Coverage Report

Created: 2024-11-21 07:03

/src/libgmp/mpn/hgcd_jacobi.c
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/* hgcd_jacobi.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 2003-2005, 2008, 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-impl.h"
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#include "longlong.h"
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/* This file is almost a copy of hgcd.c, with some added calls to
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   mpn_jacobi_update */
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struct hgcd_jacobi_ctx
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{
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  struct hgcd_matrix *M;
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  unsigned *bitsp;
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};
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static void
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hgcd_jacobi_hook (void *p, mp_srcptr gp, mp_size_t gn,
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      mp_srcptr qp, mp_size_t qn, int d)
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0
{
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  ASSERT (!gp);
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  ASSERT (d >= 0);
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  MPN_NORMALIZE (qp, qn);
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  if (qn > 0)
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    {
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      struct hgcd_jacobi_ctx *ctx = (struct hgcd_jacobi_ctx *) p;
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      /* NOTES: This is a bit ugly. A tp area is passed to
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   gcd_subdiv_step, which stores q at the start of that area. We
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   now use the rest. */
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      mp_ptr tp = (mp_ptr) qp + qn;
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      mpn_hgcd_matrix_update_q (ctx->M, qp, qn, d, tp);
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      *ctx->bitsp = mpn_jacobi_update (*ctx->bitsp, d, qp[0] & 3);
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    }
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}
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/* Perform a few steps, using some of mpn_hgcd2, subtraction and
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   division. Reduces the size by almost one limb or more, but never
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   below the given size s. Return new size for a and b, or 0 if no
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   more steps are possible.
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   If hgcd2 succeeds, needs temporary space for hgcd_matrix_mul_1, M->n
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   limbs, and hgcd_mul_matrix1_inverse_vector, n limbs. If hgcd2
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   fails, needs space for the quotient, qn <= n - s + 1 limbs, for and
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   hgcd_matrix_update_q, qn + (size of the appropriate column of M) <=
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   resulting size of M.
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   If N is the input size to the calling hgcd, then s = floor(N/2) +
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   1, M->n < N, qn + matrix size <= n - s + 1 + n - s = 2 (n - s) + 1
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   < N, so N is sufficient.
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*/
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static mp_size_t
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hgcd_jacobi_step (mp_size_t n, mp_ptr ap, mp_ptr bp, mp_size_t s,
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      struct hgcd_matrix *M, unsigned *bitsp, mp_ptr tp)
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0
{
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  struct hgcd_matrix1 M1;
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  mp_limb_t mask;
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  mp_limb_t ah, al, bh, bl;
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  ASSERT (n > s);
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  mask = ap[n-1] | bp[n-1];
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  ASSERT (mask > 0);
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  if (n == s + 1)
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    {
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      if (mask < 4)
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  goto subtract;
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      ah = ap[n-1]; al = ap[n-2];
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      bh = bp[n-1]; bl = bp[n-2];
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    }
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  else if (mask & GMP_NUMB_HIGHBIT)
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    {
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      ah = ap[n-1]; al = ap[n-2];
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      bh = bp[n-1]; bl = bp[n-2];
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    }
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  else
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    {
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      int shift;
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      count_leading_zeros (shift, mask);
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      ah = MPN_EXTRACT_NUMB (shift, ap[n-1], ap[n-2]);
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      al = MPN_EXTRACT_NUMB (shift, ap[n-2], ap[n-3]);
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      bh = MPN_EXTRACT_NUMB (shift, bp[n-1], bp[n-2]);
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      bl = MPN_EXTRACT_NUMB (shift, bp[n-2], bp[n-3]);
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    }
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  /* Try an mpn_hgcd2 step */
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  if (mpn_hgcd2_jacobi (ah, al, bh, bl, &M1, bitsp))
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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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      /* Can't swap inputs, so we need to copy. */
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      MPN_COPY (tp, ap, n);
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      /* Multiply M1^{-1} (a;b) */
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      return mpn_matrix22_mul1_inverse_vector (&M1, ap, tp, bp, n);
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    }
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 subtract:
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  {
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    struct hgcd_jacobi_ctx ctx;
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    ctx.M = M;
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    ctx.bitsp = bitsp;
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    return mpn_gcd_subdiv_step (ap, bp, n, s, hgcd_jacobi_hook, &ctx, tp);
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  }
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}
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/* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M
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   with elements of size at most (n+1)/2 - 1. Returns new size of a,
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   b, or zero if no reduction is possible. */
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/* Same scratch requirements as for mpn_hgcd. */
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mp_size_t
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mpn_hgcd_jacobi (mp_ptr ap, mp_ptr bp, mp_size_t n,
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     struct hgcd_matrix *M, unsigned *bitsp, mp_ptr tp)
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0
{
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  mp_size_t s = n/2 + 1;
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  mp_size_t nn;
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  int success = 0;
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  if (n <= s)
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    /* Happens when n <= 2, a fairly uninteresting case but exercised
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       by the random inputs of the testsuite. */
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    return 0;
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  ASSERT ((ap[n-1] | bp[n-1]) > 0);
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  ASSERT ((n+1)/2 - 1 < M->alloc);
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  if (ABOVE_THRESHOLD (n, HGCD_THRESHOLD))
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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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      nn = mpn_hgcd_jacobi (ap + p, bp + p, n - p, M, bitsp, tp);
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      if (nn > 0)
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  {
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    /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
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       = 2 (n - 1) */
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    n = mpn_hgcd_matrix_adjust (M, p + nn, ap, bp, p, tp);
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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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    /* Needs n + 1 storage */
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    nn = hgcd_jacobi_step (n, ap, bp, s, M, bitsp, tp);
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    if (!nn)
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      return success ? n : 0;
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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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    nn = mpn_hgcd_jacobi (ap + p, bp + p, n - p, &M1, bitsp, tp + scratch);
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    if (nn > 0)
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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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        /* Needs 2 (p + M->n) <= 2 (2*s - n2 + 1 + n2 - s - 1)
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     = 2*s <= 2*(floor(n/2) + 1) <= n + 2. */
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        n = mpn_hgcd_matrix_adjust (&M1, p + nn, ap, bp, p, tp + scratch);
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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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        success = 1;
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      }
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  }
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    }
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  for (;;)
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    {
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      /* Needs s+3 < n */
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      nn = hgcd_jacobi_step (n, ap, bp, s, M, bitsp, tp);
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      if (!nn)
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  return success ? n : 0;
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      n = nn;
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      success = 1;
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    }
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}