| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id$ |
| 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 | /*----- Header files ------------------------------------------------------*/ |
| 31 | |
| 32 | #include <assert.h> |
| 33 | #include <stdio.h> |
| 34 | #include <stdlib.h> |
| 35 | #include <string.h> |
| 36 | |
| 37 | #include <mLib/bits.h> |
| 38 | |
| 39 | #include "mptypes.h" |
| 40 | #include "mpx.h" |
| 41 | #include "bitops.h" |
| 42 | |
| 43 | /*----- Loading and storing -----------------------------------------------*/ |
| 44 | |
| 45 | /* --- @mpx_storel@ --- * |
| 46 | * |
| 47 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 48 | * @void *pp@ = pointer to octet array |
| 49 | * @size_t sz@ = size of octet array |
| 50 | * |
| 51 | * Returns: --- |
| 52 | * |
| 53 | * Use: Stores an MP in an octet array, least significant octet |
| 54 | * first. High-end octets are silently discarded if there |
| 55 | * isn't enough space for them. |
| 56 | */ |
| 57 | |
| 58 | void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz) |
| 59 | { |
| 60 | mpw n, w = 0; |
| 61 | octet *p = pp, *q = p + sz; |
| 62 | unsigned bits = 0; |
| 63 | |
| 64 | while (p < q) { |
| 65 | if (bits < 8) { |
| 66 | if (v >= vl) { |
| 67 | *p++ = U8(w); |
| 68 | break; |
| 69 | } |
| 70 | n = *v++; |
| 71 | *p++ = U8(w | n << bits); |
| 72 | w = n >> (8 - bits); |
| 73 | bits += MPW_BITS - 8; |
| 74 | } else { |
| 75 | *p++ = U8(w); |
| 76 | w >>= 8; |
| 77 | bits -= 8; |
| 78 | } |
| 79 | } |
| 80 | memset(p, 0, q - p); |
| 81 | } |
| 82 | |
| 83 | /* --- @mpx_loadl@ --- * |
| 84 | * |
| 85 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 86 | * @const void *pp@ = pointer to octet array |
| 87 | * @size_t sz@ = size of octet array |
| 88 | * |
| 89 | * Returns: --- |
| 90 | * |
| 91 | * Use: Loads an MP in an octet array, least significant octet |
| 92 | * first. High-end octets are ignored if there isn't enough |
| 93 | * space for them. |
| 94 | */ |
| 95 | |
| 96 | void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz) |
| 97 | { |
| 98 | unsigned n; |
| 99 | mpw w = 0; |
| 100 | const octet *p = pp, *q = p + sz; |
| 101 | unsigned bits = 0; |
| 102 | |
| 103 | if (v >= vl) |
| 104 | return; |
| 105 | while (p < q) { |
| 106 | n = U8(*p++); |
| 107 | w |= n << bits; |
| 108 | bits += 8; |
| 109 | if (bits >= MPW_BITS) { |
| 110 | *v++ = MPW(w); |
| 111 | w = n >> (MPW_BITS - bits + 8); |
| 112 | bits -= MPW_BITS; |
| 113 | if (v >= vl) |
| 114 | return; |
| 115 | } |
| 116 | } |
| 117 | *v++ = w; |
| 118 | MPX_ZERO(v, vl); |
| 119 | } |
| 120 | |
| 121 | /* --- @mpx_storeb@ --- * |
| 122 | * |
| 123 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 124 | * @void *pp@ = pointer to octet array |
| 125 | * @size_t sz@ = size of octet array |
| 126 | * |
| 127 | * Returns: --- |
| 128 | * |
| 129 | * Use: Stores an MP in an octet array, most significant octet |
| 130 | * first. High-end octets are silently discarded if there |
| 131 | * isn't enough space for them. |
| 132 | */ |
| 133 | |
| 134 | void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz) |
| 135 | { |
| 136 | mpw n, w = 0; |
| 137 | octet *p = pp, *q = p + sz; |
| 138 | unsigned bits = 0; |
| 139 | |
| 140 | while (q > p) { |
| 141 | if (bits < 8) { |
| 142 | if (v >= vl) { |
| 143 | *--q = U8(w); |
| 144 | break; |
| 145 | } |
| 146 | n = *v++; |
| 147 | *--q = U8(w | n << bits); |
| 148 | w = n >> (8 - bits); |
| 149 | bits += MPW_BITS - 8; |
| 150 | } else { |
| 151 | *--q = U8(w); |
| 152 | w >>= 8; |
| 153 | bits -= 8; |
| 154 | } |
| 155 | } |
| 156 | memset(p, 0, q - p); |
| 157 | } |
| 158 | |
| 159 | /* --- @mpx_loadb@ --- * |
| 160 | * |
| 161 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 162 | * @const void *pp@ = pointer to octet array |
| 163 | * @size_t sz@ = size of octet array |
| 164 | * |
| 165 | * Returns: --- |
| 166 | * |
| 167 | * Use: Loads an MP in an octet array, most significant octet |
| 168 | * first. High-end octets are ignored if there isn't enough |
| 169 | * space for them. |
| 170 | */ |
| 171 | |
| 172 | void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz) |
| 173 | { |
| 174 | unsigned n; |
| 175 | mpw w = 0; |
| 176 | const octet *p = pp, *q = p + sz; |
| 177 | unsigned bits = 0; |
| 178 | |
| 179 | if (v >= vl) |
| 180 | return; |
| 181 | while (q > p) { |
| 182 | n = U8(*--q); |
| 183 | w |= n << bits; |
| 184 | bits += 8; |
| 185 | if (bits >= MPW_BITS) { |
| 186 | *v++ = MPW(w); |
| 187 | w = n >> (MPW_BITS - bits + 8); |
| 188 | bits -= MPW_BITS; |
| 189 | if (v >= vl) |
| 190 | return; |
| 191 | } |
| 192 | } |
| 193 | *v++ = w; |
| 194 | MPX_ZERO(v, vl); |
| 195 | } |
| 196 | |
| 197 | /* --- @mpx_storel2cn@ --- * |
| 198 | * |
| 199 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 200 | * @void *pp@ = pointer to octet array |
| 201 | * @size_t sz@ = size of octet array |
| 202 | * |
| 203 | * Returns: --- |
| 204 | * |
| 205 | * Use: Stores a negative MP in an octet array, least significant |
| 206 | * octet first, as two's complement. High-end octets are |
| 207 | * silently discarded if there isn't enough space for them. |
| 208 | * This obviously makes the output bad. |
| 209 | */ |
| 210 | |
| 211 | void mpx_storel2cn(const mpw *v, const mpw *vl, void *pp, size_t sz) |
| 212 | { |
| 213 | unsigned c = 1; |
| 214 | unsigned b = 0; |
| 215 | mpw n, w = 0; |
| 216 | octet *p = pp, *q = p + sz; |
| 217 | unsigned bits = 0; |
| 218 | |
| 219 | while (p < q) { |
| 220 | if (bits < 8) { |
| 221 | if (v >= vl) { |
| 222 | b = w; |
| 223 | break; |
| 224 | } |
| 225 | n = *v++; |
| 226 | b = w | n << bits; |
| 227 | w = n >> (8 - bits); |
| 228 | bits += MPW_BITS - 8; |
| 229 | } else { |
| 230 | b = w; |
| 231 | w >>= 8; |
| 232 | bits -= 8; |
| 233 | } |
| 234 | b = U8(~b + c); |
| 235 | c = c && !b; |
| 236 | *p++ = b; |
| 237 | } |
| 238 | while (p < q) { |
| 239 | b = U8(~b + c); |
| 240 | c = c && !b; |
| 241 | *p++ = b; |
| 242 | b = 0; |
| 243 | } |
| 244 | } |
| 245 | |
| 246 | /* --- @mpx_loadl2cn@ --- * |
| 247 | * |
| 248 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 249 | * @const void *pp@ = pointer to octet array |
