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/* mpn_toom3_sqr -- Square {ap,an}.
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Contributed to the GNU project by Torbjorn Granlund.
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Additional improvements 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 2006-2010, 2012 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.h"
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#include "gmp-impl.h"
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/* Evaluate in: -1, 0, +1, +2, +inf
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<-s--><--n--><--n-->
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____ ______ ______
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|_a2_|___a1_|___a0_|
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v0 = a0 ^2 # A(0)^2
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v1 = (a0+ a1+ a2)^2 # A(1)^2 ah <= 2
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vm1 = (a0- a1+ a2)^2 # A(-1)^2 |ah| <= 1
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v2 = (a0+2a1+4a2)^2 # A(2)^2 ah <= 6
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vinf= a2 ^2 # A(inf)^2
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*/
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#if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY
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#define MAYBE_sqr_basecase 1
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#define MAYBE_sqr_toom3 1
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#else
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#define MAYBE_sqr_basecase \
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(SQR_TOOM3_THRESHOLD < 3 * SQR_TOOM2_THRESHOLD)
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#define MAYBE_sqr_toom3 \
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(SQR_TOOM4_THRESHOLD >= 3 * SQR_TOOM3_THRESHOLD)
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#endif
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#define TOOM3_SQR_REC(p, a, n, ws) \
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do { \
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if (MAYBE_sqr_basecase \
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&& BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD)) \
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mpn_sqr_basecase (p, a, n); \
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else if (! MAYBE_sqr_toom3 \
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|| BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \
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mpn_toom2_sqr (p, a, n, ws); \
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else \
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mpn_toom3_sqr (p, a, n, ws); \
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} while (0)
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void
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mpn_toom3_sqr (mp_ptr pp,
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mp_srcptr ap, mp_size_t an,
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mp_ptr scratch)
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{
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const int __gmpn_cpuvec_initialized = 1;
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mp_size_t n, s;
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mp_limb_t cy, vinf0;
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mp_ptr gp;
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mp_ptr as1, asm1, as2;
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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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n = (an + 2) / (size_t) 3;
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s = an - 2 * n;
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ASSERT (0 < s && s <= n);
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as1 = scratch + 4 * n + 4;
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asm1 = scratch + 2 * n + 2;
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as2 = pp + n + 1;
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gp = scratch;
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/* Compute as1 and asm1. */
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cy = mpn_add (gp, a0, n, a2, s);
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#if HAVE_NATIVE_mpn_add_n_sub_n
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if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
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{
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cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n);
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as1[n] = cy >> 1;
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asm1[n] = 0;
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}
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else
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{
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mp_limb_t cy2;
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cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n);
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as1[n] = cy + (cy2 >> 1);
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asm1[n] = cy - (cy2 & 1);
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}
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#else
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as1[n] = cy + mpn_add_n (as1, gp, a1, n);
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if (cy == 0 && mpn_cmp (gp, a1, n) < 0)
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{
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mpn_sub_n (asm1, a1, gp, n);
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asm1[n] = 0;
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}
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else
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{
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cy -= mpn_sub_n (asm1, gp, a1, n);
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asm1[n] = cy;
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}
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#endif
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/* Compute as2. */
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#if HAVE_NATIVE_mpn_rsblsh1_n
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cy = mpn_add_n (as2, a2, as1, s);
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if (s != n)
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cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
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cy += as1[n];
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cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n);
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#else
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = mpn_addlsh1_n (as2, a1, a2, s);
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if (s != n)
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cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy);
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cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
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#else
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cy = mpn_add_n (as2, a2, as1, s);
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if (s != n)
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cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy);
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cy += as1[n];
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cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
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cy -= mpn_sub_n (as2, as2, a0, n);
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#endif
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#endif
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as2[n] = cy;
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ASSERT (as1[n] <= 2);
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ASSERT (asm1[n] <= 1);
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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 + 4 * n) /* s+s */
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#define vm1 scratch /* 2n+1 */
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#define v2 (scratch + 2 * n + 1) /* 2n+2 */
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#define scratch_out (scratch + 5 * n + 5)
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/* vm1, 2n+1 limbs */
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#ifdef SMALLER_RECURSION
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TOOM3_SQR_REC (vm1, asm1, n, scratch_out);
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cy = 0;
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if (asm1[n] != 0)
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cy = asm1[n] + mpn_add_n (vm1 + n, vm1 + n, asm1, n);
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if (asm1[n] != 0)
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cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
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vm1[2 * n] = cy;
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#else
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TOOM3_SQR_REC (vm1, asm1, n + 1, scratch_out);
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#endif
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TOOM3_SQR_REC (v2, as2, n + 1, scratch_out); /* v2, 2n+1 limbs */
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TOOM3_SQR_REC (vinf, a2, s, scratch_out); /* vinf, s+s limbs */
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vinf0 = vinf[0]; /* v1 overlaps with this */
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#ifdef SMALLER_RECURSION
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/* v1, 2n+1 limbs */
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TOOM3_SQR_REC (v1, as1, n, scratch_out);
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if (as1[n] == 1)
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{
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cy = as1[n] + mpn_add_n (v1 + n, v1 + n, as1, n);
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}
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else if (as1[n] != 0)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy = 2 * as1[n] + mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
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#else
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cy = 2 * as1[n] + mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
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#endif
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}
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else
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cy = 0;
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if (as1[n] == 1)
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{
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cy += mpn_add_n (v1 + n, v1 + n, as1, n);
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}
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else if (as1[n] != 0)
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{
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#if HAVE_NATIVE_mpn_addlsh1_n
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cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
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#else
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cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
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#endif
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}
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v1[2 * n] = cy;
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#else
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cy = vinf[1];
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TOOM3_SQR_REC (v1, as1, n + 1, scratch_out);
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vinf[1] = cy;
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#endif
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TOOM3_SQR_REC (v0, ap, n, scratch_out); /* v0, 2n limbs */
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mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + s, 0, vinf0);
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}
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