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Diffstat (limited to 'mpi/mpih-div.c')
| -rw-r--r-- | mpi/mpih-div.c | 537 |
1 files changed, 0 insertions, 537 deletions
diff --git a/mpi/mpih-div.c b/mpi/mpih-div.c deleted file mode 100644 index 6eb0e1a34..000000000 --- a/mpi/mpih-div.c +++ /dev/null @@ -1,537 +0,0 @@ -/* 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 <config.h> -#include <stdio.h> -#include <stdlib.h> -#include "mpi-internal.h" -#include "longlong.h" - -#ifndef UMUL_TIME - #define UMUL_TIME 1 -#endif -#ifndef UDIV_TIME - #define UDIV_TIME UMUL_TIME -#endif - -/* FIXME: We should be using invert_limb (or invert_normalized_limb) - * here (not udiv_qrnnd). - */ - -mpi_limb_t -mpihelp_mod_1(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; - - /* Botch: Should this be handled at all? Rely on callers? */ - 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(dummy, r, r, - ((n1 << normalization_steps) - | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), - divisor_limb, divisor_limb_inverted); - n1 = n0; - } - UDIV_QRNND_PREINV(dummy, 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 - i--; - - for( ; i >= 0; i--) { - n0 = dividend_ptr[i]; - UDIV_QRNND_PREINV(dummy, 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 (dummy, r, r, - ((n1 << normalization_steps) - | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), - divisor_limb); - n1 = n0; - } - udiv_qrnnd (dummy, 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 - i--; - - for(; i >= 0; i--) { - n0 = dividend_ptr[i]; - udiv_qrnnd (dummy, r, r, n0, divisor_limb); - } - return r; - } -} - -/* 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.) */ - 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; -} - - -/**************** - * 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; - } -} - - |