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238 lines
6.9 KiB
C
238 lines
6.9 KiB
C
/* mpn_toom42_mulmid -- toom42 middle product
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Contributed by David Harvey.
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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'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2011 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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/*
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Middle product of {ap,2n-1} and {bp,n}, output written to {rp,n+2}.
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Neither ap nor bp may overlap rp.
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Must have n >= 4.
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Amount of scratch space required is given by mpn_toom42_mulmid_itch().
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FIXME: this code assumes that n is small compared to GMP_NUMB_MAX. The exact
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requirements should be clarified.
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*/
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void
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mpn_toom42_mulmid (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n,
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mp_ptr scratch)
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{
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mp_limb_t cy, e[12], zh, zl;
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mp_size_t m;
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int neg;
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ASSERT (n >= 4);
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ASSERT (! MPN_OVERLAP_P (rp, n + 2, ap, 2*n - 1));
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ASSERT (! MPN_OVERLAP_P (rp, n + 2, bp, n));
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ap += n & 1; /* handle odd row and diagonal later */
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m = n / 2;
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/* (e0h:e0l) etc are correction terms, in 2's complement */
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#define e0l (e[0])
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#define e0h (e[1])
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#define e1l (e[2])
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#define e1h (e[3])
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#define e2l (e[4])
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#define e2h (e[5])
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#define e3l (e[6])
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#define e3h (e[7])
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#define e4l (e[8])
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#define e4h (e[9])
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#define e5l (e[10])
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#define e5h (e[11])
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#define s (scratch + 2)
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#define t (rp + m + 2)
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#define p0 rp
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#define p1 scratch
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#define p2 (rp + m)
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#define next_scratch (scratch + 3*m + 1)
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/*
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rp scratch
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|---------|-----------| |---------|---------|----------|
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0 m 2m+2 0 m 2m 3m+1
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<----p2----> <-------------s------------->
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<----p0----><---t----> <----p1---->
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*/
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/* compute {s,3m-1} = {a,3m-1} + {a+m,3m-1} and error terms e0, e1, e2, e3 */
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cy = mpn_add_err1_n (s, ap, ap + m, &e0l, bp + m, m - 1, 0);
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cy = mpn_add_err2_n (s + m - 1, ap + m - 1, ap + 2*m - 1, &e1l,
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bp + m, bp, m, cy);
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mpn_add_err1_n (s + 2*m - 1, ap + 2*m - 1, ap + 3*m - 1, &e3l, bp, m, cy);
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/* compute t = (-1)^neg * ({b,m} - {b+m,m}) and error terms e4, e5 */
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if (mpn_cmp (bp + m, bp, m) < 0)
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{
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ASSERT_NOCARRY (mpn_sub_err2_n (t, bp, bp + m, &e4l,
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ap + m - 1, ap + 2*m - 1, m, 0));
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neg = 1;
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}
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else
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{
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ASSERT_NOCARRY (mpn_sub_err2_n (t, bp + m, bp, &e4l,
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ap + m - 1, ap + 2*m - 1, m, 0));
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neg = 0;
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}
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/* recursive middle products. The picture is:
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b[2m-1] A A A B B B - - - - -
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... - A A A B B B - - - -
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b[m] - - A A A B B B - - -
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b[m-1] - - - C C C D D D - -
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... - - - - C C C D D D -
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b[0] - - - - - C C C D D D
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a[0] ... a[m] ... a[2m] ... a[4m-2]
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*/
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if (m < MULMID_TOOM42_THRESHOLD)
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{
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/* A + B */
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mpn_mulmid_basecase (p0, s, 2*m - 1, bp + m, m);
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/* accumulate high limbs of p0 into e1 */
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ADDC_LIMB (cy, e1l, e1l, p0[m]);
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e1h += p0[m + 1] + cy;
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/* (-1)^neg * (B - C) (overwrites first m limbs of s) */
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mpn_mulmid_basecase (p1, ap + m, 2*m - 1, t, m);
