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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
301 lines
8.0 KiB
C
301 lines
8.0 KiB
C
/* mpn_toom62_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 3 times
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as large as bn. Or more accurately, (5/2)bn < an < 6bn.
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Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
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The idea of applying toom to unbalanced multiplication is due to Marco
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Bodrato and Alberto Zanoni.
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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 2006, 2007, 2008 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 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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/* Evaluate in:
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0, +1, -1, +2, -2, 1/2, +inf
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<-s-><--n--><--n--><--n--><--n--><--n-->
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___ ______ ______ ______ ______ ______
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|a5_|___a4_|___a3_|___a2_|___a1_|___a0_|
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|_b1_|___b0_|
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<-t--><--n-->
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v0 = a0 * b0 # A(0)*B(0)
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v1 = ( a0+ a1+ a2+ a3+ a4+ a5)*( b0+ b1) # A(1)*B(1) ah <= 5 bh <= 1
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vm1 = ( a0- a1+ a2- a3+ a4- a5)*( b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0
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v2 = ( a0+ 2a1+4a2+8a3+16a4+32a5)*( b0+2b1) # A(2)*B(2) ah <= 62 bh <= 2
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vm2 = ( a0- 2a1+4a2-8a3+16a4-32a5)*( b0-2b1) # A(-2)*B(-2) -41<=ah<=20 -1<=bh<=0
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vh = (32a0+16a1+8a2+4a3+ 2a4+ a5)*(2b0+ b1) # A(1/2)*B(1/2) ah <= 62 bh <= 2
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vinf= a5 * b1 # A(inf)*B(inf)
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*/
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void
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mpn_toom62_mul (mp_ptr pp,
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mp_srcptr ap, mp_size_t an,
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mp_srcptr bp, mp_size_t bn,
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mp_ptr scratch)
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{
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mp_size_t n, s, t;
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mp_limb_t cy;
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mp_ptr as1, asm1, as2, asm2, ash;
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mp_ptr bs1, bsm1, bs2, bsm2, bsh;
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mp_ptr gp;
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enum toom7_flags aflags, bflags;
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TMP_DECL;
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#define a0 ap
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#define a1 (ap + n)
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#define a2 (ap + 2*n)
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#define a3 (ap + 3*n)
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#define a4 (ap + 4*n)
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#define a5 (ap + 5*n)
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#define b0 bp
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#define b1 (bp + n)
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n = 1 + (an >= 3 * bn ? (an - 1) / (size_t) 6 : (bn - 1) >> 1);
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s = an - 5 * n;
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t = bn - n;
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ASSERT (0 < s && s <= n);
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ASSERT (0 < t && t <= n);
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TMP_MARK;
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as1 = TMP_SALLOC_LIMBS (n + 1);
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asm1 = TMP_SALLOC_LIMBS (n + 1);
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as2 = TMP_SALLOC_LIMBS (n + 1);
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asm2 = TMP_SALLOC_LIMBS (n + 1);
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ash = TMP_SALLOC_LIMBS (n + 1);
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bs1 = TMP_SALLOC_LIMBS (n + 1);
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bsm1 = TMP_SALLOC_LIMBS (n);
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bs2 = TMP_SALLOC_LIMBS (n + 1);
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bsm2 = TMP_SALLOC_LIMBS (n + 1);
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bsh = TMP_SALLOC_LIMBS (n + 1);
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gp = pp;
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/* Compute as1 and asm1. */
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aflags = toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 5, ap, n, s, gp);
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/* Compute as2 and asm2. */
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aflags |= toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 5, ap, n, s, gp);
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/* Compute ash = 32 a0 + 16 a1 + 8 a2 + 4 a3 + 2 a4 + a5
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= 2*(2*(2*(2*(2*a0 + a1) + a2) + a3) + a4) + a5 */
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (ash, a1, a0, n);
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cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n);
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cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n);
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cy = 2*cy + mpn_addlsh1_n (ash, a4, ash, n);
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if (s < n)
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{
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mp_limb_t cy2;
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cy2 = mpn_addlsh1_n (ash, a5, ash, s);
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ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1);
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MPN_INCR_U (ash + s, n+1-s, cy2);
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}
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else
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ash[n] = 2*cy + mpn_addlsh1_n (ash, a5, ash, n);
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#else
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cy = mpn_lshift (ash, a0, n, 1);
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cy += mpn_add_n (ash, ash, a1, n);
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cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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cy += mpn_add_n (ash, ash, a2, n);
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cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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cy += mpn_add_n (ash, ash, a3, n);
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cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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cy += mpn_add_n (ash, ash, a4, n);
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cy = 2*cy + mpn_lshift (ash, ash, n, 1);
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ash[n] = cy + mpn_add (ash, ash, n, a5, s);
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#endif
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/* Compute bs1 and bsm1. */
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if (t == n)
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{
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#if HAVE_NATIVE_mpn_add_n_sub_n
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if (mpn_cmp (b0, b1, n) < 0)
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{
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cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
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bflags = toom7_w3_neg;
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}
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else
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{
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cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
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bflags = 0;
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}
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bs1[n] = cy >> 1;
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#else
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bs1[n] = mpn_add_n (bs1, b0, b1, n);
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if (mpn_cmp (b0, b1, n) < 0)
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{
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mpn_sub_n (bsm1, b1, b0, n);
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bflags = toom7_w3_neg;
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}
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else
