mpi-genesis~ 1
mpi-genesis~ 2 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.
mpi-genesis~ 3 * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
mpi-genesis~ 4 *
mpi-genesis~ 5 * This file is part of GnuPG.
mpi-genesis~ 6 *
mpi-genesis~ 7 * GnuPG is free software; you can redistribute it and/or modify
mpi-genesis~ 8 * it under the terms of the GNU General Public License as published by
mpi-genesis~ 9 * the Free Software Foundation; either version 3 of the License, or
mpi-genesis~ 10 * (at your option) any later version.
mpi-genesis~ 11 *
mpi-genesis~ 12 * GnuPG is distributed in the hope that it will be useful,
mpi-genesis~ 13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
mpi-genesis~ 14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
mpi-genesis~ 15 * GNU General Public License for more details.
mpi-genesis~ 16 *
mpi-genesis~ 17 * You should have received a copy of the GNU General Public License
mpi-genesis~ 18 * along with this program; if not, see <http:
mpi-genesis~ 19 *
mpi-genesis~ 20 * Note: This code is heavily based on the GNU MP Library.
mpi-genesis~ 21 * Actually it's the same code with only minor changes in the
mpi-genesis~ 22 * way the data is stored; this is to support the abstraction
mpi-genesis~ 23 * of an optional secure memory allocation which may be used
mpi-genesis~ 24 * to avoid revealing of sensitive data due to paging etc.
mpi-genesis~ 25 * The GNU MP Library itself is published under the LGPL;
mpi-genesis~ 26 * however I decided to publish this code under the plain GPL.
mpi-genesis~ 27 */
mpi-genesis~ 28
mpi-genesis~ 29 #include <config.h>
mpi-genesis~ 30 #include <stdio.h>
mpi-genesis~ 31 #include <stdlib.h>
mpi-genesis~ 32 #include "mpi-internal.h"
mpi-genesis~ 33 #include "longlong.h"
mpi-genesis~ 34
mpi-genesis~ 35 #ifndef UMUL_TIME
mpi-genesis~ 36 #define UMUL_TIME 1
mpi-genesis~ 37 #endif
mpi-genesis~ 38 #ifndef UDIV_TIME
mpi-genesis~ 39 #define UDIV_TIME UMUL_TIME
mpi-genesis~ 40 #endif
mpi-genesis~ 41
mpi-genesis~ 42
mpi-genesis~ 43 * here (not udiv_qrnnd).
mpi-genesis~ 44 */
mpi-genesis~ 45
mpi-genesis~ 46 mpi_limb_t
mpi-genesis~ 47 mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
mpi-genesis~ 48 mpi_limb_t divisor_limb)
mpi-genesis~ 49 {
mpi-genesis~ 50 mpi_size_t i;
mpi-genesis~ 51 mpi_limb_t n1, n0, r;
mpi-genesis~ 52 int dummy;
mpi-genesis~ 53
mpi-genesis~ 54
mpi-genesis~ 55 if( !dividend_size )
mpi-genesis~ 56 return 0;
mpi-genesis~ 57
mpi-genesis~ 58
mpi-genesis~ 59 * dividend is large, pre-invert the divisor, and use
mpi-genesis~ 60 * only multiplications in the inner loop.
mpi-genesis~ 61 *
mpi-genesis~ 62 * This test should be read:
mpi-genesis~ 63 * Does it ever help to use udiv_qrnnd_preinv?
mpi-genesis~ 64 * && Does what we save compensate for the inversion overhead?
mpi-genesis~ 65 */
mpi-genesis~ 66 if( UDIV_TIME > (2 * UMUL_TIME + 6)
mpi-genesis~ 67 && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
mpi-genesis~ 68 int normalization_steps;
mpi-genesis~ 69
mpi-genesis~ 70 count_leading_zeros( normalization_steps, divisor_limb );
mpi-genesis~ 71 if( normalization_steps ) {
mpi-genesis~ 72 mpi_limb_t divisor_limb_inverted;
mpi-genesis~ 73
mpi-genesis~ 74 divisor_limb <<= normalization_steps;
mpi-genesis~ 75
mpi-genesis~ 76
mpi-genesis~ 77 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
mpi-genesis~ 78 * most significant bit (with weight 2**N) implicit.
