tree-optimization/95495 - use SLP_TREE_REPRESENTATIVE in assertion

[thirdparty/gcc.git] / libgcc / fp-bit.c

/* This is a software floating point library which can be used
   for targets without hardware floating point. 
   Copyright (C) 1994-2020 Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.

GCC 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.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

/* This implements IEEE 754 format arithmetic, but does not provide a
   mechanism for setting the rounding mode, or for generating or handling
   exceptions.

   The original code by Steve Chamberlain, hacked by Mark Eichin and Jim
   Wilson, all of Cygnus Support.  */

/* The intended way to use this file is to make two copies, add `#define FLOAT'
   to one copy, then compile both copies and add them to libgcc.a.  */

#include "tconfig.h"
#include "coretypes.h"
#include "tm.h"
#include "libgcc_tm.h"
#include "fp-bit.h"

/* The following macros can be defined to change the behavior of this file:
   FLOAT: Implement a `float', aka SFmode, fp library.  If this is not
     defined, then this file implements a `double', aka DFmode, fp library.
   FLOAT_ONLY: Used with FLOAT, to implement a `float' only library, i.e.
     don't include float->double conversion which requires the double library.
     This is useful only for machines which can't support doubles, e.g. some
     8-bit processors.
   CMPtype: Specify the type that floating point compares should return.
     This defaults to SItype, aka int.
   _DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding
     two integers to the FLO_union_type.
   NO_DENORMALS: Disable handling of denormals.
   NO_NANS: Disable nan and infinity handling
   SMALL_MACHINE: Useful when operations on QIs and HIs are faster
     than on an SI */

/* We don't currently support extended floats (long doubles) on machines
   without hardware to deal with them.

   These stubs are just to keep the linker from complaining about unresolved
   references which can be pulled in from libio & libstdc++, even if the
   user isn't using long doubles.  However, they may generate an unresolved
   external to abort if abort is not used by the function, and the stubs
   are referenced from within libc, since libgcc goes before and after the
   system library.  */

#ifdef DECLARE_LIBRARY_RENAMES
  DECLARE_LIBRARY_RENAMES
#endif

#ifdef EXTENDED_FLOAT_STUBS
extern void abort (void);
void __extendsfxf2 (void) { abort(); }
void __extenddfxf2 (void) { abort(); }
void __truncxfdf2 (void) { abort(); }
void __truncxfsf2 (void) { abort(); }
void __fixxfsi (void) { abort(); }
void __floatsixf (void) { abort(); }
void __addxf3 (void) { abort(); }
void __subxf3 (void) { abort(); }
void __mulxf3 (void) { abort(); }
void __divxf3 (void) { abort(); }
void __negxf2 (void) { abort(); }
void __eqxf2 (void) { abort(); }
void __nexf2 (void) { abort(); }
void __gtxf2 (void) { abort(); }
void __gexf2 (void) { abort(); }
void __lexf2 (void) { abort(); }
void __ltxf2 (void) { abort(); }

void __extendsftf2 (void) { abort(); }
void __extenddftf2 (void) { abort(); }
void __trunctfdf2 (void) { abort(); }
void __trunctfsf2 (void) { abort(); }
void __fixtfsi (void) { abort(); }
void __floatsitf (void) { abort(); }
void __addtf3 (void) { abort(); }
void __subtf3 (void) { abort(); }
void __multf3 (void) { abort(); }
void __divtf3 (void) { abort(); }
void __negtf2 (void) { abort(); }
void __eqtf2 (void) { abort(); }
void __netf2 (void) { abort(); }
void __gttf2 (void) { abort(); }
void __getf2 (void) { abort(); }
void __letf2 (void) { abort(); }
void __lttf2 (void) { abort(); }
#else   /* !EXTENDED_FLOAT_STUBS, rest of file */

/* IEEE "special" number predicates */

#ifdef NO_NANS

#define nan() 0
#define isnan(x) 0
#define isinf(x) 0
#else

#if   defined L_thenan_sf
const fp_number_type __thenan_sf = { CLASS_SNAN, 0, 0, {(fractype) 0} };
#elif defined L_thenan_df
const fp_number_type __thenan_df = { CLASS_SNAN, 0, 0, {(fractype) 0} };
#elif defined L_thenan_tf
const fp_number_type __thenan_tf = { CLASS_SNAN, 0, 0, {(fractype) 0} };
#elif defined TFLOAT
extern const fp_number_type __thenan_tf;
#elif defined FLOAT
extern const fp_number_type __thenan_sf;
#else
extern const fp_number_type __thenan_df;
#endif

INLINE
static const fp_number_type *
makenan (void)
{
#ifdef TFLOAT
  return & __thenan_tf;
#elif defined FLOAT  
  return & __thenan_sf;
#else
  return & __thenan_df;
#endif
}

INLINE
static int
isnan (const fp_number_type *x)
{
  return __builtin_expect (x->class == CLASS_SNAN || x->class == CLASS_QNAN,
                           0);
}

INLINE
static int
isinf (const fp_number_type *  x)
{
  return __builtin_expect (x->class == CLASS_INFINITY, 0);
}

#endif /* NO_NANS */

INLINE
static int
iszero (const fp_number_type *  x)
{
  return x->class == CLASS_ZERO;
}

