lib/mpi/mpi-div.c

   1 /* mpi-div.c  -  MPI functions
   2  * Copyright (C) 1994, 1996, 1998, 2001, 2002,
   3  *               2003 Free Software Foundation, Inc.
   4  *
   5  * This file is part of Libgcrypt.
   6  *
   7  * Note: This code is heavily based on the GNU MP Library.
   8  *       Actually it's the same code with only minor changes in the
   9  *       way the data is stored; this is to support the abstraction
  10  *       of an optional secure memory allocation which may be used
  11  *       to avoid revealing of sensitive data due to paging etc.
  12  */
  13
  14 #include "mpi-internal.h"
  15 #include "longlong.h"
  16
  17 void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
  18 void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
  19
  20 void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
  21 {
  22         int divisor_sign = divisor->sign;
  23         MPI temp_divisor = NULL;
  24
  25         /* We need the original value of the divisor after the remainder has been
  26          * preliminary calculated.      We have to copy it to temporary space if it's
  27          * the same variable as REM.
  28          */
  29         if (rem == divisor) {
  30                 temp_divisor = mpi_copy(divisor);
  31                 divisor = temp_divisor;
  32         }
  33
  34         mpi_tdiv_r(rem, dividend, divisor);
  35
  36         if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
  37                 mpi_add(rem, rem, divisor);
  38
  39         if (temp_divisor)
  40                 mpi_free(temp_divisor);
  41 }
  42
  43 void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
  44 {
  45         MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
  46         mpi_fdiv_qr(quot, tmp, dividend, divisor);
  47         mpi_free(tmp);
  48 }
  49
  50 void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
  51 {
  52         int divisor_sign = divisor->sign;
  53         MPI temp_divisor = NULL;
  54
  55         if (quot == divisor || rem == divisor) {
  56                 temp_divisor = mpi_copy(divisor);
  57                 divisor = temp_divisor;
  58         }
  59
  60         mpi_tdiv_qr(quot, rem, dividend, divisor);
  61
  62         if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
  63                 mpi_sub_ui(quot, quot, 1);
  64                 mpi_add(rem, rem, divisor);
  65         }
  66
  67         if (temp_divisor)
  68                 mpi_free(temp_divisor);
  69 }
  70
  71 /* If den == quot, den needs temporary storage.
  72  * If den == rem, den needs temporary storage.
  73  * If num == quot, num needs temporary storage.
  74  * If den has temporary storage, it can be normalized while being copied,
  75  *   i.e no extra storage should be allocated.
  76  */
  77
  78 void mpi_tdiv_r(MPI rem, MPI num, MPI den)
  79 {
  80         mpi_tdiv_qr(NULL, rem, num, den);
  81 }
  82
  83 void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
  84 {
  85         mpi_ptr_t np, dp;
  86         mpi_ptr_t qp, rp;
  87         mpi_size_t nsize = num->nlimbs;
  88         mpi_size_t dsize = den->nlimbs;
  89         mpi_size_t qsize, rsize;
  90         mpi_size_t sign_remainder = num->sign;
  91         mpi_size_t sign_quotient = num->sign ^ den->sign;
  92         unsigned int normalization_steps;
  93         mpi_limb_t q_limb;
  94         mpi_ptr_t marker[5];
  95         int markidx = 0;
  96
  97         /* Ensure space is enough for quotient and remainder.
  98          * We need space for an extra limb in the remainder, because it's
  99          * up-shifted (normalized) below.
 100          */
 101         rsize = nsize + 1;
 102         mpi_resize(rem, rsize);
 103
 104         qsize = rsize - dsize;    /* qsize cannot be bigger than this.  */
 105         if (qsize <= 0) {
 106                 if (num != rem) {
 107                         rem->nlimbs = num->nlimbs;
 108                         rem->sign = num->sign;
 109                         MPN_COPY(rem->d, num->d, nsize);
 110                 }
 111                 if (quot) {
 112                         /* This needs to follow the assignment to rem, in case the
 113                          * numerator and quotient are the same.