| 250 | * @size_t sz@ = size of octet array |
| 251 | * |
| 252 | * Returns: --- |
| 253 | * |
| 254 | * Use: Loads a negative MP in an octet array, least significant |
| 255 | * octet first, as two's complement. High-end octets are |
| 256 | * ignored if there isn't enough space for them. This probably |
| 257 | * means you made the wrong choice coming here. |
| 258 | */ |
| 259 | |
| 260 | void mpx_loadl2cn(mpw *v, mpw *vl, const void *pp, size_t sz) |
| 261 | { |
| 262 | unsigned n; |
| 263 | unsigned c = 1; |
| 264 | mpw w = 0; |
| 265 | const octet *p = pp, *q = p + sz; |
| 266 | unsigned bits = 0; |
| 267 | |
| 268 | if (v >= vl) |
| 269 | return; |
| 270 | while (p < q) { |
| 271 | n = U8(~(*p++) + c); |
| 272 | c = c && !n; |
| 273 | w |= n << bits; |
| 274 | bits += 8; |
| 275 | if (bits >= MPW_BITS) { |
| 276 | *v++ = MPW(w); |
| 277 | w = n >> (MPW_BITS - bits + 8); |
| 278 | bits -= MPW_BITS; |
| 279 | if (v >= vl) |
| 280 | return; |
| 281 | } |
| 282 | } |
| 283 | *v++ = w; |
| 284 | MPX_ZERO(v, vl); |
| 285 | } |
| 286 | |
| 287 | /* --- @mpx_storeb2cn@ --- * |
| 288 | * |
| 289 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 290 | * @void *pp@ = pointer to octet array |
| 291 | * @size_t sz@ = size of octet array |
| 292 | * |
| 293 | * Returns: --- |
| 294 | * |
| 295 | * Use: Stores a negative MP in an octet array, most significant |
| 296 | * octet first, as two's complement. High-end octets are |
| 297 | * silently discarded if there isn't enough space for them, |
| 298 | * which probably isn't what you meant. |
| 299 | */ |
| 300 | |
| 301 | void mpx_storeb2cn(const mpw *v, const mpw *vl, void *pp, size_t sz) |
| 302 | { |
| 303 | mpw n, w = 0; |
| 304 | unsigned b = 0; |
| 305 | unsigned c = 1; |
| 306 | octet *p = pp, *q = p + sz; |
| 307 | unsigned bits = 0; |
| 308 | |
| 309 | while (q > p) { |
| 310 | if (bits < 8) { |
| 311 | if (v >= vl) { |
| 312 | b = w; |
| 313 | break; |
| 314 | } |
| 315 | n = *v++; |
| 316 | b = w | n << bits; |
| 317 | w = n >> (8 - bits); |
| 318 | bits += MPW_BITS - 8; |
| 319 | } else { |
| 320 | b = w; |
| 321 | w >>= 8; |
| 322 | bits -= 8; |
| 323 | } |
| 324 | b = U8(~b + c); |
| 325 | c = c && !b; |
| 326 | *--q = b; |
| 327 | } |
| 328 | while (q > p) { |
| 329 | b = ~b + c; |
| 330 | c = c && !(b & 0xff); |
| 331 | *--q = b; |
| 332 | b = 0; |
| 333 | } |
| 334 | } |
| 335 | |
| 336 | /* --- @mpx_loadb2cn@ --- * |
| 337 | * |
| 338 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 339 | * @const void *pp@ = pointer to octet array |
| 340 | * @size_t sz@ = size of octet array |
| 341 | * |
| 342 | * Returns: --- |
| 343 | * |
| 344 | * Use: Loads a negative MP in an octet array, most significant octet |
| 345 | * first as two's complement. High-end octets are ignored if |
| 346 | * there isn't enough space for them. This probably means you |
| 347 | * chose this function wrongly. |
| 348 | */ |
| 349 | |
| 350 | void mpx_loadb2cn(mpw *v, mpw *vl, const void *pp, size_t sz) |
| 351 | { |
| 352 | unsigned n; |
| 353 | unsigned c = 1; |
| 354 | mpw w = 0; |
| 355 | const octet *p = pp, *q = p + sz; |
| 356 | unsigned bits = 0; |
| 357 | |
| 358 | if (v >= vl) |
| 359 | return; |
| 360 | while (q > p) { |
| 361 | n = U8(~(*--q) + c); |
| 362 | c = c && !n; |
| 363 | w |= n << bits; |
| 364 | bits += 8; |
| 365 | if (bits >= MPW_BITS) { |
| 366 | *v++ = MPW(w); |
| 367 | w = n >> (MPW_BITS - bits + 8); |
| 368 | bits -= MPW_BITS; |
| 369 | if (v >= vl) |
| 370 | return; |
| 371 | } |
| 372 | } |
| 373 | *v++ = w; |
| 374 | MPX_ZERO(v, vl); |
| 375 | } |
| 376 | |
| 377 | /*----- Logical shifting --------------------------------------------------*/ |
| 378 | |
| 379 | /* --- @mpx_lsl@ --- * |
| 380 | * |
| 381 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 382 | * @const mpw *av, *avl@ = source vector base and limit |
| 383 | * @size_t n@ = number of bit positions to shift by |
| 384 | * |
| 385 | * Returns: --- |
| 386 | * |
| 387 | * Use: Performs a logical shift left operation on an integer. |
| 388 | */ |
| 389 | |
| 390 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
| 391 | { |
| 392 | size_t nw; |
| 393 | unsigned nb; |
| 394 | |
| 395 | /* --- Trivial special case --- */ |
| 396 | |
| 397 | if (n == 0) |
| 398 | MPX_COPY(dv, dvl, av, avl); |
| 399 | |
| 400 | /* --- Single bit shifting --- */ |
| 401 | |
| 402 | else if (n == 1) { |
| 403 | mpw w = 0; |
| 404 | while (av < avl) { |
| 405 | mpw t; |
| 406 | if (dv >= dvl) |
| 407 | goto done; |
| 408 | t = *av++; |
| 409 | *dv++ = MPW((t << 1) | w); |
| 410 | w = t >> (MPW_BITS - 1); |
| 411 | } |
| 412 | if (dv >= dvl) |
| 413 | goto done; |
| 414 | *dv++ = MPW(w); |
| 415 | MPX_ZERO(dv, dvl); |
| 416 | goto done; |
| 417 | } |
| 418 | |
| 419 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
| 420 | |
| 421 | nw = n / MPW_BITS; |
| 422 | nb = n % MPW_BITS; |
| 423 | |
| 424 | /* --- Handle a shift by a multiple of the word size --- */ |
| 425 | |
| 426 | if (nb == 0) { |
| 427 | if (nw >= dvl - dv) |
| 428 | MPX_ZERO(dv, dvl); |
| 429 | else { |
| 430 | MPX_COPY(dv + nw, dvl, av, avl); |
| 431 | memset(dv, 0, MPWS(nw)); |
| 432 | } |
| 433 | } |
| 434 | |
| 435 | /* --- And finally the difficult case --- * |
| 436 | * |
| 437 | * This is a little convoluted, because I have to start from the end and |
| 438 | * work backwards to avoid overwriting the source, if they're both the same |
| 439 | * block of memory. |
| 440 | */ |
| 441 | |
| 442 | else { |
| 443 | mpw w; |
| 444 | size_t nr = MPW_BITS - nb; |
| 445 | size_t dvn = dvl - dv; |
| 446 | size_t avn = avl - av; |
| 447 | |
| 448 | if (dvn <= nw) { |
| 449 | MPX_ZERO(dv, dvl); |
| 450 | goto done; |
| 451 | } |
| 452 | |
| 453 | if (dvn > avn + nw) { |
| 454 | size_t off = avn + nw + 1; |
| 455 | MPX_ZERO(dv + off, dvl); |
| 456 | dvl = dv + off; |
| 457 | w = 0; |
| 458 | } else { |
| 459 | avl = av + dvn - nw; |
| 460 | w = *--avl << nb; |
| 461 | } |
| 462 | |
| 463 | while (avl > av) { |
| 464 | mpw t = *--avl; |
| 465 | *--dvl = (t >> nr) | w; |
| 466 | w = t << nb; |
| 467 | } |
| 468 | |
| 469 | *--dvl = w; |
| 470 | MPX_ZERO(dv, dvl); |
| 471 | } |
| 472 | |
| 473 | done:; |
| 474 | } |
| 475 | |
