/* This file was automatically imported with import_gcry.py. Please don't modify it */ /* 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.) */ grub_fatal ("mpi division by zero"); return 0; 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; } }