FreeBSD/Linux Kernel Cross Reference
sys/lib/libkern/softfloat.c

     /* $NetBSD: softfloat.c,v 1.3 2003/12/04 13:57:31 keihan Exp $ */
     
     /*
      * This version hacked for use with gcc -msoft-float by bjh21.
      * (Mostly a case of #ifdefing out things GCC doesn't need or provides
      *  itself).
      */
     
     /*
     * Things you may want to define:
     *
     * SOFTFLOAT_FOR_GCC - build only those functions necessary for GCC (with
     *   -msoft-float) to work.  Include "softfloat-for-gcc.h" to get them
     *   properly renamed.
     */
    
    /*
    ===============================================================================
    
    This C source file is part of the SoftFloat IEC/IEEE Floating-point
    Arithmetic Package, Release 2a.
    
    Written by John R. Hauser.  This work was made possible in part by the
    International Computer Science Institute, located at Suite 600, 1947 Center
    Street, Berkeley, California 94704.  Funding was partially provided by the
    National Science Foundation under grant MIP-9311980.  The original version
    of this code was written as part of a project to build a fixed-point vector
    processor in collaboration with the University of California at Berkeley,
    overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
    is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
    arithmetic/SoftFloat.html'.
    
    THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort
    has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
    TIMES RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO
    PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
    AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
    
    Derivative works are acceptable, even for commercial purposes, so long as
    (1) they include prominent notice that the work is derivative, and (2) they
    include prominent notice akin to these four paragraphs for those parts of
    this code that are retained.
    
    ===============================================================================
    */
    
    /* If you need this in a boot program, you have bigger problems... */
    #ifndef _STANDALONE
    
    #include <sys/cdefs.h>
    #if defined(LIBC_SCCS) && !defined(lint)
    __RCSID("$NetBSD: softfloat.c,v 1.3 2003/12/04 13:57:31 keihan Exp $");
    #endif /* LIBC_SCCS and not lint */
    
    #ifdef SOFTFLOAT_FOR_GCC
    #include "softfloat-for-gcc.h"
    #endif
    
    #include "milieu.h"
    #include "softfloat.h"
    
    /*
     * Conversions between floats as stored in memory and floats as
     * SoftFloat uses them
     */
    #ifndef FLOAT64_DEMANGLE
    #define FLOAT64_DEMANGLE(a)     (a)
    #endif
    #ifndef FLOAT64_MANGLE
    #define FLOAT64_MANGLE(a)       (a)
    #endif
    
    /*
    -------------------------------------------------------------------------------
    Floating-point rounding mode, extended double-precision rounding precision,
    and exception flags.
    -------------------------------------------------------------------------------
    */
    
    /*
     * XXX: This may cause options-MULTIPROCESSOR or thread problems someday.
     *      Right now, it does not.  I've removed all other dynamic global
     *      variables. [ross]
     */
    #ifdef FLOATX80
    int8 floatx80_rounding_precision = 80;
    #endif
    
    /*
    -------------------------------------------------------------------------------
    Primitive arithmetic functions, including multi-word arithmetic, and
    division and square root approximations.  (Can be specialized to target if
    desired.)
    -------------------------------------------------------------------------------
    */
    #include "softfloat-macros.h"
    
    /*
    -------------------------------------------------------------------------------
   Functions and definitions to determine:  (1) whether tininess for underflow
   is detected before or after rounding by default, (2) what (if anything)
   happens when exceptions are raised, (3) how signaling NaNs are distinguished
   from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs
   are propagated from function inputs to output.  These details are target-
   specific.
   -------------------------------------------------------------------------------
   */
   #include "softfloat-specialize.h"
   
   #ifndef SOFTFLOAT_FOR_GCC /* Not used */
   /*
   -------------------------------------------------------------------------------
   Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
   and 7, and returns the properly rounded 32-bit integer corresponding to the
   input.  If `zSign' is 1, the input is negated before being converted to an
   integer.  Bit 63 of `absZ' must be zero.  Ordinarily, the fixed-point input
   is simply rounded to an integer, with the inexact exception raised if the
   input cannot be represented exactly as an integer.  However, if the fixed-
   point input is too large, the invalid exception is raised and the largest
   positive or negative integer is returned.
   -------------------------------------------------------------------------------
   */
   static int32 roundAndPackInt32( flag zSign, bits64 absZ )
   {
       int8 roundingMode;
       flag roundNearestEven;
       int8 roundIncrement, roundBits;
       int32 z;
   
       roundingMode = float_rounding_mode();
       roundNearestEven = ( roundingMode == float_round_nearest_even );
       roundIncrement = 0x40;
       if ( ! roundNearestEven ) {
           if ( roundingMode == float_round_to_zero ) {
               roundIncrement = 0;
           }
           else {
               roundIncrement = 0x7F;
               if ( zSign ) {
                   if ( roundingMode == float_round_up ) roundIncrement = 0;
               }
               else {
                   if ( roundingMode == float_round_down ) roundIncrement = 0;
               }
           }
       }
       roundBits = absZ & 0x7F;
       absZ = ( absZ + roundIncrement )>>7;
       absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
       z = absZ;
       if ( zSign ) z = - z;
       if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
           float_raise( float_flag_invalid );
           return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
       }
       if ( roundBits ) float_set_inexact();
       return z;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
   `absZ1', with binary point between bits 63 and 64 (between the input words),
   and returns the properly rounded 64-bit integer corresponding to the input.
   If `zSign' is 1, the input is negated before being converted to an integer.
   Ordinarily, the fixed-point input is simply rounded to an integer, with
   the inexact exception raised if the input cannot be represented exactly as
   an integer.  However, if the fixed-point input is too large, the invalid
   exception is raised and the largest positive or negative integer is
   returned.
   -------------------------------------------------------------------------------
   */
   static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 )
   {
       int8 roundingMode;
       flag roundNearestEven, increment;
       int64 z;
   
