lib/mpi/mpi-div.c

   1 /* mpi-div.c  -  MPI functions
   2  *      Copyright (C) 1994, 1996 Free Software Foundation, Inc.
   3  *      Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
   4  *
   5  * This file is part of GnuPG.
   6  *
   7  * GnuPG is free software; you can redistribute it and/or modify
   8  * it under the terms of the GNU General Public License as published by
   9  * the Free Software Foundation; either version 2 of the License, or
  10  * (at your option) any later version.
  11  *
  12  * GnuPG is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  * GNU General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU General Public License
  18  * along with this program; if not, write to the Free Software
  19  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
  20  *
  21  * Note: This code is heavily based on the GNU MP Library.
  22  *       Actually it's the same code with only minor changes in the
  23  *       way the data is stored; this is to support the abstraction
  24  *       of an optional secure memory allocation which may be used
  25  *       to avoid revealing of sensitive data due to paging etc.
  26  *       The GNU MP Library itself is published under the LGPL;
  27  *       however I decided to publish this code under the plain GPL.
  28  */
  29
  30 #include <linux/string.h>
  31 #include "mpi-internal.h"
  32 #include "longlong.h"
  33
  34 int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
  35 {
  36         int rc = -ENOMEM;
  37         int divisor_sign = divisor->sign;
  38         MPI temp_divisor = NULL;
  39
  40         /* We need the original value of the divisor after the remainder has been
  41          * preliminary calculated.      We have to copy it to temporary space if it's
  42          * the same variable as REM.  */
  43         if (rem == divisor) {
  44                 if (mpi_copy(&temp_divisor, divisor) < 0)
  45                         goto nomem;
  46                 divisor = temp_divisor;
  47         }
  48
  49         if (mpi_tdiv_qr(NULL, rem, dividend, divisor) < 0)
  50                 goto nomem;
  51         if (((divisor_sign ? 1 : 0) ^ (dividend->sign ? 1 : 0)) && rem->nlimbs)
  52                 if (mpi_add(rem, rem, divisor) < 0)
  53                         goto nomem;
  54
  55         rc = 0;
  56
  57 nomem:
  58         if (temp_divisor)
  59                 mpi_free(temp_divisor);
  60         return rc;
  61 }
  62
  63 /****************
  64  * Division rounding the quotient towards -infinity.
  65  * The remainder gets the same sign as the denominator.
  66  * rem is optional
  67  */
  68
  69 ulong mpi_fdiv_r_ui(MPI rem, MPI dividend, ulong divisor)
  70 {
  71         mpi_limb_t rlimb;
  72
  73         rlimb = mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
  74         if (rlimb && dividend->sign)
  75                 rlimb = divisor - rlimb;
  76
  77         if (rem) {
  78                 rem->d[0] = rlimb;
  79                 rem->nlimbs = rlimb ? 1 : 0;
  80         }
  81         return rlimb;
  82 }
  83
  84 int mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
  85 {
  86         MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
  87         if (!tmp)
  88                 return -ENOMEM;
  89         mpi_fdiv_qr(quot, tmp, dividend, divisor);
  90         mpi_free(tmp);
  91         return 0;
  92 }
  93
  94 int mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
  95 {
  96         int divisor_sign = divisor->sign;
  97         MPI temp_divisor = NULL;
  98
  99         if (quot == divisor || rem == divisor) {
 100                 if (mpi_copy(&temp_divisor, divisor) < 0)
 101                         return -ENOMEM;
 102                 divisor = temp_divisor;
 103         }
 104
 105         if (mpi_tdiv_qr(quot, rem, dividend, divisor) < 0)
 106                 goto nomem;
 107
 108         if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
 109                 if (mpi_sub_ui(quot, quot, 1) < 0)
 110                         goto nomem;
 111                 if (mpi_add(rem, rem, divisor) < 0)
 112                         goto nomem;
 113         }
 114
 115         if (temp_divisor)
 116                 mpi_free(temp_divisor);
 117
 118         return 0;
 119
 120 nomem:
 121         mpi_free(temp_divisor);
 122         return -ENOMEM;
 123 }
 124
 125 /* If den == quot, den needs temporary storage.