INLINE 
static void
flip_sign ( fp_number_type *  x)
{
  x->sign = !x->sign;
}

/* Count leading zeroes in N.  */
INLINE
static int
clzusi (USItype n)
{
  extern int __clzsi2 (USItype);
  if (sizeof (USItype) == sizeof (unsigned int))
    return __builtin_clz (n);
  else if (sizeof (USItype) == sizeof (unsigned long))
    return __builtin_clzl (n);
  else if (sizeof (USItype) == sizeof (unsigned long long))
    return __builtin_clzll (n);
  else
    return __clzsi2 (n);
}

extern FLO_type pack_d (const fp_number_type * );

#if defined(L_pack_df) || defined(L_pack_sf) || defined(L_pack_tf)
FLO_type
pack_d (const fp_number_type *src)
{
  FLO_union_type dst;
  fractype fraction = src->fraction.ll; /* wasn't unsigned before? */
  int sign = src->sign;
  int exp = 0;

  if (isnan (src))
    {
      exp = EXPMAX;
      /* Restore the NaN's payload.  */
      fraction >>= NGARDS;
      fraction &= QUIET_NAN - 1;
      if (src->class == CLASS_QNAN || 1)
        {
#ifdef QUIET_NAN_NEGATED
          /* The quiet/signaling bit remains unset.  */
          /* Make sure the fraction has a non-zero value.  */
          if (fraction == 0)
            fraction |= QUIET_NAN - 1;
#else
          /* Set the quiet/signaling bit.  */
          fraction |= QUIET_NAN;
#endif
        }
    }
  else if (isinf (src))
    {
      exp = EXPMAX;
      fraction = 0;
    }
  else if (iszero (src))
    {
      exp = 0;
      fraction = 0;
    }
  else if (fraction == 0)
    {
      exp = 0;
    }
  else
    {
      if (__builtin_expect (src->normal_exp < NORMAL_EXPMIN, 0))
        {
#ifdef NO_DENORMALS
          /* Go straight to a zero representation if denormals are not
             supported.  The denormal handling would be harmless but
             isn't unnecessary.  */
          exp = 0;
          fraction = 0;
#else /* NO_DENORMALS */
          /* This number's exponent is too low to fit into the bits
             available in the number, so we'll store 0 in the exponent and
             shift the fraction to the right to make up for it.  */

          int shift = NORMAL_EXPMIN - src->normal_exp;

          exp = 0;

          if (shift > FRAC_NBITS - NGARDS)
            {
              /* No point shifting, since it's more that 64 out.  */
              fraction = 0;
            }
          else
            {
              int lowbit = (fraction & (((fractype)1 << shift) - 1)) ? 1 : 0;
              fraction = (fraction >> shift) | lowbit;
            }
          if ((fraction & GARDMASK) == GARDMSB)
            {
              if ((fraction & (1 << NGARDS)))
                fraction += GARDROUND + 1;
            }
          else
            {
              /* Add to the guards to round up.  */
              fraction += GARDROUND;
            }
          /* Perhaps the rounding means we now need to change the
             exponent, because the fraction is no longer denormal.  */
          if (fraction >= IMPLICIT_1)
            {
              exp += 1;
            }
          fraction >>= NGARDS;
#endif /* NO_DENORMALS */
        }
      else if (__builtin_expect (src->normal_exp > EXPBIAS, 0))
        {
          exp = EXPMAX;
          fraction = 0;
        }
      else
        {
          exp = src->normal_exp + EXPBIAS;
          /* IF the gard bits are the all zero, but the first, then we're
             half way between two numbers, choose the one which makes the
             lsb of the answer 0.  */
          if ((fraction & GARDMASK) == GARDMSB)
            {
              if (fraction & (1 << NGARDS))
                fraction += GARDROUND + 1;
            }
          else
            {
              /* Add a one to the guards to round up */
              fraction += GARDROUND;
            }
          if (fraction >= IMPLICIT_2)
            {
              fraction >>= 1;
              exp += 1;
            }
          fraction >>= NGARDS;
        }
    }

  /* We previously used bitfields to store the number, but this doesn't
     handle little/big endian systems conveniently, so use shifts and
     masks */
#if defined TFLOAT && defined HALFFRACBITS
 {
   halffractype high, low, unity;
   int lowsign, lowexp;

   unity = (halffractype) 1 << HALFFRACBITS;

   /* Set HIGH to the high double's significand, masking out the implicit 1.
      Set LOW to the low double's full significand.  */
   high = (fraction >> (FRACBITS - HALFFRACBITS)) & (unity - 1);
   low = fraction & (unity * 2 - 1);

   /* Get the initial sign and exponent of the low double.  */
   lowexp = exp - HALFFRACBITS - 1;
   lowsign = sign;

