| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mpx.c,v 1.1 1999/09/03 08:41:12 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.c,v $ |
| 33 | * Revision 1.1 1999/09/03 08:41:12 mdw |
| 34 | * Initial import. |
| 35 | * |
| 36 | */ |
| 37 | |
| 38 | /*----- Header files ------------------------------------------------------*/ |
| 39 | |
| 40 | #include <stdio.h> |
| 41 | #include <stdlib.h> |
| 42 | #include <string.h> |
| 43 | |
| 44 | #include <mLib/bits.h> |
| 45 | |
| 46 | #include "mptypes.h" |
| 47 | #include "mpx.h" |
| 48 | |
| 49 | /*----- Loading and storing -----------------------------------------------*/ |
| 50 | |
| 51 | /* --- @mpx_storel@ --- * |
| 52 | * |
| 53 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 54 | * @octet *p@ = pointer to octet array |
| 55 | * @size_t sz@ = size of octet array |
| 56 | * |
| 57 | * Returns: --- |
| 58 | * |
| 59 | * Use: Stores an MP in an octet array, least significant octet |
| 60 | * first. High-end octets are silently discarded if there |
| 61 | * isn't enough space for them. |
| 62 | */ |
| 63 | |
| 64 | void mpx_storel(const mpw *v, const mpw *vl, octet *p, size_t sz) |
| 65 | { |
| 66 | mpw n, w = 0; |
| 67 | octet *q = p + sz; |
| 68 | unsigned bits = 0; |
| 69 | |
| 70 | while (p < q) { |
| 71 | if (bits < 8) { |
| 72 | if (v >= vl) { |
| 73 | *p++ = U8(w); |
| 74 | break; |
| 75 | } |
| 76 | n = *v++; |
| 77 | *p++ = U8(w | n << bits); |
| 78 | w = n >> (8 - bits); |
| 79 | bits += MPW_BITS - 8; |
| 80 | } else { |
| 81 | *p++ = U8(w); |
| 82 | w >>= 8; |
| 83 | bits -= 8; |
| 84 | } |
| 85 | } |
| 86 | memset(p, 0, q - p); |
| 87 | } |
| 88 | |
| 89 | /* --- @mpx_loadl@ --- * |
| 90 | * |
| 91 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 92 | * @const octet *p@ = pointer to octet array |
| 93 | * @size_t sz@ = size of octet array |
| 94 | * |
| 95 | * Returns: --- |
| 96 | * |
| 97 | * Use: Loads an MP in an octet array, least significant octet |
| 98 | * first. High-end octets are ignored if there isn't enough |
| 99 | * space for them. |
| 100 | */ |
| 101 | |
| 102 | void mpx_loadl(mpw *v, const mpw *vl, const octet *p, size_t sz) |
| 103 | { |
| 104 | unsigned n; |
| 105 | const octet *q = p + sz; |
| 106 | unsigned bits = 0; |
| 107 | |
| 108 | if (v >= vl) |
| 109 | return; |
| 110 | while (p < q) { |
| 111 | n = U8(*p++); |
| 112 | w |= n << bits; |
| 113 | bits += 8; |
| 114 | if (bits >= MPW_BITS) { |
| 115 | *v++ = MPW(w); |
| 116 | w = n >> (MPW_BITS - bits + 8); |
| 117 | bits -= MPW_BITS; |
| 118 | if (v >= vl) |
| 119 | return; |
| 120 | } |
| 121 | } |
| 122 | *v++ = w; |
| 123 | MPX_ZERO(v, vl); |
| 124 | } |
| 125 | |
| 126 | /* --- @mpx_storeb@ --- * |
| 127 | * |
| 128 | * Arguments: @const mpw *v, *vl@ = base and limit of source vector |
| 129 | * @octet *p@ = pointer to octet array |
| 130 | * @size_t sz@ = size of octet array |
| 131 | * |
| 132 | * Returns: --- |
| 133 | * |