mpi-genesis~ 79 *
mpi-genesis~ 80 * Special case for DIVISOR_LIMB == 100...000.
mpi-genesis~ 81 */
mpi-genesis~ 82 if( !(divisor_limb << 1) )
mpi-genesis~ 83 divisor_limb_inverted = ~(mpi_limb_t)0;
mpi-genesis~ 84 else
mpi-genesis~ 85 udiv_qrnnd(divisor_limb_inverted, dummy,
mpi-genesis~ 86 -divisor_limb, 0, divisor_limb);
mpi-genesis~ 87
mpi-genesis~ 88 n1 = dividend_ptr[dividend_size - 1];
mpi-genesis~ 89 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
mpi-genesis~ 90
mpi-genesis~ 91
mpi-genesis~ 92 * if (r == 0
mpi-genesis~ 93 * && divisor_limb > ((n1 << normalization_steps)
mpi-genesis~ 94 * | (dividend_ptr[dividend_size - 2] >> ...)))
mpi-genesis~ 95 * ...one division less...
mpi-genesis~ 96 */
mpi-genesis~ 97 for( i = dividend_size - 2; i >= 0; i--) {
mpi-genesis~ 98 n0 = dividend_ptr[i];
mpi-genesis~ 99 UDIV_QRNND_PREINV(dummy, r, r,
mpi-genesis~ 100 ((n1 << normalization_steps)
mpi-genesis~ 101 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
mpi-genesis~ 102 divisor_limb, divisor_limb_inverted);
mpi-genesis~ 103 n1 = n0;
mpi-genesis~ 104 }
mpi-genesis~ 105 UDIV_QRNND_PREINV(dummy, r, r,
mpi-genesis~ 106 n1 << normalization_steps,
mpi-genesis~ 107 divisor_limb, divisor_limb_inverted);
mpi-genesis~ 108 return r >> normalization_steps;
mpi-genesis~ 109 }
mpi-genesis~ 110 else {
mpi-genesis~ 111 mpi_limb_t divisor_limb_inverted;
mpi-genesis~ 112
mpi-genesis~ 113
mpi-genesis~ 114 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
mpi-genesis~ 115 * most significant bit (with weight 2**N) implicit.
mpi-genesis~ 116 *
mpi-genesis~ 117 * Special case for DIVISOR_LIMB == 100...000.
mpi-genesis~ 118 */
mpi-genesis~ 119 if( !(divisor_limb << 1) )
mpi-genesis~ 120 divisor_limb_inverted = ~(mpi_limb_t)0;
mpi-genesis~ 121 else
mpi-genesis~ 122 udiv_qrnnd(divisor_limb_inverted, dummy,
mpi-genesis~ 123 -divisor_limb, 0, divisor_limb);
mpi-genesis~ 124
mpi-genesis~ 125 i = dividend_size - 1;
mpi-genesis~ 126 r = dividend_ptr[i];
mpi-genesis~ 127
mpi-genesis~ 128 if( r >= divisor_limb )
mpi-genesis~ 129 r = 0;
mpi-genesis~ 130 else
mpi-genesis~ 131 i--;
mpi-genesis~ 132
mpi-genesis~ 133 for( ; i >= 0; i--) {
mpi-genesis~ 134 n0 = dividend_ptr[i];
mpi-genesis~ 135 UDIV_QRNND_PREINV(dummy, r, r,
mpi-genesis~ 136 n0, divisor_limb, divisor_limb_inverted);
mpi-genesis~ 137 }
mpi-genesis~ 138 return r;
mpi-genesis~ 139 }
mpi-genesis~ 140 }
mpi-genesis~ 141 else {
mpi-genesis~ 142 if( UDIV_NEEDS_NORMALIZATION ) {
mpi-genesis~ 143 int normalization_steps;
mpi-genesis~ 144
mpi-genesis~ 145 count_leading_zeros(normalization_steps, divisor_limb);
mpi-genesis~ 146 if( normalization_steps ) {
mpi-genesis~ 147 divisor_limb <<= normalization_steps;
mpi-genesis~ 148
mpi-genesis~ 149 n1 = dividend_ptr[dividend_size - 1];
mpi-genesis~ 150 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
mpi-genesis~ 151
mpi-genesis~ 152
mpi-genesis~ 153 * if (r == 0
mpi-genesis~ 154 * && divisor_limb > ((n1 << normalization_steps)
mpi-genesis~ 155 * | (dividend_ptr[dividend_size - 2] >> ...)))