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{
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mpn_sub_n (bsm1, b0, b1, n);
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bflags = 0;
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}
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#endif
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}
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else
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{
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bs1[n] = mpn_add (bs1, b0, n, b1, t);
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if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
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{
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mpn_sub_n (bsm1, b1, b0, t);
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MPN_ZERO (bsm1 + t, n - t);
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bflags = toom7_w3_neg;
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}
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else
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{
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mpn_sub (bsm1, b0, n, b1, t);
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bflags = 0;
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}
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}
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/* Compute bs2 and bsm2. Recycling bs1 and bsm1; bs2=bs1+b1, bsm2 =
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bsm1 - b1 */
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mpn_add (bs2, bs1, n + 1, b1, t);
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if (bflags & toom7_w3_neg)
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{
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bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t);
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bflags |= toom7_w1_neg;
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}
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else
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{
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/* FIXME: Simplify this logic? */
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if (t < n)
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{
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if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0)
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{
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ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, t));
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MPN_ZERO (bsm2 + t, n + 1 - t);
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bflags |= toom7_w1_neg;
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}
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else
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{
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ASSERT_NOCARRY (mpn_sub (bsm2, bsm1, n, b1, t));
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bsm2[n] = 0;
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}
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}
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else
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{
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if (mpn_cmp (bsm1, b1, n) < 0)
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{
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ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, n));
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bflags |= toom7_w1_neg;
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}
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else
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{
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ASSERT_NOCARRY (mpn_sub (bsm2, bsm1, n, b1, n));
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}
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bsm2[n] = 0;
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}
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}
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/* Compute bsh, recycling bs1 and bsm1. bsh=bs1+b0; */
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mpn_add (bsh, bs1, n + 1, b0, n);
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ASSERT (as1[n] <= 5);
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ASSERT (bs1[n] <= 1);
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ASSERT (asm1[n] <= 2);
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ASSERT (as2[n] <= 62);
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ASSERT (bs2[n] <= 2);
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ASSERT (asm2[n] <= 41);
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ASSERT (bsm2[n] <= 1);
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ASSERT (ash[n] <= 62);
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ASSERT (bsh[n] <= 2);
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#define v0 pp /* 2n */
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#define v1 (pp + 2 * n) /* 2n+1 */
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#define vinf (pp + 6 * n) /* s+t */
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#define v2 scratch /* 2n+1 */
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#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
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#define vh (scratch + 4 * n + 2) /* 2n+1 */
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#define vm1 (scratch + 6 * n + 3) /* 2n+1 */
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#define scratch_out (scratch + 8 * n + 4) /* 2n+1 */
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/* Total scratch need: 10*n+5 */
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/* Must be in allocation order, as they overwrite one limb beyond
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* 2n+1. */
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mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */
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mpn_mul_n (vm2, asm2, bsm2, n + 1); /* vm2, 2n+1 limbs */
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mpn_mul_n (vh, ash, bsh, n + 1); /* vh, 2n+1 limbs */
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/* vm1, 2n+1 limbs */
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mpn_mul_n (vm1, asm1, bsm1, n);
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cy = 0;
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if (asm1[n] == 1)
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{
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cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
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}
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else if (asm1[n] == 2)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (vm1 + n, vm1 + n, bsm1, n);
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#else
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cy = mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2));
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#endif
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}
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vm1[2 * n] = cy;
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/* v1, 2n+1 limbs */
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mpn_mul_n (v1, as1, bs1, n);
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if (as1[n] == 1)
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{
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cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n);
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}
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else if (as1[n] == 2)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n);
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#else
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cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2));
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#endif
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}
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else if (as1[n] != 0)
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{
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cy = as1[n] * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, as1[n]);
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}
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else
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cy = 0;
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if (bs1[n] != 0)
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cy += mpn_add_n (v1 + n, v1 + n, as1, n);
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v1[2 * n] = cy;
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mpn_mul_n (v0, a0, b0, n); /* v0, 2n limbs */
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/* vinf, s+t limbs */
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if (s > t) mpn_mul (vinf, a5, s, b1, t);
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else mpn_mul (vinf, b1, t, a5, s);
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mpn_toom_interpolate_7pts (pp, n, aflags ^ bflags,
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vm2, vm1, v2, vh, s + t, scratch_out);
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TMP_FREE;
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}
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