| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mp.h,v 1.7 2000/06/17 11:45:09 mdw Exp $ |
| 4 | * |
| 5 | * Simple 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: mp.h,v $ |
| 33 | * Revision 1.7 2000/06/17 11:45:09 mdw |
| 34 | * Major memory management overhaul. Added arena support. Use the secure |
| 35 | * arena for secret integers. Replace and improve the MP management macros |
| 36 | * (e.g., replace MP_MODIFY by MP_DEST). |
| 37 | * |
| 38 | * Revision 1.6 1999/12/10 23:19:46 mdw |
| 39 | * Minor bugfixes. New interface for suggested destinations. |
| 40 | * |
| 41 | * Revision 1.5 1999/11/22 20:50:37 mdw |
| 42 | * Add support for computing Jacobi symbols. |
| 43 | * |
| 44 | * Revision 1.4 1999/11/21 22:13:02 mdw |
| 45 | * Add mp version of MPX_BITS. |
| 46 | * |
| 47 | * Revision 1.3 1999/11/19 13:19:14 mdw |
| 48 | * Fix const annotation. |
| 49 | * |
| 50 | * Revision 1.2 1999/11/17 18:02:16 mdw |
| 51 | * New multiprecision integer arithmetic suite. |
| 52 | * |
| 53 | */ |
| 54 | |
| 55 | #ifndef CATACOMB_MP_H |
| 56 | #define CATACOMB_MP_H |
| 57 | |
| 58 | #ifdef __cplusplus |
| 59 | extern "C" { |
| 60 | #endif |
| 61 | |
| 62 | /*----- Header files ------------------------------------------------------*/ |
| 63 | |
| 64 | #include <assert.h> |
| 65 | #include <string.h> |
| 66 | |
| 67 | #include <mLib/sub.h> |
| 68 | |
| 69 | #ifndef CATACOMB_MPW_H |
| 70 | # include "mpw.h" |
| 71 | #endif |
| 72 | |
| 73 | #ifndef CATACOMB_ARENA_H |
| 74 | # include "arena.h" |
| 75 | #endif |
| 76 | |
| 77 | #ifndef CATACOMB_MPARENA_H |
| 78 | # include "mparena.h" |
| 79 | #endif |
| 80 | |
| 81 | #ifndef CATACOMB_MPX_H |
| 82 | # include "mpx.h" |
| 83 | #endif |
| 84 | |
| 85 | /*----- Data structures ---------------------------------------------------*/ |
| 86 | |
| 87 | typedef struct mp { |
| 88 | mpw *v, *vl; |
| 89 | size_t sz; |
| 90 | mparena *a; |
| 91 | unsigned f; |
| 92 | unsigned ref; |
| 93 | } mp; |
| 94 | |
| 95 | #define MP_NEG 1u |
| 96 | #define MP_BURN 2u |
| 97 | #define MP_CONST 4u |
| 98 | #define MP_UNDEF 8u |
| 99 | #define MP_DESTROYED 16u |
| 100 | |
| 101 | /*----- Useful constants --------------------------------------------------*/ |
| 102 | |
| 103 | extern mp mp_const[]; |
| 104 | |
| 105 | #define MP_ZERO (&mp_const[0]) |
| 106 | #define MP_ONE (&mp_const[1]) |
| 107 | #define MP_TWO (&mp_const[2]) |
| 108 | #define MP_THREE (&mp_const[3]) |
| 109 | #define MP_FOUR (&mp_const[4]) |
| 110 | #define MP_FIVE (&mp_const[5]) |
| 111 | #define MP_TEN (&mp_const[6]) |
| 112 | #define MP_256 (&mp_const[7]) |
| 113 | #define MP_MONE (&mp_const[8]) |
| 114 | |
| 115 | #define MP_NEW ((mp *)0) |
| 116 | #define MP_NEWSEC (&mp_const[9]) |
| 117 | |
| 118 | /*----- Trivial macros ----------------------------------------------------*/ |
| 119 | |
| 120 | /* --- @MP_LEN@ --- * |
| 121 | * |
| 122 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 123 | * |
| 124 | * Returns: Length of the integer, in words. |
| 125 | */ |
| 126 | |
| 127 | #define MP_LEN(m) ((m)->vl - ((m)->v)) |
| 128 | |
| 129 | /*----- Memory management and reference counting --------------------------*/ |
