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Diffstat (limited to 'mpi/mpih-mul.c')
| -rw-r--r-- | mpi/mpih-mul.c | 557 |
1 files changed, 557 insertions, 0 deletions
diff --git a/mpi/mpih-mul.c b/mpi/mpih-mul.c new file mode 100644 index 000000000..c579a93fe --- /dev/null +++ b/mpi/mpih-mul.c @@ -0,0 +1,557 @@ +/* mpihelp-mul.c - MPI helper functions + * Copyright (c) 1997 by Werner Koch (dd9jn) + * + * This file is part of G10. + * + * G10 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. + * + * G10 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 + */ + +#include <config.h> +#include <stdio.h> +#include <stdlib.h> +#include "mpi-internal.h" +#include "longlong.h" + +/* If KARATSUBA_THRESHOLD is not already defined, define it to a + * value which is good on most machines. */ +#ifndef KARATSUBA_THRESHOLD + #define KARATSUBA_THRESHOLD 32 +#endif + +/* The code can't handle KARATSUBA_THRESHOLD smaller than 2. */ +#if KARATSUBA_THRESHOLD < 2 + #undef KARATSUBA_THRESHOLD + #define KARATSUBA_THRESHOLD 2 +#endif + + +#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \ + do { \ + if( (size) < KARATSUBA_THRESHOLD ) \ + mul_n_basecase (prodp, up, vp, size); \ + else \ + mul_n (prodp, up, vp, size, tspace); \ + } while (0); + +#define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \ + do { \ + if ((size) < KARATSUBA_THRESHOLD) \ + sqr_n_basecase (prodp, up, size); \ + else \ + sqr_n (prodp, up, size, tspace); \ + } while (0); + + + +mpi_limb_t +mpihelp_addmul_1( mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, + mpi_size_t s1_size, mpi_limb_t s2_limb) +{ + mpi_limb_t cy_limb; + mpi_size_t j; + mpi_limb_t prod_high, prod_low; + mpi_limb_t x; + + /* The loop counter and index J goes from -SIZE to -1. This way + * the loop becomes faster. */ + j = -s1_size; + res_ptr -= j; + s1_ptr -= j; + + cy_limb = 0; + do { + umul_ppmm( prod_high, prod_low, s1_ptr[j], s2_limb ); + + prod_low += cy_limb; + cy_limb = (prod_low < cy_limb?1:0) + prod_high; + + x = res_ptr[j]; + prod_low = x + prod_low; + cy_limb += prod_low < x?1:0; + res_ptr[j] = prod_low; + } while ( ++j ); + return cy_limb; +} + + +mpi_limb_t +mpihelp_submul_1( mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, + mpi_size_t s1_size, mpi_limb_t s2_limb) +{ + mpi_limb_t cy_limb; + mpi_size_t j; + mpi_limb_t prod_high, prod_low; + mpi_limb_t x; + + /* The loop counter and index J goes from -SIZE to -1. This way + * the loop becomes faster. */ + j = -s1_size; + res_ptr -= j; + s1_ptr -= j; + + cy_limb = 0; + do { + umul_ppmm( prod_high, prod_low, s1_ptr[j], s2_limb); + + prod_low += cy_limb; + cy_limb = (prod_low < cy_limb?1:0) + prod_high; + + x = res_ptr[j]; + prod_low = x - prod_low; + cy_limb += prod_low > x?1:0; + res_ptr[j] = prod_low; + } while( ++j ); + + return cy_limb; +} + +mpi_limb_t +mpihelp_mul_1( mpi_ptr_t res_ptr, mpi_ptr_t s1_ptr, mpi_size_t s1_size, + mpi_limb_t s2_limb) +{ + mpi_limb_t cy_limb; + mpi_size_t j; + mpi_limb_t prod_high, prod_low; + + /* The loop counter and index J goes from -S1_SIZE to -1. This way + * the loop becomes faster. */ + j = -s1_size; + + /* Offset the base pointers to compensate for the negative indices. */ + s1_ptr -= j; + res_ptr -= j; + + cy_limb = 0; + do { + umul_ppmm( prod_high, prod_low, s1_ptr[j], s2_limb ); + prod_low += cy_limb; + cy_limb = (prod_low < cy_limb?1:0) + prod_high; + res_ptr[j] = prod_low; + } while( ++j ); + + return cy_limb; +} + + +/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP), + * both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are + * always stored. Return the most significant limb. + * + * Argument constraints: + * 1. PRODP != UP and PRODP != VP, i.e. the destination + * must be distinct from the multiplier and