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/* This is a software floating point library which can be used instead of

   the floating point routines in libgcc1.c for targets without hardware

   floating point.  */

/* Copyright (C) 1994, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.

This program 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 of the License, or

(at your option) any later version.

This program 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 a copy of the GNU General Public License

along with this program.  If not, see <http://www.gnu.org/licenses/>.  */

/* As a special exception, if you link this library with other files,

   some of which are compiled with GCC, to produce an executable,

   this library does not by itself cause the resulting executable

   to be covered by the GNU General Public License.

   This exception does not however invalidate any other reasons why

   the executable file might be covered by the GNU General Public License.  */

/* 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.  */

/* The following macros can be defined to change the behaviour 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.

   US_SOFTWARE_GOFAST: This makes all entry points use the same names as the

     US Software goFast library.  If this is not defined, the entry points use

     the same names as libgcc1.c.

   _DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding

     two integers to the FLO_union_type.

   NO_NANS: Disable nan and infinity handling

   SMALL_MACHINE: Useful when operations on QIs and HIs are faster

     than on an SI */

#ifndef SFtype

typedef SFtype __attribute__ ((mode (SF)));

#endif

#ifndef DFtype

typedef DFtype __attribute__ ((mode (DF)));

#endif

#ifndef HItype

typedef int HItype __attribute__ ((mode (HI)));

#endif

#ifndef SItype

typedef int SItype __attribute__ ((mode (SI)));

#endif

#ifndef DItype

typedef int DItype __attribute__ ((mode (DI)));

#endif

/* The type of the result of a fp compare */

#ifndef CMPtype

#define CMPtype SItype

#endif

#ifndef UHItype

typedef unsigned int UHItype __attribute__ ((mode (HI)));

#endif

#ifndef USItype

typedef unsigned int USItype __attribute__ ((mode (SI)));

#endif

#ifndef UDItype

typedef unsigned int UDItype __attribute__ ((mode (DI)));

#endif

#define MAX_SI_INT   ((SItype) ((unsigned) (~0)>>1))

#define MAX_USI_INT  ((USItype) ~0)

#ifdef FLOAT_ONLY

#define NO_DI_MODE

#endif

#ifdef FLOAT

#       define NGARDS    7L

#       define GARDROUND 0x3f

#       define GARDMASK  0x7f

#       define GARDMSB   0x40

#       define EXPBITS 8

#       define EXPBIAS 127

#       define FRACBITS 23

#       define EXPMAX (0xff)

#       define QUIET_NAN 0x100000L

#       define FRAC_NBITS 32

#       define FRACHIGH  0x80000000L

#       define FRACHIGH2 0xc0000000L

        typedef USItype fractype;

        typedef UHItype halffractype;

        typedef SFtype FLO_type;

        typedef SItype intfrac;

#else

#       define PREFIXFPDP dp

#       define PREFIXSFDF df

#       define NGARDS 8L

#       define GARDROUND 0x7f

#       define GARDMASK  0xff

#       define GARDMSB   0x80

#       define EXPBITS 11

#       define EXPBIAS 1023

#       define FRACBITS 52

#       define EXPMAX (0x7ff)

#       define QUIET_NAN 0x8000000000000LL

#       define FRAC_NBITS 64

#       define FRACHIGH  0x8000000000000000LL

#       define FRACHIGH2 0xc000000000000000LL

        typedef UDItype fractype;

        typedef USItype halffractype;

        typedef DFtype FLO_type;

        typedef DItype intfrac;

