Likely GMP bug

Niels Möller nisse at
Mon May 28 20:00:32 UTC 2018

tg at (Torbjörn Granlund) writes:

> For now, I'd suggest to just rip out USE_ZEROTAB.

I've pushed a change to do just that. For making the rest of the file
clearer, I'd suggest the below (complete file, I think that's more
readable than the diff). I've also ripped out the GCD_1_METHOD==1 code,
since it appears to be disabled everywhere. Let me know if anyone has
any interest in keeping that around.

The last part of the function requires vlimb odd, but tolerates
arbitrary u, including 0. This would be a candidate gcd_11 or
gcd_11_odd. If it's made it's own function, the live zero_bits variable
prevents it from being a tail call, but maybe that's not a big deal.

I haven't done any benchmarks, and I'm not able to do any tonight.


/* mpn_gcd_1 -- mpn and limb greatest common divisor.

Copyright 1994, 1996, 2000, 2001, 2009, 2012 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of either:

  * the GNU Lesser General Public License as published by the Free
    Software Foundation; either version 3 of the License, or (at your
    option) any later version.


  * the GNU General Public License as published by the Free Software
    Foundation; either version 2 of the License, or (at your option) any
    later version.

or both in parallel, as here.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library.  If not,
see  */

#include "gmp-impl.h"
#include "longlong.h"

/* Does not work for U == 0 or V == 0.  It would be tough to make it work for
   V == 0 since gcd(x,0) = x, and U does not generally fit in an mp_limb_t.

   The threshold for doing u%v when size==1 will vary by CPU according to
   the speed of a division and the code generated for the main loop.  Any
   tuning for this is left to a CPU specific implementation.  */

mpn_gcd_1 (mp_srcptr up, mp_size_t size, mp_limb_t vlimb)
  mp_limb_t      ulimb;
  unsigned long  zero_bits, u_low_zero_bits;
  int c;

  ASSERT (size >= 1);
  ASSERT (vlimb != 0);
  ASSERT_MPN_NONZERO_P (up, size);

  ulimb = up[0];

  /* Need vlimb odd for modexact, want it odd to get common zeros. */
  count_trailing_zeros (zero_bits, vlimb);
  vlimb >>= zero_bits;

  if (size > 1)
      /* Must get common zeros before the mod reduction.  If ulimb==0 then
	 vlimb already gives the common zeros.  */
      if (ulimb != 0)
	  count_trailing_zeros (u_low_zero_bits, ulimb);
	  zero_bits = MIN (zero_bits, u_low_zero_bits);

      ulimb = MPN_MOD_OR_MODEXACT_1_ODD (up, size, vlimb);
      /* size==1, so up[0]!=0 */
      count_trailing_zeros (u_low_zero_bits, ulimb);
      ulimb >>= u_low_zero_bits;
      zero_bits = MIN (zero_bits, u_low_zero_bits);

      /* make u bigger */
      if (vlimb > ulimb)
	MP_LIMB_T_SWAP (ulimb, vlimb);

      /* if u is much bigger than v, reduce using a division rather than
	 chipping away at it bit-by-bit */
      if ((ulimb >> 16) > vlimb)
	ulimb %= vlimb;


  ASSERT (vlimb & 1);
  if (ulimb == 0)
    return vlimb << zero_bits;

  count_trailing_zeros (c, ulimb);
  /* Note that if ulimb == GMP_LIMB_HIGHBIT, c+1 is an invalid shift count. */
  ulimb >>= c;

  /* Represent the odd numbers ulimb and vlimb without the redundant
     least significant one bit. This reduction in size by one bit
     ensures that the high bit of t, below, is set if and only if
     vlimb > ulimb. And in addition, t != GMP_LIMB_HIGHBIT. */
  ulimb >>= 1;
  vlimb >>= 1;

  while (ulimb != vlimb)
      mp_limb_t t;
      mp_limb_t vgtu;

      t = ulimb - vlimb;
      vgtu = LIMB_HIGHBIT_TO_MASK (t);

      /* v <-- min (u, v) */
      vlimb += (vgtu & t);

      /* u <-- |u - v| */
      ulimb = (t ^ vgtu) - vgtu;

      count_trailing_zeros (c, t);
      ASSERT (c + 1 < GMP_LIMB_BITS);
      ulimb >>= (c + 1);

  vlimb = (vlimb << 1) | 1;
  return vlimb << zero_bits;

Niels Möller. PGP-encrypted email is preferred. Keyid 368C6677.
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