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