#endif

#ifdef US_SOFTWARE_GOFAST

#       ifdef FLOAT

#               define add              fpadd

#               define sub              fpsub

#               define multiply         fpmul

#               define divide           fpdiv

#               define compare          fpcmp

#               define si_to_float      sitofp

#               define float_to_si      fptosi

#               define float_to_usi     fptoui

#               define negate           __negsf2

#               define sf_to_df         fptodp

#               define dptofp           dptofp

#else

#               define add              dpadd

#               define sub              dpsub

#               define multiply         dpmul

#               define divide           dpdiv

#               define compare          dpcmp

#               define si_to_float      litodp

#               define float_to_si      dptoli

#               define float_to_usi     dptoul

#               define negate           __negdf2

#               define df_to_sf         dptofp

#endif

#else

#       ifdef FLOAT

#               define add              __addsf3

#               define sub              __subsf3

#               define multiply         __mulsf3

#               define divide           __divsf3

#               define compare          __cmpsf2

#               define _eq_f2           __eqsf2

#               define _ne_f2           __nesf2

#               define _gt_f2           __gtsf2

#               define _ge_f2           __gesf2

#               define _lt_f2           __ltsf2

#               define _le_f2           __lesf2

#               define si_to_float      __floatsisf

#               define float_to_si      __fixsfsi

#               define float_to_usi     __fixunssfsi

#               define negate           __negsf2

#               define sf_to_df         __extendsfdf2

#else

#               define add              __adddf3

#               define sub              __subdf3

#               define multiply         __muldf3

#               define divide           __divdf3

#               define compare          __cmpdf2

#               define _eq_f2           __eqdf2

#               define _ne_f2           __nedf2

#               define _gt_f2           __gtdf2

#               define _ge_f2           __gedf2

#               define _lt_f2           __ltdf2

#               define _le_f2           __ledf2

#               define si_to_float      __floatsidf

#               define float_to_si      __fixdfsi

#               define float_to_usi     __fixunsdfsi

#               define negate           __negdf2

#               define df_to_sf         __truncdfsf2

#       endif

#endif

#ifndef INLINE

#define INLINE __inline__

#endif

/* Preserve the sticky-bit when shifting fractions to the right.  */

#define LSHIFT(a) { a = (a & 1) | (a >> 1); }

/* numeric parameters */

/* F_D_BITOFF is the number of bits offset between the MSB of the mantissa

   of a float and of a double. Assumes there are only two float types.

   (double::FRAC_BITS+double::NGARGS-(float::FRAC_BITS-float::NGARDS))

 */

#define F_D_BITOFF (52+8-(23+7))

#define NORMAL_EXPMIN (-(EXPBIAS)+1)

#define IMPLICIT_1 (1LL<<(FRACBITS+NGARDS))

#define IMPLICIT_2 (1LL<<(FRACBITS+1+NGARDS))

/* common types */

typedef enum

{

  CLASS_SNAN,

  CLASS_QNAN,

  CLASS_ZERO,

  CLASS_NUMBER,

  CLASS_INFINITY

} fp_class_type;

typedef struct

{

#ifdef SMALL_MACHINE

  char class;

  unsigned char sign;

  short normal_exp;

#else

  fp_class_type class;

  unsigned int sign;

  int normal_exp;

#endif

  union

    {

      fractype ll;

      halffractype l[2];

    } fraction;

} fp_number_type;

typedef union

{

  FLO_type value;

#ifdef _DEBUG_BITFLOAT

  int l[2];

#endif

  struct

    {

#ifndef FLOAT_BIT_ORDER_MISMATCH

      unsigned int sign:1 __attribute__ ((packed));

      unsigned int exp:EXPBITS __attribute__ ((packed));

      fractype fraction:FRACBITS __attribute__ ((packed));

#else

      fractype fraction:FRACBITS __attribute__ ((packed));

      unsigned int exp:EXPBITS __attribute__ ((packed));

      unsigned int sign:1 __attribute__ ((packed));

#endif

    }

  bits;

}

FLO_union_type;

/* end of header */

/* IEEE "special" number predicates */

#ifdef NO_NANS

#define nan() 0

#define isnan(x) 0

#define isinf(x) 0

#else

INLINE

static fp_number_type *

nan ()

{

  static fp_number_type thenan;

  return &thenan;

}

INLINE

static int

isnan ( fp_number_type *  x)

{

  return x->class == CLASS_SNAN || x->class == CLASS_QNAN;

}

INLINE

static int

isinf ( fp_number_type *  x)

{

  return x->class == CLASS_INFINITY;

}

#endif

INLINE

static int

iszero ( fp_number_type *  x)

{

  return x->class == CLASS_ZERO;

}

INLINE

static void

flip_sign ( fp_number_type *  x)

{

  x->sign = !x->sign;

}

static FLO_type

pack_d ( fp_number_type *  src)

{

  FLO_union_type dst;

  fractype fraction = src->fraction.ll; /* wasn't unsigned before? */

  dst.bits.sign = src->sign;

  if (isnan (src))

    {

      dst.bits.exp = EXPMAX;

      dst.bits.fraction = src->fraction.ll;

      if (src->class == CLASS_QNAN || 1)

        {

          dst.bits.fraction |= QUIET_NAN;

        }

    }

  else if (isinf (src))

    {

      dst.bits.exp = EXPMAX;

      dst.bits.fraction = 0;

    }

  else if (iszero (src))

    {

      dst.bits.exp = 0;

      dst.bits.fraction = 0;

    }

  else if (fraction == 0)

    {

      dst.value = 0;

