| /* 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; |
| 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 |
| _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: |
| /* 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 || _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; |
| 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; |
| } |
| } |
| |
| |