Coverage Report

Created: 2024-11-21 06:47

/src/libgmp/mpn/mod_1.c
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/* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) --
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   Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
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   Return the single-limb remainder.
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   There are no constraints on the value of the divisor.
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Copyright 1991, 1993, 1994, 1999, 2000, 2002, 2007-2009, 2012, 2020
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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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/* The size where udiv_qrnnd_preinv should be used rather than udiv_qrnnd,
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   meaning the quotient size where that should happen, the quotient size
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   being how many udiv divisions will be done.
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   The default is to use preinv always, CPUs where this doesn't suit have
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   tuned thresholds.  Note in particular that preinv should certainly be
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   used if that's the only division available (USE_PREINV_ALWAYS).  */
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#ifndef MOD_1_NORM_THRESHOLD
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#define MOD_1_NORM_THRESHOLD  0
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#endif
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#ifndef MOD_1_UNNORM_THRESHOLD
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#define MOD_1_UNNORM_THRESHOLD  0
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#endif
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#ifndef MOD_1U_TO_MOD_1_1_THRESHOLD
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#define MOD_1U_TO_MOD_1_1_THRESHOLD  MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */
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#endif
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#ifndef MOD_1N_TO_MOD_1_1_THRESHOLD
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#define MOD_1N_TO_MOD_1_1_THRESHOLD  MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */
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#endif
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#ifndef MOD_1_1_TO_MOD_1_2_THRESHOLD
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#define MOD_1_1_TO_MOD_1_2_THRESHOLD  10
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#endif
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#ifndef MOD_1_2_TO_MOD_1_4_THRESHOLD
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#define MOD_1_2_TO_MOD_1_4_THRESHOLD  20
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#endif
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#if TUNE_PROGRAM_BUILD && !HAVE_NATIVE_mpn_mod_1_1p
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/* Duplicates declarations in tune/speed.h */
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mp_limb_t mpn_mod_1_1p_1 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4]);
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mp_limb_t mpn_mod_1_1p_2 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4]);
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void mpn_mod_1_1p_cps_1 (mp_limb_t [4], mp_limb_t);
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void mpn_mod_1_1p_cps_2 (mp_limb_t [4], mp_limb_t);
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#undef mpn_mod_1_1p
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#define mpn_mod_1_1p(ap, n, b, pre)          \
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  (mod_1_1p_method == 1 ? mpn_mod_1_1p_1 (ap, n, b, pre)     \
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   : (mod_1_1p_method == 2 ? mpn_mod_1_1p_2 (ap, n, b, pre)  \
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      : __gmpn_mod_1_1p (ap, n, b, pre)))
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#undef mpn_mod_1_1p_cps
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#define mpn_mod_1_1p_cps(pre, b)        \
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  (mod_1_1p_method == 1 ? mpn_mod_1_1p_cps_1 (pre, b)   \
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   : (mod_1_1p_method == 2 ? mpn_mod_1_1p_cps_2 (pre, b)  \
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      : __gmpn_mod_1_1p_cps (pre, b)))
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#endif /* TUNE_PROGRAM_BUILD && !HAVE_NATIVE_mpn_mod_1_1p */
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/* The comments in mpn/generic/divrem_1.c apply here too.
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   As noted in the algorithms section of the manual, the shifts in the loop
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   for the unnorm case can be avoided by calculating r = a%(d*2^n), followed
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   by a final (r*2^n)%(d*2^n).  In fact if it happens that a%(d*2^n) can
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   skip a division where (a*2^n)%(d*2^n) can't then there's the same number
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   of divide steps, though how often that happens depends on the assumed
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   distributions of dividend and divisor.  In any case this idea is left to
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   CPU specific implementations to consider.  */
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static mp_limb_t
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mpn_mod_1_unnorm (mp_srcptr up, mp_size_t un, mp_limb_t d)
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0
{
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  mp_size_t  i;
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  mp_limb_t  n1, n0, r;
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  mp_limb_t  dummy;
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  int cnt;
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  ASSERT (un > 0);
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  ASSERT (d != 0);
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  /* Skip a division if high < divisor.  Having the test here before
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     normalizing will still skip as often as possible.  */
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  r = up[un - 1];
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  if (r < d)
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    {
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      if (--un == 0)
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  return r;
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    }
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  else
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    r = 0;
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  d <<= GMP_NAIL_BITS;
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  /* If udiv_qrnnd doesn't need a normalized divisor, can use the simple
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     code above. */
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  if (! UDIV_NEEDS_NORMALIZATION
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      && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD))
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    {
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      for (i = un - 1; i >= 0; i--)
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  {
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    n0 = up[i] << GMP_NAIL_BITS;
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    udiv_qrnnd (dummy, r, r, n0, d);
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    r >>= GMP_NAIL_BITS;
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  }
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      return r;
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    }
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  count_leading_zeros (cnt, d);
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  d <<= cnt;
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  n1 = up[un - 1] << GMP_NAIL_BITS;
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  r = (r << cnt) | (n1 >> (GMP_LIMB_BITS - cnt));
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  if (UDIV_NEEDS_NORMALIZATION
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      && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD))
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    {
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      mp_limb_t nshift;