mpi-genesis~ 156 * ...one division less...
mpi-genesis~ 157 */
mpi-genesis~ 158 for(i = dividend_size - 2; i >= 0; i--) {
mpi-genesis~ 159 n0 = dividend_ptr[i];
mpi-genesis~ 160 udiv_qrnnd (dummy, r, r,
mpi-genesis~ 161 ((n1 << normalization_steps)
mpi-genesis~ 162 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
mpi-genesis~ 163 divisor_limb);
mpi-genesis~ 164 n1 = n0;
mpi-genesis~ 165 }
mpi-genesis~ 166 udiv_qrnnd (dummy, r, r,
mpi-genesis~ 167 n1 << normalization_steps,
mpi-genesis~ 168 divisor_limb);
mpi-genesis~ 169 return r >> normalization_steps;
mpi-genesis~ 170 }
mpi-genesis~ 171 }
mpi-genesis~ 172
mpi-genesis~ 173 * it, or because DIVISOR_LIMB is already normalized. */
mpi-genesis~ 174 i = dividend_size - 1;
mpi-genesis~ 175 r = dividend_ptr[i];
mpi-genesis~ 176
mpi-genesis~ 177 if(r >= divisor_limb)
mpi-genesis~ 178 r = 0;
mpi-genesis~ 179 else
mpi-genesis~ 180 i--;
mpi-genesis~ 181
mpi-genesis~ 182 for(; i >= 0; i--) {
mpi-genesis~ 183 n0 = dividend_ptr[i];
mpi-genesis~ 184 udiv_qrnnd (dummy, r, r, n0, divisor_limb);
mpi-genesis~ 185 }
mpi-genesis~ 186 return r;
mpi-genesis~ 187 }
mpi-genesis~ 188 }
mpi-genesis~ 189
mpi-genesis~ 190
mpi-genesis~ 191 * the NSIZE-DSIZE least significant quotient limbs at QP
mpi-genesis~ 192 * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
mpi-genesis~ 193 * non-zero, generate that many fraction bits and append them after the
mpi-genesis~ 194 * other quotient limbs.
mpi-genesis~ 195 * Return the most significant limb of the quotient, this is always 0 or 1.
mpi-genesis~ 196 *
mpi-genesis~ 197 * Preconditions:
mpi-genesis~ 198 * 0. NSIZE >= DSIZE.
mpi-genesis~ 199 * 1. The most significant bit of the divisor must be set.
mpi-genesis~ 200 * 2. QP must either not overlap with the input operands at all, or
mpi-genesis~ 201 * QP + DSIZE >= NP must hold true. (This means that it's
mpi-genesis~ 202 * possible to put the quotient in the high part of NUM, right after the
mpi-genesis~ 203 * remainder in NUM.
