xref: /dflybsd-src/contrib/mpfr/src/cmp2.c (revision 2786097444a0124b5d33763854de247e230c6629)

/* mpfr_cmp2 -- exponent shift when subtracting two numbers.

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
Contributed by the AriC and Caramel projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of 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 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */


#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

/* If |b| != |c|, puts the number of canceled bits when one subtracts |c|
   from |b| in *cancel. Returns the sign of the difference (-1, 0, 1).

   Assumes neither of b or c is NaN, +/- infinity, or +/- 0.

   In other terms, if |b| != |c|, mpfr_cmp2 (b, c) returns
   EXP(max(|b|,|c|)) - EXP(|b| - |c|).
*/

int
mpfr_cmp2 (mpfr_srcptr b, mpfr_srcptr c, mpfr_prec_t *cancel)
{
  mp_limb_t *bp, *cp, bb, cc = 0, lastc = 0, dif, high_dif = 0;
  mp_size_t bn, cn;
  mpfr_uexp_t diff_exp;
  mpfr_prec_t res = 0;
  int sign;

  /* b=c should not happen, since cmp2 is called only from agm (with
     different variables) and from sub1 (if b=c, then sub1sp would be
     called instead). So, no need for a particular optimization here. */

  /* the cases b=0 or c=0 are also treated apart in agm and sub
     (which calls sub1) */
  MPFR_ASSERTD (MPFR_IS_PURE_FP(b));
  MPFR_ASSERTD (MPFR_IS_PURE_FP(c));

  if (MPFR_GET_EXP (b) >= MPFR_GET_EXP (c))
    {
      sign = 1;
      diff_exp = (mpfr_uexp_t) MPFR_GET_EXP (b) - MPFR_GET_EXP (c);

      bp = MPFR_MANT(b);
      cp = MPFR_MANT(c);

      bn = (MPFR_PREC(b) - 1) / GMP_NUMB_BITS;
      cn = (MPFR_PREC(c) - 1) / GMP_NUMB_BITS; /* # of limbs of c minus 1 */

      if (MPFR_UNLIKELY( diff_exp == 0 ))
        {
          while (bn >= 0 && cn >= 0 && bp[bn] == cp[cn])
            {
              bn--;
              cn--;
              res += GMP_NUMB_BITS;
            }

          if (MPFR_UNLIKELY (bn < 0))
            {
              if (MPFR_LIKELY (cn < 0)) /* b = c */
                return 0;

              bp = cp;
              bn = cn;
              cn = -1;
              sign = -1;
            }

          if (MPFR_UNLIKELY (cn < 0))
            /* c discards exactly the upper part of b */
            {
              unsigned int z;

              MPFR_ASSERTD (bn >= 0);

              while (bp[bn] == 0)
                {
                  if (--bn < 0) /* b = c */
                    return 0;
                  res += GMP_NUMB_BITS;
                }

              count_leading_zeros(z, bp[bn]); /* bp[bn] <> 0 */
              *cancel = res + z;
              return sign;
            }

          MPFR_ASSERTD (bn >= 0);
          MPFR_ASSERTD (cn >= 0);
          MPFR_ASSERTD (bp[bn] != cp[cn]);
          if (bp[bn] < cp[cn])
            {
              mp_limb_t *tp;
              mp_size_t tn;

              tp = bp; bp = cp; cp = tp;
              tn = bn; bn = cn; cn = tn;
              sign = -1;
            }
        }
    } /* MPFR_EXP(b) >= MPFR_EXP(c) */
  else /* MPFR_EXP(b) < MPFR_EXP(c) */
    {
      sign = -1;
      diff_exp = (mpfr_uexp_t) MPFR_GET_EXP (c) - MPFR_GET_EXP (b);

      bp = MPFR_MANT(c);
      cp = MPFR_MANT(b);

      bn = (MPFR_PREC(c) - 1) / GMP_NUMB_BITS;
      cn = (MPFR_PREC(b) - 1) / GMP_NUMB_BITS;
    }

  /* now we have removed the identical upper limbs of b and c
     (can happen only when diff_exp = 0), and after the possible
     swap, we have |b| > |c|: bp[bn] > cc, bn >= 0, cn >= 0,
     diff_exp = EXP(b) - EXP(c).
  */

  if (MPFR_LIKELY (diff_exp < GMP_NUMB_BITS))
    {
      cc = cp[cn] >> diff_exp;
      /* warning: a shift by GMP_NUMB_BITS may give wrong results */
      if (diff_exp)
        lastc = cp[cn] << (GMP_NUMB_BITS - diff_exp);
      cn--;
    }
  else
    diff_exp -= GMP_NUMB_BITS; /* cc = 0 */

  dif = bp[bn--] - cc; /* necessarily dif >= 1 */
  MPFR_ASSERTD(dif >= 1);

  /* now high_dif = 0, dif >= 1, lastc is the neglected part of cp[cn+1] */

  while (MPFR_UNLIKELY ((cn >= 0 || lastc != 0)
                        && (high_dif == 0) && (dif == 1)))
    { /* dif=1 implies diff_exp = 0 or 1 */
      bb = (bn >= 0) ? bp[bn] : 0;
      cc = lastc;
      if (cn >= 0)
        {
          if (diff_exp == 0)
            {
              cc += cp[cn];
            }
          else /* diff_exp = 1 */
            {
              cc += cp[cn] >> 1;
              lastc = cp[cn] << (GMP_NUMB_BITS - 1);
            }
        }
      else
        lastc = 0;
      high_dif = 1 - mpn_sub_n (&dif, &bb, &cc, 1);
      bn--;
      cn--;
      res += GMP_NUMB_BITS;
    }

  /* (cn<0 and lastc=0) or (high_dif,dif)<>(0,1) */

  if (MPFR_UNLIKELY (high_dif != 0)) /* high_dif == 1 */
    {
      res--;
      MPFR_ASSERTD (res >= 0);
      if (dif != 0)
        {
          *cancel = res;
          return sign;
        }
    }
  else /* high_dif == 0 */
    {
      unsigned int z;

      count_leading_zeros(z, dif); /* dif > 1 here */
      res += z;
      if (MPFR_LIKELY(dif != (MPFR_LIMB_ONE << (GMP_NUMB_BITS - z - 1))))
        { /* dif is not a power of two */
          *cancel = res;
          return sign;
        }
    }

  /* now result is res + (low(b) < low(c)) */
  while (MPFR_UNLIKELY (bn >= 0 && (cn >= 0 || lastc != 0)))
    {
      if (diff_exp >= GMP_NUMB_BITS)
        diff_exp -= GMP_NUMB_BITS;
      else
        {
          cc = lastc;
          if (cn >= 0)
            {
              cc += cp[cn] >> diff_exp;
              if (diff_exp != 0)
                lastc = cp[cn] << (GMP_NUMB_BITS - diff_exp);
            }
          else
            lastc = 0;
          cn--;
        }
      if (bp[bn] != cc)
        {
          *cancel = res + (bp[bn] < cc);
          return sign;
        }
      bn--;
    }

  if (bn < 0)
    {
      if (lastc != 0)
        res++;
      else
        {
          while (cn >= 0 && cp[cn] == 0)
            cn--;
          if (cn >= 0)
            res++;
        }
    }

  *cancel = res;
  return sign;
}