| 134 | * Use: Stores an MP in an octet array, most significant octet |
| 135 | * first. High-end octets are silently discarded if there |
| 136 | * isn't enough space for them. |
| 137 | */ |
| 138 | |
| 139 | void mpx_storeb(const mpw *v, const mpw *vl, octet *p, size_t sz); |
| 140 | { |
| 141 | mpw n, w = 0; |
| 142 | octet *q = p + sz; |
| 143 | unsigned bits = 0; |
| 144 | |
| 145 | while (q > p) { |
| 146 | if (bits < 8) { |
| 147 | if (v >= vl) { |
| 148 | *--q = U8(w); |
| 149 | break; |
| 150 | } |
| 151 | n = *v++; |
| 152 | *--q = U8(w | n << bits); |
| 153 | w = n >> (8 - bits); |
| 154 | bits += MPW_BITS - 8; |
| 155 | } else { |
| 156 | *--q = U8(w); |
| 157 | w >>= 8; |
| 158 | bits -= 8; |
| 159 | } |
| 160 | } |
| 161 | memset(p, 0, q - p); |
| 162 | } |
| 163 | |
| 164 | /* --- @mpx_loadb@ --- * |
| 165 | * |
| 166 | * Arguments: @mpw *v, *vl@ = base and limit of destination vector |
| 167 | * @const octet *p@ = pointer to octet array |
| 168 | * @size_t sz@ = size of octet array |
| 169 | * |
| 170 | * Returns: --- |
| 171 | * |
| 172 | * Use: Loads an MP in an octet array, most significant octet |
| 173 | * first. High-end octets are ignored if there isn't enough |
| 174 | * space for them. |
| 175 | */ |
| 176 | |
| 177 | void mpx_loadb(mpw *v, const mpw *vl, const octet *p, size_t sz) |
| 178 | { |
| 179 | unsigned n; |
| 180 | const octet *q = p + sz; |
| 181 | unsigned bits = 0; |
| 182 | |
| 183 | if (v >= vl) |
| 184 | return; |
| 185 | while (q > p) { |
| 186 | n = U8(*--q); |
| 187 | w |= n << bits; |
| 188 | bits += 8; |
| 189 | if (bits >= MPW_BITS) { |
| 190 | *v++ = MPW(w); |
| 191 | w = n >> (MPW_BITS - bits + 8); |
| 192 | bits -= MPW_BITS; |
| 193 | if (v >= vl) |
| 194 | return; |
| 195 | } |
| 196 | } |
| 197 | *v++ = w; |
| 198 | MPX_ZERO(v, vl); |
| 199 | } |
| 200 | |
| 201 | /*----- Logical shifting --------------------------------------------------*/ |
| 202 | |
| 203 | /* --- @mpx_lsl@ --- * |
| 204 | * |
| 205 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 206 | * @const mpw *av, *avl@ = source vector base and limit |
| 207 | * @size_t n@ = number of bit positions to shift by |
| 208 | * |
| 209 | * Returns: --- |
| 210 | * |
| 211 | * Use: Performs a logical shift left operation on an integer. |
| 212 | */ |
| 213 | |
| 214 | void mpx_lsl(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
| 215 | { |
| 216 | size_t nw; |
| 217 | unsigned nb; |
| 218 | |
| 219 | /* --- Trivial special case --- */ |
| 220 | |
| 221 | if (n == 0) |
| 222 | MPX_COPY(dv, dvl, av, avl); |
| 223 | |
| 224 | /* --- Single bit shifting --- */ |
| 225 | |
| 226 | else if (n == 1) { |
| 227 | mpw w = 0; |
| 228 | while (av < avl) { |
| 229 | mpw t; |
| 230 | if (dv >= dvl) |
| 231 | goto done; |
| 232 | t = *av++; |
| 233 | *dv++ = MPW((t << 1) | w); |
| 234 | w = t >> (MPW_BITS - 1); |
| 235 | } |
| 236 | if (dv >= dvl) |
| 237 | goto done; |
| 238 | *dv++ = MPW(w); |
| 239 | MPX_ZERO(dv, dvl); |
| 240 | } |
| 241 | |
