lib/mpi/mpih-div.c

   1 /* mpihelp-div.c  -  MPI helper functions
   2  *      Copyright (C) 1994, 1996 Free Software Foundation, Inc.
   3  *      Copyright (C) 1998, 1999 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 "mpi-internal.h"
  31 #include "longlong.h"
  32
  33 #ifndef UMUL_TIME
  34 #define UMUL_TIME 1
  35 #endif
  36 #ifndef UDIV_TIME
  37 #define UDIV_TIME UMUL_TIME
  38 #endif
  39
  40 /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
  41  * the NSIZE-DSIZE least significant quotient limbs at QP
  42  * and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is
  43  * non-zero, generate that many fraction bits and append them after the
  44  * other quotient limbs.
  45  * Return the most significant limb of the quotient, this is always 0 or 1.
  46  *
  47  * Preconditions:
  48  * 0. NSIZE >= DSIZE.
  49  * 1. The most significant bit of the divisor must be set.
  50  * 2. QP must either not overlap with the input operands at all, or
  51  *    QP + DSIZE >= NP must hold true.  (This means that it's
  52  *    possible to put the quotient in the high part of NUM, right after the
  53  *    remainder in NUM.
  54  * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
  55  */
  56
  57 mpi_limb_t
  58 mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
  59                mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
  60 {
  61         mpi_limb_t most_significant_q_limb = 0;
  62
  63         switch (dsize) {
  64         case 0:
  65                 /* We are asked to divide by zero, so go ahead and do it!  (To make
  66                    the compiler not remove this statement, return the value.)  */
  67                 /*
  68                  * existing clients of this function have been modified
  69                  * not to call it with dsize == 0, so this should not happen
  70                  */
  71                 return 1 / dsize;
  72
  73         case 1:
  74                 {
  75                         mpi_size_t i;
  76                         mpi_limb_t n1;
  77                         mpi_limb_t d;
  78
  79                         d = dp[0];
  80                         n1 = np[nsize - 1];
  81
  82                         if (n1 >= d) {
  83                                 n1 -= d;
  84                                 most_significant_q_limb = 1;
  85                         }
  86
  87                         qp += qextra_limbs;
  88                         for (i = nsize - 2; i >= 0; i--)
  89                                 udiv_qrnnd(qp[i], n1, n1, np[i], d);
  90                         qp -= qextra_limbs;
  91
  92                         for (i = qextra_limbs - 1; i >= 0; i--)
  93                                 udiv_qrnnd(qp[i], n1, n1, 0, d);
  94
  95                         np[0] = n1;
  96                 }
  97                 break;
  98
  99         case 2:
 100                 {
 101                         mpi_size_t i;
 102                         mpi_limb_t n1, n0, n2;
 103                         mpi_limb_t d1, d0;
 104
 105                         np += nsize - 2;
 106                         d1 = dp[1];
 107                         d0 = dp[0];
 108                         n1 = np[1];
 109                         n0 = np[0];
 110
 111                         if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
 112                                 sub_ddmmss(n1, n0, n1, n0, d1, d0);
 113                                 most_significant_q_limb = 1;
 114                         }
 115
 116                         for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
 117                                 mpi_limb_t q;
 118                                 mpi_limb_t r;
 119
 120                                 if (i >= qextra_limbs)
 121                                         np--;
 122                                 else
 123                                         np[0] = 0;
 124
 125                                 if (n1 == d1) {
 126                                         /* Q should be either 111..111 or 111..110.  Need special
 127                                          * treatment of this rare case as normal division would
 128                                          * give overflow.  */
 129                                         q = ~(mpi_limb_t) 0;
 130
 131                                         r = n0 + d1;
 132                                         if (r < d1) {   /* Carry in the addition? */
 133                                                 add_ssaaaa(n1, n0, r - d0,
 134                                                            np[0], 0, d0);
 135                                                 qp[i] = q;
 136                                                 continue;
 137                                         }
 138                                         n1 = d0 - (d0 != 0 ? 1 : 0);
 139                                         n0 = -d0;
 140                                 } else {
 141                                         udiv_qrnnd(q, r, n1, n0, d1);
 142                                         umul_ppmm(n1, n0, d0, q);
 143                                 }
 144
 145                                 n2 = np[0];
 146 q_test:
 147                                 if (n1 > r || (n1 == r && n0 > n2)) {
 148                                         /* The estimated Q was too large.  */
 149                                         q--;
 150                                         sub_ddmmss(n1, n0, n1, n0, 0, d0);
 151                                         r += d1;
 152                                         if (r >= d1)    /* If not carry, test Q again.  */
 153                                                 goto q_test;
 154                                 }
 155
 156                                 qp[i] = q;
 157                                 sub_ddmmss(n1, n0, r, n2, n1, n0);
 158                         }
 159                         np[1] = n1;
 160                         np[0] = n0;
 161                 }
 162                 break;
 163
 164         default:
 165                 {
 166                         mpi_size_t i;
 167                         mpi_limb_t dX, d1, n0;
 168
 169                         np += nsize - dsize;
 170                         dX = dp[dsize - 1];
 171                         d1 = dp[dsize - 2];
 172                         n0 = np[dsize - 1];
 173
 174                         if (n0 >= dX) {
 175                                 if (n0 > dX
 176                                     || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
 177                                         mpihelp_sub_n(np, np, dp, dsize);
 178                                         n0 = np[dsize - 1];
 179                                         most_significant_q_limb = 1;
 180                                 }
 181                         }
 182
 183                         for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
 184                                 mpi_limb_t q;
 185                                 mpi_limb_t n1, n2;
 186                                 mpi_limb_t cy_limb;
 187
 188                                 if (i >= qextra_limbs) {
 189                                         np--;
 190                                         n2 = np[dsize];
 191                                 } else {
 192                                         n2 = np[dsize - 1];
 193                                         MPN_COPY_DECR(np + 1, np, dsize - 1);
 194                                         np[0] = 0;
 195                                 }
 196
 197                                 if (n0 == dX) {
 198                                         /* This might over-estimate q, but it's probably not worth
 199                                          * the extra code here to find out.  */
 200                                         q = ~(mpi_limb_t) 0;
 201                                 } else {
 202                                         mpi_limb_t r;
 203
 204                                         udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
 205                                         umul_ppmm(n1, n0, d1, q);
 206
 207                                         while (n1 > r
 208                                                || (n1 == r
 209                                                    && n0 > np[dsize - 2])) {
 210                                                 q--;
 211                                                 r += dX;
 212                                                 if (r < dX)     /* I.e. "carry in previous addition?" */
 213                                                         break;
 214                                                 n1 -= n0 < d1;
 215                                                 n0 -= d1;
 216                                         }
 217                                 }
 218
 219                                 /* Possible optimization: We already have (q * n0) and (1 * n1)
 220                                  * after the calculation of q.  Taking advantage of that, we
 221                                  * could make this loop make two iterations less.  */
 222                                 cy_limb = mpihelp_submul_1(np, dp, dsize, q);
 223
 224                                 if (n2 != cy_limb) {
 225                                         mpihelp_add_n(np, np, dp, dsize);
 226                                         q--;
 227                                 }
 228
 229                                 qp[i] = q;
 230                                 n0 = np[dsize - 1];
 231                         }
 232                 }
 233         }
 234
 235         return most_significant_q_limb;
 236 }