143 lines
3.9 KiB
C
143 lines
3.9 KiB
C
/* mpn_mul -- Multiply two natural numbers.
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Copyright (C) 1991-2017 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, see
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<http://www.gnu.org/licenses/>. */
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#include <gmp.h>
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#include "gmp-impl.h"
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/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
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and v (pointed to by VP, with VSIZE limbs), and store the result at
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PRODP. USIZE + VSIZE limbs are always stored, but if the input
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operands are normalized. Return the most significant limb of the
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result.
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NOTE: The space pointed to by PRODP is overwritten before finished
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with U and V, so overlap is an error.
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Argument constraints:
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1. USIZE >= VSIZE.
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2. PRODP != UP and PRODP != VP, i.e. the destination
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must be distinct from the multiplier and the multiplicand. */
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/* If KARATSUBA_THRESHOLD is not already defined, define it to a
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value which is good on most machines. */
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#ifndef KARATSUBA_THRESHOLD
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#define KARATSUBA_THRESHOLD 32
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#endif
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mp_limb_t
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mpn_mul (mp_ptr prodp,
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mp_srcptr up, mp_size_t usize,
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mp_srcptr vp, mp_size_t vsize)
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{
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mp_ptr prod_endp = prodp + usize + vsize - 1;
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mp_limb_t cy;
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mp_ptr tspace;
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TMP_DECL (marker);
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if (vsize < KARATSUBA_THRESHOLD)
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{
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/* Handle simple cases with traditional multiplication.
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This is the most critical code of the entire function. All
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multiplies rely on this, both small and huge. Small ones arrive
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here immediately. Huge ones arrive here as this is the base case
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for Karatsuba's recursive algorithm below. */
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mp_size_t i;
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mp_limb_t cy_limb;
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mp_limb_t v_limb;
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if (vsize == 0)
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return 0;
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/* Multiply by the first limb in V separately, as the result can be
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stored (not added) to PROD. We also avoid a loop for zeroing. */
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v_limb = vp[0];
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if (v_limb <= 1)
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{
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if (v_limb == 1)
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MPN_COPY (prodp, up, usize);
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else
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MPN_ZERO (prodp, usize);
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cy_limb = 0;
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}
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else
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cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
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prodp[usize] = cy_limb;
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prodp++;
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/* For each iteration in the outer loop, multiply one limb from
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U with one limb from V, and add it to PROD. */
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for (i = 1; i < vsize; i++)
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{
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v_limb = vp[i];
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if (v_limb <= 1)
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{
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cy_limb = 0;
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if (v_limb == 1)
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cy_limb = mpn_add_n (prodp, prodp, up, usize);
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}
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else
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cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
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prodp[usize] = cy_limb;
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prodp++;
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}
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return cy_limb;
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}
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TMP_MARK (marker);
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tspace = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
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MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
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prodp += vsize;
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up += vsize;
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usize -= vsize;
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if (usize >= vsize)
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{
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mp_ptr tp = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
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do
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{
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MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
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cy = mpn_add_n (prodp, prodp, tp, vsize);
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mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
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prodp += vsize;
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up += vsize;
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usize -= vsize;
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}
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while (usize >= vsize);
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}
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/* True: usize < vsize. */
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/* Make life simple: Recurse. */
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if (usize != 0)
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{
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mpn_mul (tspace, vp, vsize, up, usize);
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cy = mpn_add_n (prodp, prodp, tspace, vsize);
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mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
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}
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TMP_FREE (marker);
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return *prod_endp;
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}
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