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      for (i = un - 2; i >= 0; i--)
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  {
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    n0 = up[i] << GMP_NAIL_BITS;
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    nshift = (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt));
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    udiv_qrnnd (dummy, r, r, nshift, d);
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    r >>= GMP_NAIL_BITS;
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    n1 = n0;
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  }
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      udiv_qrnnd (dummy, r, r, n1 << cnt, d);
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      r >>= GMP_NAIL_BITS;
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      return r >> cnt;
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    }
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  else
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    {
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      mp_limb_t inv, nshift;
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      invert_limb (inv, d);
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      for (i = un - 2; i >= 0; i--)
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  {
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    n0 = up[i] << GMP_NAIL_BITS;
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    nshift = (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt));
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    udiv_rnnd_preinv (r, r, nshift, d, inv);
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    r >>= GMP_NAIL_BITS;
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    n1 = n0;
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  }
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      udiv_rnnd_preinv (r, r, n1 << cnt, d, inv);
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      r >>= GMP_NAIL_BITS;
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      return r >> cnt;
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    }
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}
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static mp_limb_t
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mpn_mod_1_norm (mp_srcptr up, mp_size_t un, mp_limb_t d)
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{
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  mp_size_t  i;
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  mp_limb_t  n0, r;
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  mp_limb_t  dummy;
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  ASSERT (un > 0);
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  d <<= GMP_NAIL_BITS;
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  ASSERT (d & GMP_LIMB_HIGHBIT);
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  /* High limb is initial remainder, possibly with one subtract of
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     d to get r<d.  */
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  r = up[un - 1] << GMP_NAIL_BITS;
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  if (r >= d)
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    r -= d;
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  r >>= GMP_NAIL_BITS;
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  un--;
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  if (un == 0)
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    return r;
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  if (BELOW_THRESHOLD (un, MOD_1_NORM_THRESHOLD))
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    {
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      for (i = un - 1; i >= 0; i--)
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  {
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    n0 = up[i] << GMP_NAIL_BITS;
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    udiv_qrnnd (dummy, r, r, n0, d);
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    r >>= GMP_NAIL_BITS;
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  }
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      return r;
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    }
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  else
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    {
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      mp_limb_t  inv;
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      invert_limb (inv, d);
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      for (i = un - 1; i >= 0; i--)
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  {
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    n0 = up[i] << GMP_NAIL_BITS;
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    udiv_rnnd_preinv (r, r, n0, d, inv);
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    r >>= GMP_NAIL_BITS;
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  }
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      return r;
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    }
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}
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mp_limb_t
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mpn_mod_1 (mp_srcptr ap, mp_size_t n, mp_limb_t b)
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{
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  ASSERT (n >= 0);
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  ASSERT (b != 0);
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  /* Should this be handled at all?  Rely on callers?  Note un==0 is currently
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     required by mpz/fdiv_r_ui.c and possibly other places.  */
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  if (n == 0)
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    return 0;
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  if (UNLIKELY ((b & GMP_NUMB_HIGHBIT) != 0))
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    {
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      if (BELOW_THRESHOLD (n, MOD_1N_TO_MOD_1_1_THRESHOLD))
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  {
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    return mpn_mod_1_norm (ap, n, b);
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  }
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      else
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  {
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    mp_limb_t pre[4];
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    mpn_mod_1_1p_cps (pre, b);
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    return mpn_mod_1_1p (ap, n, b, pre);
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  }
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    }
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  else
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    {
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      if (BELOW_THRESHOLD (n, MOD_1U_TO_MOD_1_1_THRESHOLD))
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  {
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    return mpn_mod_1_unnorm (ap, n, b);
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  }
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      else if (BELOW_THRESHOLD (n, MOD_1_1_TO_MOD_1_2_THRESHOLD))
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  {
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    mp_limb_t pre[4];
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    mpn_mod_1_1p_cps (pre, b);
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    return mpn_mod_1_1p (ap, n, b << pre[1], pre);
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  }
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      else if (BELOW_THRESHOLD (n, MOD_1_2_TO_MOD_1_4_THRESHOLD) || UNLIKELY (b > GMP_NUMB_MASK / 4))
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  {
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    mp_limb_t pre[5];
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    mpn_mod_1s_2p_cps (pre, b);
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    return mpn_mod_1s_2p (ap, n, b << pre[1], pre);
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  }
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      else
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  {
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    mp_limb_t pre[7];
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    mpn_mod_1s_4p_cps (pre, b);
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    return mpn_mod_1s_4p (ap, n, b << pre[1], pre);
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  }
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    }
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895
}