442 lines
8.8 KiB
C
442 lines
8.8 KiB
C
/* hgcd2.c
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THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
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SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 1996, 1998, 2000, 2001, 2002, 2003, 2004, 2008 Free Software
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Foundation, Inc.
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Copyright 2004, 2005 Niels Möller
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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 3 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. If not, see http://www.gnu.org/licenses/. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#include "longlong.h"
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#if GMP_NAIL_BITS == 0
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/* Copied from the old mpn/generic/gcdext.c, and modified slightly to return
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the remainder. */
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/* Single-limb division optimized for small quotients. */
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static inline mp_limb_t
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div1 (mp_ptr rp,
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mp_limb_t n0,
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mp_limb_t d0)
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{
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mp_limb_t q = 0;
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if ((mp_limb_signed_t) n0 < 0)
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{
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int cnt;
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for (cnt = 1; (mp_limb_signed_t) d0 >= 0; cnt++)
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{
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d0 = d0 << 1;
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}
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q = 0;
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while (cnt)
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{
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q <<= 1;
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if (n0 >= d0)
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{
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n0 = n0 - d0;
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q |= 1;
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}
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d0 = d0 >> 1;
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cnt--;
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}
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}
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else
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{
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int cnt;
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for (cnt = 0; n0 >= d0; cnt++)
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{
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d0 = d0 << 1;
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}
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q = 0;
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while (cnt)
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{
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d0 = d0 >> 1;
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q <<= 1;
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if (n0 >= d0)
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{
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n0 = n0 - d0;
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q |= 1;
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}
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cnt--;
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}
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}
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*rp = n0;
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return q;
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}
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/* Two-limb division optimized for small quotients. */
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static inline mp_limb_t
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div2 (mp_ptr rp,
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mp_limb_t nh, mp_limb_t nl,
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mp_limb_t dh, mp_limb_t dl)
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{
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mp_limb_t q = 0;
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if ((mp_limb_signed_t) nh < 0)
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{
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int cnt;
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for (cnt = 1; (mp_limb_signed_t) dh >= 0; cnt++)
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{
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dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
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dl = dl << 1;
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}
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while (cnt)
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{
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q <<= 1;
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if (nh > dh || (nh == dh && nl >= dl))
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{
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sub_ddmmss (nh, nl, nh, nl, dh, dl);
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q |= 1;
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}
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dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
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dh = dh >> 1;
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cnt--;
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}
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}
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else
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{
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int cnt;
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for (cnt = 0; nh > dh || (nh == dh && nl >= dl); cnt++)
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{
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dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
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dl = dl << 1;
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}
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while (cnt)
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{
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dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
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dh = dh >> 1;
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q <<= 1;
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if (nh > dh || (nh == dh && nl >= dl))
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{
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sub_ddmmss (nh, nl, nh, nl, dh, dl);
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q |= 1;
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}
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cnt--;
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}
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}
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rp[0] = nl;
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rp[1] = nh;
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return q;
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}
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#if 0
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/* This div2 uses less branches, but it seems to nevertheless be
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slightly slower than the above code. */
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static inline mp_limb_t
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div2 (mp_ptr rp,
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mp_limb_t nh, mp_limb_t nl,
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mp_limb_t dh, mp_limb_t dl)
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{
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mp_limb_t q = 0;
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int ncnt;
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int dcnt;
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count_leading_zeros (ncnt, nh);
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count_leading_zeros (dcnt, dh);
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dcnt -= ncnt;
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dh = (dh << dcnt) + (-(dcnt > 0) & (dl >> (GMP_LIMB_BITS - dcnt)));
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dl <<= dcnt;
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do
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{
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mp_limb_t bit;
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q <<= 1;
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if (UNLIKELY (nh == dh))
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bit = (nl >= dl);
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else
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bit = (nh > dh);
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q |= bit;
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sub_ddmmss (nh, nl, nh, nl, (-bit) & dh, (-bit) & dl);
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dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
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dh = dh >> 1;
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}
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while (dcnt--);
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rp[0] = nl;
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rp[1] = nh;
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return q;
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}
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#endif
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#else /* GMP_NAIL_BITS != 0 */
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/* Check all functions for nail support. */
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/* hgcd2 should be defined to take inputs including nail bits, and
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produce a matrix with elements also including nail bits. This is
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necessary, for the matrix elements to be useful with mpn_mul_1,
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mpn_addmul_1 and friends. */
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#error Not implemented
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#endif /* GMP_NAIL_BITS != 0 */
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/* Reduces a,b until |a-b| (almost) fits in one limb + 1 bit. Constructs
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matrix M. Returns 1 if we make progress, i.e. can perform at least
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one subtraction. Otherwise returns zero.. */
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/* FIXME: Possible optimizations:
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The div2 function starts with checking the most significant bit of
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the numerator. We can maintained normalized operands here, call
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hgcd with normalized operands only, which should make the code
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simpler and possibly faster.
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Experiment with table lookups on the most significant bits.
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This function is also a candidate for assembler implementation.
