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b89f57fe5d
* include/types.h (GNUPG_GCC_ATTR_UNUSED): Define for gcc >= 3.5. * mpi/mpih-div.c (mpihelp_divmod_1, mpihelp_mod_1): Mark dummy as unused. * mpi/mpi-internal.h (UDIV_QRNND_PREINV): Mark _ql as unused. -- Due to the use of macros and longlong.h, we use variables which are only used by some architectures. At least gcc 4.7.2 prints new warnings about set but not used variables. This patch silences them.
535 lines
14 KiB
C
535 lines
14 KiB
C
/* mpihelp-div.c - MPI helper functions
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* Copyright (C) 1994, 1996 Free Software Foundation, Inc.
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* Copyright (C) 1998, 1999 Free Software Foundation, Inc.
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*
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* This file is part of GnuPG.
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*
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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 3 of the License, or
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* (at your option) any later version.
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*
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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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*
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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, see <http://www.gnu.org/licenses/>.
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*
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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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*/
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#include <config.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include "mpi-internal.h"
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#include "longlong.h"
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#ifndef UMUL_TIME
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#define UMUL_TIME 1
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#endif
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#ifndef UDIV_TIME
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#define UDIV_TIME UMUL_TIME
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#endif
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/* FIXME: We should be using invert_limb (or invert_normalized_limb)
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* here (not udiv_qrnnd).
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*/
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mpi_limb_t
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mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
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mpi_limb_t divisor_limb)
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{
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mpi_size_t i;
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mpi_limb_t n1, n0, r;
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int dummy GNUPG_GCC_ATTR_UNUSED;
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/* Botch: Should this be handled at all? Rely on callers? */
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if( !dividend_size )
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return 0;
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/* If multiplication is much faster than division, and the
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* dividend is large, pre-invert the divisor, and use
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* only multiplications in the inner loop.
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*
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* This test should be read:
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* Does it ever help to use udiv_qrnnd_preinv?
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* && Does what we save compensate for the inversion overhead?
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*/
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if( UDIV_TIME > (2 * UMUL_TIME + 6)
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&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
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int normalization_steps;
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count_leading_zeros( normalization_steps, divisor_limb );
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if( normalization_steps ) {
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mpi_limb_t divisor_limb_inverted;
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divisor_limb <<= normalization_steps;
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
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* most significant bit (with weight 2**N) implicit.
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*
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* Special case for DIVISOR_LIMB == 100...000.
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*/
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if( !(divisor_limb << 1) )
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divisor_limb_inverted = ~(mpi_limb_t)0;
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else
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udiv_qrnnd(divisor_limb_inverted, dummy,
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-divisor_limb, 0, divisor_limb);
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n1 = dividend_ptr[dividend_size - 1];
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
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/* Possible optimization:
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* if (r == 0
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* && divisor_limb > ((n1 << normalization_steps)
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* | (dividend_ptr[dividend_size - 2] >> ...)))
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* ...one division less...
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*/
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for( i = dividend_size - 2; i >= 0; i--) {
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n0 = dividend_ptr[i];
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UDIV_QRNND_PREINV(dummy, r, r,
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((n1 << normalization_steps)
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
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divisor_limb, divisor_limb_inverted);
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n1 = n0;
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}
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UDIV_QRNND_PREINV(dummy, r, r,
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n1 << normalization_steps,
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divisor_limb, divisor_limb_inverted);
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return r >> normalization_steps;
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}
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else {
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mpi_limb_t divisor_limb_inverted;
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
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* most significant bit (with weight 2**N) implicit.
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*
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* Special case for DIVISOR_LIMB == 100...000.
