpw *bv, *bvl@ = pointer to second argument |
| 604 | * @mpw *sv, *svl@ = pointer to scratch workspace |
| 605 | * |
| 606 | * Returns: --- |
| 607 | * |
| 608 | * Use: Multiplies two multiprecision integers using Karatsuba's |
| 609 | * algorithm. This is rather faster than traditional long |
| 610 | * multiplication (e.g., @mpx_umul@) on large numbers, although |
| 611 | * more expensive on small ones. |
| 612 | * |
| 613 | * The destination and scratch buffers must be twice as large as |
| 614 | * the larger argument. The scratch space must be twice as |
| 615 | * large as the larger argument, plus the magic number |
| 616 | * @MPK_SLOP@. |
| 617 | */ |
| 618 | |
| 619 | extern void mpx_kmul(mpw */*dv*/, mpw */*dvl*/, |
| 620 | const mpw */*av*/, const mpw */*avl*/, |
| 621 | const mpw */*bv*/, const mpw */*bvl*/, |
| 622 | mpw */*sv*/, mpw */*svl*/); |
| 623 | |
| 624 | /* --- @mpx_ksqr@ --- * |
| 625 | * |
| 626 | * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer |
| 627 | * @const mpw *av, *avl@ = pointer to first argument |
| 628 | * @mpw *sv, *svl@ = pointer to scratch workspace |
| 629 | * |
| 630 | * Returns: --- |
| 631 | * |
| 632 | * Use: Squares a multiprecision integers using something similar to |
| 633 | * Karatsuba's multiplication algorithm. This is rather faster |
| 634 | * than traditional long multiplication (e.g., @mpx_umul@) on |
| 635 | * large numbers, although more expensive on small ones, and |
| 636 | * rather simpler than full-blown Karatsuba multiplication. |
| 637 | * |
| 638 | * The destination must be twice as large as the argument. The |
| 639 | * scratch space must be twice as large as the argument, plus |
| 640 | * the magic number @MPK_SLOP@. |
| 641 | */ |
| 642 | |
| 643 | extern void mpx_ksqr(mpw */*dv*/, mpw */*dvl*/, |
| 644 | const mpw */*av*/, const mpw */*avl*/, |
| 645 | mpw */*sv*/, mpw */*svl*/); |
| 646 | |
| 647 | /*----- That's all, folks -------------------------------------------------*/ |
| 648 | |
| 649 | #ifdef __cplusplus |
| 650 | } |
| 651 | #endif |
| 652 | |
| 653 | #endif |