mpih-div.c

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/* mpihelp-div.c  -  MPI helper functions
 *  Copyright (C) 1994, 1996 Free Software Foundation, Inc.
 *  Copyright (C) 1998, 1999 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * GnuPG is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * GnuPG is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 *
 * Note: This code is heavily based on the GNU MP Library.
 *   Actually it's the same code with only minor changes in the
 *   way the data is stored; this is to support the abstraction
 *   of an optional secure memory allocation which may be used
 *   to avoid revealing of sensitive data due to paging etc.
 *   The GNU MP Library itself is published under the LGPL;
 *   however I decided to publish this code under the plain GPL.
 */

#include "mpi-internal.h"
#include "longlong.h"

#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
 * the NSIZE-DSIZE least significant quotient limbs at QP
 * and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is
 * non-zero, generate that many fraction bits and append them after the
 * other quotient limbs.
 * Return the most significant limb of the quotient, this is always 0 or 1.
 *
 * Preconditions:
 * 0. NSIZE >= DSIZE.
 * 1. The most significant bit of the divisor must be set.
 * 2. QP must either not overlap with the input operands at all, or
 *    QP + DSIZE >= NP must hold true.  (This means that it's
 *    possible to put the quotient in the high part of NUM, right after the
 *    remainder in NUM.
 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
 */

mpi_limb_t
mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
           mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
{
    mpi_limb_t most_significant_q_limb = 0;

    switch (dsize) {
    case 0:
        /* We are asked to divide by zero, so go ahead and do it!  (To make
           the compiler not remove this statement, return the value.)  */
        /*
         * existing clients of this function have been modified
         * not to call it with dsize == 0, so this should not happen
         */
        return 1 / dsize;

    case 1:
        {
            mpi_size_t i;
            mpi_limb_t n1;
            mpi_limb_t d;

            d = dp[0];
            n1 = np[nsize - 1];

            if (n1 >= d) {
                n1 -= d;
                most_significant_q_limb = 1;
            }

            qp += qextra_limbs;
            for (i = nsize - 2; i >= 0; i--)
                udiv_qrnnd(qp[i], n1, n1, np[i], d);
            qp -= qextra_limbs;

            for (i = qextra_limbs - 1; i >= 0; i--)
                udiv_qrnnd(qp[i], n1, n1, 0, d);

            np[0] = n1;
        }
        break;

    case 2:
        {
            mpi_size_t i;
            mpi_limb_t n1, n0, n2;
            mpi_limb_t d1, d0;

            np += nsize - 2;
            d1 = dp[1];
            d0 = dp[0];
            n1 = np[1];
            n0 = np[0];

            if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
                sub_ddmmss(n1, n0, n1, n0, d1, d0);
                most_significant_q_limb = 1;
            }

            for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
                mpi_limb_t q;
                mpi_limb_t r;

                if (i >= qextra_limbs)
                    np--;
                else
                    np[0] = 0;

                if (n1 == d1) {
                    /* Q should be either 111..111 or 111..110.  Need special
                     * treatment of this rare case as normal division would
                     * give overflow.  */
                    q = ~(mpi_limb_t) 0;

                    r = n0 + d1;
                    if (r < d1) {   /* Carry in the addition? */
                        add_ssaaaa(n1, n0, r - d0,
                               np[0], 0, d0);
                        qp[i] = q;
                        continue;
                    }
                    n1 = d0 - (d0 != 0 ? 1 : 0);
                    n0 = -d0;
                } else {
                    udiv_qrnnd(q, r, n1, n0, d1);
                    umul_ppmm(n1, n0, d0, q);
                }

                n2 = np[0];
q_test:
                if (n1 > r || (n1 == r && n0 > n2)) {
                    /* The estimated Q was too large.  */
                    q--;
                    sub_ddmmss(n1, n0, n1, n0, 0, d0);
                    r += d1;
                    if (r >= d1)    /* If not carry, test Q again.  */
                        goto q_test;
                }

                qp[i] = q;
                sub_ddmmss(n1, n0, r, n2, n1, n0);
            }
            np[1] = n1;
            np[0] = n0;
        }
        break;

    default:
        {
            mpi_size_t i;
            mpi_limb_t dX, d1, n0;

            np += nsize - dsize;
            dX = dp[dsize - 1];
            d1 = dp[dsize - 2];
            n0 = np[dsize - 1];

            if (n0 >= dX) {
                if (n0 > dX
                    || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
                    mpihelp_sub_n(np, np, dp, dsize);
                    n0 = np[dsize - 1];
                    most_significant_q_limb = 1;
                }
            }

            for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
                mpi_limb_t q;
                mpi_limb_t n1, n2;
                mpi_limb_t cy_limb;

                if (i >= qextra_limbs) {
                    np--;
                    n2 = np[dsize];
                } else {
                    n2 = np[dsize - 1];
                    MPN_COPY_DECR(np + 1, np, dsize - 1);
                    np[0] = 0;
                }

                if (n0 == dX) {
                    /* This might over-estimate q, but it's probably not worth
                     * the extra code here to find out.  */
                    q = ~(mpi_limb_t) 0;
                } else {
                    mpi_limb_t r;

                    udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
                    umul_ppmm(n1, n0, d1, q);

                    while (n1 > r
                           || (n1 == r
                           && n0 > np[dsize - 2])) {
                        q--;
                        r += dX;
                        if (r < dX) /* I.e. "carry in previous addition?" */
                            break;
                        n1 -= n0 < d1;
                        n0 -= d1;
                    }
                }

                /* Possible optimization: We already have (q * n0) and (1 * n1)
                 * after the calculation of q.  Taking advantage of that, we
                 * could make this loop make two iterations less.  */
                cy_limb = mpihelp_submul_1(np, dp, dsize, q);

                if (n2 != cy_limb) {
                    mpihelp_add_n(np, np, dp, dsize);
                    q--;
                }

                qp[i] = q;
                n0 = np[dsize - 1];
            }
        }
    }

    return most_significant_q_limb;
}