lib/mpi/mpih-div.c

   1 // SPDX-License-Identifier: GPL-2.0-or-later
   2 /* mpihelp-div.c  -  MPI helper functions
   3  *      Copyright (C) 1994, 1996 Free Software Foundation, Inc.
   4  *      Copyright (C) 1998, 1999 Free Software Foundation, Inc.
   5  *
   6  * This file is part of GnuPG.
   7  *
   8  * Note: This code is heavily based on the GNU MP Library.
   9  *       Actually it's the same code with only minor changes in the
  10  *       way the data is stored; this is to support the abstraction
  11  *       of an optional secure memory allocation which may be used
  12  *       to avoid revealing of sensitive data due to paging etc.
  13  *       The GNU MP Library itself is published under the LGPL;
  14  *       however I decided to publish this code under the plain GPL.
  15  */
  16
  17 #include "mpi-internal.h"
  18 #include "longlong.h"
  19
  20 #ifndef UMUL_TIME
  21 #define UMUL_TIME 1
  22 #endif
  23 #ifndef UDIV_TIME
  24 #define UDIV_TIME UMUL_TIME
  25 #endif
  26
  27 /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
  28  * the NSIZE-DSIZE least significant quotient limbs at QP
  29  * and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is
  30  * non-zero, generate that many fraction bits and append them after the
  31  * other quotient limbs.
  32  * Return the most significant limb of the quotient, this is always 0 or 1.
  33  *
  34  * Preconditions:
  35  * 0. NSIZE >= DSIZE.
  36  * 1. The most significant bit of the divisor must be set.
  37  * 2. QP must either not overlap with the input operands at all, or
  38  *    QP + DSIZE >= NP must hold true.  (This means that it's
  39  *    possible to put the quotient in the high part of NUM, right after the
  40  *    remainder in NUM.
  41  * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
  42  */
  43
  44 mpi_limb_t
  45 mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
  46                mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
  47 {
  48         mpi_limb_t most_significant_q_limb = 0;
  49
  50         switch (dsize) {
  51         case 0:
  52                 /* We are asked to divide by zero, so go ahead and do it!  (To make
  53                    the compiler not remove this statement, return the value.)  */
  54                 /*
  55                  * existing clients of this function have been modified
  56                  * not to call it with dsize == 0, so this should not happen
  57                  */
  58                 return 1 / dsize;
  59
  60         case 1:
  61                 {
  62                         mpi_size_t i;
  63                         mpi_limb_t n1;
  64                         mpi_limb_t d;
  65
  66                         d = dp[0];
  67                         n1 = np[nsize - 1];
  68
  69                         if (n1 >= d) {
  70                                 n1 -= d;
  71                                 most_significant_q_limb = 1;
  72                         }
  73
  74                         qp += qextra_limbs;
  75                         for (i = nsize - 2; i >= 0; i--)
  76                                 udiv_qrnnd(qp[i], n1, n1, np[i], d);
  77                         qp -= qextra_limbs;
  78
  79                         for (i = qextra_limbs - 1; i >= 0; i--)
  80                                 udiv_qrnnd(qp[i], n1, n1, 0, d);
  81
  82                         np[0] = n1;
  83                 }
  84                 break;
  85
  86         case 2:
  87                 {
  88                         mpi_size_t i;
  89                         mpi_limb_t n1, n0, n2;
  90                         mpi_limb_t d1, d0;
  91
  92                         np += nsize - 2;
  93                         d1 = dp[1];
  94                         d0 = dp[0];
  95                         n1 = np[1];
  96                         n0 = np[0];
  97
  98                         if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
  99                                 sub_ddmmss(n1, n0, n1, n0, d1, d0);
 100                                 most_significant_q_limb = 1;
 101                         }
 102
 103                         for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
 104                                 mpi_limb_t q;
 105                                 mpi_limb_t r;
 106
 107                                 if (i >= qextra_limbs)
 108                                         np--;
 109                                 else
 110                                         np[0] = 0;
 111
 112                                 if (n1 == d1) {
 113                                         /* Q should be either 111..111 or 111..110.  Need special
 114                                          * treatment of this rare case as normal division would
 115                                          * give overflow.  */
 116                                         q = ~(mpi_limb_t) 0;
 117
 118                                         r = n0 + d1;
 119                                         if (r < d1) {   /* Carry in the addition? */
 120                                                 add_ssaaaa(n1, n0, r - d0,