| 476 | /* --- @mpx_lslc@ --- * |
| 477 | * |
| 478 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 479 | * @const mpw *av, *avl@ = source vector base and limit |
| 480 | * @size_t n@ = number of bit positions to shift by |
| 481 | * |
| 482 | * Returns: --- |
| 483 | * |
| 484 | * Use: Performs a logical shift left operation on an integer, only |
| 485 | * it fills in the bits with ones instead of zeroes. |
| 486 | */ |
| 487 | |
| 488 | void mpx_lslc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
| 489 | { |
| 490 | size_t nw; |
| 491 | unsigned nb; |
| 492 | |
| 493 | /* --- Trivial special case --- */ |
| 494 | |
| 495 | if (n == 0) |
| 496 | MPX_COPY(dv, dvl, av, avl); |
| 497 | |
| 498 | /* --- Single bit shifting --- */ |
| 499 | |
| 500 | else if (n == 1) { |
| 501 | mpw w = 1; |
| 502 | while (av < avl) { |
| 503 | mpw t; |
| 504 | if (dv >= dvl) |
| 505 | goto done; |
| 506 | t = *av++; |
| 507 | *dv++ = MPW((t << 1) | w); |
| 508 | w = t >> (MPW_BITS - 1); |
| 509 | } |
| 510 | if (dv >= dvl) |
| 511 | goto done; |
| 512 | *dv++ = MPW(w); |
| 513 | MPX_ZERO(dv, dvl); |
| 514 | goto done; |
| 515 | } |
| 516 | |
| 517 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
| 518 | |
| 519 | nw = n / MPW_BITS; |
| 520 | nb = n % MPW_BITS; |
| 521 | |
| 522 | /* --- Handle a shift by a multiple of the word size --- */ |
| 523 | |
| 524 | if (nb == 0) { |
| 525 | if (nw >= dvl - dv) |
| 526 | MPX_ONE(dv, dvl); |
| 527 | else { |
| 528 | MPX_COPY(dv + nw, dvl, av, avl); |
| 529 | MPX_ONE(dv, dv + nw); |
| 530 | } |
| 531 | } |
| 532 | |
| 533 | /* --- And finally the difficult case --- * |
| 534 | * |
| 535 | * This is a little convoluted, because I have to start from the end and |
| 536 | * work backwards to avoid overwriting the source, if they're both the same |
| 537 | * block of memory. |
| 538 | */ |
| 539 | |
| 540 | else { |
| 541 | mpw w; |
| 542 | size_t nr = MPW_BITS - nb; |
| 543 | size_t dvn = dvl - dv; |
| 544 | size_t avn = avl - av; |
| 545 | |
| 546 | if (dvn <= nw) { |
| 547 | MPX_ONE(dv, dvl); |
| 548 | goto done; |
| 549 | } |
| 550 | |
| 551 | if (dvn > avn + nw) { |
| 552 | size_t off = avn + nw + 1; |
| 553 | MPX_ZERO(dv + off, dvl); |
| 554 | dvl = dv + off; |
| 555 | w = 0; |
| 556 | } else { |
| 557 | avl = av + dvn - nw; |
| 558 | w = *--avl << nb; |
| 559 | } |
| 560 | |
| 561 | while (avl > av) { |
| 562 | mpw t = *--avl; |
| 563 | *--dvl = (t >> nr) | w; |
| 564 | w = t << nb; |
| 565 | } |
| 566 | |
| 567 | *--dvl = (MPW_MAX >> nr) | w; |
| 568 | MPX_ONE(dv, dvl); |
| 569 | } |
| 570 | |
| 571 | done:; |
| 572 | } |
| 573 | |
| 574 | /* --- @mpx_lsr@ --- * |
| 575 | * |
| 576 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 577 | * @const mpw *av, *avl@ = source vector base and limit |
| 578 | * @size_t n@ = number of bit positions to shift by |
| 579 | * |
| 580 | * Returns: --- |
| 581 | * |
| 582 | * Use: Performs a logical shift right operation on an integer. |
| 583 | */ |
| 584 | |
| 585 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
| 586 | { |
| 587 | size_t nw; |
| 588 | unsigned nb; |
| 589 | |
| 590 | /* --- Trivial special case --- */ |
| 591 | |
| 592 | if (n == 0) |
| 593 | MPX_COPY(dv, dvl, av, avl); |
| 594 | |
| 595 | /* --- Single bit shifting --- */ |
| 596 | |
| 597 | else if (n == 1) { |
| 598 | mpw w = av < avl ? *av++ >> 1 : 0; |
| 599 | while (av < avl) { |
| 600 | mpw t; |
| 601 | if (dv >= dvl) |
| 602 | goto done; |
| 603 | t = *av++; |
| 604 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
| 605 | w = t >> 1; |
| 606 | } |
| 607 | if (dv >= dvl) |
| 608 | goto done; |
| 609 | *dv++ = MPW(w); |
| 610 | MPX_ZERO(dv, dvl); |
| 611 | goto done; |
| 612 | } |
| 613 | |
| 614 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
| 615 | |
| 616 | nw = n / MPW_BITS; |
| 617 | nb = n % MPW_BITS; |
| 618 | |
| 619 | /* --- Handle a shift by a multiple of the word size --- */ |
| 620 | |
| 621 | if (nb == 0) { |
| 622 | if (nw >= avl - av) |
| 623 | MPX_ZERO(dv, dvl); |
| 624 | else |
| 625 | MPX_COPY(dv, dvl, av + nw, avl); |
| 626 | } |
| 627 | |
| 628 | /* --- And finally the difficult case --- */ |
| 629 | |
| 630 | else { |
| 631 | mpw w; |
| 632 | size_t nr = MPW_BITS - nb; |
| 633 | |
| 634 | av += nw; |
| 635 | w = av < avl ? *av++ : 0; |
| 636 | while (av < avl) { |
| 637 | mpw t; |
| 638 | if (dv >= dvl) |
| 639 | goto done; |
| 640 | t = *av++; |
| 641 | *dv++ = MPW((w >> nb) | (t << nr)); |
| 642 | w = t; |
| 643 | } |
| 644 | if (dv < dvl) { |
| 645 | *dv++ = MPW(w >> nb); |
| 646 | MPX_ZERO(dv, dvl); |
| 647 | } |
| 648 | } |
| 649 | |
| 650 | done:; |
| 651 | } |
| 652 | |
| 653 | /*----- Bitwise operations ------------------------------------------------*/ |
| 654 | |
| 655 | /* --- @mpx_bitop@ --- * |
| 656 | * |
| 657 | * Arguments: @mpw *dv, *dvl@ = destination vector |
| 658 | * @const mpw *av, *avl@ = first source vector |
| 659 | * @const mpw *bv, *bvl@ = second source vector |
| 660 | * |
| 661 | * Returns: --- |
| 662 | * |
| 663 | * Use; Provides the dyadic boolean functions. |
| 664 | */ |
| 665 | |
| 666 | #define MPX_BITBINOP(string) \ |
| 667 | \ |
| 668 | void mpx_bit##string(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, \ |
| 669 | const mpw *bv, const mpw *bvl) \ |
| 670 | { \ |
| 671 | MPX_SHRINK(av, avl); \ |
| 672 | MPX_SHRINK(bv, bvl); \ |
| 673 | \ |
| 674 | while (dv < dvl) { \ |
| 675 | mpw a, b; \ |
| 676 | a = (av < avl) ? *av++ : 0; \ |
| 677 | b = (bv < bvl) ? *bv++ : 0; \ |
| 678 | *dv++ = B##string(a, b); \ |
| 679 | } \ |
| 680 | } |
| 681 | |
| 682 | MPX_DOBIN(MPX_BITBINOP) |
| 683 | |
| 684 | void mpx_not(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
| 685 | { |
| 686 | MPX_SHRINK(av, avl); |
| 687 | |
| 688 | while (dv < dvl) { |
| 689 | mpw a; |
| 690 | a = (av < avl) ? *av++ : 0; |
| 691 | *dv++ = ~a; |
| 692 | } |
| 693 | } |
| 694 | |
| 695 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
| 696 | |
| 697 | /* --- @mpx_2c@ --- * |
| 698 | * |
| 699 | * Arguments: @mpw *dv, *dvl@ = destination vector |
| 700 | * @const mpw *v, *vl@ = source vector |
| 701 | * |
| 702 | * Returns: --- |
| 703 | * |
| 704 | * Use: Calculates the two's complement of @v@. |