    }

  else

    {

      if (src->normal_exp < NORMAL_EXPMIN)

        {

          /* 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;

          dst.bits.exp = 0;

          if (shift > FRAC_NBITS - NGARDS)

            {

              /* No point shifting, since it's more that 64 out.  */

              fraction = 0;

            }

          else

            {

              /* Shift by the value */

              fraction >>= shift;

            }

          fraction >>= NGARDS;

          dst.bits.fraction = fraction;

        }

      else if (src->normal_exp > EXPBIAS)

        {

          dst.bits.exp = EXPMAX;

          dst.bits.fraction = 0;

        }

      else

        {

          dst.bits.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;

              dst.bits.exp += 1;

            }

          fraction >>= NGARDS;

          dst.bits.fraction = fraction;

        }

    }

  return dst.value;

}

static void

unpack_d (FLO_union_type * src, fp_number_type * dst)

{

  fractype fraction = src->bits.fraction;

  dst->sign = src->bits.sign;

  if (src->bits.exp == 0)

    {

      /* Hmm.  Looks like 0 */

      if (fraction == 0)

        {

          /* tastes like zero */

          dst->class = CLASS_ZERO;

        }

      else

        {

          /* Zero exponent with non zero fraction - it's denormalized,

             so there isn't a leading implicit one - we'll shift it so

             it gets one.  */

          dst->normal_exp = src->bits.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 (src->bits.exp == EXPMAX)

    {

      /* Huge exponent*/

      if (fraction == 0)

        {

          /* Attached to a zero fraction - means infinity */

          dst->class = CLASS_INFINITY;

        }

      else

        {

          /* Non zero fraction, means nan */

          if (dst->sign)

            {

              dst->class = CLASS_SNAN;

            }

          else

            {

              dst->class = CLASS_QNAN;

            }

          /* Keep the fraction part as the nan number */

          dst->fraction.ll = fraction;

        }

    }

  else

    {

      /* Nothing strange about this number */

      dst->normal_exp = src->bits.exp - EXPBIAS;

      dst->class = CLASS_NUMBER;

      dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1;

    }

}

static 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 nan ();

      return a;

    }

  if (isinf (b))

    {

      return b;

    }

  if (iszero (b))

    {

      return a;

    }

  if (iszero (a))

    {

      return b;

    }

  /* Got two numbers. shift the smaller and increment the exponent till

     they're the same */

  {

    int diff;

    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;

    if (diff < 0)

      diff = -diff;

    if (diff < FRAC_NBITS)

      {

        /* ??? This does shifts one bit at a time.  Optimize.  */

        while (a_normal_exp > b_normal_exp)

          {

            b_normal_exp++;

            LSHIFT (b_fraction);

          }

        while (b_normal_exp > a_normal_exp)

          {

            a_normal_exp++;

            LSHIFT (a_fraction);

          }

      }

    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);

      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;

  fp_number_type *res;

  unpack_d ((FLO_union_type *) & arg_a, &a);

  unpack_d ((FLO_union_type *) & arg_b, &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;

  fp_number_type *res;

  unpack_d ((FLO_union_type *) & arg_a, &a);

  unpack_d ((FLO_union_type *) & arg_b, &b);

  b.sign ^= 1;

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

  return pack_d (res);

}

static 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 nan ();

      a->sign = a->sign != b->sign;

      return a;

    }

  if (isinf (b))

    {

      if (iszero (a))

        {

          return nan ();

        }

      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 64bit numbers to get a

     128 bit number */

  {

    fractype x = a->fraction.ll;

    fractype ylow = b->fraction.ll;

    fractype yhigh = 0;

    int bit;

#if defined(NO_DI_MODE)

    {

      /* ??? 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 32 bit numbers to get a 64 bit number  on

        a machine with DI, so we're safe */

      DItype answer = (DItype)(a->fraction.ll) * (DItype)(b->fraction.ll);

      high = answer >> 32;

      low = answer;

    }

#else

    /* Doing a 64*64 to 128 */

    {

      UDItype nl = a->fraction.ll & 0xffffffff;

      UDItype nh = a->fraction.ll >> 32;

      UDItype ml = b->fraction.ll & 0xffffffff;

      UDItype mh = b->fraction.ll >>32;

      UDItype pp_ll = ml * nl;

      UDItype pp_hl = mh * nl;

      UDItype pp_lh = ml * nh;

      UDItype pp_hh = mh * nh;

      UDItype res2 = 0;

      UDItype res0 = 0;

      UDItype ps_hh__ = pp_hl + pp_lh;

      if (ps_hh__ < pp_hl)