 114                          */
 115                         quot->nlimbs = 0;
 116                         quot->sign = 0;
 117                 }
 118                 return;
 119         }
 120
 121         if (quot)
 122                 mpi_resize(quot, qsize);
 123
 124         /* Read pointers here, when reallocation is finished.  */
 125         np = num->d;
 126         dp = den->d;
 127         rp = rem->d;
 128
 129         /* Optimize division by a single-limb divisor.  */
 130         if (dsize == 1) {
 131                 mpi_limb_t rlimb;
 132                 if (quot) {
 133                         qp = quot->d;
 134                         rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
 135                         qsize -= qp[qsize - 1] == 0;
 136                         quot->nlimbs = qsize;
 137                         quot->sign = sign_quotient;
 138                 } else
 139                         rlimb = mpihelp_mod_1(np, nsize, dp[0]);
 140                 rp[0] = rlimb;
 141                 rsize = rlimb != 0?1:0;
 142                 rem->nlimbs = rsize;
 143                 rem->sign = sign_remainder;
 144                 return;
 145         }
 146
 147
 148         if (quot) {
 149                 qp = quot->d;
 150                 /* Make sure QP and NP point to different objects.  Otherwise the
 151                  * numerator would be gradually overwritten by the quotient limbs.
 152                  */
 153                 if (qp == np) { /* Copy NP object to temporary space.  */
 154                         np = marker[markidx++] = mpi_alloc_limb_space(nsize);
 155                         MPN_COPY(np, qp, nsize);
 156                 }
 157         } else /* Put quotient at top of remainder. */
 158                 qp = rp + dsize;
 159
 160         normalization_steps = count_leading_zeros(dp[dsize - 1]);
 161
 162         /* Normalize the denominator, i.e. make its most significant bit set by
 163          * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
 164          * numerator the same number of steps (to keep the quotient the same!).
 165          */
 166         if (normalization_steps) {
 167                 mpi_ptr_t tp;
 168                 mpi_limb_t nlimb;
 169
 170                 /* Shift up the denominator setting the most significant bit of
 171                  * the most significant word.  Use temporary storage not to clobber
 172                  * the original contents of the denominator.
 173                  */
 174                 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
 175                 mpihelp_lshift(tp, dp, dsize, normalization_steps);
 176                 dp = tp;
 177
 178                 /* Shift up the numerator, possibly introducing a new most
 179                  * significant word.  Move the shifted numerator in the remainder
 180                  * meanwhile.
 181                  */
 182                 nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
 183                 if (nlimb) {
 184                         rp[nsize] = nlimb;
 185                         rsize = nsize + 1;
 186                 } else
 187                         rsize = nsize;
 188         } else {
 189                 /* The denominator is already normalized, as required.  Copy it to
 190                  * temporary space if it overlaps with the quotient or remainder.
 191                  */
 192                 if (dp == rp || (quot && (dp == qp))) {
 193                         mpi_ptr_t tp;
 194
 195                         tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
 196                         MPN_COPY(tp, dp, dsize);
 197                         dp = tp;
 198                 }
 199
 200                 /* Move the numerator to the remainder.  */
 201                 if (rp != np)
 202                         MPN_COPY(rp, np, nsize);
 203
 204                 rsize = nsize;
 205         }
 206
 207         q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
 208
 209         if (quot) {
 210                 qsize = rsize - dsize;
 211                 if (q_limb) {
 212                         qp[qsize] = q_limb;
 213                         qsize += 1;
 214                 }
 215
 216                 quot->nlimbs = qsize;
 217                 quot->sign = sign_quotient;
 218         }
 219
 220         rsize = dsize;
 221         MPN_NORMALIZE(rp, rsize);
 222
 223         if (normalization_steps && rsize) {
 224                 mpihelp_rshift(rp, rp, rsize, normalization_steps);
 225                 rsize -= rp[rsize - 1] == 0?1:0;
 226         }
 227
 228         rem->nlimbs = rsize;
 229         rem->sign       = sign_remainder;
 230         while (markidx) {
 231                 markidx--;
 232                 mpi_free_limb_space(marker[markidx]);
 233         }
 234 }