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*/
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if( !(divisor_limb << 1) )
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divisor_limb_inverted = ~(mpi_limb_t)0;
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else
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udiv_qrnnd(divisor_limb_inverted, dummy,
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-divisor_limb, 0, divisor_limb);
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i = dividend_size - 1;
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r = dividend_ptr[i];
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if( r >= divisor_limb )
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r = 0;
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else
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i--;
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for( ; i >= 0; i--) {
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n0 = dividend_ptr[i];
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UDIV_QRNND_PREINV(dummy, r, r,
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n0, divisor_limb, divisor_limb_inverted);
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}
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return r;
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}
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}
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else {
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if( UDIV_NEEDS_NORMALIZATION ) {
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int normalization_steps;
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count_leading_zeros(normalization_steps, divisor_limb);
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if( normalization_steps ) {
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divisor_limb <<= normalization_steps;
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n1 = dividend_ptr[dividend_size - 1];
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
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/* Possible optimization:
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* if (r == 0
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* && divisor_limb > ((n1 << normalization_steps)
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* | (dividend_ptr[dividend_size - 2] >> ...)))
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* ...one division less...
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*/
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for(i = dividend_size - 2; i >= 0; i--) {
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n0 = dividend_ptr[i];
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udiv_qrnnd (dummy, r, r,
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((n1 << normalization_steps)
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
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divisor_limb);
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n1 = n0;
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}
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udiv_qrnnd (dummy, r, r,
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n1 << normalization_steps,
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divisor_limb);
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return r >> normalization_steps;
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}
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}
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/* No normalization needed, either because udiv_qrnnd doesn't require
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* it, or because DIVISOR_LIMB is already normalized. */
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i = dividend_size - 1;
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r = dividend_ptr[i];
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if(r >= divisor_limb)
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r = 0;
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else
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i--;
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for(; i >= 0; i--) {
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n0 = dividend_ptr[i];
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udiv_qrnnd (dummy, r, r, n0, divisor_limb);
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}
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return r;
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}
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}
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/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
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* the NSIZE-DSIZE least significant quotient limbs at QP
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* and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
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* non-zero, generate that many fraction bits and append them after the
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* other quotient limbs.
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* Return the most significant limb of the quotient, this is always 0 or 1.
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*
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* Preconditions:
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* 0. NSIZE >= DSIZE.
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* 1. The most significant bit of the divisor must be set.
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* 2. QP must either not overlap with the input operands at all, or
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* QP + DSIZE >= NP must hold true. (This means that it's
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* possible to put the quotient in the high part of NUM, right after the
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* remainder in NUM.
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* 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
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*/
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mpi_limb_t
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mpihelp_divrem( mpi_ptr_t qp, mpi_size_t qextra_limbs,
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mpi_ptr_t np, mpi_size_t nsize,
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mpi_ptr_t dp, mpi_size_t dsize)
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{
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mpi_limb_t most_significant_q_limb = 0;
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switch(dsize) {
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case 0:
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/* We are asked to divide by zero, so go ahead and do it! (To make
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the compiler not remove this statement, return the value.) */
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return 1 / dsize;
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case 1:
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{
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mpi_size_t i;
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mpi_limb_t n1;
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mpi_limb_t d;
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d = dp[0];
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n1 = np[nsize - 1];
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if( n1 >= d ) {
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n1 -= d;
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most_significant_q_limb = 1;
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}
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qp += qextra_limbs;
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for( i = nsize - 2; i >= 0; i--)
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udiv_qrnnd( qp[i], n1, n1, np[i], d );
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qp -= qextra_limbs;
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for( i = qextra_limbs - 1; i >= 0; i-- )
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udiv_qrnnd (qp[i], n1, n1, 0, d);
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np[0] = n1;
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}
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break;
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case 2:
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{
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mpi_size_t i;
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mpi_limb_t n1, n0, n2;
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mpi_limb_t d1, d0;
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np += nsize - 2;
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d1 = dp[1];
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d0 = dp[0];
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n1 = np[1];
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n0 = np[0];
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if( n1 >= d1 && (n1 > d1 || n0 >= d0) ) {
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sub_ddmmss (n1, n0, n1, n0, d1, d0);
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most_significant_q_limb = 1;
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}
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for( i = qextra_limbs + nsize - 2 - 1; i >= 0; i-- ) {