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/* C + D (overwrites t) */
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mpn_mulmid_basecase (p2, s + m, 2*m - 1, bp, m);
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}
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else
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{
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/* as above, but use toom42 instead */
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mpn_toom42_mulmid (p0, s, bp + m, m, next_scratch);
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ADDC_LIMB (cy, e1l, e1l, p0[m]);
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e1h += p0[m + 1] + cy;
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mpn_toom42_mulmid (p1, ap + m, t, m, next_scratch);
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mpn_toom42_mulmid (p2, s + m, bp, m, next_scratch);
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}
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/* apply error terms */
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/* -e0 at rp[0] */
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SUBC_LIMB (cy, rp[0], rp[0], e0l);
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SUBC_LIMB (cy, rp[1], rp[1], e0h + cy);
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if (UNLIKELY (cy))
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{
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cy = (m > 2) ? mpn_sub_1 (rp + 2, rp + 2, m - 2, 1) : 1;
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SUBC_LIMB (cy, e1l, e1l, cy);
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e1h -= cy;
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}
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/* z = e1 - e2 + high(p0) */
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SUBC_LIMB (cy, zl, e1l, e2l);
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zh = e1h - e2h - cy;
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/* z at rp[m] */
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ADDC_LIMB (cy, rp[m], rp[m], zl);
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zh = (zh + cy) & GMP_NUMB_MASK;
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ADDC_LIMB (cy, rp[m + 1], rp[m + 1], zh);
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cy -= (zh >> (GMP_NUMB_BITS - 1));
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if (UNLIKELY (cy))
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{
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if (cy == 1)
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mpn_add_1 (rp + m + 2, rp + m + 2, m, 1);
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else /* cy == -1 */
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mpn_sub_1 (rp + m + 2, rp + m + 2, m, 1);
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}
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/* e3 at rp[2*m] */
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ADDC_LIMB (cy, rp[2*m], rp[2*m], e3l);
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rp[2*m + 1] = (rp[2*m + 1] + e3h + cy) & GMP_NUMB_MASK;
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/* e4 at p1[0] */
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ADDC_LIMB (cy, p1[0], p1[0], e4l);
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ADDC_LIMB (cy, p1[1], p1[1], e4h + cy);
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if (UNLIKELY (cy))
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mpn_add_1 (p1 + 2, p1 + 2, m, 1);
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/* -e5 at p1[m] */
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SUBC_LIMB (cy, p1[m], p1[m], e5l);
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p1[m + 1] = (p1[m + 1] - e5h - cy) & GMP_NUMB_MASK;
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/* adjustment if p1 ends up negative */
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cy = (p1[m + 1] >> (GMP_NUMB_BITS - 1));
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/* add (-1)^neg * (p1 - B^m * p1) to output */
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if (neg)
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{
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mpn_sub_1 (rp + m + 2, rp + m + 2, m, cy);
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mpn_add (rp, rp, 2*m + 2, p1, m + 2); /* A + C */
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mpn_sub_n (rp + m, rp + m, p1, m + 2); /* B + D */
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}
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else
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{
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mpn_add_1 (rp + m + 2, rp + m + 2, m, cy);
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mpn_sub (rp, rp, 2*m + 2, p1, m + 2); /* A + C */
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mpn_add_n (rp + m, rp + m, p1, m + 2); /* B + D */
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}
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/* odd row and diagonal */
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if (n & 1)
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{
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/*
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Products marked E are already done. We need to do products marked O.
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OOOOO----
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-EEEEO---
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--EEEEO--
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---EEEEO-
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----EEEEO
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*/
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/* first row of O's */
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cy = mpn_addmul_1 (rp, ap - 1, n, bp[n - 1]);
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ADDC_LIMB (rp[n + 1], rp[n], rp[n], cy);
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/* O's on diagonal */
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/* FIXME: should probably define an interface "mpn_mulmid_diag_1"
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that can handle the sum below. Currently we're relying on
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mulmid_basecase being pretty fast for a diagonal sum like this,
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which is true at least for the K8 asm version, but surely false
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for the generic version. */
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mpn_mulmid_basecase (e, ap + n - 1, n - 1, bp, n - 1);
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mpn_add_n (rp + n - 1, rp + n - 1, e, 3);
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}
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}
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