| 705 | */ |
| 706 | |
| 707 | void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl) |
| 708 | { |
| 709 | mpw c = 0; |
| 710 | while (dv < dvl && v < vl) |
| 711 | *dv++ = c = MPW(~*v++); |
| 712 | if (dv < dvl) { |
| 713 | if (c > MPW_MAX / 2) |
| 714 | c = MPW(~0); |
| 715 | while (dv < dvl) |
| 716 | *dv++ = c; |
| 717 | } |
| 718 | MPX_UADDN(dv, dvl, 1); |
| 719 | } |
| 720 | |
| 721 | /* --- @mpx_ueq@ --- * |
| 722 | * |
| 723 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
| 724 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 725 | * |
| 726 | * Returns: Nonzero if the two vectors are equal. |
| 727 | * |
| 728 | * Use: Performs an unsigned integer test for equality. |
| 729 | */ |
| 730 | |
| 731 | int mpx_ueq(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
| 732 | { |
| 733 | MPX_SHRINK(av, avl); |
| 734 | MPX_SHRINK(bv, bvl); |
| 735 | if (avl - av != bvl - bv) |
| 736 | return (0); |
| 737 | while (av < avl) { |
| 738 | if (*av++ != *bv++) |
| 739 | return (0); |
| 740 | } |
| 741 | return (1); |
| 742 | } |
| 743 | |
| 744 | /* --- @mpx_ucmp@ --- * |
| 745 | * |
| 746 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
| 747 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 748 | * |
| 749 | * Returns: Less than, equal to, or greater than zero depending on |
| 750 | * whether @a@ is less than, equal to or greater than @b@, |
| 751 | * respectively. |
| 752 | * |
| 753 | * Use: Performs an unsigned integer comparison. |
| 754 | */ |
| 755 | |
| 756 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
| 757 | { |
| 758 | MPX_SHRINK(av, avl); |
| 759 | MPX_SHRINK(bv, bvl); |
| 760 | |
| 761 | if (avl - av > bvl - bv) |
| 762 | return (+1); |
| 763 | else if (avl - av < bvl - bv) |
| 764 | return (-1); |
| 765 | else while (avl > av) { |
| 766 | mpw a = *--avl, b = *--bvl; |
| 767 | if (a > b) |
| 768 | return (+1); |
| 769 | else if (a < b) |
| 770 | return (-1); |
| 771 | } |
| 772 | return (0); |
| 773 | } |
| 774 | |
| 775 | /* --- @mpx_uadd@ --- * |
| 776 | * |
| 777 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 778 | * @const mpw *av, *avl@ = first addend vector base and limit |
| 779 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
| 780 | * |
| 781 | * Returns: --- |
| 782 | * |
| 783 | * Use: Performs unsigned integer addition. If the result overflows |
| 784 | * the destination vector, high-order bits are discarded. This |
| 785 | * means that two's complement addition happens more or less for |
| 786 | * free, although that's more a side-effect than anything else. |
| 787 | * The result vector may be equal to either or both source |
| 788 | * vectors, but may not otherwise overlap them. |
| 789 | */ |
| 790 | |
| 791 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 792 | const mpw *bv, const mpw *bvl) |
| 793 | { |
| 794 | mpw c = 0; |
| 795 | |
| 796 | while (av < avl || bv < bvl) { |
| 797 | mpw a, b; |
| 798 | mpd x; |
| 799 | if (dv >= dvl) |
| 800 | return; |
| 801 | a = (av < avl) ? *av++ : 0; |
| 802 | b = (bv < bvl) ? *bv++ : 0; |
| 803 | x = (mpd)a + (mpd)b + c; |
| 804 | *dv++ = MPW(x); |
| 805 | c = x >> MPW_BITS; |
| 806 | } |
| 807 | if (dv < dvl) { |
| 808 | *dv++ = c; |
| 809 | MPX_ZERO(dv, dvl); |
| 810 | } |
| 811 | } |
| 812 | |
| 813 | /* --- @mpx_uaddn@ --- * |
| 814 | * |
| 815 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
| 816 | * @mpw n@ = other addend |
| 817 | * |
| 818 | * Returns: --- |
| 819 | * |
| 820 | * Use: Adds a small integer to a multiprecision number. |
| 821 | */ |
| 822 | |
| 823 | void mpx_uaddn(mpw *dv, mpw *dvl, mpw n) { MPX_UADDN(dv, dvl, n); } |
| 824 | |
| 825 | /* --- @mpx_uaddnlsl@ --- * |
| 826 | * |
| 827 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector |
| 828 | * @mpw a@ = second argument |
| 829 | * @unsigned o@ = offset in bits |
| 830 | * |
| 831 | * Returns: --- |
| 832 | * |
| 833 | * Use: Computes %$d + 2^o a$%. If the result overflows then |
| 834 | * high-order bits are discarded, as usual. We must have |
| 835 | * @0 < o < MPW_BITS@. |
| 836 | */ |
| 837 | |
| 838 | void mpx_uaddnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o) |
| 839 | { |
| 840 | mpd x = (mpd)a << o; |
| 841 | |
| 842 | while (x && dv < dvl) { |
| 843 | x += *dv; |
| 844 | *dv++ = MPW(x); |
| 845 | x >>= MPW_BITS; |
| 846 | } |
| 847 | } |
| 848 | |
| 849 | /* --- @mpx_usub@ --- * |
| 850 | * |
| 851 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 852 | * @const mpw *av, *avl@ = first argument vector base and limit |
| 853 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 854 | * |
| 855 | * Returns: --- |
| 856 | * |
| 857 | * Use: Performs unsigned integer subtraction. If the result |
| 858 | * overflows the destination vector, high-order bits are |
| 859 | * discarded. This means that two's complement subtraction |
| 860 | * happens more or less for free, althuogh that's more a side- |
| 861 | * effect than anything else. The result vector may be equal to |
| 862 | * either or both source vectors, but may not otherwise overlap |
| 863 | * them. |
| 864 | */ |
| 865 | |
| 866 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 867 | const mpw *bv, const mpw *bvl) |
| 868 | { |
| 869 | mpw c = 0; |
| 870 | |
| 871 | while (av < avl || bv < bvl) { |
| 872 | mpw a, b; |
| 873 | mpd x; |
| 874 | if (dv >= dvl) |
| 875 | return; |
| 876 | a = (av < avl) ? *av++ : 0; |
| 877 | b = (bv < bvl) ? *bv++ : 0; |
| 878 | x = (mpd)a - (mpd)b - c; |
| 879 | *dv++ = MPW(x); |
| 880 | if (x >> MPW_BITS) |
| 881 | c = 1; |
| 882 | else |
| 883 | c = 0; |
| 884 | } |
| 885 | if (c) |
| 886 | c = MPW_MAX; |
| 887 | while (dv < dvl) |
| 888 | *dv++ = c; |
| 889 | } |
| 890 | |
| 891 | /* --- @mpx_usubn@ --- * |
| 892 | * |
| 893 | * Arguments: @mpw *dv, *dvl@ = source and destination base and limit |
| 894 | * @n@ = subtrahend |
| 895 | * |
| 896 | * Returns: --- |
| 897 | * |
| 898 | * Use: Subtracts a small integer from a multiprecision number. |
| 899 | */ |
| 900 | |
| 901 | void mpx_usubn(mpw *dv, mpw *dvl, mpw n) { MPX_USUBN(dv, dvl, n); } |
| 902 | |
| 903 | /* --- @mpx_uaddnlsl@ --- * |
| 904 | * |
| 905 | * Arguments: @mpw *dv, *dvl@ = destination and first argument vector |