| 130 | |
| 131 | /* --- @mp_new@ --- * |
| 132 | * |
| 133 | * Arguments: @size_t sz@ = size of vector required |
| 134 | * @unsigned f@ = flags to set |
| 135 | * |
| 136 | * Returns: Pointer to a new MP structure. |
| 137 | * |
| 138 | * Use: Allocates a new multiprecision integer. The data space is |
| 139 | * allocated from either the standard global or secret arena, |
| 140 | * depending on the initial flags requested. |
| 141 | */ |
| 142 | |
| 143 | extern mp *mp_new(size_t /*sz*/, unsigned /*f*/); |
| 144 | |
| 145 | /* --- @mp_create@ --- * |
| 146 | * |
| 147 | * Arguments: @size_t sz@ = size of vector required |
| 148 | * |
| 149 | * Returns: Pointer to pristine new MP structure with enough memory |
| 150 | * bolted onto it. |
| 151 | * |
| 152 | * Use: Creates a new multiprecision integer with indeterminate |
| 153 | * contents. The integer has a single reference. |
| 154 | */ |
| 155 | |
| 156 | extern mp *mp_create(size_t /*sz*/); |
| 157 | |
| 158 | /* --- @mp_createsecure@ --- * |
| 159 | * |
| 160 | * Arguments: @size_t sz@ = size of vector required |
| 161 | * |
| 162 | * Returns: Pointer to pristine new MP structure with enough memory |
| 163 | * bolted onto it. |
| 164 | * |
| 165 | * Use: Creates a new multiprecision integer with indeterminate |
| 166 | * contents. The integer has a single reference. The integer's |
| 167 | * data space is allocated from the secure arena. Its burn flag |
| 168 | * is set. |
| 169 | */ |
| 170 | |
| 171 | extern mp *mp_createsecure(size_t /*sz*/); |
| 172 | |
| 173 | /* --- @mp_build@ --- * |
| 174 | * |
| 175 | * Arguments: @mp *m@ = pointer to an MP block to fill in |
| 176 | * @mpw *v@ = pointer to a word array |
| 177 | * @mpw *vl@ = pointer just past end of array |
| 178 | * |
| 179 | * Returns: --- |
| 180 | * |
| 181 | * Use: Creates a multiprecision integer representing some smallish |
| 182 | * number. You must provide storage for the number and dispose |
| 183 | * of it when you've finished with it. The number is marked as |
| 184 | * constant while it exists. |
| 185 | */ |
| 186 | |
| 187 | extern void mp_build(mp */*m*/, mpw */*v*/, mpw */*vl*/); |
| 188 | |
| 189 | /* --- @mp_destroy@ --- * |
| 190 | * |
| 191 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 192 | * |
| 193 | * Returns: --- |
| 194 | * |
| 195 | * Use: Destroys a multiprecision integer. The reference count isn't |
| 196 | * checked. Don't use this function if you don't know what |
| 197 | * you're doing: use @mp_drop@ instead. |
| 198 | */ |
| 199 | |
| 200 | extern void mp_destroy(mp */*m*/); |
| 201 | |
| 202 | /* --- @mp_copy@ --- * |
| 203 | * |
| 204 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 205 | * |
| 206 | * Returns: A copy of the given multiprecision integer. |
| 207 | * |
| 208 | * Use: Copies the given integer. In fact you just get another |
| 209 | * reference to the same old one again. |
| 210 | */ |
| 211 | |
| 212 | extern mp *mp_copy(mp */*m*/); |
| 213 | |
| 214 | #define MP_COPY(m) ((m)->ref++, (m)) |
| 215 | |
| 216 | /* --- @mp_drop@ --- * |
| 217 | * |
| 218 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 219 | * |
