542 lines
14 KiB
C
542 lines
14 KiB
C
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/* 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 2 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, 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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*
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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 "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;
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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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(BITS_PER_MPI_LIMB -
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normalization_steps))),
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divisor_limb,
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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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} 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,
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divisor_limb_inverted);
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}
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return r;
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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 -
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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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(BITS_PER_MPI_LIMB -
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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, 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,
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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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} 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
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|| 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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} 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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} 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
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&& 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
|
||
|
|
* 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;
|
||
|
|
}
|
||
|
|
|
||
|
|
/****************
|
||
|
|
* Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
|
||
|
|
* Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
|
||
|
|
* Return the single-limb remainder.
|
||
|
|
* There are no constraints on the value of the divisor.
|
||
|
|
*
|
||
|
|
* QUOT_PTR and DIVIDEND_PTR might point to the same limb.
|
||
|
|
*/
|
||
|
|
|
||
|
|
mpi_limb_t
|
||
|
|
mpihelp_divmod_1(mpi_ptr_t quot_ptr,
|
||
|
|
mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
|
||
|
|
mpi_limb_t divisor_limb)
|
||
|
|
{
|
||
|
|
mpi_size_t i;
|
||
|
|
mpi_limb_t n1, n0, r;
|
||
|
|
int dummy;
|
||
|
|
|
||
|
|
if (!dividend_size)
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* If multiplication is much faster than division, and the
|
||
|
|
* dividend is large, pre-invert the divisor, and use
|
||
|
|
* only multiplications in the inner loop.
|
||
|
|
*
|
||
|
|
* This test should be read:
|
||
|
|
* Does it ever help to use udiv_qrnnd_preinv?
|
||
|
|
* && Does what we save compensate for the inversion overhead?
|
||
|
|
*/
|
||
|
|
if (UDIV_TIME > (2 * UMUL_TIME + 6)
|
||
|
|
&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
|
||
|
|
int normalization_steps;
|
||
|
|
|
||
|
|
count_leading_zeros(normalization_steps, divisor_limb);
|
||
|
|
if (normalization_steps) {
|
||
|
|
mpi_limb_t divisor_limb_inverted;
|
||
|
|
|
||
|
|
divisor_limb <<= normalization_steps;
|
||
|
|
|
||
|
|
/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
|
||
|
|
* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
|
||
|
|
* most significant bit (with weight 2**N) implicit.
|
||
|
|
*/
|
||
|
|
/* Special case for DIVISOR_LIMB == 100...000. */
|
||
|
|
if (!(divisor_limb << 1))
|
||
|
|
divisor_limb_inverted = ~(mpi_limb_t) 0;
|
||
|
|
else
|
||
|
|
udiv_qrnnd(divisor_limb_inverted, dummy,
|
||
|
|
-divisor_limb, 0, divisor_limb);
|
||
|
|
|
||
|
|
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_PREINV(quot_ptr[i + 1], r, r,
|
||
|
|
((n1 << normalization_steps)
|
||
|
|
| (n0 >>
|
||
|
|
(BITS_PER_MPI_LIMB -
|
||
|
|
normalization_steps))),
|
||
|
|
divisor_limb,
|
||
|
|
divisor_limb_inverted);
|
||
|
|
n1 = n0;
|
||
|
|
}
|
||
|
|
UDIV_QRNND_PREINV(quot_ptr[0], r, r,
|
||
|
|
n1 << normalization_steps,
|
||
|
|
divisor_limb, divisor_limb_inverted);
|
||
|
|
return r >> normalization_steps;
|
||
|
|
} else {
|
||
|
|
mpi_limb_t divisor_limb_inverted;
|
||
|
|
|
||
|
|
/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
|
||
|
|
* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
|
||
|
|
* most significant bit (with weight 2**N) implicit.
|
||
|
|
*/
|
||
|
|
/* Special case for DIVISOR_LIMB == 100...000. */
|
||
|
|
if (!(divisor_limb << 1))
|
||
|
|
divisor_limb_inverted = ~(mpi_limb_t) 0;
|
||
|
|
else
|
||
|
|
udiv_qrnnd(divisor_limb_inverted, dummy,
|
||
|
|
-divisor_limb, 0, divisor_limb);
|
||
|
|
|
||
|
|
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_PREINV(quot_ptr[i], r, r,
|
||
|
|
n0, divisor_limb,
|
||
|
|
divisor_limb_inverted);
|
||
|
|
}
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
} 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;
|
||
|
|
}
|
||
|
|
}
|