| 906 | * @mpw a@ = second argument |
| 907 | * @unsigned o@ = offset in bits |
| 908 | * |
| 909 | * Returns: --- |
| 910 | * |
| 911 | * Use: Computes %$d + 2^o a$%. If the result overflows then |
| 912 | * high-order bits are discarded, as usual. We must have |
| 913 | * @0 < o < MPW_BITS@. |
| 914 | */ |
| 915 | |
| 916 | void mpx_usubnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o) |
| 917 | { |
| 918 | mpw b = a >> (MPW_BITS - o); |
| 919 | a <<= o; |
| 920 | |
| 921 | if (dv < dvl) { |
| 922 | mpd x = (mpd)*dv - (mpd)a; |
| 923 | *dv++ = MPW(x); |
| 924 | if (x >> MPW_BITS) |
| 925 | b++; |
| 926 | MPX_USUBN(dv, dvl, b); |
| 927 | } |
| 928 | } |
| 929 | |
| 930 | /* --- @mpx_umul@ --- * |
| 931 | * |
| 932 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 933 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 934 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
| 935 | * |
| 936 | * Returns: --- |
| 937 | * |
| 938 | * Use: Performs unsigned integer multiplication. If the result |
| 939 | * overflows the desination vector, high-order bits are |
| 940 | * discarded. The result vector may not overlap the argument |
| 941 | * vectors in any way. |
| 942 | */ |
| 943 | |
| 944 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 945 | const mpw *bv, const mpw *bvl) |
| 946 | { |
| 947 | /* --- This is probably worthwhile on a multiply --- */ |
| 948 | |
| 949 | MPX_SHRINK(av, avl); |
| 950 | MPX_SHRINK(bv, bvl); |
| 951 | |
| 952 | /* --- Deal with a multiply by zero --- */ |
| 953 | |
| 954 | if (bv == bvl) { |
| 955 | MPX_ZERO(dv, dvl); |
| 956 | return; |
| 957 | } |
| 958 | |
| 959 | /* --- Do the initial multiply and initialize the accumulator --- */ |
| 960 | |
| 961 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
| 962 | |
| 963 | /* --- Do the remaining multiply/accumulates --- */ |
| 964 | |
| 965 | while (dv < dvl && bv < bvl) { |
| 966 | mpw m = *bv++; |
| 967 | mpw c = 0; |
| 968 | const mpw *avv = av; |
| 969 | mpw *dvv = ++dv; |
| 970 | |
| 971 | while (avv < avl) { |
| 972 | mpd x; |
| 973 | if (dvv >= dvl) |
| 974 | goto next; |
| 975 | x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c; |
| 976 | *dvv++ = MPW(x); |
| 977 | c = x >> MPW_BITS; |
| 978 | } |
| 979 | MPX_UADDN(dvv, dvl, c); |
| 980 | next:; |
| 981 | } |
| 982 | } |
| 983 | |
| 984 | /* --- @mpx_umuln@ --- * |
| 985 | * |
| 986 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 987 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 988 | * @mpw m@ = multiplier |
| 989 | * |
| 990 | * Returns: --- |
| 991 | * |
| 992 | * Use: Multiplies a multiprecision integer by a single-word value. |
| 993 | * The destination and source may be equal. The destination |
| 994 | * is completely cleared after use. |
| 995 | */ |
| 996 | |
| 997 | void mpx_umuln(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
| 998 | { MPX_UMULN(dv, dvl, av, avl, m); } |
| 999 | |
| 1000 | /* --- @mpx_umlan@ --- * |
| 1001 | * |
| 1002 | * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit |
| 1003 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 1004 | * @mpw m@ = multiplier |
| 1005 | * |
| 1006 | * Returns: --- |
| 1007 | * |
| 1008 | * Use: Multiplies a multiprecision integer by a single-word value |
| 1009 | * and adds the result to an accumulator. |
| 1010 | */ |
| 1011 | |
| 1012 | void mpx_umlan(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m) |
| 1013 | { MPX_UMLAN(dv, dvl, av, avl, m); } |
| 1014 | |
| 1015 | /* --- @mpx_usqr@ --- * |
| 1016 | * |
| 1017 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 1018 | * @const mpw *av, *av@ = source vector base and limit |
| 1019 | * |
| 1020 | * Returns: --- |
| 1021 | * |
| 1022 | * Use: Performs unsigned integer squaring. The result vector must |
| 1023 | * not overlap the source vector in any way. |
| 1024 | */ |
| 1025 | |
| 1026 | void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl) |
| 1027 | { |
| 1028 | MPX_ZERO(dv, dvl); |
| 1029 | |
| 1030 | /* --- Main loop --- */ |
| 1031 | |
| 1032 | while (av < avl) { |
| 1033 | const mpw *avv = av; |
| 1034 | mpw *dvv = dv; |
| 1035 | mpw a = *av; |
| 1036 | mpd c; |
| 1037 | |
| 1038 | /* --- Stop if I've run out of destination --- */ |
| 1039 | |
| 1040 | if (dvv >= dvl) |
| 1041 | break; |
| 1042 | |
| 1043 | /* --- Work out the square at this point in the proceedings --- */ |
| 1044 | |
| 1045 | { |
| 1046 | mpd x = (mpd)a * (mpd)a + *dvv; |
| 1047 | *dvv++ = MPW(x); |
| 1048 | c = MPW(x >> MPW_BITS); |
| 1049 | } |
| 1050 | |
| 1051 | /* --- Now fix up the rest of the vector upwards --- */ |
| 1052 | |
| 1053 | avv++; |
| 1054 | while (dvv < dvl && avv < avl) { |
| 1055 | mpd x = (mpd)a * (mpd)*avv++; |
| 1056 | mpd y = ((x << 1) & MPW_MAX) + c + *dvv; |
| 1057 | c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS); |
| 1058 | *dvv++ = MPW(y); |
| 1059 | } |
| 1060 | while (dvv < dvl && c) { |
| 1061 | mpd x = c + *dvv; |
| 1062 | *dvv++ = MPW(x); |
| 1063 | c = x >> MPW_BITS; |
| 1064 | } |
| 1065 | |
| 1066 | /* --- Get ready for the next round --- */ |
| 1067 | |
| 1068 | av++; |
| 1069 | dv += 2; |
| 1070 | } |
| 1071 | } |
| 1072 | |
| 1073 | /* --- @mpx_udiv@ --- * |
| 1074 | * |
| 1075 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
| 1076 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
| 1077 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
| 1078 | * @mpw *sv, *svl@ = scratch workspace |
| 1079 | * |
| 1080 | * Returns: --- |
| 1081 | * |
| 1082 | * Use: Performs unsigned integer division. If the result overflows |
| 1083 | * the quotient vector, high-order bits are discarded. (Clearly |
| 1084 | * the remainder vector can't overflow.) The various vectors |
| 1085 | * may not overlap in any way. Yes, I know it's a bit odd |
| 1086 | * requiring the dividend to be in the result position but it |
| 1087 | * does make some sense really. The remainder must have |
| 1088 | * headroom for at least two extra words. The scratch space |
| 1089 | * must be at least one word larger than the divisor. |
| 1090 | */ |
| 1091 | |
| 1092 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
| 1093 | const mpw *dv, const mpw *dvl, |
| 1094 | mpw *sv, mpw *svl) |