| 220 | * Returns: --- |
| 221 | * |
| 222 | * Use: Drops a reference to an integer which isn't wanted any more. |
| 223 | * If there are no more references, the integer is destroyed. |
| 224 | */ |
| 225 | |
| 226 | extern void mp_drop(mp */*m*/); |
| 227 | |
| 228 | #define MP_DROP(m) do { \ |
| 229 | mp *_mm = (m); \ |
| 230 | _mm->ref--; \ |
| 231 | if (_mm->ref == 0 && !(_mm->f & MP_CONST)) \ |
| 232 | mp_destroy(_mm); \ |
| 233 | } while (0) |
| 234 | |
| 235 | /* --- @mp_split@ --- * |
| 236 | * |
| 237 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 238 | * |
| 239 | * Returns: A reference to the same integer, possibly with a different |
| 240 | * address. |
| 241 | * |
| 242 | * Use: Splits off a modifiable version of the integer referred to. |
| 243 | */ |
| 244 | |
| 245 | extern mp *mp_split(mp */*m*/); |
| 246 | |
| 247 | #define MP_SPLIT(m) do { \ |
| 248 | mp *_m = (m); \ |
| 249 | if ((_m->f & MP_CONST) || _m->ref > 1) { \ |
| 250 | size_t _len = MP_LEN(_m); \ |
| 251 | mp *_mm = mp_new(_len, _m->f); \ |
| 252 | if (!(_m->f & MP_UNDEF)) \ |
| 253 | memcpy(_mm->v, _m->v, MPWS(_len)); \ |
| 254 | _m->ref--; \ |
| 255 | _m = _mm; \ |
| 256 | } \ |
| 257 | (m) = _m; \ |
| 258 | } while (0) |
| 259 | |
| 260 | /* --- @mp_resize@ --- * |
| 261 | * |
| 262 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 263 | * @size_t sz@ = new size |
| 264 | * |
| 265 | * Returns: --- |
| 266 | * |
| 267 | * Use: Resizes the vector containing the integer's digits. The new |
| 268 | * size must be at least as large as the current integer's |
| 269 | * length. This isn't really intended for client use. |
| 270 | */ |
| 271 | |
| 272 | extern void mp_resize(mp */*m*/, size_t /*sz*/); |
| 273 | |
| 274 | #define MP_RESIZE(m, ssz) do { \ |
| 275 | mp *_m = (m); \ |
| 276 | size_t _sz = (ssz); \ |
| 277 | mparena *_a = (_m->f & MP_BURN) ? MPARENA_SECURE : MPARENA_GLOBAL; \ |
| 278 | mpw *_v; \ |
| 279 | size_t _len = MP_LEN(_m); \ |
| 280 | assert(((void)"can't make size less than length", _sz >= _len)); \ |
| 281 | _v = mpalloc(_a, _sz); \ |
| 282 | if (!(_m->f & MP_UNDEF)) \ |
| 283 | memcpy(_v, _m->v, MPWS(_len)); \ |
| 284 | if (_m->f & MP_BURN) \ |
| 285 | memset(_m->v, 0, MPWS(_m->sz)); \ |
| 286 | mpfree(_m->a, _m->v); \ |
| 287 | _m->a = _a; \ |
| 288 | _m->v = _v; \ |
| 289 | _m->vl = _v + _len; \ |
| 290 | } while (0) |
| 291 | |
| 292 | /* --- @mp_ensure@ --- * |
| 293 | * |
| 294 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 295 | * @size_t sz@ = required size |
| 296 | * |
| 297 | * Returns: --- |
| 298 | * |
| 299 | * Use: Ensures that the integer has enough space for @sz@ digits. |
| 300 | * The value is not changed. |
| 301 | */ |
| 302 | |
| 303 | extern void mp_ensure(mp */*m*/, size_t /*sz*/); |
| 304 | |
| 305 | #define MP_ENSURE(m, ssz) do { \ |
| 306 | mp *_m = (m); \ |
| 307 | size_t _ssz = (ssz); \ |
| 308 | size_t _len = MP_LEN(_m); \ |
| 309 | if (_ssz >= _len) { \ |
| 310 | if (_ssz > _m->sz) \ |
| 311 | mp_resize(_m, _ssz); \ |
| 312 | if (!(_m->f & MP_UNDEF) && _ssz > _len) \ |
| 313 | memset(_m->vl, 0, MPWS(_ssz - _len)); \ |
| 314 | _m->vl = _m->v + _ssz; \ |
| 315 | } \ |