| 242 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
| 243 | |
| 244 | nw = n / MPW_BITS; |
| 245 | nb = n % MPW_BITS; |
| 246 | |
| 247 | /* --- Handle a shift by a multiple of the word size --- */ |
| 248 | |
| 249 | if (nb == 0) { |
| 250 | MPX_COPY(dv + nw, dvl, av, avl); |
| 251 | memset(dv, 0, MPWS(nw)); |
| 252 | } |
| 253 | |
| 254 | /* --- And finally the difficult case --- */ |
| 255 | |
| 256 | else { |
| 257 | mpw w; |
| 258 | size_t nr = MPW_BITS - nb; |
| 259 | |
| 260 | if (dv + nw >= dvl) { |
| 261 | MPX_ZERO(dv, dvl); |
| 262 | goto done; |
| 263 | } |
| 264 | memset(dv, 0, MPWS(nw)); |
| 265 | dv += nw; |
| 266 | w = *av++; |
| 267 | |
| 268 | while (av < avl) { |
| 269 | mpw t; |
| 270 | if (dv >= dvl) |
| 271 | goto done; |
| 272 | t = *av++; |
| 273 | *dv++ = MPW((w >> nr) | (t << nb)); |
| 274 | w = t; |
| 275 | } |
| 276 | |
| 277 | if (dv < dvl) { |
| 278 | *dv++ = MPW(w >> nr); |
| 279 | MPX_ZERO(dv, dvl); |
| 280 | } |
| 281 | } |
| 282 | |
| 283 | done:; |
| 284 | } |
| 285 | |
| 286 | /* --- @mpx_lsr@ --- * |
| 287 | * |
| 288 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 289 | * @const mpw *av, *avl@ = source vector base and limit |
| 290 | * @size_t n@ = number of bit positions to shift by |
| 291 | * |
| 292 | * Returns: --- |
| 293 | * |
| 294 | * Use: Performs a logical shift right operation on an integer. |
| 295 | */ |
| 296 | |
| 297 | void mpx_lsr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n) |
| 298 | { |
| 299 | size_t nw; |
| 300 | unsigned nb; |
| 301 | |
| 302 | /* --- Trivial special case --- */ |
| 303 | |
| 304 | if (n == 0) |
| 305 | MPX_COPY(dv, dvl, av, avl); |
| 306 | |
| 307 | /* --- Single bit shifting --- */ |
| 308 | |
| 309 | else if (n == 1) { |
| 310 | mpw w = *av++ >> 1; |
| 311 | while (av < avl) { |
| 312 | mpw t; |
| 313 | if (dv >= dvl) |
| 314 | goto done; |
| 315 | t = *av++; |
| 316 | *dv++ = MPW((t << (MPW_BITS - 1)) | w); |
| 317 | w = t >> 1; |
| 318 | } |
| 319 | if (dv >= dvl) |
| 320 | goto done; |
| 321 | *dv++ = MPW(w); |
| 322 | MPX_ZERO(dv, dvl); |
| 323 | } |
| 324 | |
| 325 | /* --- Break out word and bit shifts for more sophisticated work --- */ |
| 326 | |
| 327 | nw = n / MPW_BITS; |
| 328 | nb = n % MPW_BITS; |
| 329 | |
| 330 | /* --- Handle a shift by a multiple of the word size --- */ |
| 331 | |
| 332 | if (nb == 0) |
| 333 | MPX_COPY(dv, dvl, av + nw, avl); |
| 334 | |
| 335 | /* --- And finally the difficult case --- */ |
| 336 | |
| 337 | else { |
| 338 | mpw w; |
| 339 | size_t nr = MPW_BITS - nb; |
| 340 | |
| 341 | av += nw; |
| 342 | w = *av++; |
| 343 | while (av < avl) { |
| 344 | mpw t; |
| 345 | if (dv >= dvl) |
| 346 | goto done; |
| 347 | t = *av++; |
| 348 | *dv++ = MPW((w >> nb) | (t << nr)); |
| 349 | w = t; |
| 350 | } |
| 351 | if (dv < dvl) { |
| 352 | *dv++ = MPW(w >> nb); |
| 353 | MPX_ZERO(dv, dvl); |
| 354 | } |
| 355 | } |
| 356 | |
| 357 | done:; |
| 358 | } |
| 359 | |