   /* HIGH should be rounded like a normal double, making |LOW| <=
      0.5 ULP of HIGH.  Assume round-to-nearest.  */
   if (exp < EXPMAX)
     if (low > unity || (low == unity && (high & 1) == 1))
       {
         /* Round HIGH up and adjust LOW to match.  */
         high++;
         if (high == unity)
           {
             /* May make it infinite, but that's OK.  */
             high = 0;
             exp++;
           }
         low = unity * 2 - low;
         lowsign ^= 1;
       }

   high |= (halffractype) exp << HALFFRACBITS;
   high |= (halffractype) sign << (HALFFRACBITS + EXPBITS);

   if (exp == EXPMAX || exp == 0 || low == 0)
     low = 0;
   else
     {
       while (lowexp > 0 && low < unity)
         {
           low <<= 1;
           lowexp--;
         }

       if (lowexp <= 0)
         {
           halffractype roundmsb, round;
           int shift;

           shift = 1 - lowexp;
           roundmsb = (1 << (shift - 1));
           round = low & ((roundmsb << 1) - 1);

           low >>= shift;
           lowexp = 0;

           if (round > roundmsb || (round == roundmsb && (low & 1) == 1))
             {
               low++;
               if (low == unity)
                 /* LOW rounds up to the smallest normal number.  */
                 lowexp++;
             }
         }

       low &= unity - 1;
       low |= (halffractype) lowexp << HALFFRACBITS;
       low |= (halffractype) lowsign << (HALFFRACBITS + EXPBITS);
     }
   dst.value_raw = ((fractype) high << HALFSHIFT) | low;
 }
#else
  dst.value_raw = fraction & ((((fractype)1) << FRACBITS) - (fractype)1);
  dst.value_raw |= ((fractype) (exp & ((1 << EXPBITS) - 1))) << FRACBITS;
  dst.value_raw |= ((fractype) (sign & 1)) << (FRACBITS | EXPBITS);
#endif

#if defined(FLOAT_WORD_ORDER_MISMATCH) && !defined(FLOAT)
#ifdef TFLOAT
  {
    qrtrfractype tmp1 = dst.words[0];
    qrtrfractype tmp2 = dst.words[1];
    dst.words[0] = dst.words[3];
    dst.words[1] = dst.words[2];
    dst.words[2] = tmp2;
    dst.words[3] = tmp1;
  }
#else
  {
    halffractype tmp = dst.words[0];
    dst.words[0] = dst.words[1];
    dst.words[1] = tmp;
  }
#endif
#endif

  return dst.value;
}
#endif

#if defined(L_unpack_df) || defined(L_unpack_sf) || defined(L_unpack_tf)
void
unpack_d (FLO_union_type * src, fp_number_type * dst)
{
  /* We previously used bitfields to store the number, but this doesn't
     handle little/big endian systems conveniently, so use shifts and
     masks */
  fractype fraction;
  int exp;
  int sign;

#if defined(FLOAT_WORD_ORDER_MISMATCH) && !defined(FLOAT)
  FLO_union_type swapped;

#ifdef TFLOAT
  swapped.words[0] = src->words[3];
  swapped.words[1] = src->words[2];
  swapped.words[2] = src->words[1];
  swapped.words[3] = src->words[0];
#else
  swapped.words[0] = src->words[1];
  swapped.words[1] = src->words[0];
#endif
  src = &swapped;
#endif
  
#if defined TFLOAT && defined HALFFRACBITS
 {
   halffractype high, low;
   
   high = src->value_raw >> HALFSHIFT;
   low = src->value_raw & (((fractype)1 << HALFSHIFT) - 1);

   fraction = high & ((((fractype)1) << HALFFRACBITS) - 1);
   fraction <<= FRACBITS - HALFFRACBITS;
   exp = ((int)(high >> HALFFRACBITS)) & ((1 << EXPBITS) - 1);
   sign = ((int)(high >> (((HALFFRACBITS + EXPBITS))))) & 1;

   if (exp != EXPMAX && exp != 0 && low != 0)
     {
       int lowexp = ((int)(low >> HALFFRACBITS)) & ((1 << EXPBITS) - 1);
       int lowsign = ((int)(low >> (((HALFFRACBITS + EXPBITS))))) & 1;
       int shift;
       fractype xlow;

       xlow = low & ((((fractype)1) << HALFFRACBITS) - 1);
       if (lowexp)
         xlow |= (((halffractype)1) << HALFFRACBITS);
       else
         lowexp = 1;
       shift = (FRACBITS - HALFFRACBITS) - (exp - lowexp);
       if (shift > 0)
         xlow <<= shift;
       else if (shift < 0)
         xlow >>= -shift;
       if (sign == lowsign)
         fraction += xlow;
       else if (fraction >= xlow)
         fraction -= xlow;
       else
         {
           /* The high part is a power of two but the full number is lower.
              This code will leave the implicit 1 in FRACTION, but we'd
              have added that below anyway.  */
           fraction = (((fractype) 1 << FRACBITS) - xlow) << 1;
           exp--;
         }
     }
 }
#else
  fraction = src->value_raw & ((((fractype)1) << FRACBITS) - 1);
  exp = ((int)(src->value_raw >> FRACBITS)) & ((1 << EXPBITS) - 1);
  sign = ((int)(src->value_raw >> (FRACBITS + EXPBITS))) & 1;
#endif

  dst->sign = sign;
  if (exp == 0)
    {
      /* Hmm.  Looks like 0 */
      if (fraction == 0
#ifdef NO_DENORMALS
          || 1
#endif
          )
        {
          /* tastes like zero */
          dst->class = CLASS_ZERO;
        }
      else
        {
          /* Zero exponent with nonzero fraction - it's denormalized,
             so there isn't a leading implicit one - we'll shift it so
             it gets one.  */
          dst->normal_exp = exp - EXPBIAS + 1;
          fraction <<= NGARDS;

