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gnupg/mpi/mpi-div.c

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/* mpi-div.c - MPI functions
* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
* Copyright (C) 1998, 1999, 2000, 2001 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 <config.h>
#include <stdio.h>
#include <stdlib.h>
#include "mpi-internal.h"
#include "longlong.h"
void
mpi_fdiv_r( MPI rem, MPI dividend, MPI divisor )
{
int divisor_sign = divisor->sign;
MPI temp_divisor = NULL;
/* We need the original value of the divisor after the remainder has been
* preliminary calculated. We have to copy it to temporary space if it's
* the same variable as REM. */
if( rem == divisor ) {
temp_divisor = mpi_copy( divisor );
divisor = temp_divisor;
}
mpi_tdiv_r( rem, dividend, divisor );
if( ((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs )
mpi_add( rem, rem, divisor);
if( temp_divisor )
mpi_free(temp_divisor);
}
/****************
* Division rounding the quotient towards -infinity.
* The remainder gets the same sign as the denominator.
* rem is optional
*/
ulong
mpi_fdiv_r_ui( MPI rem, MPI dividend, ulong divisor )
{
mpi_limb_t rlimb;
rlimb = mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
if( rlimb && dividend->sign )
rlimb = divisor - rlimb;
if( rem ) {
rem->d[0] = rlimb;
rem->nlimbs = rlimb? 1:0;
}
return rlimb;
}
void
mpi_fdiv_q( MPI quot, MPI dividend, MPI divisor )
{
MPI tmp = mpi_alloc( mpi_get_nlimbs(quot) );
mpi_fdiv_qr( quot, tmp, dividend, divisor);
mpi_free(tmp);
}
void
mpi_fdiv_qr( MPI quot, MPI rem, MPI dividend, MPI divisor )
{
int divisor_sign = divisor->sign;
MPI temp_divisor = NULL;
if( quot == divisor || rem == divisor ) {
temp_divisor = mpi_copy( divisor );
divisor = temp_divisor;
}
mpi_tdiv_qr( quot, rem, dividend, divisor );
if( (divisor_sign ^ dividend->sign) && rem->nlimbs ) {
mpi_sub_ui( quot, quot, 1 );
mpi_add( rem, rem, divisor);
}
if( temp_divisor )
mpi_free(temp_divisor);
}
/* If den == quot, den needs temporary storage.
* If den == rem, den needs temporary storage.
* If num == quot, num needs temporary storage.
* If den has temporary storage, it can be normalized while being copied,
* i.e no extra storage should be allocated.
*/
void
mpi_tdiv_r( MPI rem, MPI num, MPI den)
{
mpi_tdiv_qr(NULL, rem, num, den );
}
void
mpi_tdiv_qr( MPI quot, MPI rem, MPI num, MPI den)
{
mpi_ptr_t np, dp;
mpi_ptr_t qp, rp;
mpi_size_t nsize = num->nlimbs;
mpi_size_t dsize = den->nlimbs;
mpi_size_t qsize, rsize;
mpi_size_t sign_remainder = num->sign;
mpi_size_t sign_quotient = num->sign ^ den->sign;
unsigned normalization_steps;
mpi_limb_t q_limb;
mpi_ptr_t marker[5];
int markidx=0;
/* Ensure space is enough for quotient and remainder.