       roundingMode = float_rounding_mode();
       roundNearestEven = ( roundingMode == float_round_nearest_even );
       increment = ( (sbits64) absZ1 < 0 );
       if ( ! roundNearestEven ) {
           if ( roundingMode == float_round_to_zero ) {
               increment = 0;
           }
           else {
               if ( zSign ) {
                   increment = ( roundingMode == float_round_down ) && absZ1;
               }
               else {
                   increment = ( roundingMode == float_round_up ) && absZ1;
               }
           }
       }
       if ( increment ) {
           ++absZ0;
           if ( absZ0 == 0 ) goto overflow;
           absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven );
       }
       z = absZ0;
       if ( zSign ) z = - z;
       if ( z && ( ( z < 0 ) ^ zSign ) ) {
    overflow:
           float_raise( float_flag_invalid );
           return
                 zSign ? (sbits64) LIT64( 0x8000000000000000 )
               : LIT64( 0x7FFFFFFFFFFFFFFF );
       }
       if ( absZ1 ) float_set_inexact();
       return z;
   
   }
   #endif
   
   /*
   -------------------------------------------------------------------------------
   Returns the fraction bits of the single-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE bits32 extractFloat32Frac( float32 a )
   {
   
       return a & 0x007FFFFF;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the exponent bits of the single-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE int16 extractFloat32Exp( float32 a )
   {
   
       return ( a>>23 ) & 0xFF;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the sign bit of the single-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE flag extractFloat32Sign( float32 a )
   {
   
       return a>>31;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Normalizes the subnormal single-precision floating-point value represented
   by the denormalized significand `aSig'.  The normalized exponent and
   significand are stored at the locations pointed to by `zExpPtr' and
   `zSigPtr', respectively.
   -------------------------------------------------------------------------------
   */
   static void
    normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
   {
       int8 shiftCount;
   
       shiftCount = countLeadingZeros32( aSig ) - 8;
       *zSigPtr = aSig<<shiftCount;
       *zExpPtr = 1 - shiftCount;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
   single-precision floating-point value, returning the result.  After being
   shifted into the proper positions, the three fields are simply added
   together to form the result.  This means that any integer portion of `zSig'
   will be added into the exponent.  Since a properly normalized significand
   will have an integer portion equal to 1, the `zExp' input should be 1 less
   than the desired result exponent whenever `zSig' is a complete, normalized
   significand.
   -------------------------------------------------------------------------------
   */
   INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
   {
   
       return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent `zExp',
   and significand `zSig', and returns the proper single-precision floating-
   point value corresponding to the abstract input.  Ordinarily, the abstract
   value is simply rounded and packed into the single-precision format, with
   the inexact exception raised if the abstract input cannot be represented
   exactly.  However, if the abstract value is too large, the overflow and
   inexact exceptions are raised and an infinity or maximal finite value is
   returned.  If the abstract value is too small, the input value is rounded to
   a subnormal number, and the underflow and inexact exceptions are raised if
   the abstract input cannot be represented exactly as a subnormal single-
   precision floating-point number.
       The input significand `zSig' has its binary point between bits 30
   and 29, which is 7 bits to the left of the usual location.  This shifted
   significand must be normalized or smaller.  If `zSig' is not normalized,
   `zExp' must be 0; in that case, the result returned is a subnormal number,
   and it must not require rounding.  In the usual case that `zSig' is
   normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
   The handling of underflow and overflow follows the IEC/IEEE Standard for
   Binary Floating-Point Arithmetic.
   -------------------------------------------------------------------------------
   */
   static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
   {
       int8 roundingMode;
       flag roundNearestEven;
       int8 roundIncrement, roundBits;
       flag isTiny;
   
       roundingMode = float_rounding_mode();
       roundNearestEven = ( roundingMode == float_round_nearest_even );
       roundIncrement = 0x40;
       if ( ! roundNearestEven ) {
           if ( roundingMode == float_round_to_zero ) {
               roundIncrement = 0;
           }
           else {
               roundIncrement = 0x7F;
               if ( zSign ) {
                   if ( roundingMode == float_round_up ) roundIncrement = 0;
               }
               else {
                   if ( roundingMode == float_round_down ) roundIncrement = 0;
               }
           }
       }
       roundBits = zSig & 0x7F;
       if ( 0xFD <= (bits16) zExp ) {
           if (    ( 0xFD < zExp )
                || (    ( zExp == 0xFD )
                     && ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
              ) {
               float_raise( float_flag_overflow | float_flag_inexact );
               return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
           }
           if ( zExp < 0 ) {
               isTiny =
                      ( float_detect_tininess == float_tininess_before_rounding )
                   || ( zExp < -1 )
                   || ( zSig + roundIncrement < 0x80000000 );
               shift32RightJamming( zSig, - zExp, &zSig );
               zExp = 0;
               roundBits = zSig & 0x7F;
               if ( isTiny && roundBits ) float_raise( float_flag_underflow );
           }
       }
       if ( roundBits ) float_set_inexact();
       zSig = ( zSig + roundIncrement )>>7;
       zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
       if ( zSig == 0 ) zExp = 0;
       return packFloat32( zSign, zExp, zSig );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent `zExp',
   and significand `zSig', and returns the proper single-precision floating-
   point value corresponding to the abstract input.  This routine is just like
   `roundAndPackFloat32' except that `zSig' does not have to be normalized.
   Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
   floating-point exponent.
   -------------------------------------------------------------------------------
   */
   static float32
    normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
   {
       int8 shiftCount;
   