| 316 | } while (0) |
| 317 | |
| 318 | /* --- @mp_dest@ --- * |
| 319 | * |
| 320 | * Arguments: @mp *m@ = a suggested destination integer |
| 321 | * @size_t sz@ = size required for result, in digits |
| 322 | * @unsigned f@ = various flags |
| 323 | * |
| 324 | * Returns: A pointer to an appropriate destination. |
| 325 | * |
| 326 | * Use: Converts a suggested destination into a real destination with |
| 327 | * the required properties. If the real destination is @d@, |
| 328 | * then the following properties will hold: |
| 329 | * |
| 330 | * * @d@ will have exactly one reference. |
| 331 | * |
| 332 | * * If @m@ is not @MP_NEW@, then the contents of @m@ will not |
| 333 | * change, unless @f@ has the @MP_UNDEF@ flag set. |
| 334 | * |
| 335 | * * If @m@ is not @MP_NEW@, then he reference count of @m@ on |
| 336 | * entry is equal to the sum of the counts of @d@ and @m@ on |
| 337 | * exit. |
| 338 | * |
| 339 | * * The size of @d@ will be at least @sz@. |
| 340 | * |
| 341 | * * If @f@ has the @MP_BURN@ flag set, then @d@ will be |
| 342 | * allocated from @MPARENA_SECURE@. |
| 343 | * |
| 344 | * Understanding this function is crucial to using Catacomb's |
| 345 | * multiprecision integer library effectively. |
| 346 | */ |
| 347 | |
| 348 | extern mp *mp_dest(mp */*m*/, size_t /*sz*/, unsigned /*f*/); |
| 349 | |
| 350 | #define MP_DEST(m, ssz, f) do { \ |
| 351 | mp *_m = (m); \ |
| 352 | size_t _ssz = (ssz); \ |
| 353 | unsigned _f = (f); \ |
| 354 | _m = mp_dest(_m, _ssz, _f); \ |
| 355 | (m) = _m; \ |
| 356 | } while (0) |
| 357 | |
| 358 | /*----- Size manipulation -------------------------------------------------*/ |
| 359 | |
| 360 | /* --- @mp_shrink@ --- * |
| 361 | * |
| 362 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 363 | * |
| 364 | * Returns: --- |
| 365 | * |
| 366 | * Use: Reduces the recorded length of an integer. This doesn't |
| 367 | * reduce the amount of memory used, although it can improve |
| 368 | * performance a bit. To reduce memory, use @mp_minimize@ |
| 369 | * instead. This can't change the value of an integer, and is |
| 370 | * therefore safe to use even when there are multiple |
| 371 | * references. |
| 372 | */ |
| 373 | |
| 374 | extern void mp_shrink(mp */*m*/); |
| 375 | |
| 376 | #define MP_SHRINK(m) do { \ |
| 377 | mp *_mm = (m); \ |
| 378 | MPX_SHRINK(_mm->v, _mm->vl); \ |
| 379 | if (!MP_LEN(_mm)) \ |
| 380 | _mm->f &= ~MP_NEG; \ |
| 381 | } while (0) |
| 382 | |
| 383 | /* --- @mp_minimize@ --- * |
| 384 | * |
| 385 | * Arguments: @mp *m@ = pointer to a multiprecision integer |
| 386 | * |
| 387 | * Returns: --- |
| 388 | * |
| 389 | * Use: Reduces the amount of memory an integer uses. It's best to |
| 390 | * do this to numbers which aren't going to change in the |
| 391 | * future. |
| 392 | */ |
| 393 | |
| 394 | extern void mp_minimize(mp */*m*/); |
| 395 | |
| 396 | /*----- Bit scanning ------------------------------------------------------*/ |
| 397 | |
| 398 | #ifndef CATACOMB_MPSCAN_H |
| 399 | # include "mpscan.h" |
| 400 | #endif |
| 401 | |
| 402 | /* --- @mp_scan@ --- * |
| 403 | * |
| 404 | * Arguments: @mpscan *sc@ = pointer to bitscanner block |
