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Release 4.9 lib/mpi/mpih-div.c

Directory: lib/mpi
/* 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; }

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Directory: lib/mpi