 121                                                            np[0], 0, d0);
 122                                                 qp[i] = q;
 123                                                 continue;
 124                                         }
 125                                         n1 = d0 - (d0 != 0 ? 1 : 0);
 126                                         n0 = -d0;
 127                                 } else {
 128                                         udiv_qrnnd(q, r, n1, n0, d1);
 129                                         umul_ppmm(n1, n0, d0, q);
 130                                 }
 131
 132                                 n2 = np[0];
 133 q_test:
 134                                 if (n1 > r || (n1 == r && n0 > n2)) {
 135                                         /* The estimated Q was too large.  */
 136                                         q--;
 137                                         sub_ddmmss(n1, n0, n1, n0, 0, d0);
 138                                         r += d1;
 139                                         if (r >= d1)    /* If not carry, test Q again.  */
 140                                                 goto q_test;
 141                                 }
 142
 143                                 qp[i] = q;
 144                                 sub_ddmmss(n1, n0, r, n2, n1, n0);
 145                         }
 146                         np[1] = n1;
 147                         np[0] = n0;
 148                 }
 149                 break;
 150
 151         default:
 152                 {
 153                         mpi_size_t i;
 154                         mpi_limb_t dX, d1, n0;
 155
 156                         np += nsize - dsize;
 157                         dX = dp[dsize - 1];
 158                         d1 = dp[dsize - 2];
 159                         n0 = np[dsize - 1];
 160
 161                         if (n0 >= dX) {
 162                                 if (n0 > dX
 163                                     || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
 164                                         mpihelp_sub_n(np, np, dp, dsize);
 165                                         n0 = np[dsize - 1];
 166                                         most_significant_q_limb = 1;
 167                                 }
 168                         }
 169
 170                         for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
 171                                 mpi_limb_t q;
 172                                 mpi_limb_t n1, n2;
 173                                 mpi_limb_t cy_limb;
 174
 175                                 if (i >= qextra_limbs) {
 176                                         np--;
 177                                         n2 = np[dsize];
 178                                 } else {
 179                                         n2 = np[dsize - 1];
 180                                         MPN_COPY_DECR(np + 1, np, dsize - 1);
 181                                         np[0] = 0;
 182                                 }
 183
 184                                 if (n0 == dX) {
 185                                         /* This might over-estimate q, but it's probably not worth
 186                                          * the extra code here to find out.  */
 187                                         q = ~(mpi_limb_t) 0;
 188                                 } else {
 189                                         mpi_limb_t r;
 190
 191                                         udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
 192                                         umul_ppmm(n1, n0, d1, q);
 193
 194                                         while (n1 > r
 195                                                || (n1 == r
 196                                                    && n0 > np[dsize - 2])) {
 197                                                 q--;
 198                                                 r += dX;
 199                                                 if (r < dX)     /* I.e. "carry in previous addition?" */
 200                                                         break;
 201                                                 n1 -= n0 < d1;
 202                                                 n0 -= d1;
 203                                         }
 204                                 }
 205
 206                                 /* Possible optimization: We already have (q * n0) and (1 * n1)
 207                                  * after the calculation of q.  Taking advantage of that, we
 208                                  * could make this loop make two iterations less.  */
 209                                 cy_limb = mpihelp_submul_1(np, dp, dsize, q);
 210
 211                                 if (n2 != cy_limb) {
 212                                         mpihelp_add_n(np, np, dp, dsize);
 213                                         q--;
 214                                 }
 215
 216                                 qp[i] = q;
 217                                 n0 = np[dsize - 1];
 218                         }
 219                 }
 220         }
 221
 222         return most_significant_q_limb;
 223 }