Coverage Report

Created: 2024-11-21 07:03

/src/libgmp/mpn/divis.c
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/* mpn_divisible_p -- mpn by mpn divisibility test
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   THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
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   CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
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   FUTURE GNU MP RELEASES.
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Copyright 2001, 2002, 2005, 2009, 2014, 2017, 2018 Free Software
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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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/* Determine whether A={ap,an} is divisible by D={dp,dn}.  Must have both
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   operands normalized, meaning high limbs non-zero, except that an==0 is
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   allowed.
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   There usually won't be many low zero bits on D, but the checks for this
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   are fast and might pick up a few operand combinations, in particular they
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   might reduce D to fit the single-limb mod_1/modexact_1 code.
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   Future:
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   Getting the remainder limb by limb would make an early exit possible on
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   finding a non-zero.  This would probably have to be bdivmod style so
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   there's no addback, but it would need a multi-precision inverse and so
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   might be slower than the plain method (on small sizes at least).
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   When D must be normalized (shifted to low bit set), it's possible to
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   suppress the bit-shifting of A down, as long as it's already been checked
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   that A has at least as many trailing zero bits as D.  */
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int
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mpn_divisible_p (mp_srcptr ap, mp_size_t an,
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     mp_srcptr dp, mp_size_t dn)
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{
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  mp_limb_t  alow, dlow, dmask;
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  mp_ptr     qp, rp, tp;
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  mp_limb_t di;
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  unsigned  twos;
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  int c;
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  TMP_DECL;
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  ASSERT (an >= 0);
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  ASSERT (an == 0 || ap[an-1] != 0);
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  ASSERT (dn >= 1);
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  ASSERT (dp[dn-1] != 0);
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  ASSERT_MPN (ap, an);
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  ASSERT_MPN (dp, dn);
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  /* When a<d only a==0 is divisible.
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     Notice this test covers all cases of an==0. */
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  if (an < dn)
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    return (an == 0);
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  /* Strip low zero limbs from d, requiring a==0 on those. */
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  for (;;)
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    {
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      alow = *ap;
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      dlow = *dp;
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      if (dlow != 0)
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  break;
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      if (alow != 0)
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  return 0;  /* a has fewer low zero limbs than d, so not divisible */
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      /* a!=0 and d!=0 so won't get to n==0 */
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      an--; ASSERT (an >= 1);
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      dn--; ASSERT (dn >= 1);
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      ap++;
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      dp++;
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    }
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  /* a must have at least as many low zero bits as d */
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  dmask = LOW_ZEROS_MASK (dlow);
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  if ((alow & dmask) != 0)
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    return 0;
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  if (dn == 1)
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    {
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      if (ABOVE_THRESHOLD (an, BMOD_1_TO_MOD_1_THRESHOLD))
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  return mpn_mod_1 (ap, an, dlow) == 0;
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      count_trailing_zeros (twos, dlow);
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      dlow >>= twos;
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      return mpn_modexact_1_odd (ap, an, dlow) == 0;
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    }
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  count_trailing_zeros (twos, dlow);
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  if (dn == 2)
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    {
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      mp_limb_t  dsecond = dp[1];
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      if (dsecond <= dmask)
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  {
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    dlow = (dlow >> twos) | (dsecond << (GMP_NUMB_BITS-twos));
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    ASSERT_LIMB (dlow);
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    return MPN_MOD_OR_MODEXACT_1_ODD (ap, an, dlow) == 0;
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0
  }
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    }
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  /* Should we compute Q = A * D^(-1) mod B^k,
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                       R = A - Q * D  mod B^k
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     here, for some small values of k?  Then check if R = 0 (mod B^k).  */
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  /* We could also compute A' = A mod T and D' = D mod P, for some
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     P = 3 * 5 * 7 * 11 ..., and then check if any prime factor from P
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     dividing D' also divides A'.  */
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  TMP_MARK;
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  TMP_ALLOC_LIMBS_2 (rp, an + 1,
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         qp, an - dn + 1); /* FIXME: Could we avoid this? */
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  if (twos != 0)
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    {
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      tp = TMP_ALLOC_LIMBS (dn);
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      ASSERT_NOCARRY (mpn_rshift (tp, dp, dn, twos));
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      dp = tp;
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      ASSERT_NOCARRY (mpn_rshift (rp, ap, an, twos));
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    }
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  else
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    {
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      MPN_COPY (rp, ap, an);
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    }
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  if (rp[an - 1] >= dp[dn - 1])
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    {
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      rp[an] = 0;
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      an++;
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    }
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  else if (an == dn)
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    {
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      TMP_FREE;
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      return 0;
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    }
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  ASSERT (an > dn);   /* requirement of functions below */
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  if (BELOW_THRESHOLD (dn, DC_BDIV_QR_THRESHOLD) ||
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      BELOW_THRESHOLD (an - dn, DC_BDIV_QR_THRESHOLD))
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    {
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      binvert_limb (di, dp[0]);
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      mpn_sbpi1_bdiv_qr (qp, rp, an, dp, dn, -di);
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      rp += an - dn;
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    }
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  else if (BELOW_THRESHOLD (dn, MU_BDIV_QR_THRESHOLD))
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    {
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      binvert_limb (di, dp[0]);
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      mpn_dcpi1_bdiv_qr (qp, rp, an, dp, dn, -di);
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      rp += an - dn;
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    }
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  else
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    {
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      tp = TMP_ALLOC_LIMBS (mpn_mu_bdiv_qr_itch (an, dn));
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      mpn_mu_bdiv_qr (qp, rp, rp, an, dp, dn, tp);
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    }
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  /* In general, bdiv may return either R = 0 or R = D when D divides
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     A. But R = 0 can happen only when A = 0, which we already have
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     excluded. Furthermore, R == D (mod B^{dn}) implies no carry, so
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     we don't need to check the carry returned from bdiv. */
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  MPN_CMP (c, rp, dp, dn);
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  TMP_FREE;
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  return c == 0;
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}