       shiftCount = countLeadingZeros32( zSig ) - 1;
       return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the fraction bits of the double-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE bits64 extractFloat64Frac( float64 a )
   {
   
       return FLOAT64_DEMANGLE(a) & LIT64( 0x000FFFFFFFFFFFFF );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the exponent bits of the double-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE int16 extractFloat64Exp( float64 a )
   {
   
       return ( FLOAT64_DEMANGLE(a)>>52 ) & 0x7FF;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the sign bit of the double-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE flag extractFloat64Sign( float64 a )
   {
   
       return FLOAT64_DEMANGLE(a)>>63;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Normalizes the subnormal double-precision floating-point value represented
   by the denormalized significand `aSig'.  The normalized exponent and
   significand are stored at the locations pointed to by `zExpPtr' and
   `zSigPtr', respectively.
   -------------------------------------------------------------------------------
   */
   static void
    normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr )
   {
       int8 shiftCount;
   
       shiftCount = countLeadingZeros64( aSig ) - 11;
       *zSigPtr = aSig<<shiftCount;
       *zExpPtr = 1 - shiftCount;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
   double-precision floating-point value, returning the result.  After being
   shifted into the proper positions, the three fields are simply added
   together to form the result.  This means that any integer portion of `zSig'
   will be added into the exponent.  Since a properly normalized significand
   will have an integer portion equal to 1, the `zExp' input should be 1 less
   than the desired result exponent whenever `zSig' is a complete, normalized
   significand.
   -------------------------------------------------------------------------------
   */
   INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
   {
   
       return FLOAT64_MANGLE( ( ( (bits64) zSign )<<63 ) +
                              ( ( (bits64) zExp )<<52 ) + zSig );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent `zExp',
   and significand `zSig', and returns the proper double-precision floating-
   point value corresponding to the abstract input.  Ordinarily, the abstract
   value is simply rounded and packed into the double-precision format, with
   the inexact exception raised if the abstract input cannot be represented
   exactly.  However, if the abstract value is too large, the overflow and
   inexact exceptions are raised and an infinity or maximal finite value is
   returned.  If the abstract value is too small, the input value is rounded to
   a subnormal number, and the underflow and inexact exceptions are raised if
   the abstract input cannot be represented exactly as a subnormal double-
   precision floating-point number.
       The input significand `zSig' has its binary point between bits 62
   and 61, which is 10 bits to the left of the usual location.  This shifted
   significand must be normalized or smaller.  If `zSig' is not normalized,
   `zExp' must be 0; in that case, the result returned is a subnormal number,
   and it must not require rounding.  In the usual case that `zSig' is
   normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
   The handling of underflow and overflow follows the IEC/IEEE Standard for
   Binary Floating-Point Arithmetic.
   -------------------------------------------------------------------------------
   */
   static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig )
   {
       int8 roundingMode;
       flag roundNearestEven;
       int16 roundIncrement, roundBits;
       flag isTiny;
   
       roundingMode = float_rounding_mode();
       roundNearestEven = ( roundingMode == float_round_nearest_even );
       roundIncrement = 0x200;
       if ( ! roundNearestEven ) {
           if ( roundingMode == float_round_to_zero ) {
               roundIncrement = 0;
           }
           else {
               roundIncrement = 0x3FF;
               if ( zSign ) {
                   if ( roundingMode == float_round_up ) roundIncrement = 0;
               }
               else {
                   if ( roundingMode == float_round_down ) roundIncrement = 0;
               }
           }
       }
       roundBits = zSig & 0x3FF;
       if ( 0x7FD <= (bits16) zExp ) {
           if (    ( 0x7FD < zExp )
                || (    ( zExp == 0x7FD )
                     && ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
              ) {
               float_raise( float_flag_overflow | float_flag_inexact );
               return FLOAT64_MANGLE(
                   FLOAT64_DEMANGLE(packFloat64( zSign, 0x7FF, 0 )) -
                   ( roundIncrement == 0 ));
           }
           if ( zExp < 0 ) {
               isTiny =
                      ( float_detect_tininess == float_tininess_before_rounding )
                   || ( zExp < -1 )
                   || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
               shift64RightJamming( zSig, - zExp, &zSig );
               zExp = 0;
               roundBits = zSig & 0x3FF;
               if ( isTiny && roundBits ) float_raise( float_flag_underflow );
           }
       }
       if ( roundBits ) float_set_inexact();
       zSig = ( zSig + roundIncrement )>>10;
       zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
       if ( zSig == 0 ) zExp = 0;
       return packFloat64( zSign, zExp, zSig );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent `zExp',
   and significand `zSig', and returns the proper double-precision floating-
   point value corresponding to the abstract input.  This routine is just like
   `roundAndPackFloat64' except that `zSig' does not have to be normalized.
   Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
   floating-point exponent.
   -------------------------------------------------------------------------------
   */
   static float64
    normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig )
   {
       int8 shiftCount;
   
       shiftCount = countLeadingZeros64( zSig ) - 1;
       return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount );
   