| 1095 | { |
| 1096 | unsigned norm = 0; |
| 1097 | size_t scale; |
| 1098 | mpw d, dd; |
| 1099 | |
| 1100 | /* --- Initialize the quotient --- */ |
| 1101 | |
| 1102 | MPX_ZERO(qv, qvl); |
| 1103 | |
| 1104 | /* --- Perform some sanity checks --- */ |
| 1105 | |
| 1106 | MPX_SHRINK(dv, dvl); |
| 1107 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
| 1108 | |
| 1109 | /* --- Normalize the divisor --- * |
| 1110 | * |
| 1111 | * The algorithm requires that the divisor be at least two digits long. |
| 1112 | * This is easy to fix. |
| 1113 | */ |
| 1114 | |
| 1115 | { |
| 1116 | unsigned b; |
| 1117 | |
| 1118 | d = dvl[-1]; |
| 1119 | for (b = MPW_BITS / 2; b; b >>= 1) { |
| 1120 | if (d <= (MPW_MAX >> b)) { |
| 1121 | d <<= b; |
| 1122 | norm += b; |
| 1123 | } |
| 1124 | } |
| 1125 | if (dv + 1 == dvl) |
| 1126 | norm += MPW_BITS; |
| 1127 | } |
| 1128 | |
| 1129 | /* --- Normalize the dividend/remainder to match --- */ |
| 1130 | |
| 1131 | if (norm) { |
| 1132 | mpx_lsl(rv, rvl, rv, rvl, norm); |
| 1133 | mpx_lsl(sv, svl, dv, dvl, norm); |
| 1134 | dv = sv; |
| 1135 | dvl = svl; |
| 1136 | MPX_SHRINK(dv, dvl); |
| 1137 | } |
| 1138 | |
| 1139 | MPX_SHRINK(rv, rvl); |
| 1140 | d = dvl[-1]; |
| 1141 | dd = dvl[-2]; |
| 1142 | |
| 1143 | /* --- Work out the relative scales --- */ |
| 1144 | |
| 1145 | { |
| 1146 | size_t rvn = rvl - rv; |
| 1147 | size_t dvn = dvl - dv; |
| 1148 | |
| 1149 | /* --- If the divisor is clearly larger, notice this --- */ |
| 1150 | |
| 1151 | if (dvn > rvn) { |
| 1152 | mpx_lsr(rv, rvl, rv, rvl, norm); |
| 1153 | return; |
| 1154 | } |
| 1155 | |
| 1156 | scale = rvn - dvn; |
| 1157 | } |
| 1158 | |
| 1159 | /* --- Calculate the most significant quotient digit --- * |
| 1160 | * |
| 1161 | * Because the divisor has its top bit set, this can only happen once. The |
| 1162 | * pointer arithmetic is a little contorted, to make sure that the |
| 1163 | * behaviour is defined. |
| 1164 | */ |
| 1165 | |
| 1166 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
| 1167 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
| 1168 | if (qvl - qv > scale) |
| 1169 | qv[scale] = 1; |
| 1170 | } |
| 1171 | |
| 1172 | /* --- Now for the main loop --- */ |
| 1173 | |
| 1174 | { |
| 1175 | mpw *rvv = rvl - 2; |
| 1176 | |
| 1177 | while (scale) { |
| 1178 | mpw q; |
| 1179 | mpd rh; |
| 1180 | |
| 1181 | /* --- Get an estimate for the next quotient digit --- */ |
| 1182 | |
| 1183 | mpw r = rvv[1]; |
| 1184 | mpw rr = rvv[0]; |
| 1185 | mpw rrr = *--rvv; |
| 1186 | |
| 1187 | scale--; |
| 1188 | rh = ((mpd)r << MPW_BITS) | rr; |
| 1189 | if (r == d) |
| 1190 | q = MPW_MAX; |
| 1191 | else |
| 1192 | q = MPW(rh / d); |
| 1193 | |
| 1194 | /* --- Refine the estimate --- */ |
| 1195 | |
| 1196 | { |
| 1197 | mpd yh = (mpd)d * q; |
| 1198 | mpd yy = (mpd)dd * q; |
| 1199 | mpw yl; |
| 1200 | |
| 1201 | if (yy > MPW_MAX) |
| 1202 | yh += yy >> MPW_BITS; |
| 1203 | yl = MPW(yy); |
| 1204 | |
| 1205 | while (yh > rh || (yh == rh && yl > rrr)) { |
| 1206 | q--; |
| 1207 | yh -= d; |
| 1208 | if (yl < dd) |
| 1209 | yh--; |
| 1210 | yl = MPW(yl - dd); |
| 1211 | } |
| 1212 | } |
| 1213 | |
| 1214 | /* --- Remove a chunk from the dividend --- */ |
| 1215 | |
| 1216 | { |
| 1217 | mpw *svv; |
| 1218 | const mpw *dvv; |
| 1219 | mpw mc = 0, sc = 0; |
| 1220 | |
| 1221 | /* --- Calculate the size of the chunk --- * |
| 1222 | * |
| 1223 | * This does the whole job of calculating @r >> scale - qd@. |
| 1224 | */ |
| 1225 | |
| 1226 | for (svv = rv + scale, dvv = dv; |
| 1227 | dvv < dvl && svv < rvl; |
| 1228 | svv++, dvv++) { |
| 1229 | mpd x = (mpd)*dvv * (mpd)q + mc; |
| 1230 | mc = x >> MPW_BITS; |
| 1231 | x = (mpd)*svv - MPW(x) - sc; |
| 1232 | *svv = MPW(x); |
| 1233 | if (x >> MPW_BITS) |
| 1234 | sc = 1; |
| 1235 | else |
| 1236 | sc = 0; |
| 1237 | } |
| 1238 | |
| 1239 | if (svv < rvl) { |
| 1240 | mpd x = (mpd)*svv - mc - sc; |
| 1241 | *svv++ = MPW(x); |
| 1242 | if (x >> MPW_BITS) |
| 1243 | sc = MPW_MAX; |
| 1244 | else |
| 1245 | sc = 0; |
| 1246 | while (svv < rvl) |
| 1247 | *svv++ = sc; |
| 1248 | } |
| 1249 | |
| 1250 | /* --- Fix if the quotient was too large --- * |
| 1251 | * |
| 1252 | * This doesn't seem to happen very often. |
| 1253 | */ |
| 1254 | |
| 1255 | if (rvl[-1] > MPW_MAX / 2) { |
| 1256 | mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
| 1257 | q--; |
| 1258 | } |
| 1259 | } |
| 1260 | |
| 1261 | /* --- Done for another iteration --- */ |
| 1262 | |
| 1263 | if (qvl - qv > scale) |
| 1264 | qv[scale] = q; |
| 1265 | r = rr; |
| 1266 | rr = rrr; |
| 1267 | } |
| 1268 | } |
| 1269 | |
| 1270 | /* --- Now fiddle with unnormalizing and things --- */ |
| 1271 | |
| 1272 | mpx_lsr(rv, rvl, rv, rvl, norm); |
| 1273 | } |
| 1274 | |
| 1275 | /* --- @mpx_udivn@ --- * |
| 1276 | * |
| 1277 | * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap |
| 1278 | * dividend) |
| 1279 | * @const mpw *rv, *rvl@ = dividend |
| 1280 | * @mpw d@ = single-precision divisor |
| 1281 | * |
| 1282 | * Returns: Remainder after divison. |
| 1283 | * |
| 1284 | * Use: Performs a single-precision division operation. |
| 1285 | */ |
| 1286 | |
| 1287 | mpw mpx_udivn(mpw *qv, mpw *qvl, const mpw *rv, const mpw *rvl, mpw d) |
| 1288 | { |
| 1289 | size_t i; |
| 1290 | size_t ql = qvl - qv; |
| 1291 | mpd r = 0; |
| 1292 | |
| 1293 | i = rvl - rv; |
| 1294 | while (i > 0) { |
| 1295 | i--; |
| 1296 | r = (r << MPW_BITS) | rv[i]; |
| 1297 | if (i < ql) |
| 1298 | qv[i] = r / d; |
| 1299 | r %= d; |
| 1300 | } |
| 1301 | return (MPW(r)); |
| 1302 | } |
| 1303 | |
| 1304 | /*----- Test rig ----------------------------------------------------------*/ |
| 1305 | |
| 1306 | #ifdef TEST_RIG |
| 1307 | |
| 1308 | #include <mLib/alloc.h> |
| 1309 | #include <mLib/dstr.h> |
| 1310 | #include <mLib/quis.h> |
| 1311 | #include <mLib/testrig.h> |
| 1312 | |
| 1313 | #include "mpscan.h" |
| 1314 | |
| 1315 | #define ALLOC(v, vl, sz) do { \ |
| 1316 | size_t _sz = (sz); \ |
| 1317 | mpw *_vv = xmalloc(MPWS(_sz)); \ |
| 1318 | mpw *_vvl = _vv + _sz; \ |
| 1319 | (v) = _vv; \ |
| 1320 | (vl) = _vvl; \ |
| 1321 | } while (0) |
| 1322 | |
| 1323 | #define LOAD(v, vl, d) do { \ |
