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4c74403188
Change-Id: Iae65e95cfa0d92091b8b0a424ae36d88efa76aa9 Reviewed-on: https://review.haiku-os.org/c/buildtools/+/3020 Reviewed-by: Adrien Destugues <pulkomandy@gmail.com>
371 lines
11 KiB
C
371 lines
11 KiB
C
/* Interpolation for the algorithm Toom-Cook 6.5-way.
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Contributed to the GNU project by Marco Bodrato.
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THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
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SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2009, 2010, 2012, 2015 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 either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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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 General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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#if HAVE_NATIVE_mpn_sublsh_n
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#define DO_mpn_sublsh_n(dst,src,n,s,ws) mpn_sublsh_n(dst,dst,src,n,s)
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#else
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static mp_limb_t
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DO_mpn_sublsh_n(mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws)
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{
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#if USE_MUL_1 && 0
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return mpn_submul_1(dst,src,n,CNST_LIMB(1) <<(s));
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#else
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mp_limb_t __cy;
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__cy = mpn_lshift(ws,src,n,s);
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return __cy + mpn_sub_n(dst,dst,ws,n);
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#endif
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}
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#endif
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#if HAVE_NATIVE_mpn_addlsh_n
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#define DO_mpn_addlsh_n(dst,src,n,s,ws) mpn_addlsh_n(dst,dst,src,n,s)
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#else
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static mp_limb_t
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DO_mpn_addlsh_n(mp_ptr dst, mp_srcptr src, mp_size_t n, unsigned int s, mp_ptr ws)
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{
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#if USE_MUL_1 && 0
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return mpn_addmul_1(dst,src,n,CNST_LIMB(1) <<(s));
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#else
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mp_limb_t __cy;
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__cy = mpn_lshift(ws,src,n,s);
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return __cy + mpn_add_n(dst,dst,ws,n);
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#endif
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}
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#endif
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#if HAVE_NATIVE_mpn_subrsh
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#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) mpn_subrsh(dst,nd,src,ns,s)
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#else
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/* FIXME: This is not a correct definition, it assumes no carry */
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#define DO_mpn_subrsh(dst,nd,src,ns,s,ws) \
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do { \
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mp_limb_t __cy; \
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MPN_DECR_U (dst, nd, src[0] >> s); \
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__cy = DO_mpn_sublsh_n (dst, src + 1, ns - 1, GMP_NUMB_BITS - s, ws); \
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MPN_DECR_U (dst + ns - 1, nd - ns + 1, __cy); \
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} while (0)
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#endif
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#if GMP_NUMB_BITS < 21
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#error Not implemented: Both sublsh_n(,,,20) should be corrected.
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#endif
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#if GMP_NUMB_BITS < 16
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#error Not implemented: divexact_by42525 needs splitting.
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#endif
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#if GMP_NUMB_BITS < 12
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#error Not implemented: Hard to adapt...
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#endif
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/* FIXME: tuneup should decide the best variant */
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#ifndef AORSMUL_FASTER_AORS_AORSLSH
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#define AORSMUL_FASTER_AORS_AORSLSH 1
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#endif
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#ifndef AORSMUL_FASTER_AORS_2AORSLSH
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#define AORSMUL_FASTER_AORS_2AORSLSH 1
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#endif
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#ifndef AORSMUL_FASTER_2AORSLSH
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#define AORSMUL_FASTER_2AORSLSH 1
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#endif
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#ifndef AORSMUL_FASTER_3AORSLSH
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#define AORSMUL_FASTER_3AORSLSH 1
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#endif
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#define BINVERT_9 \