| 405 | * @const mp *m@ = pointer to a multiprecision integer |
| 406 | * |
| 407 | * Returns: --- |
| 408 | * |
| 409 | * Use: Initializes a bitscanner on a multiprecision integer. |
| 410 | */ |
| 411 | |
| 412 | extern void mp_scan(mpscan */*sc*/, const mp */*m*/); |
| 413 | |
| 414 | #define MP_SCAN(sc, m) do { \ |
| 415 | const mp *_mm = (m); \ |
| 416 | mpscan *_sc = (sc); \ |
| 417 | MPSCAN_INITX(_sc, _mm->v, _mm->vl); \ |
| 418 | } while (0) |
| 419 | |
| 420 | /* --- Other bitscanning aliases --- */ |
| 421 | |
| 422 | #define mp_step mpscan_step |
| 423 | #define mp_bit mpscan_bit |
| 424 | |
| 425 | #define MP_STEP MPSCAN_STEP |
| 426 | #define MP_BIT MPSCAN_BIT |
| 427 | |
| 428 | /*----- Loading and storing -----------------------------------------------*/ |
| 429 | |
| 430 | /* --- @mp_octets@ --- * |
| 431 | * |
| 432 | * Arguments: @const mp *m@ = a multiprecision integer |
| 433 | * |
| 434 | * Returns: The number of octets required to represent @m@. |
| 435 | * |
| 436 | * Use: Calculates the external storage required for a multiprecision |
| 437 | * integer. |
| 438 | */ |
| 439 | |
| 440 | extern size_t mp_octets(const mp */*m*/); |
| 441 | |
| 442 | /* --- @mp_bits@ --- * |
| 443 | * |
| 444 | * Arguments: @const mp *m@ = a multiprecision integer |
| 445 | * |
| 446 | * Returns: The number of bits required to represent @m@. |
| 447 | * |
| 448 | * Use: Calculates the external storage required for a multiprecision |
| 449 | * integer. |
| 450 | */ |
| 451 | |
| 452 | extern unsigned long mp_bits(const mp */*m*/); |
| 453 | |
| 454 | /* --- @mp_loadl@ --- * |
| 455 | * |
| 456 | * Arguments: @mp *d@ = destination |
| 457 | * @const void *pv@ = pointer to source data |
| 458 | * @size_t sz@ = size of the source data |
| 459 | * |
| 460 | * Returns: Resulting multiprecision number. |
| 461 | * |
| 462 | * Use: Loads a multiprecision number from an array of octets. The |
| 463 | * first byte in the array is the least significant. More |
| 464 | * formally, if the bytes are %$b_0, b_1, \ldots, b_{n-1}$% |
| 465 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
| 466 | */ |
| 467 | |
| 468 | extern mp *mp_loadl(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
| 469 | |
| 470 | /* --- @mp_storel@ --- * |
| 471 | * |
| 472 | * Arguments: @const mp *m@ = source |
| 473 | * @void *pv@ = pointer to output array |
| 474 | * @size_t sz@ = size of the output array |
| 475 | * |
| 476 | * Returns: --- |
| 477 | * |
| 478 | * Use: Stores a multiprecision number in an array of octets. The |
| 479 | * first byte in the array is the least significant. If the |
| 480 | * array is too small to represent the number, high-order bits |
| 481 | * are truncated; if the array is too large, high order bytes |
| 482 | * are filled with zeros. More formally, if the number is |
| 483 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
| 484 | * then the array is %$b_0, b_1, \ldots, b_{n-1}$%. |
| 485 | */ |
| 486 | |
| 487 | extern void mp_storel(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
| 488 | |
| 489 | /* --- @mp_loadb@ --- * |
| 490 | * |
| 491 | * Arguments: @mp *d@ = destination |
