[Bug-gmp] Bug in GMP 3.1

[Gerardo Ballabio]

I downloaded GMP 3.1 today. I experienced some minor problems and one
real bug (which I was able to fix).

The problems:
1) shared libraries fail to compile under this power-ibm-aix4.2.1.0
machine (triplet determined by configure). The documentation reports
this problem, but for some reason shared libraries aren't disabled as
they should be. I had to disable them manually by passing
--disable-shared to configure.
2) the include file mpfr.h doesn't have an #ifdef _MPFR_H_ ... #endif
test surrounding the declarations to prevent them from being read more
than once, so that errors are generated if mpfr.h is included twice.
3) nor does mpfr.h declare the function prototypes extern "C" when
__cplusplus is defined, so that mpfr functions can't be linked to C++
code.
4) the manual contains no documentation at all about the mpfr
functions. A short notice, at least, saying that they are there and
must be explicitly invoked with --enable-mpfr, would be useful.

The bug:
comparison between mpfr_t numbers behaves incorrectly if one of the
operands is zero, and the other is positive and less than 1 (i.e.,
zero is reported to be the greater one). The cause is a flaw in the
algorithm in the file mpfr/cmp.c. I had already sent a patch for this
bug to the MPFR maintainers a couple of months ago, but the GMP 3.1
distribution still contains the buggy version.
The patched file is included below; the patch consisted in adding two
lines of code (and a blank line, for clarity) in the function
mpfr_cmp3.

Bye
 Gerardo

Dr. Gerardo Ballabio
c/o SISSA/ISAS
Scuola Internazionale Superiore di Studi Avanzati
International School for Advanced Studies
via Beirut 2-4
34013 Trieste Miramare-Grignano (Italy)
room 18 - tel. +39/0403787505
E-mail: address@hidden

--------------------------------------------

/* mpfr_cmp -- compare two floating-point numbers

Copyright (C) 1999 PolKA project, Inria Lorraine and Loria

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Library General Public License as published by
the Free Software Foundation; either version 2 of the License, or (at your
option) any later version.

The MPFR 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 Library General Public
License for more details.

You should have received a copy of the GNU Library General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"

/* returns 0 iff b = c
            a positive value iff b > c
            a negative value iff b < c

More precisely, in case b and c are of same sign, the absolute value 
of the result is one plus the absolute difference between the exponents 
of b and c, i.e. one plus the number of bits shifts to align b and c
(this value is useful in mpfr_sub).

*/

/* #define DEBUG */

/* compares b and sign(s)*c */
int 
#if __STDC__
mpfr_cmp3 ( mpfr_srcptr b, mpfr_srcptr c, long int s)
#else
mpfr_cmp3(b, c, s)
     mpfr_srcptr b;
     mpfr_srcptr c; 
     long int s;
#endif
{
   long int diff_exp;
   unsigned long bn, cn;
   mp_limb_t *bp, *cp;

   if (!NOTZERO(b) && !NOTZERO(c)) { return 0; }
   if (!NOTZERO(b)) { return -SIGN(c); }
   if (!NOTZERO(c)) { return SIGN(b); }

   s = s*SIGN(b)*SIGN(c);
   if (s<0) return(SIGN(b));

   /* now signs are equal */

   diff_exp = EXP(b)-EXP(c);
   s = (SIGN(b)>0) ? 1 : -1;

   if (diff_exp>0) return(s*(1+diff_exp));
   else if (diff_exp<0) return(s*(-1+diff_exp));
   /* both signs and exponents are equal */

   bn = (PREC(b)-1)/mp_bits_per_limb+1;
   cn = (PREC(c)-1)/mp_bits_per_limb+1;
   bp = MANT(b); cp = MANT(c);

   while (bn && cn) {
     if (bp[--bn] != cp[--cn])
       return((bp[bn]>cp[cn]) ? s : -s);
   }

   if (bn) { while (bn) if (bp[--bn]) return(s); }
   else if (cn) while (cn) if (cp[--cn]) return(-s);

   return 0;
}

/* returns the number of cancelled bits when one subtracts abs(c) from abs(b). 
   Assumes b>=c, which implies EXP(b)>=EXP(c).
   if b=c, returns prec(b).
*/
int 
#if __STDC__
mpfr_cmp2 ( mpfr_srcptr b, mpfr_srcptr c )
#else
mpfr_cmp2(b, c)
     mpfr_srcptr b; 
     mpfr_srcptr c; 
#endif
{
  long int d, bn, cn, k, z;
  mp_limb_t *bp, *cp, t, u=0, cc=0;