          dst->class = CLASS_NUMBER;
#if 1
          while (fraction < IMPLICIT_1)
            {
              fraction <<= 1;
              dst->normal_exp--;
            }
#endif
          dst->fraction.ll = fraction;
        }
    }
  else if (__builtin_expect (exp == EXPMAX, 0))
    {
      /* Huge exponent*/
      if (fraction == 0)
        {
          /* Attached to a zero fraction - means infinity */
          dst->class = CLASS_INFINITY;
        }
      else
        {
          /* Nonzero fraction, means nan */
#ifdef QUIET_NAN_NEGATED
          if ((fraction & QUIET_NAN) == 0)
#else
          if (fraction & QUIET_NAN)
#endif
            {
              dst->class = CLASS_QNAN;
            }
          else
            {
              dst->class = CLASS_SNAN;
            }
          /* Now that we know which kind of NaN we got, discard the
             quiet/signaling bit, but do preserve the NaN payload.  */
          fraction &= ~QUIET_NAN;
          dst->fraction.ll = fraction << NGARDS;
        }
    }
  else
    {
      /* Nothing strange about this number */
      dst->normal_exp = exp - EXPBIAS;
      dst->class = CLASS_NUMBER;
      dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1;
    }
}
#endif /* L_unpack_df || L_unpack_sf */

#if defined(L_addsub_sf) || defined(L_addsub_df) || defined(L_addsub_tf)
static const fp_number_type *
_fpadd_parts (fp_number_type * a,
              fp_number_type * b,
              fp_number_type * tmp)
{
  intfrac tfraction;

  /* Put commonly used fields in local variables.  */
  int a_normal_exp;
  int b_normal_exp;
  fractype a_fraction;
  fractype b_fraction;

  if (isnan (a))
    {
      return a;
    }
  if (isnan (b))
    {
      return b;
    }
  if (isinf (a))
    {
      /* Adding infinities with opposite signs yields a NaN.  */
      if (isinf (b) && a->sign != b->sign)
        return makenan ();
      return a;
    }
  if (isinf (b))
    {
      return b;
    }
  if (iszero (b))
    {
      if (iszero (a))
        {
          *tmp = *a;
          tmp->sign = a->sign & b->sign;
          return tmp;
        }
      return a;
    }
  if (iszero (a))
    {
      return b;
    }

  /* Got two numbers. shift the smaller and increment the exponent till
     they're the same */
  {
    int diff;
    int sdiff;

    a_normal_exp = a->normal_exp;
    b_normal_exp = b->normal_exp;
    a_fraction = a->fraction.ll;
    b_fraction = b->fraction.ll;

    diff = a_normal_exp - b_normal_exp;
    sdiff = diff;

    if (diff < 0)
      diff = -diff;
    if (diff < FRAC_NBITS)
      {
        if (sdiff > 0)
          {
            b_normal_exp += diff;
            LSHIFT (b_fraction, diff);
          }
        else if (sdiff < 0)
          {
            a_normal_exp += diff;
            LSHIFT (a_fraction, diff);
          }
      }
    else
      {
        /* Somethings's up.. choose the biggest */
        if (a_normal_exp > b_normal_exp)
          {
            b_normal_exp = a_normal_exp;
            b_fraction = 0;
          }
        else
          {
            a_normal_exp = b_normal_exp;
            a_fraction = 0;
          }
      }
  }

  if (a->sign != b->sign)
    {
      if (a->sign)
        {
          tfraction = -a_fraction + b_fraction;
        }
      else
        {
          tfraction = a_fraction - b_fraction;
        }
      if (tfraction >= 0)
        {
          tmp->sign = 0;
          tmp->normal_exp = a_normal_exp;
          tmp->fraction.ll = tfraction;
        }
      else
        {
          tmp->sign = 1;
          tmp->normal_exp = a_normal_exp;
          tmp->fraction.ll = -tfraction;
        }
      /* and renormalize it */

      while (tmp->fraction.ll < IMPLICIT_1 && tmp->fraction.ll)
        {
          tmp->fraction.ll <<= 1;
          tmp->normal_exp--;
        }
    }
  else
    {
      tmp->sign = a->sign;
      tmp->normal_exp = a_normal_exp;
      tmp->fraction.ll = a_fraction + b_fraction;
    }
  tmp->class = CLASS_NUMBER;
  /* Now the fraction is added, we have to shift down to renormalize the
     number */

  if (tmp->fraction.ll >= IMPLICIT_2)
    {
      LSHIFT (tmp->fraction.ll, 1);
      tmp->normal_exp++;
    }
  return tmp;
}