| 1324 | const dstr *_d = (d); \ |
| 1325 | mpw *_v, *_vl; \ |
| 1326 | ALLOC(_v, _vl, MPW_RQ(_d->len)); \ |
| 1327 | mpx_loadb(_v, _vl, _d->buf, _d->len); \ |
| 1328 | (v) = _v; \ |
| 1329 | (vl) = _vl; \ |
| 1330 | } while (0) |
| 1331 | |
| 1332 | #define MAX(x, y) ((x) > (y) ? (x) : (y)) |
| 1333 | |
| 1334 | static void dumpbits(const char *msg, const void *pp, size_t sz) |
| 1335 | { |
| 1336 | const octet *p = pp; |
| 1337 | fputs(msg, stderr); |
| 1338 | for (; sz; sz--) |
| 1339 | fprintf(stderr, " %02x", *p++); |
| 1340 | fputc('\n', stderr); |
| 1341 | } |
| 1342 | |
| 1343 | static void dumpmp(const char *msg, const mpw *v, const mpw *vl) |
| 1344 | { |
| 1345 | fputs(msg, stderr); |
| 1346 | MPX_SHRINK(v, vl); |
| 1347 | while (v < vl) |
| 1348 | fprintf(stderr, " %08lx", (unsigned long)*--vl); |
| 1349 | fputc('\n', stderr); |
| 1350 | } |
| 1351 | |
| 1352 | static int chkscan(const mpw *v, const mpw *vl, |
| 1353 | const void *pp, size_t sz, int step) |
| 1354 | { |
| 1355 | mpscan mps; |
| 1356 | const octet *p = pp; |
| 1357 | unsigned bit = 0; |
| 1358 | int ok = 1; |
| 1359 | |
| 1360 | mpscan_initx(&mps, v, vl); |
| 1361 | while (sz) { |
| 1362 | unsigned x = *p; |
| 1363 | int i; |
| 1364 | p += step; |
| 1365 | for (i = 0; i < 8 && MPSCAN_STEP(&mps); i++) { |
| 1366 | if (MPSCAN_BIT(&mps) != (x & 1)) { |
| 1367 | fprintf(stderr, |
| 1368 | "\n*** error, step %i, bit %u, expected %u, found %u\n", |
| 1369 | step, bit, x & 1, MPSCAN_BIT(&mps)); |
| 1370 | ok = 0; |
| 1371 | } |
| 1372 | x >>= 1; |
| 1373 | bit++; |
| 1374 | } |
| 1375 | sz--; |
| 1376 | } |
| 1377 | |
| 1378 | return (ok); |
| 1379 | } |
| 1380 | |
| 1381 | static int loadstore(dstr *v) |
| 1382 | { |
| 1383 | dstr d = DSTR_INIT; |
| 1384 | size_t sz = MPW_RQ(v->len) * 2, diff; |
| 1385 | mpw *m, *ml; |
| 1386 | int ok = 1; |
| 1387 | |
| 1388 | dstr_ensure(&d, v->len); |
| 1389 | m = xmalloc(MPWS(sz)); |
| 1390 | |
| 1391 | for (diff = 0; diff < sz; diff += 5) { |
| 1392 | size_t oct; |
| 1393 | |
| 1394 | ml = m + sz - diff; |
| 1395 | |
| 1396 | mpx_loadl(m, ml, v->buf, v->len); |
| 1397 | if (!chkscan(m, ml, v->buf, v->len, +1)) |
| 1398 | ok = 0; |
| 1399 | MPX_OCTETS(oct, m, ml); |
| 1400 | mpx_storel(m, ml, d.buf, d.sz); |
| 1401 | if (memcmp(d.buf, v->buf, oct) != 0) { |
| 1402 | dumpbits("\n*** storel failed", d.buf, d.sz); |
| 1403 | ok = 0; |
| 1404 | } |
| 1405 | |
| 1406 | mpx_loadb(m, ml, v->buf, v->len); |
| 1407 | if (!chkscan(m, ml, v->buf + v->len - 1, v->len, -1)) |
| 1408 | ok = 0; |
| 1409 | MPX_OCTETS(oct, m, ml); |
| 1410 | mpx_storeb(m, ml, d.buf, d.sz); |
| 1411 | if (memcmp(d.buf + d.sz - oct, v->buf + v->len - oct, oct) != 0) { |
| 1412 | dumpbits("\n*** storeb failed", d.buf, d.sz); |
| 1413 | ok = 0; |
| 1414 | } |
| 1415 | } |
| 1416 | |
| 1417 | if (!ok) |
| 1418 | dumpbits("input data", v->buf, v->len); |
| 1419 | |
| 1420 | xfree(m); |
| 1421 | dstr_destroy(&d); |
| 1422 | return (ok); |
| 1423 | } |
| 1424 | |
| 1425 | static int twocl(dstr *v) |
| 1426 | { |
| 1427 | dstr d = DSTR_INIT; |
| 1428 | mpw *m, *ml; |
| 1429 | size_t sz; |
| 1430 | int ok = 1; |
| 1431 | |
| 1432 | sz = v[0].len; if (v[1].len > sz) sz = v[1].len; |
| 1433 | dstr_ensure(&d, sz); |
| 1434 | |
| 1435 | sz = MPW_RQ(sz); |
| 1436 | m = xmalloc(MPWS(sz)); |
| 1437 | ml = m + sz; |
| 1438 | |
| 1439 | mpx_loadl(m, ml, v[0].buf, v[0].len); |
| 1440 | mpx_storel2cn(m, ml, d.buf, v[1].len); |
| 1441 | if (memcmp(d.buf, v[1].buf, v[1].len)) { |
| 1442 | dumpbits("\n*** storel2cn failed", d.buf, v[1].len); |
| 1443 | ok = 0; |
| 1444 | } |
| 1445 | |
| 1446 | mpx_loadl2cn(m, ml, v[1].buf, v[1].len); |
| 1447 | mpx_storel(m, ml, d.buf, v[0].len); |
| 1448 | if (memcmp(d.buf, v[0].buf, v[0].len)) { |
| 1449 | dumpbits("\n*** loadl2cn failed", d.buf, v[0].len); |
| 1450 | ok = 0; |
| 1451 | } |
| 1452 | |
| 1453 | if (!ok) { |
| 1454 | dumpbits("pos", v[0].buf, v[0].len); |
| 1455 | dumpbits("neg", v[1].buf, v[1].len); |
| 1456 | } |
| 1457 | |
| 1458 | xfree(m); |
| 1459 | dstr_destroy(&d); |
| 1460 | |
| 1461 | return (ok); |
| 1462 | } |
| 1463 | |
| 1464 | static int twocb(dstr *v) |
| 1465 | { |
| 1466 | dstr d = DSTR_INIT; |
| 1467 | mpw *m, *ml; |
| 1468 | size_t sz; |
| 1469 | int ok = 1; |
| 1470 | |
| 1471 | sz = v[0].len; if (v[1].len > sz) sz = v[1].len; |
| 1472 | dstr_ensure(&d, sz); |
| 1473 | |
| 1474 | sz = MPW_RQ(sz); |
| 1475 | m = xmalloc(MPWS(sz)); |
| 1476 | ml = m + sz; |
| 1477 | |
| 1478 | mpx_loadb(m, ml, v[0].buf, v[0].len); |
| 1479 | mpx_storeb2cn(m, ml, d.buf, v[1].len); |
| 1480 | if (memcmp(d.buf, v[1].buf, v[1].len)) { |
| 1481 | dumpbits("\n*** storeb2cn failed", d.buf, v[1].len); |
| 1482 | ok = 0; |
| 1483 | } |
| 1484 | |
| 1485 | mpx_loadb2cn(m, ml, v[1].buf, v[1].len); |
| 1486 | mpx_storeb(m, ml, d.buf, v[0].len); |
| 1487 | if (memcmp(d.buf, v[0].buf, v[0].len)) { |
| 1488 | dumpbits("\n*** loadb2cn failed", d.buf, v[0].len); |
| 1489 | ok = 0; |
| 1490 | } |
| 1491 | |
| 1492 | if (!ok) { |
| 1493 | dumpbits("pos", v[0].buf, v[0].len); |
| 1494 | dumpbits("neg", v[1].buf, v[1].len); |
| 1495 | } |
| 1496 | |
| 1497 | xfree(m); |
| 1498 | dstr_destroy(&d); |
| 1499 | |
| 1500 | return (ok); |
| 1501 | } |
| 1502 | |
| 1503 | static int lsl(dstr *v) |
| 1504 | { |
| 1505 | mpw *a, *al; |
| 1506 | int n = *(int *)v[1].buf; |
| 1507 | mpw *c, *cl; |
| 1508 | mpw *d, *dl; |
| 1509 | int ok = 1; |
| 1510 | |
| 1511 | LOAD(a, al, &v[0]); |
| 1512 | LOAD(c, cl, &v[2]); |
| 1513 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); |
| 1514 | |
| 1515 | mpx_lsl(d, dl, a, al, n); |
| 1516 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1517 | fprintf(stderr, "\n*** lsl(%i) failed\n", n); |
| 1518 | dumpmp(" a", a, al); |
| 1519 | dumpmp("expected", c, cl); |
| 1520 | dumpmp(" result", d, dl); |
| 1521 | ok = 0; |
| 1522 | } |
| 1523 | |
| 1524 | xfree(a); xfree(c); xfree(d); |
| 1525 | return (ok); |
| 1526 | } |
| 1527 | |
| 1528 | static int lslc(dstr *v) |
| 1529 | { |
| 1530 | mpw *a, *al; |
| 1531 | int n = *(int *)v[1].buf; |
| 1532 | mpw *c, *cl; |
| 1533 | mpw *d, *dl; |
| 1534 | int ok = 1; |
| 1535 | |
| 1536 | LOAD(a, al, &v[0]); |
| 1537 | LOAD(c, cl, &v[2]); |