   }
   
   #ifdef FLOATX80
   
   /*
   -------------------------------------------------------------------------------
   Returns the fraction bits of the extended double-precision floating-point
   value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE bits64 extractFloatx80Frac( floatx80 a )
   {
   
       return a.low;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the exponent bits of the extended double-precision floating-point
   value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE int32 extractFloatx80Exp( floatx80 a )
   {
   
       return a.high & 0x7FFF;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the sign bit of the extended double-precision floating-point value
   `a'.
   -------------------------------------------------------------------------------
   */
   INLINE flag extractFloatx80Sign( floatx80 a )
   {
   
       return a.high>>15;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Normalizes the subnormal extended double-precision floating-point value
   represented by the denormalized significand `aSig'.  The normalized exponent
   and significand are stored at the locations pointed to by `zExpPtr' and
   `zSigPtr', respectively.
   -------------------------------------------------------------------------------
   */
   static void
    normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
   {
       int8 shiftCount;
   
       shiftCount = countLeadingZeros64( aSig );
       *zSigPtr = aSig<<shiftCount;
       *zExpPtr = 1 - shiftCount;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
   extended double-precision floating-point value, returning the result.
   -------------------------------------------------------------------------------
   */
   INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
   {
       floatx80 z;
   
       z.low = zSig;
       z.high = ( ( (bits16) zSign )<<15 ) + zExp;
       return z;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent `zExp',
   and extended significand formed by the concatenation of `zSig0' and `zSig1',
   and returns the proper extended double-precision floating-point value
   corresponding to the abstract input.  Ordinarily, the abstract value is
   rounded and packed into the extended double-precision format, with the
   inexact exception raised if the abstract input cannot be represented
   exactly.  However, if the abstract value is too large, the overflow and
   inexact exceptions are raised and an infinity or maximal finite value is
   returned.  If the abstract value is too small, the input value is rounded to
   a subnormal number, and the underflow and inexact exceptions are raised if
   the abstract input cannot be represented exactly as a subnormal extended
   double-precision floating-point number.
       If `roundingPrecision' is 32 or 64, the result is rounded to the same
   number of bits as single or double precision, respectively.  Otherwise, the
   result is rounded to the full precision of the extended double-precision
   format.
       The input significand must be normalized or smaller.  If the input
   significand is not normalized, `zExp' must be 0; in that case, the result
   returned is a subnormal number, and it must not require rounding.  The
   handling of underflow and overflow follows the IEC/IEEE Standard for Binary
   Floating-Point Arithmetic.
   -------------------------------------------------------------------------------
   */
   static floatx80
    roundAndPackFloatx80(
        int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
    )
   {
       int8 roundingMode;
       flag roundNearestEven, increment, isTiny;
       int64 roundIncrement, roundMask, roundBits;
   
       roundingMode = float_rounding_mode();
       roundNearestEven = ( roundingMode == float_round_nearest_even );
       if ( roundingPrecision == 80 ) goto precision80;
       if ( roundingPrecision == 64 ) {
           roundIncrement = LIT64( 0x0000000000000400 );
           roundMask = LIT64( 0x00000000000007FF );
       }
       else if ( roundingPrecision == 32 ) {
           roundIncrement = LIT64( 0x0000008000000000 );
           roundMask = LIT64( 0x000000FFFFFFFFFF );
       }
       else {
           goto precision80;
       }
       zSig0 |= ( zSig1 != 0 );
       if ( ! roundNearestEven ) {
           if ( roundingMode == float_round_to_zero ) {
               roundIncrement = 0;
           }
           else {
               roundIncrement = roundMask;
               if ( zSign ) {
                   if ( roundingMode == float_round_up ) roundIncrement = 0;
               }
               else {
                   if ( roundingMode == float_round_down ) roundIncrement = 0;
               }
           }
       }
       roundBits = zSig0 & roundMask;
       if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
           if (    ( 0x7FFE < zExp )
                || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
              ) {
               goto overflow;
           }
           if ( zExp <= 0 ) {
               isTiny =
                      ( float_detect_tininess == float_tininess_before_rounding )
                   || ( zExp < 0 )
                   || ( zSig0 <= zSig0 + roundIncrement );
               shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
               zExp = 0;
               roundBits = zSig0 & roundMask;
               if ( isTiny && roundBits ) float_raise( float_flag_underflow );
               if ( roundBits ) float_set_inexact();
               zSig0 += roundIncrement;
               if ( (sbits64) zSig0 < 0 ) zExp = 1;
               roundIncrement = roundMask + 1;
               if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
                   roundMask |= roundIncrement;
               }
               zSig0 &= ~ roundMask;
               return packFloatx80( zSign, zExp, zSig0 );
           }
       }
       if ( roundBits ) float_set_inexact();
       zSig0 += roundIncrement;
       if ( zSig0 < roundIncrement ) {
           ++zExp;
           zSig0 = LIT64( 0x8000000000000000 );
       }
       roundIncrement = roundMask + 1;
       if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
           roundMask |= roundIncrement;
       }
       zSig0 &= ~ roundMask;
       if ( zSig0 == 0 ) zExp = 0;
       return packFloatx80( zSign, zExp, zSig0 );
    precision80:
       increment = ( (sbits64) zSig1 < 0 );
       if ( ! roundNearestEven ) {
           if ( roundingMode == float_round_to_zero ) {
               increment = 0;
           }
           else {
               if ( zSign ) {
                   increment = ( roundingMode == float_round_down ) && zSig1;
               }
               else {
                   increment = ( roundingMode == float_round_up ) && zSig1;
               }
           }
       }
       if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
           if (    ( 0x7FFE < zExp )
                || (    ( zExp == 0x7FFE )
                     && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
                     && increment
                   )
              ) {
               roundMask = 0;
    overflow:
               float_raise( float_flag_overflow | float_flag_inexact );
               if (    ( roundingMode == float_round_to_zero )
                    || ( zSign && ( roundingMode == float_round_up ) )
                    || ( ! zSign && ( roundingMode == float_round_down ) )
                  ) {
                   return packFloatx80( zSign, 0x7FFE, ~ roundMask );
               }
               return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
           }
           if ( zExp <= 0 ) {
               isTiny =
                      ( float_detect_tininess == float_tininess_before_rounding )
                   || ( zExp < 0 )
                   || ! increment
                   || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
               shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
               zExp = 0;
               if ( isTiny && zSig1 ) float_raise( float_flag_underflow );
               if ( zSig1 ) float_set_inexact();
               if ( roundNearestEven ) {
                   increment = ( (sbits64) zSig1 < 0 );
               }
               else {
                   if ( zSign ) {
                       increment = ( roundingMode == float_round_down ) && zSig1;
                   }
                   else {
                       increment = ( roundingMode == float_round_up ) && zSig1;
                   }
               }
               if ( increment ) {
                   ++zSig0;
                   zSig0 &=
                       ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
                   if ( (sbits64) zSig0 < 0 ) zExp = 1;
               }
               return packFloatx80( zSign, zExp, zSig0 );
           }
       }
       if ( zSig1 ) float_set_inexact();
       if ( increment ) {
           ++zSig0;
           if ( zSig0 == 0 ) {
               ++zExp;
               zSig0 = LIT64( 0x8000000000000000 );
           }
           else {
               zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
           }
       }
       else {
           if ( zSig0 == 0 ) zExp = 0;
       }
       return packFloatx80( zSign, zExp, zSig0 );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent
   `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
   and returns the proper extended double-precision floating-point value
   corresponding to the abstract input.  This routine is just like
   `roundAndPackFloatx80' except that the input significand does not have to be
   normalized.
   -------------------------------------------------------------------------------
   */
   static floatx80
    normalizeRoundAndPackFloatx80(
        int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
    )
   {
       int8 shiftCount;
   
