linux/lib/mpi/mpih-div.c
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   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
  57mpi_limb_t
  58mpihelp_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];
 146q_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}
 237
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