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/* mpi-div.c - MPI functions
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* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
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* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
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* This file is part of GnuPG.
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* GnuPG is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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* GnuPG is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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* Note: This code is heavily based on the GNU MP Library.
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* Actually it's the same code with only minor changes in the
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* way the data is stored; this is to support the abstraction
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* of an optional secure memory allocation which may be used
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* to avoid revealing of sensitive data due to paging etc.
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* The GNU MP Library itself is published under the LGPL;
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* however I decided to publish this code under the plain GPL.
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#include "mpi-internal.h"
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mpi_fdiv_r( MPI rem, MPI dividend, MPI divisor )
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int divisor_sign = divisor->sign;
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MPI temp_divisor = NULL;
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/* We need the original value of the divisor after the remainder has been
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* preliminary calculated. We have to copy it to temporary space if it's
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* the same variable as REM. */
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if( rem == divisor ) {
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temp_divisor = mpi_copy( divisor );
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divisor = temp_divisor;
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mpi_tdiv_r( rem, dividend, divisor );
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if( ((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs )
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mpi_add( rem, rem, divisor);
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mpi_free(temp_divisor);
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* Division rounding the quotient towards -infinity.
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* The remainder gets the same sign as the denominator.
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mpi_fdiv_r_ui( MPI rem, MPI dividend, ulong divisor )
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rlimb = mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
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if( rlimb && dividend->sign )
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rlimb = divisor - rlimb;
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rem->nlimbs = rlimb? 1:0;
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mpi_fdiv_q( MPI quot, MPI dividend, MPI divisor )
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MPI tmp = mpi_alloc( mpi_get_nlimbs(quot) );
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mpi_fdiv_qr( quot, tmp, dividend, divisor);
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mpi_fdiv_qr( MPI quot, MPI rem, MPI dividend, MPI divisor )
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int divisor_sign = divisor->sign;
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MPI temp_divisor = NULL;
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if( quot == divisor || rem == divisor ) {
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temp_divisor = mpi_copy( divisor );
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divisor = temp_divisor;
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mpi_tdiv_qr( quot, rem, dividend, divisor );
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if( (divisor_sign ^ dividend->sign) && rem->nlimbs ) {
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mpi_sub_ui( quot, quot, 1 );
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mpi_add( rem, rem, divisor);
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mpi_free(temp_divisor);
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/* If den == quot, den needs temporary storage.
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* If den == rem, den needs temporary storage.
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* If num == quot, num needs temporary storage.
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* If den has temporary storage, it can be normalized while being copied,
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* i.e no extra storage should be allocated.
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mpi_tdiv_r( MPI rem, MPI num, MPI den)
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mpi_tdiv_qr(NULL, rem, num, den );
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mpi_tdiv_qr( MPI quot, MPI rem, MPI num, MPI den)
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mpi_size_t nsize = num->nlimbs;
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mpi_size_t dsize = den->nlimbs;
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mpi_size_t qsize, rsize;
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mpi_size_t sign_remainder = num->sign;
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mpi_size_t sign_quotient = num->sign ^ den->sign;
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unsigned normalization_steps;
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/* Ensure space is enough for quotient and remainder.
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* We need space for an extra limb in the remainder, because it's
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* up-shifted (normalized) below. */
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mpi_resize( rem, rsize);
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qsize = rsize - dsize; /* qsize cannot be bigger than this. */
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rem->nlimbs = num->nlimbs;
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rem->sign = num->sign;
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MPN_COPY(rem->d, num->d, nsize);
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/* This needs to follow the assignment to rem, in case the
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* numerator and quotient are the same. */
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mpi_resize( quot, qsize);
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/* Read pointers here, when reallocation is finished. */
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/* Optimize division by a single-limb divisor. */
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rlimb = mpihelp_divmod_1( qp, np, nsize, dp[0] );
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qsize -= qp[qsize - 1] == 0;
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quot->nlimbs = qsize;
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quot->sign = sign_quotient;
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rlimb = mpihelp_mod_1( np, nsize, dp[0] );
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rsize = rlimb != 0?1:0;
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rem->sign = sign_remainder;
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/* Make sure QP and NP point to different objects. Otherwise the
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* numerator would be gradually overwritten by the quotient limbs. */
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if(qp == np) { /* Copy NP object to temporary space. */
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np = marker[markidx++] = mpi_alloc_limb_space(nsize,
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mpi_is_secure(quot));
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MPN_COPY(np, qp, nsize);
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else /* Put quotient at top of remainder. */
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count_leading_zeros( normalization_steps, dp[dsize - 1] );
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/* Normalize the denominator, i.e. make its most significant bit set by
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* shifting it NORMALIZATION_STEPS bits to the left. Also shift the
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* numerator the same number of steps (to keep the quotient the same!).
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if( normalization_steps ) {
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/* Shift up the denominator setting the most significant bit of
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* the most significant word. Use temporary storage not to clobber
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* the original contents of the denominator. */
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tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den));
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mpihelp_lshift( tp, dp, dsize, normalization_steps );
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/* Shift up the numerator, possibly introducing a new most
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* significant word. Move the shifted numerator in the remainder
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nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
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/* The denominator is already normalized, as required. Copy it to
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* temporary space if it overlaps with the quotient or remainder. */
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if( dp == rp || (quot && (dp == qp))) {
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tp = marker[markidx++] = mpi_alloc_limb_space(dsize, mpi_is_secure(den));
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MPN_COPY( tp, dp, dsize );
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/* Move the numerator to the remainder. */
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MPN_COPY(rp, np, nsize);
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q_limb = mpihelp_divrem( qp, 0, rp, rsize, dp, dsize );
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qsize = rsize - dsize;
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quot->nlimbs = qsize;
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quot->sign = sign_quotient;
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MPN_NORMALIZE (rp, rsize);
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if( normalization_steps && rsize ) {
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mpihelp_rshift(rp, rp, rsize, normalization_steps);
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rsize -= rp[rsize - 1] == 0?1:0;
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rem->sign = sign_remainder;
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mpi_free_limb_space(marker[--markidx]);
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mpi_tdiv_q_2exp( MPI w, MPI u, unsigned count )
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mpi_size_t usize, wsize;
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limb_cnt = count / BITS_PER_MPI_LIMB;
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wsize = usize - limb_cnt;
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if( limb_cnt >= usize )
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RESIZE_IF_NEEDED( w, wsize );
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count %= BITS_PER_MPI_LIMB;
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mpihelp_rshift( wp, up + limb_cnt, wsize, count );
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wsize -= !wp[wsize - 1];
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MPN_COPY_INCR( wp, up + limb_cnt, wsize);
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* Check whether dividend is divisible by divisor
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* (note: divisor must fit into a limb)
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mpi_divisible_ui(MPI dividend, ulong divisor )
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return !mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
added
removed
mpi/mpi-div.c