FLO_type
add (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  fp_number_type tmp;
  const fp_number_type *res;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  res = _fpadd_parts (&a, &b, &tmp);

  return pack_d (res);
}

FLO_type
sub (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  fp_number_type tmp;
  const fp_number_type *res;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  b.sign ^= 1;

  res = _fpadd_parts (&a, &b, &tmp);

  return pack_d (res);
}
#endif /* L_addsub_sf || L_addsub_df */

#if defined(L_mul_sf) || defined(L_mul_df) || defined(L_mul_tf)
static inline __attribute__ ((__always_inline__)) const fp_number_type *
_fpmul_parts ( fp_number_type *  a,
               fp_number_type *  b,
               fp_number_type * tmp)
{
  fractype low = 0;
  fractype high = 0;

  if (isnan (a))
    {
      a->sign = a->sign != b->sign;
      return a;
    }
  if (isnan (b))
    {
      b->sign = a->sign != b->sign;
      return b;
    }
  if (isinf (a))
    {
      if (iszero (b))
        return makenan ();
      a->sign = a->sign != b->sign;
      return a;
    }
  if (isinf (b))
    {
      if (iszero (a))
        {
          return makenan ();
        }
      b->sign = a->sign != b->sign;
      return b;
    }
  if (iszero (a))
    {
      a->sign = a->sign != b->sign;
      return a;
    }
  if (iszero (b))
    {
      b->sign = a->sign != b->sign;
      return b;
    }

  /* Calculate the mantissa by multiplying both numbers to get a
     twice-as-wide number.  */
  {
#if defined(NO_DI_MODE) || defined(TFLOAT)
    {
      fractype x = a->fraction.ll;
      fractype ylow = b->fraction.ll;
      fractype yhigh = 0;
      int bit;

      /* ??? This does multiplies one bit at a time.  Optimize.  */
      for (bit = 0; bit < FRAC_NBITS; bit++)
        {
          int carry;

          if (x & 1)
            {
              carry = (low += ylow) < ylow;
              high += yhigh + carry;
            }
          yhigh <<= 1;
          if (ylow & FRACHIGH)
            {
              yhigh |= 1;
            }
          ylow <<= 1;
          x >>= 1;
        }
    }
#elif defined(FLOAT) 
    /* Multiplying two USIs to get a UDI, we're safe.  */
    {
      UDItype answer = (UDItype)a->fraction.ll * (UDItype)b->fraction.ll;
      
      high = answer >> BITS_PER_SI;
      low = answer;
    }
#else
    /* fractype is DImode, but we need the result to be twice as wide.
       Assuming a widening multiply from DImode to TImode is not
       available, build one by hand.  */
    {
      USItype nl = a->fraction.ll;
      USItype nh = a->fraction.ll >> BITS_PER_SI;
      USItype ml = b->fraction.ll;
      USItype mh = b->fraction.ll >> BITS_PER_SI;
      UDItype pp_ll = (UDItype) ml * nl;
      UDItype pp_hl = (UDItype) mh * nl;
      UDItype pp_lh = (UDItype) ml * nh;
      UDItype pp_hh = (UDItype) mh * nh;
      UDItype res2 = 0;
      UDItype res0 = 0;
      UDItype ps_hh__ = pp_hl + pp_lh;
      if (ps_hh__ < pp_hl)
        res2 += (UDItype)1 << BITS_PER_SI;
      pp_hl = (UDItype)(USItype)ps_hh__ << BITS_PER_SI;
      res0 = pp_ll + pp_hl;
      if (res0 < pp_ll)
        res2++;
      res2 += (ps_hh__ >> BITS_PER_SI) + pp_hh;
      high = res2;
      low = res0;
    }
#endif
  }

  tmp->normal_exp = a->normal_exp + b->normal_exp
    + FRAC_NBITS - (FRACBITS + NGARDS);
  tmp->sign = a->sign != b->sign;
  while (high >= IMPLICIT_2)
    {
      tmp->normal_exp++;
      if (high & 1)
        {
          low >>= 1;
          low |= FRACHIGH;
        }
      high >>= 1;
    }
  while (high < IMPLICIT_1)
    {
      tmp->normal_exp--;

      high <<= 1;
      if (low & FRACHIGH)
        high |= 1;
      low <<= 1;
    }

  if ((high & GARDMASK) == GARDMSB)
    {
      if (high & (1 << NGARDS))
        {
          /* Because we're half way, we would round to even by adding
             GARDROUND + 1, except that's also done in the packing
             function, and rounding twice will lose precision and cause
             the result to be too far off.  Example: 32-bit floats with
             bit patterns 0xfff * 0x3f800400 ~= 0xfff (less than 0.5ulp
             off), not 0x1000 (more than 0.5ulp off).  */
        }
      else if (low)
        {
          /* We're a further than half way by a small amount corresponding
             to the bits set in "low".  Knowing that, we round here and
             not in pack_d, because there we don't have "low" available
             anymore.  */
          high += GARDROUND + 1;

          /* Avoid further rounding in pack_d.  */
          high &= ~(fractype) GARDMASK;
        }
    }
  tmp->fraction.ll = high;
  tmp->class = CLASS_NUMBER;
  return tmp;
}

FLO_type
multiply (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  fp_number_type tmp;
  const fp_number_type *res;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  res = _fpmul_parts (&a, &b, &tmp);

  return pack_d (res);
}
#endif /* L_mul_sf || L_mul_df || L_mul_tf */

#if defined(L_div_sf) || defined(L_div_df) || defined(L_div_tf)
static inline __attribute__ ((__always_inline__)) const fp_number_type *
_fpdiv_parts (fp_number_type * a,
              fp_number_type * b)
{
  fractype bit;
  fractype numerator;
  fractype denominator;
  fractype quotient;

  if (isnan (a))
    {
      return a;
    }
  if (isnan (b))
    {
      return b;
    }

  a->sign = a->sign ^ b->sign;

  if (isinf (a) || iszero (a))
    {
      if (a->class == b->class)
        return makenan ();
      return a;
    }

  if (isinf (b))
    {
      a->fraction.ll = 0;
      a->normal_exp = 0;
      return a;
    }
  if (iszero (b))
    {
      a->class = CLASS_INFINITY;
      return a;
    }