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((((GMP_NUMB_MAX / 9) << (6 - GMP_NUMB_BITS % 6)) * 8 & GMP_NUMB_MAX) | 0x39)
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#define BINVERT_255 \
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(GMP_NUMB_MAX - ((GMP_NUMB_MAX / 255) << (8 - GMP_NUMB_BITS % 8)))
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/* FIXME: find some more general expressions for 2835^-1, 42525^-1 */
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#if GMP_LIMB_BITS == 32
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#define BINVERT_2835 (GMP_NUMB_MASK & CNST_LIMB(0x53E3771B))
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#define BINVERT_42525 (GMP_NUMB_MASK & CNST_LIMB(0x9F314C35))
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#else
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#if GMP_LIMB_BITS == 64
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#define BINVERT_2835 (GMP_NUMB_MASK & CNST_LIMB(0x938CC70553E3771B))
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#define BINVERT_42525 (GMP_NUMB_MASK & CNST_LIMB(0xE7B40D449F314C35))
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#endif
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#endif
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#ifndef mpn_divexact_by255
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#if GMP_NUMB_BITS % 8 == 0
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#define mpn_divexact_by255(dst,src,size) \
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(255 & 1 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 255)))
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#else
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#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
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#define mpn_divexact_by255(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(255),BINVERT_255,0)
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#else
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#define mpn_divexact_by255(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(255))
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#endif
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#endif
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#endif
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#ifndef mpn_divexact_by9x4
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#if HAVE_NATIVE_mpn_pi1_bdiv_q_1
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#define mpn_divexact_by9x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(9),BINVERT_9,2)
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#else
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#define mpn_divexact_by9x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(9)<<2)
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#endif
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#endif
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#ifndef mpn_divexact_by42525
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#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_42525)
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#define mpn_divexact_by42525(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(42525),BINVERT_42525,0)
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#else
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#define mpn_divexact_by42525(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(42525))
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#endif
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#endif
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#ifndef mpn_divexact_by2835x4
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#if HAVE_NATIVE_mpn_pi1_bdiv_q_1 && defined(BINVERT_2835)
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#define mpn_divexact_by2835x4(dst,src,size) mpn_pi1_bdiv_q_1(dst,src,size,CNST_LIMB(2835),BINVERT_2835,2)
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#else
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#define mpn_divexact_by2835x4(dst,src,size) mpn_divexact_1(dst,src,size,CNST_LIMB(2835)<<2)
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#endif
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#endif
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/* Interpolation for Toom-6.5 (or Toom-6), using the evaluation
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points: infinity(6.5 only), +-4, +-2, +-1, +-1/4, +-1/2, 0. More precisely,
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we want to compute f(2^(GMP_NUMB_BITS * n)) for a polynomial f of
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degree 11 (or 10), given the 12 (rsp. 11) values:
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r0 = limit at infinity of f(x) / x^11,
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r1 = f(4),f(-4),
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r2 = f(2),f(-2),
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r3 = f(1),f(-1),
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r4 = f(1/4),f(-1/4),
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r5 = f(1/2),f(-1/2),
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r6 = f(0).
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All couples of the form f(n),f(-n) must be already mixed with
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toom_couple_handling(f(n),...,f(-n),...)
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The result is stored in {pp, spt + 7*n (or 6*n)}.
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At entry, r6 is stored at {pp, 2n},
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r4 is stored at {pp + 3n, 3n + 1}.
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r2 is stored at {pp + 7n, 3n + 1}.
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r0 is stored at {pp +11n, spt}.
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The other values are 3n+1 limbs each (with most significant limbs small).
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Negative intermediate results are stored two-complemented.
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Inputs are destroyed.