| 360 | /*----- Unsigned arithmetic -----------------------------------------------*/ |
| 361 | |
| 362 | /* --- @mpx_ucmp@ --- * |
| 363 | * |
| 364 | * Arguments: @const mpw *av, *avl@ = first argument vector base and limit |
| 365 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 366 | * |
| 367 | * Returns: Less than, equal to, or greater than zero depending on |
| 368 | * whether @a@ is less than, equal to or greater than @b@, |
| 369 | * respectively. |
| 370 | * |
| 371 | * Use: Performs an unsigned integer comparison. |
| 372 | */ |
| 373 | |
| 374 | int mpx_ucmp(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl) |
| 375 | { |
| 376 | MPX_SHRINK(av, avl); |
| 377 | MPX_SHRINK(bv, bvl); |
| 378 | |
| 379 | if (avl - av > bvl - bv) |
| 380 | return (+1); |
| 381 | else if (avl - av < bvl - bv) |
| 382 | return (-1); |
| 383 | else while (avl > av) { |
| 384 | mpw a = *--avl, b = *--bvl; |
| 385 | if (a > b) |
| 386 | return (+1); |
| 387 | else if (a < b) |
| 388 | return (-1); |
| 389 | } |
| 390 | return (0); |
| 391 | } |
| 392 | |
| 393 | /* --- @mpx_uadd@ --- * |
| 394 | * |
| 395 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 396 | * @const mpw *av, *avl@ = first addend vector base and limit |
| 397 | * @const mpw *bv, *bvl@ = second addend vector base and limit |
| 398 | * |
| 399 | * Returns: --- |
| 400 | * |
| 401 | * Use: Performs unsigned integer addition. If the result overflows |
| 402 | * the destination vector, high-order bits are discarded. This |
| 403 | * means that two's complement addition happens more or less for |
| 404 | * free, although that's more a side-effect than anything else. |
| 405 | * The result vector may be equal to either or both source |
| 406 | * vectors, but may not otherwise overlap them. |
| 407 | */ |
| 408 | |
| 409 | void mpx_uadd(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 410 | const mpw *bv, const mpw *bvl) |
| 411 | { |
| 412 | mpw c = 0; |
| 413 | |
| 414 | while (av < avl || bv < bvl) { |
| 415 | mpw a, b; |
| 416 | mpd x; |
| 417 | if (dv >= dvl) |
| 418 | return; |
| 419 | a = (av < avl) ? *av++ : 0; |
| 420 | b = (bv < bvl) ? *bv++ : 0; |
| 421 | x = (mpd)a + (mpd)b + c; |
| 422 | *dv++ = MPW(x); |
| 423 | c = x >> MPW_BITS; |
| 424 | } |
| 425 | if (dv < dvl) { |
| 426 | *dv++ = c; |
| 427 | MPX_ZERO(dv, dvl); |
| 428 | } |
| 429 | } |
| 430 | |
| 431 | /* --- @mpx_usub@ --- * |
| 432 | * |
| 433 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 434 | * @const mpw *av, *avl@ = first argument vector base and limit |
| 435 | * @const mpw *bv, *bvl@ = second argument vector base and limit |
| 436 | * |
| 437 | * Returns: --- |
| 438 | * |
| 439 | * Use: Performs unsigned integer subtraction. If the result |
| 440 | * overflows the destination vector, high-order bits are |
| 441 | * discarded. This means that two's complement subtraction |
| 442 | * happens more or less for free, althuogh that's more a side- |
| 443 | * effect than anything else. The result vector may be equal to |