  /* Calculate the mantissa by multiplying both 64bit numbers to get a
     128 bit number */
  {
    /* quotient =
       ( numerator / denominator) * 2^(numerator exponent -  denominator exponent)
     */

    a->normal_exp = a->normal_exp - b->normal_exp;
    numerator = a->fraction.ll;
    denominator = b->fraction.ll;

    if (numerator < denominator)
      {
        /* Fraction will be less than 1.0 */
        numerator *= 2;
        a->normal_exp--;
      }
    bit = IMPLICIT_1;
    quotient = 0;
    /* ??? Does divide one bit at a time.  Optimize.  */
    while (bit)
      {
        if (numerator >= denominator)
          {
            quotient |= bit;
            numerator -= denominator;
          }
        bit >>= 1;
        numerator *= 2;
      }

    if ((quotient & GARDMASK) == GARDMSB)
      {
        if (quotient & (1 << NGARDS))
          {
            /* Because we're half way, we would round to even by adding
               GARDROUND + 1, except that's also done in the packing
               function, and rounding twice will lose precision and cause
               the result to be too far off.  */
          }
        else if (numerator)
          {
            /* We're a further than half way by the small amount
               corresponding to the bits set in "numerator".  Knowing
               that, we round here and not in pack_d, because there we
               don't have "numerator" available anymore.  */
            quotient += GARDROUND + 1;

            /* Avoid further rounding in pack_d.  */
            quotient &= ~(fractype) GARDMASK;
          }
      }

    a->fraction.ll = quotient;
    return (a);
  }
}

FLO_type
divide (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  const fp_number_type *res;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  res = _fpdiv_parts (&a, &b);

  return pack_d (res);
}
#endif /* L_div_sf || L_div_df */

#if defined(L_fpcmp_parts_sf) || defined(L_fpcmp_parts_df) \
    || defined(L_fpcmp_parts_tf)
/* according to the demo, fpcmp returns a comparison with 0... thus
   a<b -> -1
   a==b -> 0
   a>b -> +1
 */

int
__fpcmp_parts (fp_number_type * a, fp_number_type * b)
{
#if 0
  /* either nan -> unordered. Must be checked outside of this routine.  */
  if (isnan (a) && isnan (b))
    {
      return 1;                 /* still unordered! */
    }
#endif

  if (isnan (a) || isnan (b))
    {
      return 1;                 /* how to indicate unordered compare? */
    }
  if (isinf (a) && isinf (b))
    {
      /* +inf > -inf, but +inf != +inf */
      /* b    \a| +inf(0)| -inf(1)
       ______\+--------+--------
       +inf(0)| a==b(0)| a<b(-1)
       -------+--------+--------
       -inf(1)| a>b(1) | a==b(0)
       -------+--------+--------
       So since unordered must be nonzero, just line up the columns...
       */
      return b->sign - a->sign;
    }
  /* but not both...  */
  if (isinf (a))
    {
      return a->sign ? -1 : 1;
    }
  if (isinf (b))
    {
      return b->sign ? 1 : -1;
    }
  if (iszero (a) && iszero (b))
    {
      return 0;
    }
  if (iszero (a))
    {
      return b->sign ? 1 : -1;
    }
  if (iszero (b))
    {
      return a->sign ? -1 : 1;
    }
  /* now both are "normal".  */
  if (a->sign != b->sign)
    {
      /* opposite signs */
      return a->sign ? -1 : 1;
    }
  /* same sign; exponents? */
  if (a->normal_exp > b->normal_exp)
    {
      return a->sign ? -1 : 1;
    }
  if (a->normal_exp < b->normal_exp)
    {
      return a->sign ? 1 : -1;
    }
  /* same exponents; check size.  */
  if (a->fraction.ll > b->fraction.ll)
    {
      return a->sign ? -1 : 1;
    }
  if (a->fraction.ll < b->fraction.ll)
    {
      return a->sign ? 1 : -1;
    }
  /* after all that, they're equal.  */
  return 0;
}
#endif

#if defined(L_compare_sf) || defined(L_compare_df) || defined(L_compoare_tf)
CMPtype
compare (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  return __fpcmp_parts (&a, &b);
}
#endif /* L_compare_sf || L_compare_df */