       if ( zSig0 == 0 ) {
           zSig0 = zSig1;
           zSig1 = 0;
           zExp -= 64;
       }
       shiftCount = countLeadingZeros64( zSig0 );
       shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
       zExp -= shiftCount;
       return
           roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 );
   
   }
   
   #endif
   
   #ifdef FLOAT128
   
   /*
   -------------------------------------------------------------------------------
   Returns the least-significant 64 fraction bits of the quadruple-precision
   floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE bits64 extractFloat128Frac1( float128 a )
   {
   
       return a.low;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the most-significant 48 fraction bits of the quadruple-precision
   floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE bits64 extractFloat128Frac0( float128 a )
   {
   
       return a.high & LIT64( 0x0000FFFFFFFFFFFF );
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the exponent bits of the quadruple-precision floating-point value
   `a'.
   -------------------------------------------------------------------------------
   */
   INLINE int32 extractFloat128Exp( float128 a )
   {
   
       return ( a.high>>48 ) & 0x7FFF;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Returns the sign bit of the quadruple-precision floating-point value `a'.
   -------------------------------------------------------------------------------
   */
   INLINE flag extractFloat128Sign( float128 a )
   {
   
       return a.high>>63;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Normalizes the subnormal quadruple-precision floating-point value
   represented by the denormalized significand formed by the concatenation of
   `aSig0' and `aSig1'.  The normalized exponent is stored at the location
   pointed to by `zExpPtr'.  The most significant 49 bits of the normalized
   significand are stored at the location pointed to by `zSig0Ptr', and the
   least significant 64 bits of the normalized significand are stored at the
   location pointed to by `zSig1Ptr'.
   -------------------------------------------------------------------------------
   */
   static void
    normalizeFloat128Subnormal(
        bits64 aSig0,
        bits64 aSig1,
        int32 *zExpPtr,
        bits64 *zSig0Ptr,
        bits64 *zSig1Ptr
    )
   {
       int8 shiftCount;
   
       if ( aSig0 == 0 ) {
           shiftCount = countLeadingZeros64( aSig1 ) - 15;
           if ( shiftCount < 0 ) {
               *zSig0Ptr = aSig1>>( - shiftCount );
               *zSig1Ptr = aSig1<<( shiftCount & 63 );
           }
           else {
               *zSig0Ptr = aSig1<<shiftCount;
               *zSig1Ptr = 0;
           }
           *zExpPtr = - shiftCount - 63;
       }
       else {
           shiftCount = countLeadingZeros64( aSig0 ) - 15;
           shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
           *zExpPtr = 1 - shiftCount;
       }
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Packs the sign `zSign', the exponent `zExp', and the significand formed
   by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
   floating-point value, returning the result.  After being shifted into the
   proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
   added together to form the most significant 32 bits of the result.  This
   means that any integer portion of `zSig0' will be added into the exponent.
   Since a properly normalized significand will have an integer portion equal
   to 1, the `zExp' input should be 1 less than the desired result exponent
   whenever `zSig0' and `zSig1' concatenated form a complete, normalized
   significand.
   -------------------------------------------------------------------------------
   */
   INLINE float128
    packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
   {
       float128 z;
   
       z.low = zSig1;
       z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0;
       return z;
   
   }
   
   /*
   -------------------------------------------------------------------------------
   Takes an abstract floating-point value having sign `zSign', exponent `zExp',
   and extended significand formed by the concatenation of `zSig0', `zSig1',
   and `zSig2', and returns the proper quadruple-precision floating-point value
   corresponding to the abstract input.  Ordinarily, the abstract value is
   simply rounded and packed into the quadruple-precision format, with the
   inexact exception raised if the abstract input cannot be represented
   exactly.  However, if the abstract value is too large, the overflow and
   inexact exceptions are raised and an infinity or maximal finite value is
   returned.  If the abstract value is too small, the input value is rounded to
   a subnormal number, and the underflow and inexact exceptions are raised if
   the abstract input cannot be represented exactly as a subnormal quadruple-
   precision floating-point number.
       The input significand must be normalized or smaller.  If the input
   significand is not normalized, `zExp' must be 0; in that case, the result
   returned is a subnormal number, and it must not require rounding.  In the
   usual case that the input significand is normalized, `zExp' must be 1 less
   than the ``true'' floating-point exponent.  The handling of underflow and
   overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
   -------------------------------------------------------------------------------
   */
   static float128
    roundAndPackFloat128(
        flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 )
   {
       int8 roundingMode;
       flag roundNearestEven, increment, isTiny;
   