 126  * If den == rem, den needs temporary storage.
 127  * If num == quot, num needs temporary storage.
 128  * If den has temporary storage, it can be normalized while being copied,
 129  *   i.e no extra storage should be allocated.
 130  */
 131
 132 int mpi_tdiv_r(MPI rem, MPI num, MPI den)
 133 {
 134         return mpi_tdiv_qr(NULL, rem, num, den);
 135 }
 136
 137 int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
 138 {
 139         int rc = -ENOMEM;
 140         mpi_ptr_t np, dp;
 141         mpi_ptr_t qp, rp;
 142         mpi_size_t nsize = num->nlimbs;
 143         mpi_size_t dsize = den->nlimbs;
 144         mpi_size_t qsize, rsize;
 145         mpi_size_t sign_remainder = num->sign;
 146         mpi_size_t sign_quotient = num->sign ^ den->sign;
 147         unsigned normalization_steps;
 148         mpi_limb_t q_limb;
 149         mpi_ptr_t marker[5];
 150         int markidx = 0;
 151
 152         if (!dsize)
 153                 return -EINVAL;
 154
 155         memset(marker, 0, sizeof(marker));
 156
 157         /* Ensure space is enough for quotient and remainder.
 158          * We need space for an extra limb in the remainder, because it's
 159          * up-shifted (normalized) below.  */
 160         rsize = nsize + 1;
 161         if (mpi_resize(rem, rsize) < 0)
 162                 goto nomem;
 163
 164         qsize = rsize - dsize;  /* qsize cannot be bigger than this.  */
 165         if (qsize <= 0) {
 166                 if (num != rem) {
 167                         rem->nlimbs = num->nlimbs;
 168                         rem->sign = num->sign;
 169                         MPN_COPY(rem->d, num->d, nsize);
 170                 }
 171                 if (quot) {
 172                         /* This needs to follow the assignment to rem, in case the
 173                          * numerator and quotient are the same.  */
 174                         quot->nlimbs = 0;
 175                         quot->sign = 0;
 176                 }
 177                 return 0;
 178         }
 179
 180         if (quot)
 181                 if (mpi_resize(quot, qsize) < 0)
 182                         goto nomem;
 183
 184         /* Read pointers here, when reallocation is finished.  */
 185         np = num->d;
 186         dp = den->d;
 187         rp = rem->d;
 188
 189         /* Optimize division by a single-limb divisor.  */
 190         if (dsize == 1) {
 191                 mpi_limb_t rlimb;
 192                 if (quot) {
 193                         qp = quot->d;
 194                         rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
 195                         qsize -= qp[qsize - 1] == 0;
 196                         quot->nlimbs = qsize;
 197                         quot->sign = sign_quotient;
 198                 } else
 199                         rlimb = mpihelp_mod_1(np, nsize, dp[0]);
 200                 rp[0] = rlimb;
 201                 rsize = rlimb != 0 ? 1 : 0;
 202                 rem->nlimbs = rsize;
 203                 rem->sign = sign_remainder;
 204                 return 0;
 205         }
 206
 207         if (quot) {
 208                 qp = quot->d;
 209                 /* Make sure QP and NP point to different objects.  Otherwise the
 210                  * numerator would be gradually overwritten by the quotient limbs.  */
 211                 if (qp == np) { /* Copy NP object to temporary space.  */
 212                         np = marker[markidx++] = mpi_alloc_limb_space(nsize);
 213                         if (!np)
 214                                 goto nomem;
 215                         MPN_COPY(np, qp, nsize);
 216                 }
 217         } else                  /* Put quotient at top of remainder. */
 218                 qp = rp + dsize;
 219
 220         count_leading_zeros(normalization_steps, dp[dsize - 1]);
 221
 222         /* Normalize the denominator, i.e. make its most significant bit set by
 223          * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
 224          * numerator the same number of steps (to keep the quotient the same!).