/* These should be optimized for their specific tasks someday.  */

#if defined(L_eq_sf) || defined(L_eq_df) || defined(L_eq_tf)
CMPtype
_eq_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  if (isnan (&a) || isnan (&b))
    return 1;                   /* false, truth == 0 */

  return __fpcmp_parts (&a, &b) ;
}
#endif /* L_eq_sf || L_eq_df */

#if defined(L_ne_sf) || defined(L_ne_df) || defined(L_ne_tf)
CMPtype
_ne_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  if (isnan (&a) || isnan (&b))
    return 1;                   /* true, truth != 0 */

  return  __fpcmp_parts (&a, &b) ;
}
#endif /* L_ne_sf || L_ne_df */

#if defined(L_gt_sf) || defined(L_gt_df) || defined(L_gt_tf)
CMPtype
_gt_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  if (isnan (&a) || isnan (&b))
    return -1;                  /* false, truth > 0 */

  return __fpcmp_parts (&a, &b);
}
#endif /* L_gt_sf || L_gt_df */

#if defined(L_ge_sf) || defined(L_ge_df) || defined(L_ge_tf)
CMPtype
_ge_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  if (isnan (&a) || isnan (&b))
    return -1;                  /* false, truth >= 0 */
  return __fpcmp_parts (&a, &b) ;
}
#endif /* L_ge_sf || L_ge_df */

#if defined(L_lt_sf) || defined(L_lt_df) || defined(L_lt_tf)
CMPtype
_lt_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  if (isnan (&a) || isnan (&b))
    return 1;                   /* false, truth < 0 */

  return __fpcmp_parts (&a, &b);
}
#endif /* L_lt_sf || L_lt_df */

#if defined(L_le_sf) || defined(L_le_df) || defined(L_le_tf)
CMPtype
_le_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  if (isnan (&a) || isnan (&b))
    return 1;                   /* false, truth <= 0 */

  return __fpcmp_parts (&a, &b) ;
}
#endif /* L_le_sf || L_le_df */

#if defined(L_unord_sf) || defined(L_unord_df) || defined(L_unord_tf)
CMPtype
_unord_f2 (FLO_type arg_a, FLO_type arg_b)
{
  fp_number_type a;
  fp_number_type b;
  FLO_union_type au, bu;

  au.value = arg_a;
  bu.value = arg_b;

  unpack_d (&au, &a);
  unpack_d (&bu, &b);

  return (isnan (&a) || isnan (&b));
}
#endif /* L_unord_sf || L_unord_df */

#if defined(L_si_to_sf) || defined(L_si_to_df) || defined(L_si_to_tf)
FLO_type
si_to_float (SItype arg_a)
{
  fp_number_type in;

  in.class = CLASS_NUMBER;
  in.sign = arg_a < 0;
  if (!arg_a)
    {
      in.class = CLASS_ZERO;
    }
  else
    {
      USItype uarg;
      int shift;
      in.normal_exp = FRACBITS + NGARDS;
      if (in.sign) 
        {
          /* Special case for minint, since there is no +ve integer
             representation for it */
          if (arg_a == (- MAX_SI_INT - 1))
            {
              return (FLO_type)(- MAX_SI_INT - 1);
            }
          uarg = (-arg_a);
        }
      else
        uarg = arg_a;

      in.fraction.ll = uarg;
      shift = clzusi (uarg) - (BITS_PER_SI - 1 - FRACBITS - NGARDS);
      if (shift > 0)
        {
          in.fraction.ll <<= shift;
          in.normal_exp -= shift;
        }
    }
  return pack_d (&in);
}
#endif /* L_si_to_sf || L_si_to_df */

#if defined(L_usi_to_sf) || defined(L_usi_to_df) || defined(L_usi_to_tf)
FLO_type
usi_to_float (USItype arg_a)
{
  fp_number_type in;

  in.sign = 0;
  if (!arg_a)
    {
      in.class = CLASS_ZERO;
    }
  else
    {
      int shift;
      in.class = CLASS_NUMBER;
      in.normal_exp = FRACBITS + NGARDS;
      in.fraction.ll = arg_a;

      shift = clzusi (arg_a) - (BITS_PER_SI - 1 - FRACBITS - NGARDS);
      if (shift < 0)
        {
          fractype guard = in.fraction.ll & (((fractype)1 << -shift) - 1);
          in.fraction.ll >>= -shift;
          in.fraction.ll |= (guard != 0);
          in.normal_exp -= shift;
        }
      else if (shift > 0)
        {
          in.fraction.ll <<= shift;
          in.normal_exp -= shift;
        }
    }
  return pack_d (&in);
}
#endif

#if defined(L_sf_to_si) || defined(L_df_to_si) || defined(L_tf_to_si)
SItype
float_to_si (FLO_type arg_a)
{
  fp_number_type a;
  SItype tmp;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &a);

  if (iszero (&a))
    return 0;
  if (isnan (&a))
    return 0;
  /* get reasonable MAX_SI_INT...  */
  if (isinf (&a))
    return a.sign ? (-MAX_SI_INT)-1 : MAX_SI_INT;
  /* it is a number, but a small one */
  if (a.normal_exp < 0)
    return 0;
  if (a.normal_exp > BITS_PER_SI - 2)
    return a.sign ? (-MAX_SI_INT)-1 : MAX_SI_INT;
  tmp = a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp);
  return a.sign ? (-tmp) : (tmp);
}
#endif /* L_sf_to_si || L_df_to_si */

#if defined(L_tf_to_usi)
USItype
float_to_usi (FLO_type arg_a)
{
  fp_number_type a;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &a);

  if (iszero (&a))
    return 0;
  if (isnan (&a))
    return 0;
  /* it is a negative number */
  if (a.sign)
    return 0;
  /* get reasonable MAX_USI_INT...  */
  if (isinf (&a))
    return MAX_USI_INT;
  /* it is a number, but a small one */
  if (a.normal_exp < 0)
    return 0;
  if (a.normal_exp > BITS_PER_SI - 1)
    return MAX_USI_INT;
  else if (a.normal_exp > (FRACBITS + NGARDS))
    return a.fraction.ll << (a.normal_exp - (FRACBITS + NGARDS));
  else
    return a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp);
}
#endif /* L_tf_to_usi */

