diff options
Diffstat (limited to 'comm/third_party/libgcrypt/mpi/mpih-div.c')
| -rw-r--r-- | comm/third_party/libgcrypt/mpi/mpih-div.c | 532 |
1 files changed, 532 insertions, 0 deletions
diff --git a/comm/third_party/libgcrypt/mpi/mpih-div.c b/comm/third_party/libgcrypt/mpi/mpih-div.c new file mode 100644 index 0000000000..57c1b58487 --- /dev/null +++ b/comm/third_party/libgcrypt/mpi/mpih-div.c @@ -0,0 +1,532 @@ +/* mpih-div.c - MPI helper functions + * Copyright (C) 1994, 1996, 1998, 2000, + * 2001, 2002 Free Software Foundation, Inc. + * + * This file is part of Libgcrypt. + * + * Libgcrypt is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as + * published by the Free Software Foundation; either version 2.1 of + * the License, or (at your option) any later version. + * + * Libgcrypt 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 Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser 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. + */ + +#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 +_gcry_mpih_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; + mpi_limb_t dummy GCC_ATTR_UNUSED; + + /* 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 +_gcry_mpih_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: + _gcry_divide_by_zero(); + break; + + 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 || _gcry_mpih_cmp(np, dp, dsize - 1) >= 0 ) { + _gcry_mpih_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 = _gcry_mpih_submul_1(np, dp, dsize, q); + + if( n2 != cy_limb ) { + _gcry_mpih_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 +_gcry_mpih_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; + mpi_limb_t dummy GCC_ATTR_UNUSED; + + 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; + } +} |