| 492 | * @const void *pv@ = pointer to source data |
| 493 | * @size_t sz@ = size of the source data |
| 494 | * |
| 495 | * Returns: Resulting multiprecision number. |
| 496 | * |
| 497 | * Use: Loads a multiprecision number from an array of octets. The |
| 498 | * last byte in the array is the least significant. More |
| 499 | * formally, if the bytes are %$b_{n-1}, b_{n-2}, \ldots, b_0$% |
| 500 | * then the result is %$N = \sum_{0 \le i < n} b_i 2^{8i}$%. |
| 501 | */ |
| 502 | |
| 503 | extern mp *mp_loadb(mp */*d*/, const void */*pv*/, size_t /*sz*/); |
| 504 | |
| 505 | /* --- @mp_storeb@ --- * |
| 506 | * |
| 507 | * Arguments: @const mp *m@ = source |
| 508 | * @void *pv@ = pointer to output array |
| 509 | * @size_t sz@ = size of the output array |
| 510 | * |
| 511 | * Returns: --- |
| 512 | * |
| 513 | * Use: Stores a multiprecision number in an array of octets. The |
| 514 | * last byte in the array is the least significant. If the |
| 515 | * array is too small to represent the number, high-order bits |
| 516 | * are truncated; if the array is too large, high order bytes |
| 517 | * are filled with zeros. More formally, if the number is |
| 518 | * %$N = \sum{0 \le i} b_i 2^{8i}$% where %$0 \le b_i < 256$%, |
| 519 | * then the array is %$b_{n-1}, b_{n-2}, \ldots, b_0$%. |
| 520 | */ |
| 521 | |
| 522 | extern void mp_storeb(const mp */*m*/, void */*pv*/, size_t /*sz*/); |
| 523 | |
| 524 | /*----- Simple arithmetic -------------------------------------------------*/ |
| 525 | |
| 526 | /* --- @mp_2c@ --- * |
| 527 | * |
| 528 | * Arguments: @mp *d@ = destination |
| 529 | * @mp *a@ = source |
| 530 | * |
| 531 | * Returns: Result, @a@ converted to two's complement notation. |
| 532 | */ |
| 533 | |
| 534 | extern mp *mp_2c(mp */*d*/, mp */*a*/); |
| 535 | |
| 536 | /* --- @mp_sm@ --- * |
| 537 | * |
| 538 | * Arguments: @mp *d@ = destination |
| 539 | * @mp *a@ = source |
| 540 | * |
| 541 | * Returns: Result, @a@ converted to the native signed-magnitude |
| 542 | * notation. |
| 543 | */ |
| 544 | |
| 545 | extern mp *mp_sm(mp */*d*/, mp */*a*/); |
| 546 | |
| 547 | /* --- @mp_lsl@ --- * |
| 548 | * |
| 549 | * Arguments: @mp *d@ = destination |
| 550 | * @mp *a@ = source |
| 551 | * @size_t n@ = number of bits to move |
| 552 | * |
| 553 | * Returns: Result, @a@ shifted left by @n@. |
| 554 | */ |
| 555 | |
| 556 | extern mp *mp_lsl(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 557 | |
| 558 | /* --- @mp_lsr@ --- * |
| 559 | * |
| 560 | * Arguments: @mp *d@ = destination |
| 561 | * @mp *a@ = source |
| 562 | * @size_t n@ = number of bits to move |
| 563 | * |
| 564 | * Returns: Result, @a@ shifted left by @n@. |
| 565 | */ |
| 566 | |
| 567 | extern mp *mp_lsr(mp */*d*/, mp */*a*/, size_t /*n*/); |
| 568 | |
| 569 | /* --- @mp_cmp@ --- * |
| 570 | * |
| 571 | * Arguments: @const mp *a, *b@ = two numbers |
| 572 | * |
| 573 | * Returns: Less than, equal to or greater than zero, according to |
| 574 | * whether @a@ is less than, equal to or greater than @b@. |
| 575 | */ |
| 576 | |
| 577 | extern int mp_cmp(const mp */*a*/, const mp */*b*/); |
| 578 | |
| 579 | #define MP_CMP(a, op, b) (mp_cmp((a), (b)) op 0) |