       roundingMode = float_rounding_mode();
       roundNearestEven = ( roundingMode == float_round_nearest_even );
      increment = ( (sbits64) zSig2 < 0 );
      if ( ! roundNearestEven ) {
          if ( roundingMode == float_round_to_zero ) {
              increment = 0;
          }
          else {
              if ( zSign ) {
                  increment = ( roundingMode == float_round_down ) && zSig2;
              }
              else {
                  increment = ( roundingMode == float_round_up ) && zSig2;
              }
          }
      }
      if ( 0x7FFD <= (bits32) zExp ) {
          if (    ( 0x7FFD < zExp )
               || (    ( zExp == 0x7FFD )
                    && eq128(
                           LIT64( 0x0001FFFFFFFFFFFF ),
                           LIT64( 0xFFFFFFFFFFFFFFFF ),
                           zSig0,
                           zSig1
                       )
                    && increment
                  )
             ) {
              float_raise( float_flag_overflow | float_flag_inexact );
              if (    ( roundingMode == float_round_to_zero )
                   || ( zSign && ( roundingMode == float_round_up ) )
                   || ( ! zSign && ( roundingMode == float_round_down ) )
                 ) {
                  return
                      packFloat128(
                          zSign,
                          0x7FFE,
                          LIT64( 0x0000FFFFFFFFFFFF ),
                          LIT64( 0xFFFFFFFFFFFFFFFF )
                      );
              }
              return packFloat128( zSign, 0x7FFF, 0, 0 );
          }
          if ( zExp < 0 ) {
              isTiny =
                     ( float_detect_tininess == float_tininess_before_rounding )
                  || ( zExp < -1 )
                  || ! increment
                  || lt128(
                         zSig0,
                         zSig1,
                         LIT64( 0x0001FFFFFFFFFFFF ),
                         LIT64( 0xFFFFFFFFFFFFFFFF )
                     );
              shift128ExtraRightJamming(
                  zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
              zExp = 0;
              if ( isTiny && zSig2 ) float_raise( float_flag_underflow );
              if ( roundNearestEven ) {
                  increment = ( (sbits64) zSig2 < 0 );
              }
              else {
                  if ( zSign ) {
                      increment = ( roundingMode == float_round_down ) && zSig2;
                  }
                  else {
                      increment = ( roundingMode == float_round_up ) && zSig2;
                  }
              }
          }
      }
      if ( zSig2 ) float_set_inexact();
      if ( increment ) {
          add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
          zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
      }
      else {
          if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
      }
      return packFloat128( zSign, zExp, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Takes an abstract floating-point value having sign `zSign', exponent `zExp',
  and significand formed by the concatenation of `zSig0' and `zSig1', and
  returns the proper quadruple-precision floating-point value corresponding
  to the abstract input.  This routine is just like `roundAndPackFloat128'
  except that the input significand has fewer bits and does not have to be
  normalized.  In all cases, `zExp' must be 1 less than the ``true'' floating-
  point exponent.
  -------------------------------------------------------------------------------
  */
  static float128
   normalizeRoundAndPackFloat128(
       flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
  {
      int8 shiftCount;
      bits64 zSig2;
  
      if ( zSig0 == 0 ) {
          zSig0 = zSig1;
          zSig1 = 0;
          zExp -= 64;
      }
      shiftCount = countLeadingZeros64( zSig0 ) - 15;
      if ( 0 <= shiftCount ) {
          zSig2 = 0;
          shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
      }
      else {
          shift128ExtraRightJamming(
              zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
      }
      zExp -= shiftCount;
      return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
  
  }
  
  #endif
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 32-bit two's complement integer `a'
  to the single-precision floating-point format.  The conversion is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 int32_to_float32( int32 a )
  {
      flag zSign;
  
      if ( a == 0 ) return 0;
      if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
      zSign = ( a < 0 );
      return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 32-bit two's complement integer `a'
  to the double-precision floating-point format.  The conversion is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 int32_to_float64( int32 a )
  {
      flag zSign;
      uint32 absA;
      int8 shiftCount;
      bits64 zSig;
  
      if ( a == 0 ) return 0;
      zSign = ( a < 0 );
      absA = zSign ? - a : a;
      shiftCount = countLeadingZeros32( absA ) + 21;
      zSig = absA;
      return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount );
  
  }
  
  #ifdef FLOATX80
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 32-bit two's complement integer `a'
  to the extended double-precision floating-point format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 int32_to_floatx80( int32 a )
  {
      flag zSign;
      uint32 absA;
      int8 shiftCount;
      bits64 zSig;
  
      if ( a == 0 ) return packFloatx80( 0, 0, 0 );
      zSign = ( a < 0 );
      absA = zSign ? - a : a;
      shiftCount = countLeadingZeros32( absA ) + 32;
      zSig = absA;
      return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
  
  }
  
  #endif
  
  #ifdef FLOAT128
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 32-bit two's complement integer `a' to
  the quadruple-precision floating-point format.  The conversion is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 int32_to_float128( int32 a )
  {
      flag zSign;
      uint32 absA;
      int8 shiftCount;
      bits64 zSig0;
  
      if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
      zSign = ( a < 0 );
      absA = zSign ? - a : a;
      shiftCount = countLeadingZeros32( absA ) + 17;
      zSig0 = absA;
      return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 );
  