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mpi_limb_t q;
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mpi_limb_t r;
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if( i >= qextra_limbs )
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np--;
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else
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np[0] = 0;
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if( n1 == d1 ) {
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/* Q should be either 111..111 or 111..110. Need special
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* treatment of this rare case as normal division would
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* give overflow. */
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q = ~(mpi_limb_t)0;
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r = n0 + d1;
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if( r < d1 ) { /* Carry in the addition? */
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add_ssaaaa( n1, n0, r - d0, np[0], 0, d0 );
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qp[i] = q;
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continue;
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}
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n1 = d0 - (d0 != 0?1:0);
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n0 = -d0;
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}
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else {
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udiv_qrnnd (q, r, n1, n0, d1);
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umul_ppmm (n1, n0, d0, q);
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}
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n2 = np[0];
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q_test:
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if( n1 > r || (n1 == r && n0 > n2) ) {
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/* The estimated Q was too large. */
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q--;
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sub_ddmmss (n1, n0, n1, n0, 0, d0);
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r += d1;
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if( r >= d1 ) /* If not carry, test Q again. */
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goto q_test;
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}
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qp[i] = q;
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sub_ddmmss (n1, n0, r, n2, n1, n0);
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}
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np[1] = n1;
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np[0] = n0;
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}
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break;
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default:
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{
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mpi_size_t i;
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mpi_limb_t dX, d1, n0;
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np += nsize - dsize;
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dX = dp[dsize - 1];
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d1 = dp[dsize - 2];
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n0 = np[dsize - 1];
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if( n0 >= dX ) {
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if(n0 > dX || mpihelp_cmp(np, dp, dsize - 1) >= 0 ) {
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mpihelp_sub_n(np, np, dp, dsize);
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n0 = np[dsize - 1];
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most_significant_q_limb = 1;
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}
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}
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for( i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
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mpi_limb_t q;
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mpi_limb_t n1, n2;
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mpi_limb_t cy_limb;
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if( i >= qextra_limbs ) {
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np--;
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n2 = np[dsize];
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}
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else {
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n2 = np[dsize - 1];
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MPN_COPY_DECR (np + 1, np, dsize - 1);
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np[0] = 0;
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}
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if( n0 == dX ) {
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/* This might over-estimate q, but it's probably not worth
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* the extra code here to find out. */
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q = ~(mpi_limb_t)0;
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}
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else {
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mpi_limb_t r;
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udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
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umul_ppmm(n1, n0, d1, q);
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while( n1 > r || (n1 == r && n0 > np[dsize - 2])) {
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q--;
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r += dX;
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if( r < dX ) /* I.e. "carry in previous addition?" */
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break;
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n1 -= n0 < d1;
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n0 -= d1;
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}
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}
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/* Possible optimization: We already have (q * n0) and (1 * n1)
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* after the calculation of q. Taking advantage of that, we
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* could make this loop make two iterations less. */
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cy_limb = mpihelp_submul_1(np, dp, dsize, q);
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if( n2 != cy_limb ) {
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mpihelp_add_n(np, np, dp, dsize);
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q--;
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}
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qp[i] = q;
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n0 = np[dsize - 1];
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}
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}
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}
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return most_significant_q_limb;
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}
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/****************
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* Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
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* Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
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* Return the single-limb remainder.
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* There are no constraints on the value of the divisor.
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*
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* QUOT_PTR and DIVIDEND_PTR might point to the same limb.
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*/
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mpi_limb_t
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mpihelp_divmod_1( mpi_ptr_t quot_ptr,
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mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
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mpi_limb_t divisor_limb)
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{
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mpi_size_t i;
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mpi_limb_t n1, n0, r;
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int dummy GNUPG_GCC_ATTR_UNUSED;
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if( !dividend_size )
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return 0;
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|
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/* If multiplication is much faster than division, and the
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* dividend is large, pre-invert the divisor, and use
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* only multiplications in the inner loop.
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*
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* This test should be read:
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* Does it ever help to use udiv_qrnnd_preinv?
|
|
* && Does what we save compensate for the inversion overhead?