mpi-genesis~ 204 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
mpi-genesis~ 205 */
mpi-genesis~ 206
mpi-genesis~ 207 mpi_limb_t
mpi-genesis~ 208 mpihelp_divrem( mpi_ptr_t qp, mpi_size_t qextra_limbs,
mpi-genesis~ 209 mpi_ptr_t np, mpi_size_t nsize,
mpi-genesis~ 210 mpi_ptr_t dp, mpi_size_t dsize)
mpi-genesis~ 211 {
mpi-genesis~ 212 mpi_limb_t most_significant_q_limb = 0;
mpi-genesis~ 213
mpi-genesis~ 214 switch(dsize) {
mpi-genesis~ 215 case 0:
mpi-genesis~ 216
mpi-genesis~ 217 the compiler not remove this statement, return the value.) */
mpi-genesis~ 218 return 1 / dsize;
mpi-genesis~ 219
mpi-genesis~ 220 case 1:
mpi-genesis~ 221 {
mpi-genesis~ 222 mpi_size_t i;
mpi-genesis~ 223 mpi_limb_t n1;
mpi-genesis~ 224 mpi_limb_t d;
mpi-genesis~ 225
mpi-genesis~ 226 d = dp[0];
mpi-genesis~ 227 n1 = np[nsize - 1];
mpi-genesis~ 228
mpi-genesis~ 229 if( n1 >= d ) {
mpi-genesis~ 230 n1 -= d;
mpi-genesis~ 231 most_significant_q_limb = 1;
mpi-genesis~ 232 }
mpi-genesis~ 233
mpi-genesis~ 234 qp += qextra_limbs;
mpi-genesis~ 235 for( i = nsize - 2; i >= 0; i--)
mpi-genesis~ 236 udiv_qrnnd( qp[i], n1, n1, np[i], d );
mpi-genesis~ 237 qp -= qextra_limbs;
mpi-genesis~ 238
mpi-genesis~ 239 for( i = qextra_limbs - 1; i >= 0; i-- )
mpi-genesis~ 240 udiv_qrnnd (qp[i], n1, n1, 0, d);
mpi-genesis~ 241
mpi-genesis~ 242 np[0] = n1;
mpi-genesis~ 243 }
mpi-genesis~ 244 break;
mpi-genesis~ 245
mpi-genesis~ 246 case 2:
mpi-genesis~ 247 {
mpi-genesis~ 248 mpi_size_t i;
mpi-genesis~ 249 mpi_limb_t n1, n0, n2;
mpi-genesis~ 250 mpi_limb_t d1, d0;
mpi-genesis~ 251
mpi-genesis~ 252 np += nsize - 2;
mpi-genesis~ 253 d1 = dp[1];
mpi-genesis~ 254 d0 = dp[0];
mpi-genesis~ 255 n1 = np[1];
mpi-genesis~ 256 n0 = np[0];
mpi-genesis~ 257
mpi-genesis~ 258 if( n1 >= d1 && (n1 > d1 || n0 >= d0) ) {
mpi-genesis~ 259 sub_ddmmss (n1, n0, n1, n0, d1, d0);
mpi-genesis~ 260 most_significant_q_limb = 1;
mpi-genesis~ 261 }
mpi-genesis~ 262
mpi-genesis~ 263 for( i = qextra_limbs + nsize - 2 - 1; i >= 0; i-- ) {
mpi-genesis~ 264 mpi_limb_t q;
mpi-genesis~ 265 mpi_limb_t r;
mpi-genesis~ 266
mpi-genesis~ 267 if( i >= qextra_limbs )
mpi-genesis~ 268 np--;
mpi-genesis~ 269 else
mpi-genesis~ 270 np[0] = 0;
mpi-genesis~ 271
mpi-genesis~ 272 if( n1 == d1 ) {
mpi-genesis~ 273
mpi-genesis~ 274 * treatment of this rare case as normal division would
mpi-genesis~ 275 * give overflow. */
mpi-genesis~ 276 q = ~(mpi_limb_t)0;
mpi-genesis~ 277
mpi-genesis~ 278 r = n0 + d1;
mpi-genesis~ 279 if( r < d1 ) {
mpi-genesis~ 280 add_ssaaaa( n1, n0, r - d0, np[0], 0, d0 );
mpi-genesis~ 281 qp[i] = q;
mpi-genesis~ 282 continue;
mpi-genesis~ 283 }
mpi-genesis~ 284 n1 = d0 - (d0 != 0?1:0);
mpi-genesis~ 285 n0 = -d0;
mpi-genesis~ 286 }
mpi-genesis~ 287 else {
mpi-genesis~ 288 udiv_qrnnd (q, r, n1, n0, d1);
mpi-genesis~ 289 umul_ppmm (n1, n0, d0, q);
mpi-genesis~ 290 }
mpi-genesis~ 291
mpi-genesis~ 292 n2 = np[0];
mpi-genesis~ 293 q_test:
mpi-genesis~ 294 if( n1 > r || (n1 == r && n0 > n2) ) {
mpi-genesis~ 295