#ifdef DEBUG
  printf("b="); mpfr_print_raw(b); putchar('\n');
  printf("c="); mpfr_print_raw(c); putchar('\n');
#endif  
  if (NOTZERO(c)==0) return (NOTZERO(b)) ? 0 : PREC(b);
  d = EXP(b)-EXP(c);
  k = 0; /* result can be d or d+1 if d>1, or >= d otherwise */
  /* k is the number of identical bits in the high part,
     then z is the number of possibly cancelled bits */
#ifdef DEBUG
  if (d<0) { printf("assumption EXP(b)<EXP(c) violated\n"); exit(1); }
#endif
  bn = (PREC(b)-1)/mp_bits_per_limb;
  cn = (PREC(c)-1)/mp_bits_per_limb;
  bp = MANT(b); cp = MANT(c);
  /* subtract c from b from most significant to less significant limbs,
     and first determines first non zero limb difference */
  if (d)
    {
      cc = bp[bn--];
      if (d<mp_bits_per_limb)
        cc -= cp[cn]>>d; 
    }
  else { /* d=0 */
    while (bn>=0 && cn>=0 && (cc=(bp[bn--]-cp[cn--]))==0) {
      k+=mp_bits_per_limb;
    }

    if (cc==0) { /* either bn<0 or cn<0 */
      while (bn>=0 && (cc=bp[bn--])==0) k+=mp_bits_per_limb;
    }
    /* now bn<0 or cc<>0 */
    if (cc==0 && bn<0) return(PREC(b));
  }

  /* the first non-zero limb difference is cc, and the number
     of cancelled bits in the upper limbs is k */

  count_leading_zeros(u, cc);
  k += u; 

  if (cc != (1<<(mp_bits_per_limb-u-1))) return k;

  /* now cc is an exact power of two */
  if (cc != 1) 
    /* We just need to compare the following limbs */
    /* until two of them differ. The result is either k or k+1. */
    {
      /* First flush all the unmatched limbs of b ; they all have to
         be 0 in order for the process to go on */
      while (bn >= 0)
        {
          if (cn < 0) { return k; }
          t = bp[bn--]; 
          if (d < mp_bits_per_limb)
            {
              if (d) 
                { 
                  u = cp[cn--] << (mp_bits_per_limb - d); 
                  if (cn >= 0) u+=(cp[cn]>>d); 
                }
              else u = cp[cn--]; 
              
              if (t > u || (t == u && cn < 0)) return k; 
              if (t < u) return k+1; 
            }
          else
            if (t) return k; else d -= mp_bits_per_limb; 
        }
          
      /* bn < 0; if some limb of c is nonzero, return k+1, otherwise return k*/

      if (cn>=0 && (cp[cn--] << (mp_bits_per_limb - d))) { return k+1; }

      while (cn >= 0) 
        if (cp[cn--]) return k+1; 
      return k; 
    }

  /* cc = 1. Too bad. */
  z = 0; /* number of possibly cancelled bits - 1 */
  /* thus result is either k if low(b) >= low(c)
                        or k+z+1 if low(b) < low(c) */
  if (d > mp_bits_per_limb) { return k; }

  while (bn >= 0)
    { 
      if (cn < 0) { return k; }

      if (d) 
         { 
           u = cp[cn--] << (mp_bits_per_limb - d); 
           if (cn >= 0) u+=(cp[cn]>>d);
         }
       else u = cp[cn--]; 

      /* bp[bn--] > cp[cn--] : no borrow possible, k unchanged
         bp[bn--] = cp[cn--] : need to consider next limbs
         bp[bn--] < cp[cn--] : borrow
      */
       if ((cc = bp[bn--]) != u) {
         if (cc>u) return k;
         else { count_leading_zeros(u, cc-u); return k + 1 + z + u; }
       }
       else z += mp_bits_per_limb; 
    }

  if (cn >= 0)
    count_leading_zeros(cc, ~(cp[cn--] << (mp_bits_per_limb - d))); 
  else { cc = 0; }

  k += cc; 
  if (cc < d) return k;
  
  while (cn >= 0 && !~cp[cn--]) { z += mp_bits_per_limb; } 
  if (cn >= 0) { count_leading_zeros(cc, ~cp[cn--]); return (k + z + cc); }

  return k; /* We **need** that the nonsignificant limbs of c are set
               to zero there */        
}