207 lines
6.5 KiB
C
207 lines
6.5 KiB
C
/* mpn_mul -- Multiply two natural numbers.
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THE HELPER FUNCTIONS IN THIS FILE (meaning everything except mpn_mul)
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ARE INTERNAL FUNCTIONS WITH MUTABLE INTERFACES. IT IS ONLY SAFE TO REACH
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THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST GUARANTEED
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THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 1991, 1993, 1994, 1996, 1997, 1999, 2000, 2001, 2002, 2003, 2005
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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, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#ifndef MUL_BASECASE_MAX_UN
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#define MUL_BASECASE_MAX_UN 500
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#endif
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/* Multiply the natural numbers u (pointed to by UP, with UN limbs) and v
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(pointed to by VP, with VN limbs), and store the result at PRODP. The
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result is UN + VN limbs. Return the most significant limb of the result.
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NOTE: The space pointed to by PRODP is overwritten before finished with U
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and V, so overlap is an error.
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Argument constraints:
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1. UN >= VN.
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2. PRODP != UP and PRODP != VP, i.e. the destination must be distinct from
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the multiplier and the multiplicand. */
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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 un,
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mp_srcptr vp, mp_size_t vn)
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{
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mp_size_t l;
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mp_limb_t c;
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ASSERT (un >= vn);
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ASSERT (vn >= 1);
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ASSERT (! MPN_OVERLAP_P (prodp, un+vn, up, un));
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ASSERT (! MPN_OVERLAP_P (prodp, un+vn, vp, vn));
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if (up == vp && un == vn)
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{
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mpn_sqr_n (prodp, up, un);
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return prodp[2 * un - 1];
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}
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if (vn < MUL_KARATSUBA_THRESHOLD)
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{ /* plain schoolbook multiplication */
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if (un <= MUL_BASECASE_MAX_UN)
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mpn_mul_basecase (prodp, up, un, vp, vn);
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else
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{
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/* We have un >> MUL_BASECASE_MAX_UN > vn. For better memory
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locality, split up[] into MUL_BASECASE_MAX_UN pieces and multiply
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these pieces with the vp[] operand. After each such partial
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multiplication (but the last) we copy the most significant vn
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limbs into a temporary buffer since that part would otherwise be
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overwritten by the next multiplication. After the next
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multiplication, we add it back. This illustrates the situation:
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-->vn<--
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| |<------- un ------->|
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_____________________|
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X /|
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/XX__________________/ |
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_____________________ |
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X / |
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/XX__________________/ |
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_____________________ |
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/ / |
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/____________________/ |
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==================================================================
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The parts marked with X are the parts whose sums are copied into
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the temporary buffer. */
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mp_limb_t tp[MUL_KARATSUBA_THRESHOLD_LIMIT];
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mp_limb_t cy;
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ASSERT (MUL_KARATSUBA_THRESHOLD <= MUL_KARATSUBA_THRESHOLD_LIMIT);
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mpn_mul_basecase (prodp, up, MUL_BASECASE_MAX_UN, vp, vn);
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prodp += MUL_BASECASE_MAX_UN;
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MPN_COPY (tp, prodp, vn); /* preserve high triangle */
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up += MUL_BASECASE_MAX_UN;
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un -= MUL_BASECASE_MAX_UN;
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while (un > MUL_BASECASE_MAX_UN)
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{
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mpn_mul_basecase (prodp, up, MUL_BASECASE_MAX_UN, vp, vn);
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cy = mpn_add_n (prodp, prodp, tp, vn); /* add back preserved triangle */
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mpn_incr_u (prodp + vn, cy); /* safe? */
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prodp += MUL_BASECASE_MAX_UN;
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MPN_COPY (tp, prodp, vn); /* preserve high triangle */
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up += MUL_BASECASE_MAX_UN;
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un -= MUL_BASECASE_MAX_UN;
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}
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if (un > vn)
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{
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mpn_mul_basecase (prodp, up, un, vp, vn);
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}
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else
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{
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ASSERT_ALWAYS (un > 0);
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mpn_mul_basecase (prodp, vp, vn, up, un);
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}
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cy = mpn_add_n (prodp, prodp, tp, vn); /* add back preserved triangle */
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mpn_incr_u (prodp + vn, cy); /* safe? */
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}
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return prodp[un + vn - 1];
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}
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if (ABOVE_THRESHOLD (vn, MUL_FFT_THRESHOLD))
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{
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mpn_mul_fft_full (prodp, up, un, vp, vn);
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return prodp[un + vn - 1];
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}
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mpn_mul_n (prodp, up, vp, vn);
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if (un != vn)
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{ mp_limb_t t;
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mp_ptr ws;
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TMP_DECL;
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TMP_MARK;
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prodp += vn;
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l = vn;
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up += vn;
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un -= vn;
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if (un < vn)
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{
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/* Swap u's and v's. */
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MPN_SRCPTR_SWAP (up,un, vp,vn);
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}
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ws = TMP_ALLOC_LIMBS ((vn >= MUL_KARATSUBA_THRESHOLD ? vn : un) + vn);
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t = 0;
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while (vn >= MUL_KARATSUBA_THRESHOLD)
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{
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mpn_mul_n (ws, up, vp, vn);
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if (l <= 2*vn)
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{
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t += mpn_add_n (prodp, prodp, ws, l);
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if (l != 2*vn)
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{
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t = mpn_add_1 (prodp + l, ws + l, 2*vn - l, t);
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l = 2*vn;
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}
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}
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else
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{
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c = mpn_add_n (prodp, prodp, ws, 2*vn);
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t += mpn_add_1 (prodp + 2*vn, prodp + 2*vn, l - 2*vn, c);
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}
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prodp += vn;
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l -= vn;
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up += vn;
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un -= vn;
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if (un < vn)
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{
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/* Swap u's and v's. */
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MPN_SRCPTR_SWAP (up,un, vp,vn);
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}
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}
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if (vn != 0)
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{
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mpn_mul_basecase (ws, up, un, vp, vn);
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if (l <= un + vn)
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{
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t += mpn_add_n (prodp, prodp, ws, l);
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if (l != un + vn)
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t = mpn_add_1 (prodp + l, ws + l, un + vn - l, t);
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}
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else
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{
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c = mpn_add_n (prodp, prodp, ws, un + vn);
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t += mpn_add_1 (prodp + un + vn, prodp + un + vn, l - un - vn, c);
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}
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}
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TMP_FREE;
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}
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return prodp[un + vn - 1];
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}
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