mpi-genesis~ 296 q--;
mpi-genesis~ 297 sub_ddmmss (n1, n0, n1, n0, 0, d0);
mpi-genesis~ 298 r += d1;
mpi-genesis~ 299 if( r >= d1 )
mpi-genesis~ 300 goto q_test;
mpi-genesis~ 301 }
mpi-genesis~ 302
mpi-genesis~ 303 qp[i] = q;
mpi-genesis~ 304 sub_ddmmss (n1, n0, r, n2, n1, n0);
mpi-genesis~ 305 }
mpi-genesis~ 306 np[1] = n1;
mpi-genesis~ 307 np[0] = n0;
mpi-genesis~ 308 }
mpi-genesis~ 309 break;
mpi-genesis~ 310
mpi-genesis~ 311 default:
mpi-genesis~ 312 {
mpi-genesis~ 313 mpi_size_t i;
mpi-genesis~ 314 mpi_limb_t dX, d1, n0;
mpi-genesis~ 315
mpi-genesis~ 316 np += nsize - dsize;
mpi-genesis~ 317 dX = dp[dsize - 1];
mpi-genesis~ 318 d1 = dp[dsize - 2];
mpi-genesis~ 319 n0 = np[dsize - 1];
mpi-genesis~ 320
mpi-genesis~ 321 if( n0 >= dX ) {
mpi-genesis~ 322 if(n0 > dX || mpihelp_cmp(np, dp, dsize - 1) >= 0 ) {
mpi-genesis~ 323 mpihelp_sub_n(np, np, dp, dsize);
mpi-genesis~ 324 n0 = np[dsize - 1];
mpi-genesis~ 325 most_significant_q_limb = 1;
mpi-genesis~ 326 }
mpi-genesis~ 327 }
mpi-genesis~ 328
mpi-genesis~ 329 for( i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
mpi-genesis~ 330 mpi_limb_t q;
mpi-genesis~ 331 mpi_limb_t n1, n2;
mpi-genesis~ 332 mpi_limb_t cy_limb;
mpi-genesis~ 333
mpi-genesis~ 334 if( i >= qextra_limbs ) {
mpi-genesis~ 335 np--;
mpi-genesis~ 336 n2 = np[dsize];
mpi-genesis~ 337 }
mpi-genesis~ 338 else {
mpi-genesis~ 339 n2 = np[dsize - 1];
mpi-genesis~ 340 MPN_COPY_DECR (np + 1, np, dsize - 1);
mpi-genesis~ 341 np[0] = 0;
mpi-genesis~ 342 }
mpi-genesis~ 343
mpi-genesis~ 344 if( n0 == dX ) {
mpi-genesis~ 345
mpi-genesis~ 346 * the extra code here to find out. */
mpi-genesis~ 347 q = ~(mpi_limb_t)0;
mpi-genesis~ 348 }
mpi-genesis~ 349 else {
mpi-genesis~ 350 mpi_limb_t r;
mpi-genesis~ 351
mpi-genesis~ 352 udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
mpi-genesis~ 353 umul_ppmm(n1, n0, d1, q);
mpi-genesis~ 354
mpi-genesis~ 355 while( n1 > r || (n1 == r && n0 > np[dsize - 2])) {
mpi-genesis~ 356 q--;
mpi-genesis~ 357 r += dX;
mpi-genesis~ 358 if( r < dX )
mpi-genesis~ 359 break;
mpi-genesis~ 360 n1 -= n0 < d1;
mpi-genesis~ 361 n0 -= d1;
mpi-genesis~ 362 }
mpi-genesis~ 363 }
mpi-genesis~ 364
mpi-genesis~ 365
mpi-genesis~ 366 * after the calculation of q. Taking advantage of that, we
mpi-genesis~ 367 * could make this loop make two iterations less. */
mpi-genesis~ 368 cy_limb = mpihelp_submul_1(np, dp, dsize, q);
mpi-genesis~ 369
mpi-genesis~ 370 if( n2 != cy_limb ) {
mpi-genesis~ 371 mpihelp_add_n(np, np, dp, dsize);
mpi-genesis~ 372 q--;
mpi-genesis~ 373 }
mpi-genesis~ 374
mpi-genesis~ 375 qp[i] = q;
mpi-genesis~ 376 n0 = np[dsize - 1];
mpi-genesis~ 377 }
mpi-genesis~ 378 }
mpi-genesis~ 379 }
mpi-genesis~ 380
mpi-genesis~ 381 return most_significant_q_limb;
mpi-genesis~ 382 }
mpi-genesis~ 383
mpi-genesis~ 384
mpi-genesis~ 385
mpi-genesis~ 386 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
mpi-genesis~ 387 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
mpi-genesis~ 388 * Return the single-limb remainder.
