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[/] [openrisc/] [trunk/] [gnu-dev/] [or1k-gcc/] [libquadmath/] [printf/] [mul_n.c] - Rev 746
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/* 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 <config.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); } }
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