  }
  
  #endif
  
  #ifndef SOFTFLOAT_FOR_GCC /* __floatdi?f is in libgcc2.c */
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 64-bit two's complement integer `a'
  to the single-precision floating-point format.  The conversion is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 int64_to_float32( int64 a )
  {
      flag zSign;
      uint64 absA;
      int8 shiftCount;
  
      if ( a == 0 ) return 0;
      zSign = ( a < 0 );
      absA = zSign ? - a : a;
      shiftCount = countLeadingZeros64( absA ) - 40;
      if ( 0 <= shiftCount ) {
          return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount );
      }
      else {
          shiftCount += 7;
          if ( shiftCount < 0 ) {
              shift64RightJamming( absA, - shiftCount, &absA );
          }
          else {
              absA <<= shiftCount;
          }
          return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 64-bit two's complement integer `a'
  to the double-precision floating-point format.  The conversion is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 int64_to_float64( int64 a )
  {
      flag zSign;
  
      if ( a == 0 ) return 0;
      if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) {
          return packFloat64( 1, 0x43E, 0 );
      }
      zSign = ( a < 0 );
      return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a );
  
  }
  
  #ifdef FLOATX80
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 64-bit two's complement integer `a'
  to the extended double-precision floating-point format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 int64_to_floatx80( int64 a )
  {
      flag zSign;
      uint64 absA;
      int8 shiftCount;
  
      if ( a == 0 ) return packFloatx80( 0, 0, 0 );
      zSign = ( a < 0 );
      absA = zSign ? - a : a;
      shiftCount = countLeadingZeros64( absA );
      return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount );
  
  }
  
  #endif
  
  #ifdef FLOAT128
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the 64-bit two's complement integer `a' to
  the quadruple-precision floating-point format.  The conversion is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 int64_to_float128( int64 a )
  {
      flag zSign;
      uint64 absA;
      int8 shiftCount;
      int32 zExp;
      bits64 zSig0, zSig1;
  
      if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
      zSign = ( a < 0 );
      absA = zSign ? - a : a;
      shiftCount = countLeadingZeros64( absA ) + 49;
      zExp = 0x406E - shiftCount;
      if ( 64 <= shiftCount ) {
          zSig1 = 0;
          zSig0 = absA;
          shiftCount -= 64;
      }
      else {
          zSig1 = absA;
          zSig0 = 0;
      }
      shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
      return packFloat128( zSign, zExp, zSig0, zSig1 );
  
  }
  
  #endif
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the 32-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic---which means in particular that the conversion is rounded
  according to the current rounding mode.  If `a' is a NaN, the largest
  positive integer is returned.  Otherwise, if the conversion overflows, the
  largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int32 float32_to_int32( float32 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits32 aSig;
      bits64 aSig64;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      if ( ( aExp == 0xFF ) && aSig ) aSign = 0;
      if ( aExp ) aSig |= 0x00800000;
      shiftCount = 0xAF - aExp;
      aSig64 = aSig;
      aSig64 <<= 32;
      if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 );
      return roundAndPackInt32( aSign, aSig64 );
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the 32-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic, except that the conversion is always rounded toward zero.
  If `a' is a NaN, the largest positive integer is returned.  Otherwise, if
  the conversion overflows, the largest integer with the same sign as `a' is
  returned.
  -------------------------------------------------------------------------------
  */
  int32 float32_to_int32_round_to_zero( float32 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits32 aSig;
      int32 z;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      shiftCount = aExp - 0x9E;
      if ( 0 <= shiftCount ) {
          if ( a != 0xCF000000 ) {
              float_raise( float_flag_invalid );
              if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
          }
          return (sbits32) 0x80000000;
      }
      else if ( aExp <= 0x7E ) {
          if ( aExp | aSig ) float_set_inexact();
          return 0;
      }
      aSig = ( aSig | 0x00800000 )<<8;
      z = aSig>>( - shiftCount );
      if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
          float_set_inexact();
      }
      if ( aSign ) z = - z;
      return z;
  
  }
  
  #ifndef SOFTFLOAT_FOR_GCC /* __fix?fdi provided by libgcc2.c */
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the 64-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic---which means in particular that the conversion is rounded
  according to the current rounding mode.  If `a' is a NaN, the largest
  positive integer is returned.  Otherwise, if the conversion overflows, the
  largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int64 float32_to_int64( float32 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits32 aSig;
      bits64 aSig64, aSigExtra;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      shiftCount = 0xBE - aExp;
      if ( shiftCount < 0 ) {
          float_raise( float_flag_invalid );
          if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
              return LIT64( 0x7FFFFFFFFFFFFFFF );
          }
          return (sbits64) LIT64( 0x8000000000000000 );
      }
      if ( aExp ) aSig |= 0x00800000;
      aSig64 = aSig;
      aSig64 <<= 40;
      shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra );
      return roundAndPackInt64( aSign, aSig64, aSigExtra );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the 64-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic, except that the conversion is always rounded toward zero.  If
  `a' is a NaN, the largest positive integer is returned.  Otherwise, if the
  conversion overflows, the largest integer with the same sign as `a' is
  returned.
  -------------------------------------------------------------------------------
  */
  int64 float32_to_int64_round_to_zero( float32 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits32 aSig;
      bits64 aSig64;
      int64 z;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      shiftCount = aExp - 0xBE;
      if ( 0 <= shiftCount ) {
          if ( a != 0xDF000000 ) {
              float_raise( float_flag_invalid );
              if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
                  return LIT64( 0x7FFFFFFFFFFFFFFF );
              }
          }
          return (sbits64) LIT64( 0x8000000000000000 );
      }
      else if ( aExp <= 0x7E ) {
          if ( aExp | aSig ) float_set_inexact();
          return 0;
      }
      aSig64 = aSig | 0x00800000;
      aSig64 <<= 40;
      z = aSig64>>( - shiftCount );
      if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) {
          float_set_inexact();
      }
      if ( aSign ) z = - z;
      return z;
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the double-precision floating-point format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float32_to_float64( float32 a )
  {
      flag aSign;
      int16 aExp;
      bits32 aSig;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      if ( aExp == 0xFF ) {
          if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) );
          return packFloat64( aSign, 0x7FF, 0 );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat64( aSign, 0, 0 );
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
          --aExp;
      }
      return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );
  