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*/
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int
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mpn_nhgcd2 (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,
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struct ngcd_matrix1 *M)
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{
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mp_limb_t u00, u01, u10, u11;
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if (ah < 2 || bh < 2)
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return 0;
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if (ah > bh || (ah == bh && al > bl))
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{
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sub_ddmmss (ah, al, ah, al, bh, bl);
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if (ah < 2)
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return 0;
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u00 = u01 = u11 = 1;
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u10 = 0;
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}
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else
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{
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sub_ddmmss (bh, bl, bh, bl, ah, al);
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if (bh < 2)
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return 0;
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u00 = u10 = u11 = 1;
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u01 = 0;
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}
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if (ah < bh)
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goto subtract_a;
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for (;;)
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{
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ASSERT (ah >= bh);
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if (ah == bh)
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goto done;
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if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
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{
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ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
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bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));
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break;
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}
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/* Subtract a -= q b, and multiply M from the right by (1 q ; 0
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1), affecting the second column of M. */
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ASSERT (ah > bh);
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sub_ddmmss (ah, al, ah, al, bh, bl);
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if (ah < 2)
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goto done;
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if (ah <= bh)
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{
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/* Use q = 1 */
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u01 += u00;
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u11 += u10;
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}
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else
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{
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mp_limb_t r[2];
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mp_limb_t q = div2 (r, ah, al, bh, bl);
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al = r[0]; ah = r[1];
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if (ah < 2)
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{
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/* A is too small, but q is correct. */
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u01 += q * u00;
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u11 += q * u10;
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goto done;
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}
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q++;
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u01 += q * u00;
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u11 += q * u10;
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}
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subtract_a:
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ASSERT (bh >= ah);
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if (ah == bh)
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goto done;
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if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
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{
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ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
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bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));
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goto subtract_a1;
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}
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/* Subtract b -= q a, and multiply M from the right by (1 0 ; q
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1), affecting the first column of M. */
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sub_ddmmss (bh, bl, bh, bl, ah, al);
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if (bh < 2)
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goto done;
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if (bh <= ah)
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{
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/* Use q = 1 */
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u00 += u01;
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u10 += u11;
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}
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else
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{
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mp_limb_t r[2];
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mp_limb_t q = div2 (r, bh, bl, ah, al);
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bl = r[0]; bh = r[1];
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if (bh < 2)
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{
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/* B is too small, but q is correct. */
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u00 += q * u01;
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u10 += q * u11;
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goto done;
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}
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q++;
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u00 += q * u01;
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u10 += q * u11;
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}
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}
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/* NOTE: Since we discard the least significant half limb, we don't
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get a truly maximal M (corresponding to |a - b| <
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2^{GMP_LIMB_BITS +1}). */
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/* Single precision loop */
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for (;;)
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{
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ASSERT (ah >= bh);
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if (ah == bh)
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break;
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ah -= bh;
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if (ah < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
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break;
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if (ah <= bh)
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{
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/* Use q = 1 */
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u01 += u00;
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u11 += u10;
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}
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else
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{
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mp_limb_t r;
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mp_limb_t q = div1 (&r, ah, bh);
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ah = r;
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if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
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{
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/* A is too small, but q is correct. */
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u01 += q * u00;
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u11 += q * u10;
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break;
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}
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q++;
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u01 += q * u00;
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u11 += q * u10;
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}
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subtract_a1:
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ASSERT (bh >= ah);
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if (ah == bh)
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break;
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bh -= ah;
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if (bh < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
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break;
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if (bh <= ah)
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{
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/* Use q = 1 */
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u00 += u01;
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u10 += u11;
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}
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else
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{
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mp_limb_t r;
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mp_limb_t q = div1 (&r, bh, ah);
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bh = r;
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if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
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{
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/* B is too small, but q is correct. */
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u00 += q * u01;
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u10 += q * u11;
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break;
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}
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q++;
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u00 += q * u01;
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u10 += q * u11;
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}
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}
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done:
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M->u[0][0] = u00; M->u[0][1] = u01;
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M->u[1][0] = u10; M->u[1][1] = u11;
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return 1;
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}
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/* Multiply (a;b) by M^{-1} = (r11, -r01; -r10, r00). Needs n limbs of
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temporary storage. */
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mp_size_t
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mpn_ngcd_matrix1_vector (struct ngcd_matrix1 *M, mp_size_t n, mp_ptr ap, mp_ptr bp, mp_ptr tp)
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{
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mp_limb_t h0, h1;
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/* Compute (a;b) <-- (u11 a - u01 b, -u10 a + u00 b) as
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t = a
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a *= u11
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a -= u01 * b
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b *= u00
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b -= u10 * t
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*/
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MPN_COPY (tp, ap, n);
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h0 = mpn_mul_1 (ap, ap, n, M->u[1][1]);
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h1 = mpn_submul_1 (ap, bp, n, M->u[0][1]);
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ASSERT (h0 == h1);
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h0 = mpn_mul_1 (bp, bp, n, M->u[0][0]);
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h1 = mpn_submul_1 (bp, tp, n, M->u[1][0]);
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ASSERT (h0 == h1);
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n -= (ap[n-1] | bp[n-1]) == 0;
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return n;
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}
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