* We need space for an extra limb in the remainder, because it's
* up-shifted (normalized) below. */
rsize = nsize + 1;
mpi_resize( rem, rsize);
qsize = rsize - dsize; /* qsize cannot be bigger than this. */
if( qsize <= 0 ) {
if( num != rem ) {
rem->nlimbs = num->nlimbs;
rem->sign = num->sign;
MPN_COPY(rem->d, num->d, nsize);
}
if( quot ) {
/* This needs to follow the assignment to rem, in case the
* numerator and quotient are the same. */
quot->nlimbs = 0;
quot->sign = 0;
}
return;
}
if( quot )
mpi_resize( quot, qsize);
/* Read pointers here, when reallocation is finished. */
np = num->d;
dp = den->d;
rp = rem->d;
/* Optimize division by a single-limb divisor. */
if( dsize == 1 ) {
mpi_limb_t rlimb;
if( quot ) {
qp = quot->d;
rlimb = mpihelp_divmod_1( qp, np, nsize, dp[0] );
qsize -= qp[qsize - 1] == 0;
quot->nlimbs = qsize;
quot->sign = sign_quotient;
}
else
rlimb = mpihelp_mod_1( np, nsize, dp[0] );
rp[0] = rlimb;
rsize = rlimb != 0?1:0;
rem->nlimbs = rsize;
rem->sign = sign_remainder;
return;
}
if( quot ) {
qp = quot->d;
/* Make sure QP and NP point to different objects. Otherwise the
* numerator would be gradually overwritten by the quotient limbs. */
if(qp == np) { /* Copy NP object to temporary space. */
np = marker[markidx++] = mpi_alloc_limb_space(nsize,
mpi_is_secure(quot));
MPN_COPY(np, qp, nsize);
}
}
else /* Put quotient at top of remainder. */
qp = rp + dsize;
count_leading_zeros( normalization_steps, dp[dsize - 1] );
/* Normalize the denominator, i.e. make its most significant bit set by
* shifting it NORMALIZATION_STEPS bits to the left. Also shift the
* numerator the same number of steps (to keep the quotient the same!).
*/
if( normalization_steps ) {
mpi_ptr_t tp;
mpi_limb_t nlimb;
/* Shift up the denominator setting the most significant bit of
* the most significant word. Use temporary storage not to clobber
* the original contents of the denominator. */
tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den));
mpihelp_lshift( tp, dp, dsize, normalization_steps );
dp = tp;
/* Shift up the numerator, possibly introducing a new most
* significant word. Move the shifted numerator in the remainder
* meanwhile. */
nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
if( nlimb ) {
rp[nsize] = nlimb;
rsize = nsize + 1;
}
else
rsize = nsize;
}
else {
/* The denominator is already normalized, as required. Copy it to
* temporary space if it overlaps with the quotient or remainder. */
if( dp == rp || (quot && (dp == qp))) {
mpi_ptr_t tp;
tp = marker[markidx++] = mpi_alloc_limb_space(dsize, mpi_is_secure(den));
MPN_COPY( tp, dp, dsize );
dp = tp;
}
/* Move the numerator to the remainder. */
if( rp != np )
MPN_COPY(rp, np, nsize);
rsize = nsize;
}
q_limb = mpihelp_divrem( qp, 0, rp, rsize, dp, dsize );
if( quot ) {
qsize = rsize - dsize;
if(q_limb) {
qp[qsize] = q_limb;
qsize += 1;
}
quot->nlimbs = qsize;
quot->sign = sign_quotient;
}
rsize = dsize;
MPN_NORMALIZE (rp, rsize);
if( normalization_steps && rsize ) {
mpihelp_rshift(rp, rp, rsize, normalization_steps);
rsize -= rp[rsize - 1] == 0?1:0;
}
rem->nlimbs = rsize;
rem->sign = sign_remainder;
while( markidx )
mpi_free_limb_space(marker[--markidx]);
}
void
mpi_tdiv_q_2exp( MPI w, MPI u, unsigned count )
{
mpi_size_t usize, wsize;
mpi_size_t limb_cnt;
usize = u->nlimbs;
limb_cnt = count / BITS_PER_MPI_LIMB;
wsize = usize - limb_cnt;
if( limb_cnt >= usize )
w->nlimbs = 0;
else {
mpi_ptr_t wp;
mpi_ptr_t up;
RESIZE_IF_NEEDED( w, wsize );
wp = w->d;
up = u->d;
count %= BITS_PER_MPI_LIMB;
if( count ) {
mpihelp_rshift( wp, up + limb_cnt, wsize, count );
wsize -= !wp[wsize - 1];
}
else {
MPN_COPY_INCR( wp, up + limb_cnt, wsize);
}
w->nlimbs = wsize;
}
}
/****************
* Check whether dividend is divisible by divisor
* (note: divisor must fit into a limb)
*/
int
mpi_divisible_ui(MPI dividend, ulong divisor )
{
return !mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
}
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