| 580 | |
| 581 | /* --- @mp_add@ --- * |
| 582 | * |
| 583 | * Arguments: @mp *d@ = destination |
| 584 | * @mp *a, *b@ = sources |
| 585 | * |
| 586 | * Returns: Result, @a@ added to @b@. |
| 587 | */ |
| 588 | |
| 589 | extern mp *mp_add(mp */*d*/, mp */*a*/, mp */*b*/); |
| 590 | |
| 591 | /* --- @mp_sub@ --- * |
| 592 | * |
| 593 | * Arguments: @mp *d@ = destination |
| 594 | * @mp *a, *b@ = sources |
| 595 | * |
| 596 | * Returns: Result, @b@ subtracted from @a@. |
| 597 | */ |
| 598 | |
| 599 | extern mp *mp_sub(mp */*d*/, mp */*a*/, mp */*b*/); |
| 600 | |
| 601 | /* --- @mp_mul@ --- * |
| 602 | * |
| 603 | * Arguments: @mp *d@ = destination |
| 604 | * @mp *a, *b@ = sources |
| 605 | * |
| 606 | * Returns: Result, @a@ multiplied by @b@. |
| 607 | */ |
| 608 | |
| 609 | extern mp *mp_mul(mp */*d*/, mp */*a*/, mp */*b*/); |
| 610 | |
| 611 | /* --- @mp_sqr@ --- * |
| 612 | * |
| 613 | * Arguments: @mp *d@ = destination |
| 614 | * @mp *a@ = source |
| 615 | * |
| 616 | * Returns: Result, @a@ squared. |
| 617 | */ |
| 618 | |
| 619 | extern mp *mp_sqr(mp */*d*/, mp */*a*/); |
| 620 | |
| 621 | /* --- @mp_div@ --- * |
| 622 | * |
| 623 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
| 624 | * @mp *a, *b@ = sources |
| 625 | * |
| 626 | * Use: Calculates the quotient and remainder when @a@ is divided by |
| 627 | * @b@. |
| 628 | */ |
| 629 | |
| 630 | extern void mp_div(mp **/*qq*/, mp **/*rr*/, mp */*a*/, mp */*b*/); |
| 631 | |
| 632 | /*----- More advanced algorithms ------------------------------------------*/ |
| 633 | |
| 634 | /* --- @mp_gcd@ --- * |
| 635 | * |
| 636 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
| 637 | * @mp *a, *b@ = sources (must be nonzero) |
| 638 | * |
| 639 | * Returns: --- |
| 640 | * |
| 641 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
| 642 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
| 643 | * inverses. Neither @a@ nor @b@ may be zero. |
| 644 | */ |
| 645 | |
| 646 | extern void mp_gcd(mp **/*gcd*/, mp **/*xx*/, mp **/*yy*/, |
| 647 | mp */*a*/, mp */*b*/); |
| 648 | |
| 649 | /* --- @mp_jacobi@ --- * |
| 650 | * |
| 651 | * Arguments: @mp *a@ = an integer less than @n@ |
| 652 | * @mp *n@ = an odd integer |
| 653 | * |
| 654 | * Returns: @-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%. |
| 655 | * |
| 656 | * Use: Computes the Jacobi symbol. If @n@ is prime, this is the |
| 657 | * Legendre symbol and is equal to 1 if and only if @a@ is a |
| 658 | * quadratic residue mod @n@. The result is zero if and only if |
| 659 | * @a@ and @n@ have a common factor greater than one. |
| 660 | */ |
| 661 | |
| 662 | int mp_jacobi(mp */*a*/, mp */*n*/); |
| 663 | |
| 664 | /*----- Test harness support ----------------------------------------------*/ |
| 665 | |
| 666 | #include <mLib/testrig.h> |
| 667 | |
| 668 | #ifndef CATACOMB_MPTEXT_H |
| 669 | # include "mptext.h" |
| 670 | #endif |
| 671 | |
| 672 | extern const test_type type_mp; |
| 673 | |
| 674 | /*----- That's all, folks -------------------------------------------------*/ |
| 675 | |
| 676 | #ifdef __cplusplus |
| 677 | } |
| 678 | #endif |
| 679 | |
| 680 | #endif |