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/* hgcd_appr.c.
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THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
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SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2011, 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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#include "longlong.h"
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/* Identical to mpn_hgcd_itch. FIXME: Do we really need to add
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HGCD_THRESHOLD at the end? */
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mp_size_t
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mpn_hgcd_appr_itch (mp_size_t n)
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{
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if (BELOW_THRESHOLD (n, HGCD_APPR_THRESHOLD))
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return n;
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else
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{
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unsigned k;
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int count;
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mp_size_t nscaled;
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/* Get the recursion depth. */
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nscaled = (n - 1) / (HGCD_APPR_THRESHOLD - 1);
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count_leading_zeros (count, nscaled);
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k = GMP_LIMB_BITS - count;
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return 20 * ((n+3) / 4) + 22 * k + HGCD_THRESHOLD;
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}
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}
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/* Destroys inputs. */
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int
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mpn_hgcd_appr (mp_ptr ap, mp_ptr bp, mp_size_t n,
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struct hgcd_matrix *M, mp_ptr tp)
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{
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mp_size_t s;
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int success = 0;
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ASSERT (n > 0);
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ASSERT ((ap[n-1] | bp[n-1]) != 0);
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if (n <= 2)
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/* Implies s = n. A fairly uninteresting case but exercised by the
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random inputs of the testsuite. */
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return 0;
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ASSERT ((n+1)/2 - 1 < M->alloc);
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/* We aim for reduction of to GMP_NUMB_BITS * s bits. But each time
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we discard some of the least significant limbs, we must keep one
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additional bit to account for the truncation error. We maintain
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the GMP_NUMB_BITS * s - extra_bits as the current target size. */
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s = n/2 + 1;
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if (BELOW_THRESHOLD (n, HGCD_APPR_THRESHOLD))
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{
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unsigned extra_bits = 0;
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while (n > 2)
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{
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mp_size_t nn;
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ASSERT (n > s);
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ASSERT (n <= 2*s);
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nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
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if (!nn)
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break;
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n = nn;
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success = 1;
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/* We can truncate and discard the lower p bits whenever nbits <=
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2*sbits - p. To account for the truncation error, we must
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adjust
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sbits <-- sbits + 1 - p,
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rather than just sbits <-- sbits - p. This adjustment makes
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the produced matrix slightly smaller than it could be. */
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if (GMP_NUMB_BITS * (n + 1) + 2 * extra_bits <= 2*GMP_NUMB_BITS * s)
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{
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mp_size_t p = (GMP_NUMB_BITS * (2*s - n) - 2*extra_bits) / GMP_NUMB_BITS;
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if (extra_bits == 0)
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{
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/* We cross a limb boundary and bump s. We can't do that
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if the result is that it makes makes min(U, V)
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smaller than 2^{GMP_NUMB_BITS} s. */
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if (s + 1 == n
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|| mpn_zero_p (ap + s + 1, n - s - 1)
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|| mpn_zero_p (bp + s + 1, n - s - 1))
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continue;
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extra_bits = GMP_NUMB_BITS - 1;
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s++;
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}
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else
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{
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extra_bits--;
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}
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/* Drop the p least significant limbs */
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ap += p; bp += p; n -= p; s -= p;
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}
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}
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ASSERT (s > 0);
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if (extra_bits > 0)
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{
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/* We can get here only of we have dropped at least one of the least
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significant bits, so we can decrement ap and bp. We can then shift
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left extra bits using mpn_rshift. */
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/* NOTE: In the unlikely case that n is large, it would be preferable
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to do an initial subdiv step to reduce the size before shifting,
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but that would mean duplicating mpn_gcd_subdiv_step with a bit
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count rather than a limb count. */
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ap--; bp--;
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ap[0] = mpn_rshift (ap+1, ap+1, n, GMP_NUMB_BITS - extra_bits);
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bp[0] = mpn_rshift (bp+1, bp+1, n, GMP_NUMB_BITS - extra_bits);
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n += (ap[n] | bp[n]) > 0;
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ASSERT (success);
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while (n > 2)
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{
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mp_size_t nn;
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ASSERT (n > s);
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ASSERT (n <= 2*s);
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nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
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if (!nn)
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return 1;
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n = nn;
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}
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}
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if (n == 2)
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{
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struct hgcd_matrix1 M1;
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ASSERT (s == 1);
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if (mpn_hgcd2 (ap[1], ap[0], bp[1], bp[0], &M1))
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{
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/* Multiply M <- M * M1 */
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mpn_hgcd_matrix_mul_1 (M, &M1, tp);
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success = 1;
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}
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}
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return success;
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}
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else
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{
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mp_size_t n2 = (3*n)/4 + 1;
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mp_size_t p = n/2;
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mp_size_t nn;
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nn = mpn_hgcd_reduce (M, ap, bp, n, p, tp);
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if (nn)
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{
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n = nn;
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/* FIXME: Discard some of the low limbs immediately? */
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success = 1;
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}
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while (n > n2)
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{
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mp_size_t nn;
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/* Needs n + 1 storage */
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nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
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if (!nn)
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return success;
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n = nn;
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success = 1;
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}
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if (n > s + 2)
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{
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struct hgcd_matrix M1;
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mp_size_t scratch;
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p = 2*s - n + 1;
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scratch = MPN_HGCD_MATRIX_INIT_ITCH (n-p);
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mpn_hgcd_matrix_init(&M1, n - p, tp);
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if (mpn_hgcd_appr (ap + p, bp + p, n - p, &M1, tp + scratch))
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{
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/* We always have max(M) > 2^{-(GMP_NUMB_BITS + 1)} max(M1) */
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ASSERT (M->n + 2 >= M1.n);
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/* Furthermore, assume M ends with a quotient (1, q; 0, 1),
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then either q or q + 1 is a correct quotient, and M1 will
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start with either (1, 0; 1, 1) or (2, 1; 1, 1). This
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rules out the case that the size of M * M1 is much
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smaller than the expected M->n + M1->n. */
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ASSERT (M->n + M1.n < M->alloc);
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/* We need a bound for of M->n + M1.n. Let n be the original
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input size. Then
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ceil(n/2) - 1 >= size of product >= M.n + M1.n - 2
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and it follows that
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M.n + M1.n <= ceil(n/2) + 1
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Then 3*(M.n + M1.n) + 5 <= 3 * ceil(n/2) + 8 is the
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amount of needed scratch space. */
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mpn_hgcd_matrix_mul (M, &M1, tp + scratch);
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return 1;
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}
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}
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for(;;)
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{
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mp_size_t nn;
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ASSERT (n > s);
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ASSERT (n <= 2*s);
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nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
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if (!nn)
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return success;
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n = nn;
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success = 1;
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}
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}
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}
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