mpi-genesis~ 389 * There are no constraints on the value of the divisor.
mpi-genesis~ 390 *
mpi-genesis~ 391 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
mpi-genesis~ 392 */
mpi-genesis~ 393
mpi-genesis~ 394 mpi_limb_t
mpi-genesis~ 395 mpihelp_divmod_1( mpi_ptr_t quot_ptr,
mpi-genesis~ 396 mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
mpi-genesis~ 397 mpi_limb_t divisor_limb)
mpi-genesis~ 398 {
mpi-genesis~ 399 mpi_size_t i;
mpi-genesis~ 400 mpi_limb_t n1, n0, r;
mpi-genesis~ 401 int dummy;
mpi-genesis~ 402
mpi-genesis~ 403 if( !dividend_size )
mpi-genesis~ 404 return 0;
mpi-genesis~ 405
mpi-genesis~ 406
mpi-genesis~ 407 * dividend is large, pre-invert the divisor, and use
mpi-genesis~ 408 * only multiplications in the inner loop.
mpi-genesis~ 409 *
mpi-genesis~ 410 * This test should be read:
mpi-genesis~ 411 * Does it ever help to use udiv_qrnnd_preinv?
mpi-genesis~ 412 * && Does what we save compensate for the inversion overhead?
mpi-genesis~ 413 */
mpi-genesis~ 414 if( UDIV_TIME > (2 * UMUL_TIME + 6)
mpi-genesis~ 415 && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
mpi-genesis~ 416 int normalization_steps;
mpi-genesis~ 417
mpi-genesis~ 418 count_leading_zeros( normalization_steps, divisor_limb );
mpi-genesis~ 419 if( normalization_steps ) {
mpi-genesis~ 420 mpi_limb_t divisor_limb_inverted;
mpi-genesis~ 421
mpi-genesis~ 422 divisor_limb <<= normalization_steps;
mpi-genesis~ 423
mpi-genesis~ 424
mpi-genesis~ 425 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
mpi-genesis~ 426 * most significant bit (with weight 2**N) implicit.
mpi-genesis~ 427 */
mpi-genesis~ 428
mpi-genesis~ 429 if( !(divisor_limb << 1) )
mpi-genesis~ 430 divisor_limb_inverted = ~(mpi_limb_t)0;
mpi-genesis~ 431 else
mpi-genesis~ 432 udiv_qrnnd(divisor_limb_inverted, dummy,
mpi-genesis~ 433 -divisor_limb, 0, divisor_limb);
mpi-genesis~ 434
mpi-genesis~ 435 n1 = dividend_ptr[dividend_size - 1];
mpi-genesis~ 436 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
mpi-genesis~ 437
mpi-genesis~ 438
mpi-genesis~ 439 * if (r == 0
mpi-genesis~ 440 * && divisor_limb > ((n1 << normalization_steps)
mpi-genesis~ 441 * | (dividend_ptr[dividend_size - 2] >> ...)))
mpi-genesis~ 442 * ...one division less...
mpi-genesis~ 443 */
mpi-genesis~ 444 for( i = dividend_size - 2; i >= 0; i--) {
mpi-genesis~ 445 n0 = dividend_ptr[i];
mpi-genesis~ 446 UDIV_QRNND_PREINV( quot_ptr[i + 1], r, r,
mpi-genesis~ 447 ((n1 << normalization_steps)
mpi-genesis~ 448 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
mpi-genesis~ 449 divisor_limb, divisor_limb_inverted);
mpi-genesis~ 450 n1 = n0;
mpi-genesis~ 451 }
mpi-genesis~ 452 UDIV_QRNND_PREINV( quot_ptr[0], r, r,
mpi-genesis~ 453 n1 << normalization_steps,
mpi-genesis~ 454 divisor_limb, divisor_limb_inverted);
mpi-genesis~ 455 return r >> normalization_steps;
mpi-genesis~ 456 }
mpi-genesis~ 457 else {
mpi-genesis~ 458 mpi_limb_t divisor_limb_inverted;
mpi-genesis~ 459
mpi-genesis~ 460
mpi-genesis~ 461 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
mpi-genesis~ 462 * most significant bit (with weight 2**N) implicit.