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*/
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void
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mpn_toom_interpolate_12pts (mp_ptr pp, mp_ptr r1, mp_ptr r3, mp_ptr r5,
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mp_size_t n, mp_size_t spt, int half, mp_ptr wsi)
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{
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mp_limb_t cy;
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mp_size_t n3;
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mp_size_t n3p1;
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n3 = 3 * n;
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n3p1 = n3 + 1;
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#define r4 (pp + n3) /* 3n+1 */
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#define r2 (pp + 7 * n) /* 3n+1 */
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#define r0 (pp +11 * n) /* s+t <= 2*n */
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/******************************* interpolation *****************************/
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if (half != 0) {
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cy = mpn_sub_n (r3, r3, r0, spt);
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MPN_DECR_U (r3 + spt, n3p1 - spt, cy);
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cy = DO_mpn_sublsh_n (r2, r0, spt, 10, wsi);
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MPN_DECR_U (r2 + spt, n3p1 - spt, cy);
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DO_mpn_subrsh(r5, n3p1, r0, spt, 2, wsi);
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cy = DO_mpn_sublsh_n (r1, r0, spt, 20, wsi);
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MPN_DECR_U (r1 + spt, n3p1 - spt, cy);
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DO_mpn_subrsh(r4, n3p1, r0, spt, 4, wsi);
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};
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r4[n3] -= DO_mpn_sublsh_n (r4 + n, pp, 2 * n, 20, wsi);
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DO_mpn_subrsh(r1 + n, 2 * n + 1, pp, 2 * n, 4, wsi);
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#if HAVE_NATIVE_mpn_add_n_sub_n
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mpn_add_n_sub_n (r1, r4, r4, r1, n3p1);
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#else
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ASSERT_NOCARRY(mpn_add_n (wsi, r1, r4, n3p1));
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mpn_sub_n (r4, r4, r1, n3p1); /* can be negative */
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MP_PTR_SWAP(r1, wsi);
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#endif
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r5[n3] -= DO_mpn_sublsh_n (r5 + n, pp, 2 * n, 10, wsi);
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DO_mpn_subrsh(r2 + n, 2 * n + 1, pp, 2 * n, 2, wsi);
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#if HAVE_NATIVE_mpn_add_n_sub_n
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mpn_add_n_sub_n (r2, r5, r5, r2, n3p1);
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#else
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mpn_sub_n (wsi, r5, r2, n3p1); /* can be negative */
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ASSERT_NOCARRY(mpn_add_n (r2, r2, r5, n3p1));
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MP_PTR_SWAP(r5, wsi);
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#endif
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r3[n3] -= mpn_sub_n (r3+n, r3+n, pp, 2 * n);
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#if AORSMUL_FASTER_AORS_AORSLSH
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mpn_submul_1 (r4, r5, n3p1, 257); /* can be negative */
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#else
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mpn_sub_n (r4, r4, r5, n3p1); /* can be negative */
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DO_mpn_sublsh_n (r4, r5, n3p1, 8, wsi); /* can be negative */
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#endif
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/* A division by 2835x4 follows. Warning: the operand can be negative! */
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mpn_divexact_by2835x4(r4, r4, n3p1);
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if ((r4[n3] & (GMP_NUMB_MAX << (GMP_NUMB_BITS-3))) != 0)
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r4[n3] |= (GMP_NUMB_MAX << (GMP_NUMB_BITS-2));
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#if AORSMUL_FASTER_2AORSLSH
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mpn_addmul_1 (r5, r4, n3p1, 60); /* can be negative */
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#else
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DO_mpn_sublsh_n (r5, r4, n3p1, 2, wsi); /* can be negative */
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DO_mpn_addlsh_n (r5, r4, n3p1, 6, wsi); /* can give a carry */
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#endif
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mpn_divexact_by255(r5, r5, n3p1);
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ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r3, n3p1, 5, wsi));
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#if AORSMUL_FASTER_3AORSLSH
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ASSERT_NOCARRY(mpn_submul_1 (r1, r2, n3p1, 100));
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#else
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ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 6, wsi));
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ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 5, wsi));
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ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r2, n3p1, 2, wsi));
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#endif
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ASSERT_NOCARRY(DO_mpn_sublsh_n (r1, r3, n3p1, 9, wsi));
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mpn_divexact_by42525(r1, r1, n3p1);
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#if AORSMUL_FASTER_AORS_2AORSLSH
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ASSERT_NOCARRY(mpn_submul_1 (r2, r1, n3p1, 225));
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#else
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ASSERT_NOCARRY(mpn_sub_n (r2, r2, r1, n3p1));
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ASSERT_NOCARRY(DO_mpn_addlsh_n (r2, r1, n3p1, 5, wsi));