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*/
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if( UDIV_TIME > (2 * UMUL_TIME + 6)
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&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME ) {
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int normalization_steps;
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count_leading_zeros( normalization_steps, divisor_limb );
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if( normalization_steps ) {
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mpi_limb_t divisor_limb_inverted;
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divisor_limb <<= normalization_steps;
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
|
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* most significant bit (with weight 2**N) implicit.
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*/
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/* Special case for DIVISOR_LIMB == 100...000. */
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if( !(divisor_limb << 1) )
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divisor_limb_inverted = ~(mpi_limb_t)0;
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else
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udiv_qrnnd(divisor_limb_inverted, dummy,
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-divisor_limb, 0, divisor_limb);
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n1 = dividend_ptr[dividend_size - 1];
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
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/* Possible optimization:
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* if (r == 0
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* && divisor_limb > ((n1 << normalization_steps)
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* | (dividend_ptr[dividend_size - 2] >> ...)))
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* ...one division less...
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*/
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for( i = dividend_size - 2; i >= 0; i--) {
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n0 = dividend_ptr[i];
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UDIV_QRNND_PREINV( quot_ptr[i + 1], r, r,
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((n1 << normalization_steps)
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
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divisor_limb, divisor_limb_inverted);
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n1 = n0;
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}
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UDIV_QRNND_PREINV( quot_ptr[0], r, r,
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n1 << normalization_steps,
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divisor_limb, divisor_limb_inverted);
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return r >> normalization_steps;
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}
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else {
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mpi_limb_t divisor_limb_inverted;
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
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* most significant bit (with weight 2**N) implicit.
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*/
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/* Special case for DIVISOR_LIMB == 100...000. */
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if( !(divisor_limb << 1) )
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divisor_limb_inverted = ~(mpi_limb_t) 0;
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else
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udiv_qrnnd(divisor_limb_inverted, dummy,
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-divisor_limb, 0, divisor_limb);
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i = dividend_size - 1;
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r = dividend_ptr[i];
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if( r >= divisor_limb )
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r = 0;
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else
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quot_ptr[i--] = 0;
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for( ; i >= 0; i-- ) {
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n0 = dividend_ptr[i];
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UDIV_QRNND_PREINV( quot_ptr[i], r, r,
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n0, divisor_limb, divisor_limb_inverted);
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}
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return r;
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}
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|
}
|
|
else {
|
|
if(UDIV_NEEDS_NORMALIZATION) {
|
|
int normalization_steps;
|
|
|
|
count_leading_zeros (normalization_steps, divisor_limb);
|
|
if( normalization_steps ) {
|
|
divisor_limb <<= normalization_steps;
|
|
|
|
n1 = dividend_ptr[dividend_size - 1];
|
|
r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
|
|
|
|
/* Possible optimization:
|
|
* if (r == 0
|
|
* && divisor_limb > ((n1 << normalization_steps)
|
|
* | (dividend_ptr[dividend_size - 2] >> ...)))
|
|
* ...one division less...
|
|
*/
|
|
for( i = dividend_size - 2; i >= 0; i--) {
|
|
n0 = dividend_ptr[i];
|
|
udiv_qrnnd (quot_ptr[i + 1], r, r,
|
|
((n1 << normalization_steps)
|
|
| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),
|
|
divisor_limb);
|
|
n1 = n0;
|
|
}
|
|
udiv_qrnnd (quot_ptr[0], r, r,
|
|
n1 << normalization_steps,
|
|
divisor_limb);
|
|
return r >> normalization_steps;
|
|
}
|
|
}
|
|
/* No normalization needed, either because udiv_qrnnd doesn't require
|
|
* it, or because DIVISOR_LIMB is already normalized. */
|
|
i = dividend_size - 1;
|
|
r = dividend_ptr[i];
|
|
|
|
if(r >= divisor_limb)
|
|
r = 0;
|
|
else
|
|
quot_ptr[i--] = 0;
|
|
|
|
for(; i >= 0; i--) {
|
|
n0 = dividend_ptr[i];
|
|
udiv_qrnnd( quot_ptr[i], r, r, n0, divisor_limb );
|
|
}
|
|
return r;
|
|
}
|
|
}
|