| 444 | * either or both source vectors, but may not otherwise overlap |
| 445 | * them. |
| 446 | */ |
| 447 | |
| 448 | void mpx_usub(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 449 | const mpw *bv, const mpw *bvl) |
| 450 | { |
| 451 | mpw c = 0; |
| 452 | |
| 453 | while (av < avl || bv < bvl) { |
| 454 | mpw a, b; |
| 455 | mpd x; |
| 456 | if (dv >= dvl) |
| 457 | return; |
| 458 | a = (av < avl) ? *av++ : 0; |
| 459 | b = (bv < bvl) ? *bv++ : 0; |
| 460 | x = (mpd)a - (mpd)b + c; |
| 461 | *dv++ = MPW(x); |
| 462 | if (c >> MPW_BITS) |
| 463 | c = MPW(~0u); |
| 464 | } |
| 465 | c = c ? ~0u : 0; |
| 466 | while (dv < dvl) |
| 467 | *dv++ = c |
| 468 | } |
| 469 | |
| 470 | /* --- @mpx_umul@ --- * |
| 471 | * |
| 472 | * Arguments: @mpw *dv, *dvl@ = destination vector base and limit |
| 473 | * @const mpw *av, *avl@ = multiplicand vector base and limit |
| 474 | * @const mpw *bv, *bvl@ = multiplier vector base and limit |
| 475 | * |
| 476 | * Returns: --- |
| 477 | * |
| 478 | * Use: Performs unsigned integer multiplication. If the result |
| 479 | * overflows the desination vector, high-order bits are |
| 480 | * discarded. The result vector may not overlap the argument |
| 481 | * vectors in any way. |
| 482 | */ |
| 483 | |
| 484 | void mpx_umul(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, |
| 485 | const mpw *bv, const mpw *bvl) |
| 486 | { |
| 487 | /* --- This is probably worthwhile on a multiply --- */ |
| 488 | |
| 489 | MPX_SHRINK(av, avl); |
| 490 | MPX_SHRINK(bv, bvl); |
| 491 | |
| 492 | /* --- Deal with a multiply by zero --- */ |
| 493 | |
| 494 | if (bv == bvl) { |
| 495 | MPX_COPY(dv, dvl, bv, bvl); |
| 496 | return; |
| 497 | } |
| 498 | |
| 499 | /* --- Do the initial multiply and initialize the accumulator --- */ |
| 500 | |
| 501 | MPX_UMULN(dv, dvl, av, avl, *bv++); |
| 502 | |
| 503 | /* --- Do the remaining multiply/accumulates --- */ |
| 504 | |
| 505 | while (bv < bvl) { |
| 506 | mpw m = *bv++; |
| 507 | mpw c = ; |
| 508 | const mpw *avv = av; |
| 509 | mpw *dvv = ++dv; |
| 510 | |
| 511 | while (avv < avl) { |
| 512 | mpd x; |
| 513 | if (dvv >= dvl) |
| 514 | goto next; |
| 515 | x = *dvv + m * *av++ + c; |
| 516 | *dv++ = MPW(x); |
| 517 | c = x >> MPW_BITS; |
| 518 | } |
| 519 | if (dvv < dvl) |
| 520 | *dvv++ = MPW(c); |
| 521 | next:; |
| 522 | } |
| 523 | } |
| 524 | |
| 525 | /* --- @mpx_udiv@ --- * |
| 526 | * |
| 527 | * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit |
| 528 | * @mpw *rv, *rvl@ = dividend/remainder vector base and limit |
| 529 | * @const mpw *dv, *dvl@ = divisor vector base and limit |
| 530 | * |
| 531 | * Returns: --- |
| 532 | * |
| 533 | * Use: Performs unsigned integer division. If the result overflows |
| 534 | * the quotient vector, high-order bits are discarded. (Clearly |
| 535 | * the remainder vector can't overflow.) The various vectors |
| 536 | * may not overlap in any way. Yes, I know it's a bit odd |