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ASSERT_NOCARRY(DO_mpn_sublsh_n (r2, r1, n3p1, 8, wsi));
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#endif
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mpn_divexact_by9x4(r2, r2, n3p1);
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ASSERT_NOCARRY(mpn_sub_n (r3, r3, r2, n3p1));
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#ifdef HAVE_NATIVE_mpn_rsh1sub_n
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mpn_rsh1sub_n (r4, r2, r4, n3p1);
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r4 [n3p1 - 1] &= GMP_NUMB_MASK >> 1;
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#else
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mpn_sub_n (r4, r2, r4, n3p1);
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ASSERT_NOCARRY(mpn_rshift(r4, r4, n3p1, 1));
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#endif
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ASSERT_NOCARRY(mpn_sub_n (r2, r2, r4, n3p1));
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#ifdef HAVE_NATIVE_mpn_rsh1add_n
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mpn_rsh1add_n (r5, r5, r1, n3p1);
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r5 [n3p1 - 1] &= GMP_NUMB_MASK >> 1;
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#else
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mpn_add_n (r5, r5, r1, n3p1);
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ASSERT_NOCARRY(mpn_rshift(r5, r5, n3p1, 1));
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#endif
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/* last interpolation steps... */
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ASSERT_NOCARRY(mpn_sub_n (r3, r3, r1, n3p1));
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ASSERT_NOCARRY(mpn_sub_n (r1, r1, r5, n3p1));
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/* ... could be mixed with recomposition
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||H-r5|M-r5|L-r5| ||H-r1|M-r1|L-r1|
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*/
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/***************************** recomposition *******************************/
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/*
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pp[] prior to operations:
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|M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|____|H_r6|L r6|pp
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summation scheme for remaining operations:
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|__12|n_11|n_10|n__9|n__8|n__7|n__6|n__5|n__4|n__3|n__2|n___|n___|pp
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|M r0|L r0|___||H r2|M r2|L r2|___||H r4|M r4|L r4|____|H_r6|L r6|pp
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||H r1|M r1|L r1| ||H r3|M r3|L r3| ||H_r5|M_r5|L_r5|
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*/
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cy = mpn_add_n (pp + n, pp + n, r5, n);
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cy = mpn_add_1 (pp + 2 * n, r5 + n, n, cy);
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#if HAVE_NATIVE_mpn_add_nc
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cy = r5[n3] + mpn_add_nc(pp + n3, pp + n3, r5 + 2 * n, n, cy);
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#else
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MPN_INCR_U (r5 + 2 * n, n + 1, cy);
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cy = r5[n3] + mpn_add_n (pp + n3, pp + n3, r5 + 2 * n, n);
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#endif
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MPN_INCR_U (pp + n3 + n, 2 * n + 1, cy);
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pp[2 * n3]+= mpn_add_n (pp + 5 * n, pp + 5 * n, r3, n);
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cy = mpn_add_1 (pp + 2 * n3, r3 + n, n, pp[2 * n3]);
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#if HAVE_NATIVE_mpn_add_nc
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cy = r3[n3] + mpn_add_nc(pp + 7 * n, pp + 7 * n, r3 + 2 * n, n, cy);
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#else
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MPN_INCR_U (r3 + 2 * n, n + 1, cy);
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cy = r3[n3] + mpn_add_n (pp + 7 * n, pp + 7 * n, r3 + 2 * n, n);
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#endif
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MPN_INCR_U (pp + 8 * n, 2 * n + 1, cy);
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pp[10*n]+=mpn_add_n (pp + 9 * n, pp + 9 * n, r1, n);
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if (half) {
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cy = mpn_add_1 (pp + 10 * n, r1 + n, n, pp[10 * n]);
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#if HAVE_NATIVE_mpn_add_nc
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if (LIKELY (spt > n)) {
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cy = r1[n3] + mpn_add_nc(pp + 11 * n, pp + 11 * n, r1 + 2 * n, n, cy);
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MPN_INCR_U (pp + 4 * n3, spt - n, cy);
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} else {
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ASSERT_NOCARRY(mpn_add_nc(pp + 11 * n, pp + 11 * n, r1 + 2 * n, spt, cy));
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}
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#else
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MPN_INCR_U (r1 + 2 * n, n + 1, cy);
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if (LIKELY (spt > n)) {
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cy = r1[n3] + mpn_add_n (pp + 11 * n, pp + 11 * n, r1 + 2 * n, n);
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MPN_INCR_U (pp + 4 * n3, spt - n, cy);
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} else {
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ASSERT_NOCARRY(mpn_add_n (pp + 11 * n, pp + 11 * n, r1 + 2 * n, spt));
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}
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#endif
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} else {
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ASSERT_NOCARRY(mpn_add_1 (pp + 10 * n, r1 + n, spt, pp[10 * n]));
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}
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#undef r0
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#undef r2
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#undef r4
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}
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