#if defined(L_negate_sf) || defined(L_negate_df) || defined(L_negate_tf)
FLO_type
negate (FLO_type arg_a)
{
  fp_number_type a;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &a);

  flip_sign (&a);
  return pack_d (&a);
}
#endif /* L_negate_sf || L_negate_df */

#ifdef FLOAT

#if defined(L_make_sf)
SFtype
__make_fp(fp_class_type class,
             unsigned int sign,
             int exp, 
             USItype frac)
{
  fp_number_type in;

  in.class = class;
  in.sign = sign;
  in.normal_exp = exp;
  in.fraction.ll = frac;
  return pack_d (&in);
}
#endif /* L_make_sf */

#ifndef FLOAT_ONLY

/* This enables one to build an fp library that supports float but not double.
   Otherwise, we would get an undefined reference to __make_dp.
   This is needed for some 8-bit ports that can't handle well values that
   are 8-bytes in size, so we just don't support double for them at all.  */

#if defined(L_sf_to_df)
DFtype
sf_to_df (SFtype arg_a)
{
  fp_number_type in;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &in);

  return __make_dp (in.class, in.sign, in.normal_exp,
                    ((UDItype) in.fraction.ll) << F_D_BITOFF);
}
#endif /* L_sf_to_df */

#if defined(L_sf_to_tf) && defined(TMODES)
TFtype
sf_to_tf (SFtype arg_a)
{
  fp_number_type in;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &in);

  return __make_tp (in.class, in.sign, in.normal_exp,
                    ((UTItype) in.fraction.ll) << F_T_BITOFF);
}
#endif /* L_sf_to_df */

#endif /* ! FLOAT_ONLY */
#endif /* FLOAT */

#ifndef FLOAT

extern SFtype __make_fp (fp_class_type, unsigned int, int, USItype);

#if defined(L_make_df)
DFtype
__make_dp (fp_class_type class, unsigned int sign, int exp, UDItype frac)
{
  fp_number_type in;

  in.class = class;
  in.sign = sign;
  in.normal_exp = exp;
  in.fraction.ll = frac;
  return pack_d (&in);
}
#endif /* L_make_df */

#if defined(L_df_to_sf)
SFtype
df_to_sf (DFtype arg_a)
{
  fp_number_type in;
  USItype sffrac;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &in);

  sffrac = in.fraction.ll >> F_D_BITOFF;

  /* We set the lowest guard bit in SFFRAC if we discarded any non
     zero bits.  */
  if ((in.fraction.ll & (((USItype) 1 << F_D_BITOFF) - 1)) != 0)
    sffrac |= 1;

  return __make_fp (in.class, in.sign, in.normal_exp, sffrac);
}
#endif /* L_df_to_sf */

#if defined(L_df_to_tf) && defined(TMODES) \
    && !defined(FLOAT) && !defined(TFLOAT)
TFtype
df_to_tf (DFtype arg_a)
{
  fp_number_type in;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &in);

  return __make_tp (in.class, in.sign, in.normal_exp,
                    ((UTItype) in.fraction.ll) << D_T_BITOFF);
}
#endif /* L_sf_to_df */

#ifdef TFLOAT
#if defined(L_make_tf)
TFtype
__make_tp(fp_class_type class,
             unsigned int sign,
             int exp, 
             UTItype frac)
{
  fp_number_type in;

  in.class = class;
  in.sign = sign;
  in.normal_exp = exp;
  in.fraction.ll = frac;
  return pack_d (&in);
}
#endif /* L_make_tf */

#if defined(L_tf_to_df)
DFtype
tf_to_df (TFtype arg_a)
{
  fp_number_type in;
  UDItype sffrac;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &in);

  sffrac = in.fraction.ll >> D_T_BITOFF;

  /* We set the lowest guard bit in SFFRAC if we discarded any non
     zero bits.  */
  if ((in.fraction.ll & (((UTItype) 1 << D_T_BITOFF) - 1)) != 0)
    sffrac |= 1;

  return __make_dp (in.class, in.sign, in.normal_exp, sffrac);
}
#endif /* L_tf_to_df */

#if defined(L_tf_to_sf)
SFtype
tf_to_sf (TFtype arg_a)
{
  fp_number_type in;
  USItype sffrac;
  FLO_union_type au;

  au.value = arg_a;
  unpack_d (&au, &in);

  sffrac = in.fraction.ll >> F_T_BITOFF;

  /* We set the lowest guard bit in SFFRAC if we discarded any non
     zero bits.  */
  if ((in.fraction.ll & (((UTItype) 1 << F_T_BITOFF) - 1)) != 0)
    sffrac |= 1;

  return __make_fp (in.class, in.sign, in.normal_exp, sffrac);
}
#endif /* L_tf_to_sf */
#endif /* TFLOAT */

#endif /* ! FLOAT */
#endif /* !EXTENDED_FLOAT_STUBS */