 225          */
 226         if (normalization_steps) {
 227                 mpi_ptr_t tp;
 228                 mpi_limb_t nlimb;
 229
 230                 /* Shift up the denominator setting the most significant bit of
 231                  * the most significant word.  Use temporary storage not to clobber
 232                  * the original contents of the denominator.  */
 233                 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
 234                 if (!tp)
 235                         goto nomem;
 236                 mpihelp_lshift(tp, dp, dsize, normalization_steps);
 237                 dp = tp;
 238
 239                 /* Shift up the numerator, possibly introducing a new most
 240                  * significant word.  Move the shifted numerator in the remainder
 241                  * meanwhile.  */
 242                 nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
 243                 if (nlimb) {
 244                         rp[nsize] = nlimb;
 245                         rsize = nsize + 1;
 246                 } else
 247                         rsize = nsize;
 248         } else {
 249                 /* The denominator is already normalized, as required.  Copy it to
 250                  * temporary space if it overlaps with the quotient or remainder.  */
 251                 if (dp == rp || (quot && (dp == qp))) {
 252                         mpi_ptr_t tp;
 253
 254                         tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
 255                         if (!tp)
 256                                 goto nomem;
 257                         MPN_COPY(tp, dp, dsize);
 258                         dp = tp;
 259                 }
 260
 261                 /* Move the numerator to the remainder.  */
 262                 if (rp != np)
 263                         MPN_COPY(rp, np, nsize);
 264
 265                 rsize = nsize;
 266         }
 267
 268         q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
 269
 270         if (quot) {
 271                 qsize = rsize - dsize;
 272                 if (q_limb) {
 273                         qp[qsize] = q_limb;
 274                         qsize += 1;
 275                 }
 276
 277                 quot->nlimbs = qsize;
 278                 quot->sign = sign_quotient;
 279         }
 280
 281         rsize = dsize;
 282         MPN_NORMALIZE(rp, rsize);
 283
 284         if (normalization_steps && rsize) {
 285                 mpihelp_rshift(rp, rp, rsize, normalization_steps);
 286                 rsize -= rp[rsize - 1] == 0 ? 1 : 0;
 287         }
 288
 289         rem->nlimbs = rsize;
 290         rem->sign = sign_remainder;
 291
 292         rc = 0;
 293 nomem:
 294         while (markidx)
 295                 mpi_free_limb_space(marker[--markidx]);
 296         return rc;
 297 }
 298
 299 int mpi_tdiv_q_2exp(MPI w, MPI u, unsigned count)
 300 {
 301         mpi_size_t usize, wsize;
 302         mpi_size_t limb_cnt;
 303
 304         usize = u->nlimbs;
 305         limb_cnt = count / BITS_PER_MPI_LIMB;
 306         wsize = usize - limb_cnt;
 307         if (limb_cnt >= usize)
 308                 w->nlimbs = 0;
 309         else {
 310                 mpi_ptr_t wp;
 311                 mpi_ptr_t up;
 312
 313                 if (RESIZE_IF_NEEDED(w, wsize) < 0)
 314                         return -ENOMEM;
 315                 wp = w->d;
 316                 up = u->d;
 317
 318                 count %= BITS_PER_MPI_LIMB;
 319                 if (count) {
 320                         mpihelp_rshift(wp, up + limb_cnt, wsize, count);
 321                         wsize -= !wp[wsize - 1];
 322                 } else {
 323                         MPN_COPY_INCR(wp, up + limb_cnt, wsize);
 324                 }
 325
 326                 w->nlimbs = wsize;
 327         }
 328         return 0;
 329 }
 330
 331 /****************
 332  * Check whether dividend is divisible by divisor
 333  * (note: divisor must fit into a limb)
 334  */
 335 int mpi_divisible_ui(MPI dividend, ulong divisor)
 336 {
 337         return !mpihelp_mod_1(dividend->d, dividend->nlimbs, divisor);
 338 }