mpi-genesis~ 463 */
mpi-genesis~ 464
mpi-genesis~ 465 if( !(divisor_limb << 1) )
mpi-genesis~ 466 divisor_limb_inverted = ~(mpi_limb_t) 0;
mpi-genesis~ 467 else
mpi-genesis~ 468 udiv_qrnnd(divisor_limb_inverted, dummy,
mpi-genesis~ 469 -divisor_limb, 0, divisor_limb);
mpi-genesis~ 470
mpi-genesis~ 471 i = dividend_size - 1;
mpi-genesis~ 472 r = dividend_ptr[i];
mpi-genesis~ 473
mpi-genesis~ 474 if( r >= divisor_limb )
mpi-genesis~ 475 r = 0;
mpi-genesis~ 476 else
mpi-genesis~ 477 quot_ptr[i--] = 0;
mpi-genesis~ 478
mpi-genesis~ 479 for( ; i >= 0; i-- ) {
mpi-genesis~ 480 n0 = dividend_ptr[i];
mpi-genesis~ 481 UDIV_QRNND_PREINV( quot_ptr[i], r, r,
mpi-genesis~ 482 n0, divisor_limb, divisor_limb_inverted);
mpi-genesis~ 483 }
mpi-genesis~ 484 return r;
mpi-genesis~ 485 }
mpi-genesis~ 486 }
mpi-genesis~ 487 else {
mpi-genesis~ 488 if(UDIV_NEEDS_NORMALIZATION) {
mpi-genesis~ 489 int normalization_steps;
mpi-genesis~ 490
mpi-genesis~ 491 count_leading_zeros (normalization_steps, divisor_limb);
mpi-genesis~ 492 if( normalization_steps ) {
mpi-genesis~ 493 divisor_limb <<= normalization_steps;
mpi-genesis~ 494
mpi-genesis~ 495 n1 = dividend_ptr[dividend_size - 1];
mpi-genesis~ 496 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
mpi-genesis~ 497
mpi-genesis~ 498
mpi-genesis~ 499 * if (r == 0
mpi-genesis~ 500 * && divisor_limb > ((n1 << normalization_steps)
mpi-genesis~ 501 * | (dividend_ptr[dividend_size - 2] >> ...)))
mpi-genesis~ 502 * ...one division less...
mpi-genesis~ 503 */
mpi-genesis~ 504 for( i = dividend_size - 2; i >= 0; i--) {
mpi-genesis~ 505 n0 = dividend_ptr[i];
mpi-genesis~ 506 udiv_qrnnd (quot_ptr[i + 1], r, r,
mpi-genesis~ 507 ((n1 << normalization_steps)
mpi-genesis~ 508 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
mpi-genesis~ 509 divisor_limb);
mpi-genesis~ 510 n1 = n0;
mpi-genesis~ 511 }
mpi-genesis~ 512 udiv_qrnnd (quot_ptr[0], r, r,
mpi-genesis~ 513 n1 << normalization_steps,
mpi-genesis~ 514 divisor_limb);
mpi-genesis~ 515 return r >> normalization_steps;
mpi-genesis~ 516 }
mpi-genesis~ 517 }
mpi-genesis~ 518
mpi-genesis~ 519 * it, or because DIVISOR_LIMB is already normalized. */
mpi-genesis~ 520 i = dividend_size - 1;
mpi-genesis~ 521 r = dividend_ptr[i];
mpi-genesis~ 522
mpi-genesis~ 523 if(r >= divisor_limb)
mpi-genesis~ 524 r = 0;
mpi-genesis~ 525 else
mpi-genesis~ 526 quot_ptr[i--] = 0;
mpi-genesis~ 527
mpi-genesis~ 528 for(; i >= 0; i--) {
mpi-genesis~ 529 n0 = dividend_ptr[i];
mpi-genesis~ 530 udiv_qrnnd( quot_ptr[i], r, r, n0, divisor_limb );
mpi-genesis~ 531 }
mpi-genesis~ 532 return r;
mpi-genesis~ 533 }
mpi-genesis~ 534 }