the multiplicand. + * + * + * Handle simple cases with traditional multiplication. + * + * This is the most critical code of multiplication. All multiplies rely + * on this, both small and huge. Small ones arrive here immediately. Huge + * ones arrive here as this is the base case for Karatsuba's recursive + * algorithm below. + */ + +static mpi_limb_t +mul_n_basecase( mpi_ptr_t prodp, mpi_ptr_t up, + mpi_ptr_t vp, mpi_size_t size) +{ + mpi_size_t i; + mpi_limb_t cy; + mpi_limb_t v_limb; + + /* Multiply by the first limb in V separately, as the result can be + * stored (not added) to PROD. We also avoid a loop for zeroing. */ + v_limb = vp[0]; + if( v_limb <= 1 ) { + if( v_limb == 1 ) + MPN_COPY( prodp, up, size ); + else + MPN_ZERO( prodp, size ); + cy = 0; + } + else + cy = mpihelp_mul_1( prodp, up, size, v_limb ); + + prodp[size] = cy; + prodp++; + + /* For each iteration in the outer loop, multiply one limb from + * U with one limb from V, and add it to PROD. */ + for( i = 1; i < size; i++ ) { + v_limb = vp[i]; + if( v_limb <= 1 ) { + cy = 0; + if( v_limb == 1 ) + cy = mpihelp_add_n(prodp, prodp, up, size); + } + else + cy = mpihelp_addmul_1(prodp, up, size, v_limb); + + prodp[size] = cy; + prodp++; + } + + return cy; +} + + +static void +mul_n( mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, + mpi_size_t size, mpi_ptr_t tspace ) +{ + if( size & 1 ) { + /* The size is odd, the code code below doesn't handle that. + * Multiply the least significant (size - 1) limbs with a recursive + * call, and handle the most significant limb of S1 and S2 + * separately. + * A slightly faster way to do this would be to make the Karatsuba + * code below behave as if the size were even, and let it check for + * odd size in the end. I.e., in essence move this code to the end. + * Doing so would save us a recursive call, and potentially make the + * stack grow a lot less. + */ + mpi_size_t esize = size - 1; /* even size */ + mpi_limb_t cy_limb; + + MPN_MUL_N_RECURSE( prodp, up, vp, esize, tspace ); + cy_limb = mpihelp_addmul_1( prodp + esize, up, esize, vp[esize] ); + prodp[esize + esize] = cy_limb; + cy_limb = mpihelp_addmul_1( prodp + esize, vp, size, up[esize] ); + prodp[esize + size] = cy_limb; + } + else { + /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm. + * + * Split U in two pieces, U1 and U0, such that + * U = U0 + U1*(B**n), + * and V in V1 and V0, such that + * V = V0 + V1*(B**n). + * + * UV is then computed recursively using the identity + * + * 2n n n n + * UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V + * 1 1 1 0 0 1 0 0 + * + * Where B = 2**BITS_PER_MP_LIMB. + */ + mpi_size_t hsize = size >> 1; + mpi_limb_t cy; + int negflg; + + /* Product H. ________________ ________________ + * |_____U1 x V1____||____U0 x V0_____| + * Put result in upper part of PROD and pass low part of TSPACE + * as new TSPACE. + */ + MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize, tspace); + + /* Product M. ________________ + * |_(U1-U0)(V0-V1)_| + */ + if( mpihelp_cmp(up + hsize, up, hsize) >= 0 ) { + mpihelp_sub_n(prodp, up + hsize, up, hsize); + negflg = 0; + } + else { + mpihelp_sub_n(prodp, up, up + hsize, hsize); + negflg = 1; + } + if( mpihelp_cmp(vp + hsize, vp, hsize) >= 0 ) { + mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize); + negflg ^= 1; + } + else { + mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize); + /* No change of NEGFLG. */ + } + /* Read temporary operands from low part of PROD. + * Put result in low part of TSPACE using upper part of TSPACE + * as new TSPACE. + */ + MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize, tspace + size); + + /* Add/copy product H. */ + MPN_COPY (prodp + hsize, prodp + size, hsize); + cy = mpihelp_add_n( prodp + size, prodp + size, + prodp + size + hsize, hsize); + + /* Add product M (if NEGFLG M is a negative number) */ + if(negflg) + cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size); + else + cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size); + + /* Product L. ________________ ________________ + * |________________||____U0 x V0_____| + * Read temporary operands from low part of PROD. + * Put result in low part of TSPACE using upper part of TSPACE + * as new TSPACE. + */ + MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size); + + /* Add/copy Product L (twice) */ + + cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size); + if( cy ) + mpihelp_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy); + + MPN_COPY(prodp, tspace, hsize); + cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize); + if( cy ) + mpihelp_add_1(prodp + size, prodp + size, size, 1); + } +} + + +static void +sqr_n_basecase( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size ) +{ + mpi_size_t i; + mpi_limb_t cy_limb; + mpi_limb_t v_limb; + + /* Multiply by the first limb in V separately, as the result can be + * stored (not added) to PROD. We also avoid a loop for zeroing. */ + v_limb = up[0]; + if( v_limb <= 1 ) { + if( v_limb == 1 ) + MPN_COPY( prodp, up, size ); + else + MPN_ZERO(prodp, size); + cy_limb = 0; + } + else + cy_limb = mpihelp_mul_1( prodp, up, size, v_limb ); + + prodp[size] = cy_limb; + prodp++; + + /* For each iteration in the outer loop, multiply one limb from + * U with one limb from V, and add it to PROD. */ + for( i=1; i < size; i++) { + v_limb = up[i]; + if( v_limb <= 1 ) { + cy_limb = 0; + if( v_limb == 1 ) + cy_limb = mpihelp_add_n(prodp, prodp, up, size); + } + else + cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb); + + prodp[size] = cy_limb; + prodp++; + } +} + + +static void +sqr_n( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace) +{ + if( size & 1 ) { + /* The size is odd, the code code below doesn't handle that. + * Multiply the least significant (size - 1) limbs with a recursive + * call, and handle the most significant limb of S1 and S2 + * separately. + * A slightly faster way to do this would be to make the Karatsuba + * code below behave as if the size were even, and let it check for + * odd size in the end. I.e., in essence move this code to the end. + * Doing so would save us a recursive call, and potentially make the + * stack grow a lot less. + */ + mpi_size_t esize = size - 1; /* even size */ + mpi_limb_t cy_limb; + + MPN_SQR_N_RECURSE( prodp, up, esize, tspace ); + cy_limb = mpihelp_addmul_1( prodp + esize, up, esize, up[esize] ); + prodp[esize + esize] = cy_limb; + cy_limb = mpihelp_addmul_1( prodp + esize, up, size, up[esize] ); + + prodp[esize + size] = cy_limb; + } + else { + mpi_size_t hsize = size >> 1; + mpi_limb_t cy; + + /* Product H. ________________ ________________ + * |_____U1 x U1____||____U0 x U0_____| + * Put result in upper part of PROD and pass low part of TSPACE + * as new TSPACE. + */ + MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace); + + /* Product M. ________________ + * |_(U1-U0)(U0-U1)_| + */ + if( mpihelp_cmp( up + hsize, up, hsize) >= 0 ) + mpihelp_sub_n( prodp, up + hsize, up, hsize); + else + mpihelp_sub_n (prodp, up, up + hsize, hsize); + + /* Read temporary operands from low part of PROD. + * Put result in low part of TSPACE using upper part of TSPACE + * as new TSPACE. */ + MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size); + + /* Add/copy product H */ + MPN_COPY(prodp + hsize, prodp + size, hsize); + cy = mpihelp_add_n(prodp + size, prodp + size, + prodp + size + hsize, hsize); + + /* Add product M (if NEGFLG M is a negative number). */ + cy -= mpihelp_sub_n (prodp + hsize, prodp + hsize, tspace, size); + + /* Product L. ________________ ________________ + * |________________||____U0 x U0_____| + * Read temporary operands from low part of PROD. + * Put result in low part of TSPACE using upper part of TSPACE + * as new TSPACE. */ + MPN_SQR_N_RECURSE (tspace, up, hsize, tspace + size); + + /* Add/copy Product L (twice). */ + cy += mpihelp_add_n (prodp + hsize, prodp + hsize, tspace, size); + if( cy ) + mpihelp_add_1(prodp + hsize + size, prodp + hsize + size, + hsize, cy); + + MPN_COPY(prodp, tspace, hsize); + cy = mpihelp_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize); + if( cy ) + mpihelp_add_1 (prodp + size, prodp + size, size, 1); + } +} + + +/* This should be made into an inline function in gmp.h. */ +void +mpihelp_mul_n( mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size) +{ + if( up == vp ) { + if( size < KARATSUBA_THRESHOLD ) + sqr_n_basecase( prodp, up, size ); + else { + mpi_ptr_t tspace; + tspace = mpi_alloc_limb_space( 2 * size ); + sqr_n( prodp, up, size, tspace ); + mpi_free_limb_space( tspace ); + } + } + else { + if( size < KARATSUBA_THRESHOLD ) + mul_n_basecase( prodp, up, vp, size ); + else { + mpi_ptr_t tspace; + tspace = mpi_alloc_limb_space( 2 * size ); + mul_n (prodp, up, vp, size, tspace); + mpi_free_limb_space( tspace ); + } + } +} + + +/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs) + * and v (pointed to by VP, with VSIZE limbs), and store the result at + * PRODP. USIZE + VSIZE limbs are always stored, but if the input + * operands are normalized. Return the most significant limb of the + * result. + * + * NOTE: The space pointed to by PRODP is overwritten before finished + * with U and V, so overlap is an error. + * + * Argument constraints: + * 1. USIZE >= VSIZE. + * 2. PRODP != UP and PRODP != VP, i.e. the destination + * must be distinct from the multiplier and the multiplicand. + */ + +mpi_limb_t +mpihelp_mul( mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize, + mpi_ptr_t vp, mpi_size_t vsize) +{ + mpi_ptr_t prod_endp = prodp + usize + vsize - 1; + mpi_limb_t cy; + mpi_ptr_t tspace; + + if( vsize < KARATSUBA_THRESHOLD ) { + mpi_size_t i; + mpi_limb_t v_limb; + + if( !vsize ) + return 0; + + /* Multiply by the first limb in V separately, as the result can be + * stored (not added) to PROD. We also avoid a loop for zeroing. */ + v_limb = vp[0]; + if( v_limb <= 1 ) { + if( v_limb == 1 ) + MPN_COPY( prodp, up, usize ); + else + MPN_ZERO( prodp, usize ); + cy = 0; + } + else + cy = mpihelp_mul_1( prodp, up, usize, v_limb ); + + prodp[usize] = cy; + prodp++; + + /* For each iteration in the outer loop, multiply one limb from + * U with one limb from V, and add it to PROD. */ + for( i = 1; i < vsize; i++ ) { + v_limb = vp[i]; + if( v_limb <= 1 ) { + cy = 0; + if( v_limb == 1 ) + cy = mpihelp_add_n(prodp, prodp, up, usize); + } + else + cy = mpihelp_addmul_1(prodp, up, usize, v_limb); + + prodp[usize] = cy; + prodp++; + } + + return cy; + } + + tspace = mpi_alloc_limb_space( 2 * vsize ); + MPN_MUL_N_RECURSE( prodp, up, vp, vsize, tspace ); + + prodp += vsize; + up += vsize; + usize -= vsize; + if( usize >= vsize ) { + mpi_ptr_t tp = mpi_alloc_limb_space( 2 * vsize ); + do { + MPN_MUL_N_RECURSE( tp, up, vp, vsize, tspace ); + cy = mpihelp_add_n( prodp, prodp, tp, vsize ); + mpihelp_add_1( prodp + vsize, tp + vsize, vsize, cy ); + prodp += vsize; + up += vsize; + usize -= vsize; + } while( usize >= vsize ); + mpi_free_limb_space( tp ); + } + + if( usize ) { + mpihelp_mul( tspace, vp, vsize, up, usize ); + cy = mpihelp_add_n( prodp, prodp, tspace, vsize); + mpihelp_add_1( prodp + vsize, tspace + vsize, usize, cy ); + } + + mpi_free_limb_space( tspace ); + return *prod_endp; +} + + |