| 1538 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS); |
| 1539 | |
| 1540 | mpx_lslc(d, dl, a, al, n); |
| 1541 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1542 | fprintf(stderr, "\n*** lslc(%i) failed\n", n); |
| 1543 | dumpmp(" a", a, al); |
| 1544 | dumpmp("expected", c, cl); |
| 1545 | dumpmp(" result", d, dl); |
| 1546 | ok = 0; |
| 1547 | } |
| 1548 | |
| 1549 | xfree(a); xfree(c); xfree(d); |
| 1550 | return (ok); |
| 1551 | } |
| 1552 | |
| 1553 | static int lsr(dstr *v) |
| 1554 | { |
| 1555 | mpw *a, *al; |
| 1556 | int n = *(int *)v[1].buf; |
| 1557 | mpw *c, *cl; |
| 1558 | mpw *d, *dl; |
| 1559 | int ok = 1; |
| 1560 | |
| 1561 | LOAD(a, al, &v[0]); |
| 1562 | LOAD(c, cl, &v[2]); |
| 1563 | ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS + 1); |
| 1564 | |
| 1565 | mpx_lsr(d, dl, a, al, n); |
| 1566 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1567 | fprintf(stderr, "\n*** lsr(%i) failed\n", n); |
| 1568 | dumpmp(" a", a, al); |
| 1569 | dumpmp("expected", c, cl); |
| 1570 | dumpmp(" result", d, dl); |
| 1571 | ok = 0; |
| 1572 | } |
| 1573 | |
| 1574 | xfree(a); xfree(c); xfree(d); |
| 1575 | return (ok); |
| 1576 | } |
| 1577 | |
| 1578 | static int uadd(dstr *v) |
| 1579 | { |
| 1580 | mpw *a, *al; |
| 1581 | mpw *b, *bl; |
| 1582 | mpw *c, *cl; |
| 1583 | mpw *d, *dl; |
| 1584 | int ok = 1; |
| 1585 | |
| 1586 | LOAD(a, al, &v[0]); |
| 1587 | LOAD(b, bl, &v[1]); |
| 1588 | LOAD(c, cl, &v[2]); |
| 1589 | ALLOC(d, dl, MAX(al - a, bl - b) + 1); |
| 1590 | |
| 1591 | mpx_uadd(d, dl, a, al, b, bl); |
| 1592 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1593 | fprintf(stderr, "\n*** uadd failed\n"); |
| 1594 | dumpmp(" a", a, al); |
| 1595 | dumpmp(" b", b, bl); |
| 1596 | dumpmp("expected", c, cl); |
| 1597 | dumpmp(" result", d, dl); |
| 1598 | ok = 0; |
| 1599 | } |
| 1600 | |
| 1601 | xfree(a); xfree(b); xfree(c); xfree(d); |
| 1602 | return (ok); |
| 1603 | } |
| 1604 | |
| 1605 | static int usub(dstr *v) |
| 1606 | { |
| 1607 | mpw *a, *al; |
| 1608 | mpw *b, *bl; |
| 1609 | mpw *c, *cl; |
| 1610 | mpw *d, *dl; |
| 1611 | int ok = 1; |
| 1612 | |
| 1613 | LOAD(a, al, &v[0]); |
| 1614 | LOAD(b, bl, &v[1]); |
| 1615 | LOAD(c, cl, &v[2]); |
| 1616 | ALLOC(d, dl, al - a); |
| 1617 | |
| 1618 | mpx_usub(d, dl, a, al, b, bl); |
| 1619 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1620 | fprintf(stderr, "\n*** usub failed\n"); |
| 1621 | dumpmp(" a", a, al); |
| 1622 | dumpmp(" b", b, bl); |
| 1623 | dumpmp("expected", c, cl); |
| 1624 | dumpmp(" result", d, dl); |
| 1625 | ok = 0; |
| 1626 | } |
| 1627 | |
| 1628 | xfree(a); xfree(b); xfree(c); xfree(d); |
| 1629 | return (ok); |
| 1630 | } |
| 1631 | |
| 1632 | static int umul(dstr *v) |
| 1633 | { |
| 1634 | mpw *a, *al; |
| 1635 | mpw *b, *bl; |
| 1636 | mpw *c, *cl; |
| 1637 | mpw *d, *dl; |
| 1638 | int ok = 1; |
| 1639 | |
| 1640 | LOAD(a, al, &v[0]); |
| 1641 | LOAD(b, bl, &v[1]); |
| 1642 | LOAD(c, cl, &v[2]); |
| 1643 | ALLOC(d, dl, (al - a) + (bl - b)); |
| 1644 | |
| 1645 | mpx_umul(d, dl, a, al, b, bl); |
| 1646 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1647 | fprintf(stderr, "\n*** umul failed\n"); |
| 1648 | dumpmp(" a", a, al); |
| 1649 | dumpmp(" b", b, bl); |
| 1650 | dumpmp("expected", c, cl); |
| 1651 | dumpmp(" result", d, dl); |
| 1652 | ok = 0; |
| 1653 | } |
| 1654 | |
| 1655 | xfree(a); xfree(b); xfree(c); xfree(d); |
| 1656 | return (ok); |
| 1657 | } |
| 1658 | |
| 1659 | static int usqr(dstr *v) |
| 1660 | { |
| 1661 | mpw *a, *al; |
| 1662 | mpw *c, *cl; |
| 1663 | mpw *d, *dl; |
| 1664 | int ok = 1; |
| 1665 | |
| 1666 | LOAD(a, al, &v[0]); |
| 1667 | LOAD(c, cl, &v[1]); |
| 1668 | ALLOC(d, dl, 2 * (al - a)); |
| 1669 | |
| 1670 | mpx_usqr(d, dl, a, al); |
| 1671 | if (!mpx_ueq(d, dl, c, cl)) { |
| 1672 | fprintf(stderr, "\n*** usqr failed\n"); |
| 1673 | dumpmp(" a", a, al); |
| 1674 | dumpmp("expected", c, cl); |
| 1675 | dumpmp(" result", d, dl); |
| 1676 | ok = 0; |
| 1677 | } |
| 1678 | |
| 1679 | xfree(a); xfree(c); xfree(d); |
| 1680 | return (ok); |
| 1681 | } |
| 1682 | |
| 1683 | static int udiv(dstr *v) |
| 1684 | { |
| 1685 | mpw *a, *al; |
| 1686 | mpw *b, *bl; |
| 1687 | mpw *q, *ql; |
| 1688 | mpw *r, *rl; |
| 1689 | mpw *qq, *qql; |
| 1690 | mpw *s, *sl; |
| 1691 | int ok = 1; |
| 1692 | |
| 1693 | ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len); |
| 1694 | LOAD(b, bl, &v[1]); |
| 1695 | LOAD(q, ql, &v[2]); |
| 1696 | LOAD(r, rl, &v[3]); |
| 1697 | ALLOC(qq, qql, al - a); |
| 1698 | ALLOC(s, sl, (bl - b) + 1); |
| 1699 | |
| 1700 | mpx_udiv(qq, qql, a, al, b, bl, s, sl); |
| 1701 | if (!mpx_ueq(qq, qql, q, ql) || |
| 1702 | !mpx_ueq(a, al, r, rl)) { |
| 1703 | fprintf(stderr, "\n*** udiv failed\n"); |
| 1704 | dumpmp(" divisor", b, bl); |
| 1705 | dumpmp("expect r", r, rl); |
| 1706 | dumpmp("result r", a, al); |
| 1707 | dumpmp("expect q", q, ql); |
| 1708 | dumpmp("result q", qq, qql); |
| 1709 | ok = 0; |
| 1710 | } |
| 1711 | |
| 1712 | xfree(a); xfree(b); xfree(r); xfree(q); xfree(s); xfree(qq); |
| 1713 | return (ok); |
| 1714 | } |
| 1715 | |
| 1716 | static test_chunk defs[] = { |
| 1717 | { "load-store", loadstore, { &type_hex, 0 } }, |
| 1718 | { "2cl", twocl, { &type_hex, &type_hex, } }, |
| 1719 | { "2cb", twocb, { &type_hex, &type_hex, } }, |
| 1720 | { "lsl", lsl, { &type_hex, &type_int, &type_hex, 0 } }, |
| 1721 | { "lslc", lslc, { &type_hex, &type_int, &type_hex, 0 } }, |
| 1722 | { "lsr", lsr, { &type_hex, &type_int, &type_hex, 0 } }, |
| 1723 | { "uadd", uadd, { &type_hex, &type_hex, &type_hex, 0 } }, |
| 1724 | { "usub", usub, { &type_hex, &type_hex, &type_hex, 0 } }, |
| 1725 | { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } }, |
| 1726 | { "usqr", usqr, { &type_hex, &type_hex, 0 } }, |
| 1727 | { "udiv", udiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } }, |
| 1728 | { 0, 0, { 0 } } |
| 1729 | }; |
| 1730 | |
| 1731 | int main(int argc, char *argv[]) |
| 1732 | { |
| 1733 | test_run(argc, argv, defs, SRCDIR"/tests/mpx"); |
| 1734 | return (0); |
| 1735 | } |
| 1736 | |
| 1737 | #endif |
| 1738 | |
| 1739 | /*----- That's all, folks -------------------------------------------------*/ |