| 537 | * requiring the dividend to be in the result position but it |
| 538 | * does make some sense really. The remainder must have |
| 539 | * headroom for at least two extra words. |
| 540 | */ |
| 541 | |
| 542 | void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl, |
| 543 | const mpw *dv, const mpw *dvl) |
| 544 | { |
| 545 | mpw spare[2]; |
| 546 | unsigned norm = 0; |
| 547 | size_t scale; |
| 548 | mpw d, dd; |
| 549 | |
| 550 | /* --- Initialize the quotient --- */ |
| 551 | |
| 552 | MPX_ZERO(qv, qvl); |
| 553 | |
| 554 | /* --- Normalize the divisor --- * |
| 555 | * |
| 556 | * The algorithm requires that the divisor be at least two digits long. |
| 557 | * This is easy to fix. |
| 558 | */ |
| 559 | |
| 560 | MPX_SHRINK(dv, dvl); |
| 561 | |
| 562 | assert(((void)"division by zero in mpx_udiv", dv < dvl)); |
| 563 | |
| 564 | d = dvl[-1]; |
| 565 | if (dv + 1 == dvl) { |
| 566 | spare[0] = 0; |
| 567 | spare[1] = d; |
| 568 | dv = spare; |
| 569 | dvl = spare + 2; |
| 570 | norm += MPW_BITS; |
| 571 | } |
| 572 | |
| 573 | while (d < MPW_MAX / 2) { |
| 574 | d <<= 1; |
| 575 | norm += 1; |
| 576 | } |
| 577 | dd = dvl[-2]; |
| 578 | |
| 579 | /* --- Normalize the dividend/remainder to match --- */ |
| 580 | |
| 581 | mpx_lsl(rv, rvl, rv, rvl, norm); |
| 582 | MPX_SHRINK(rv, rvl); |
| 583 | |
| 584 | /* --- Work out the relative scales --- */ |
| 585 | |
| 586 | { |
| 587 | size_t rvn = rvl - rv; |
| 588 | size_t dvn = dvn - dv; |
| 589 | |
| 590 | /* --- If the divisor is clearly larger, notice this --- */ |
| 591 | |
| 592 | if (dvn > rvn) { |
| 593 | mpx_lsr(rv, rvl, rv, rvl, norm); |
| 594 | return; |
| 595 | } |
| 596 | |
| 597 | scale = rvn - dvn; |
| 598 | } |
| 599 | |
| 600 | /* --- Calculate the most significant quotient digit --- * |
| 601 | * |
| 602 | * Because the divisor has its top bit set, this can only happen once. The |
| 603 | * pointer arithmetic is a little contorted, to make sure that the |
| 604 | * behaviour is defined. |
| 605 | */ |
| 606 | |
| 607 | if (MPX_UCMP(rv + scale, rvl, >=, dv, dvl)) { |
| 608 | mpx_usub(rv + scale, rvl, rv + scale, rvl, dv, dvl); |
| 609 | if (qvl - qv > scale) |
| 610 | qv[scale] = 1; |
| 611 | } |
| 612 | |
| 613 | /* --- Now for the main loop --- */ |
| 614 | |
| 615 | { |
| 616 | mpw *rvv; |
| 617 | mpw r; |
| 618 | |
| 619 | scale--; |
| 620 | rvv = rvl - 2; |
| 621 | r = rvv[1]; |
| 622 | |
| 623 | while (scale) { |
| 624 | mpw q, rr; |
| 625 | |
| 626 | /* --- Get an estimate for the next quotient digit --- */ |
| 627 | |
| 628 | rr = *rvv--; |
| 629 | if (r == d) |
| 630 | q = MPW_MAX; |
| 631 | else { |
| 632 | mpd rx = (r << MPW_BITS) | rr; |
| 633 | q = MPW(rx / d); |
| 634 | } |
| 635 | |
| 636 | /* --- Refine the estimate --- */ |
| 637 | |
| 638 | { |
| 639 | mpd yh = (mpd)d * q; |
| 640 | mpd yl = (mpd)dd * q; |
| 641 | |
| 642 | } |
| 643 | |
| 644 | /*----- That's all, folks -------------------------------------------------*/ |