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Diffstat (limited to 'stdlib/mul_n.c')
| -rw-r--r-- | stdlib/mul_n.c | 401 |
1 files changed, 401 insertions, 0 deletions
diff --git a/stdlib/mul_n.c b/stdlib/mul_n.c new file mode 100644 index 0000000..b478c76 --- /dev/null +++ b/stdlib/mul_n.c @@ -0,0 +1,401 @@ +/* mpn_mul_n -- Multiply two natural numbers of length n. + +Copyright (C) 1991, 1992, 1993, 1994, 1996 Free Software Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library 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. + +The GNU MP Library 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 the GNU MP Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, +MA 02111-1307, USA. */ + +#include <gmp.h> +#include "gmp-impl.h" + +/* 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. */ + +/* 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 + +/* 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. */ + +void +#if __STDC__ +impn_mul_n_basecase (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size) +#else +impn_mul_n_basecase (prodp, up, vp, size) + mp_ptr prodp; + mp_srcptr up; + mp_srcptr vp; + mp_size_t size; +#endif +{ + mp_size_t i; + mp_limb_t cy_limb; + mp_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_limb = 0; + } + else + cy_limb = mpn_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 = vp[i]; + if (v_limb <= 1) + { + cy_limb = 0; + if (v_limb == 1) + cy_limb = mpn_add_n (prodp, prodp, up, size); + } + else + cy_limb = mpn_addmul_1 (prodp, up, size, v_limb); + + prodp[size] = cy_limb; + prodp++; + } +} + +void +#if __STDC__ +impn_mul_n (mp_ptr prodp, + mp_srcptr up, mp_srcptr vp, mp_size_t size, mp_ptr tspace) +#else +impn_mul_n (prodp, up, vp, size, tspace) + mp_ptr prodp; + mp_srcptr up; + mp_srcptr vp; + mp_size_t size; + mp_ptr tspace; +#endif +{ + if ((size & 1) != 0) + { + /* 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. */ + + mp_size_t esize = size - 1; /* even size */ + mp_limb_t cy_limb; + + MPN_MUL_N_RECURSE (prodp, up, vp, esize, tspace); + cy_limb = mpn_addmul_1 (prodp + esize, up, esize, vp[esize]); + prodp[esize + esize] = cy_limb; + cy_limb = mpn_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. */ + + mp_size_t hsize = size >> 1; + mp_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 (mpn_cmp (up + hsize, up, hsize) >= 0) + { + mpn_sub_n (prodp, up + hsize, up, hsize); + negflg = 0; + } + else + { + mpn_sub_n (prodp, up, up + hsize, hsize); + negflg = 1; + } + if (mpn_cmp (vp + hsize, vp, hsize) >= 0) + { + mpn_sub_n (prodp + hsize, vp + hsize, vp, hsize); + negflg ^= 1; + } + else + { + mpn_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 = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize); + + /*** Add product M (if NEGFLG M is a negative number). */ + if (negflg) + cy -= mpn_sub_n (prodp + hsize, prodp + hsize, tspace, size); + else + cy += mpn_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 += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size); + if (cy) + mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy); + + MPN_COPY (prodp, tspace, hsize); + cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize); + if (cy) + mpn_add_1 (prodp + size, prodp + size, size, 1); + } +} + +void +#if __STDC__ +impn_sqr_n_basecase (mp_ptr prodp, mp_srcptr up, mp_size_t size) +#else +impn_sqr_n_basecase (prodp, up, size) + mp_ptr prodp; + mp_srcptr up; + mp_size_t size; +#endif +{ + mp_size_t i; + mp_limb_t cy_limb; + mp_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 = mpn_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 = mpn_add_n (prodp, prodp, up, size); + } + else + cy_limb = mpn_addmul_1 (prodp, up, size, v_limb); + + prodp[size] = cy_limb; + prodp++; + } +} + +void +#if __STDC__ +impn_sqr_n (mp_ptr prodp, + mp_srcptr up, mp_size_t size, mp_ptr tspace) +#else +impn_sqr_n (prodp, up, size, tspace) + mp_ptr prodp; + mp_srcptr up; + mp_size_t size; + mp_ptr tspace; +#endif +{ + if ((size & 1) != 0) + { + /* 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. */ + + mp_size_t esize = size - 1; /* even size */ + mp_limb_t cy_limb; + + MPN_SQR_N_RECURSE (prodp, up, esize, tspace); + cy_limb = mpn_addmul_1 (prodp + esize, up, esize, up[esize]); + prodp[esize + esize] = cy_limb; + cy_limb = mpn_addmul_1 (prodp + esize, up, size, up[esize]); + + prodp[esize + size] = cy_limb; + } + else + { + mp_size_t hsize = size >> 1; + mp_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 (mpn_cmp (up + hsize, up, hsize) >= 0) + { + mpn_sub_n (prodp, up + hsize, up, hsize); + } + else + { + mpn_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 = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize); + + /*** Add product M (if NEGFLG M is a negative number). */ + cy -= mpn_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 += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size); + if (cy) + mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy); + + MPN_COPY (prodp, tspace, hsize); + cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize); + if (cy) + mpn_add_1 (prodp + size, prodp + size, size, 1); + } +} + +/* This should be made into an inline function in gmp.h. */ +void +#if __STDC__ +mpn_mul_n (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size) +#else +mpn_mul_n (prodp, up, vp, size) + mp_ptr prodp; + mp_srcptr up; + mp_srcptr vp; + mp_size_t size; +#endif +{ + TMP_DECL (marker); + TMP_MARK (marker); + if (up == vp) + { + if (size < KARATSUBA_THRESHOLD) + { + impn_sqr_n_basecase (prodp, up, size); + } + else + { + mp_ptr tspace; + tspace = (mp_ptr) TMP_ALLOC (2 * size * BYTES_PER_MP_LIMB); + impn_sqr_n (prodp, up, size, tspace); + } + } + else + { + if (size < KARATSUBA_THRESHOLD) + { + impn_mul_n_basecase (prodp, up, vp, size); + } + else + { + mp_ptr tspace; + tspace = (mp_ptr) TMP_ALLOC (2 * size * BYTES_PER_MP_LIMB); + impn_mul_n (prodp, up, vp, size, tspace); + } + } + TMP_FREE (marker); +} |