  }
  
  #ifdef FLOATX80
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the extended double-precision floating-point format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 float32_to_floatx80( float32 a )
  {
      flag aSign;
      int16 aExp;
      bits32 aSig;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      if ( aExp == 0xFF ) {
          if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) );
          return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
      }
      aSig |= 0x00800000;
      return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );
  
  }
  
  #endif
  
  #ifdef FLOAT128
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the double-precision floating-point format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float32_to_float128( float32 a )
  {
      flag aSign;
      int16 aExp;
      bits32 aSig;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      if ( aExp == 0xFF ) {
          if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a ) );
          return packFloat128( aSign, 0x7FFF, 0, 0 );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
          --aExp;
      }
      return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 );
  
  }
  
  #endif
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Rounds the single-precision floating-point value `a' to an integer, and
  returns the result as a single-precision floating-point value.  The
  operation is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_round_to_int( float32 a )
  {
      flag aSign;
      int16 aExp;
      bits32 lastBitMask, roundBitsMask;
      int8 roundingMode;
      float32 z;
  
      aExp = extractFloat32Exp( a );
      if ( 0x96 <= aExp ) {
          if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
              return propagateFloat32NaN( a, a );
          }
          return a;
      }
      if ( aExp <= 0x7E ) {
          if ( (bits32) ( a<<1 ) == 0 ) return a;
          float_set_inexact();
          aSign = extractFloat32Sign( a );
          switch ( float_rounding_mode() ) {
           case float_round_nearest_even:
              if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
                  return packFloat32( aSign, 0x7F, 0 );
              }
              break;
           case float_round_down:
              return aSign ? 0xBF800000 : 0;
           case float_round_up:
              return aSign ? 0x80000000 : 0x3F800000;
          }
          return packFloat32( aSign, 0, 0 );
      }
      lastBitMask = 1;
      lastBitMask <<= 0x96 - aExp;
      roundBitsMask = lastBitMask - 1;
      z = a;
      roundingMode = float_rounding_mode();
      if ( roundingMode == float_round_nearest_even ) {
          z += lastBitMask>>1;
          if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
      }
      else if ( roundingMode != float_round_to_zero ) {
          if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
              z += roundBitsMask;
          }
      }
      z &= ~ roundBitsMask;
      if ( z != a ) float_set_inexact();
      return z;
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the absolute values of the single-precision
  floating-point values `a' and `b'.  If `zSign' is 1, the sum is negated
  before being returned.  `zSign' is ignored if the result is a NaN.
  The addition is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static float32 addFloat32Sigs( float32 a, float32 b, flag zSign )
  {
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig, zSig;
      int16 expDiff;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      bSig = extractFloat32Frac( b );
      bExp = extractFloat32Exp( b );
      expDiff = aExp - bExp;
      aSig <<= 6;
      bSig <<= 6;
      if ( 0 < expDiff ) {
          if ( aExp == 0xFF ) {
              if ( aSig ) return propagateFloat32NaN( a, b );
              return a;
          }
          if ( bExp == 0 ) {
              --expDiff;
          }
          else {
              bSig |= 0x20000000;
          }
          shift32RightJamming( bSig, expDiff, &bSig );
          zExp = aExp;
      }
      else if ( expDiff < 0 ) {
          if ( bExp == 0xFF ) {
              if ( bSig ) return propagateFloat32NaN( a, b );
              return packFloat32( zSign, 0xFF, 0 );
          }
          if ( aExp == 0 ) {
              ++expDiff;
          }
          else {
              aSig |= 0x20000000;
          }
          shift32RightJamming( aSig, - expDiff, &aSig );
          zExp = bExp;
      }
      else {
          if ( aExp == 0xFF ) {
              if ( aSig | bSig ) return propagateFloat32NaN( a, b );
              return a;
          }
          if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
          zSig = 0x40000000 + aSig + bSig;
          zExp = aExp;
          goto roundAndPack;
      }
      aSig |= 0x20000000;
      zSig = ( aSig + bSig )<<1;
      --zExp;
      if ( (sbits32) zSig < 0 ) {
          zSig = aSig + bSig;
          ++zExp;
      }
   roundAndPack:
      return roundAndPackFloat32( zSign, zExp, zSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the absolute values of the single-
  precision floating-point values `a' and `b'.  If `zSign' is 1, the
  difference is negated before being returned.  `zSign' is ignored if the
  result is a NaN.  The subtraction is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static float32 subFloat32Sigs( float32 a, float32 b, flag zSign )
  {
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig, zSig;
      int16 expDiff;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      bSig = extractFloat32Frac( b );
      bExp = extractFloat32Exp( b );
      expDiff = aExp - bExp;
      aSig <<= 7;
      bSig <<= 7;
      if ( 0 < expDiff ) goto aExpBigger;
      if ( expDiff < 0 ) goto bExpBigger;
      if ( aExp == 0xFF ) {
          if ( aSig | bSig ) return propagateFloat32NaN( a, b );
          float_raise( float_flag_invalid );
          return float32_default_nan;
      }
      if ( aExp == 0 ) {
          aExp = 1;
          bExp = 1;
      }
      if ( bSig < aSig ) goto aBigger;
      if ( aSig < bSig ) goto bBigger;
      return packFloat32( float_rounding_mode() == float_round_down, 0, 0 );
   bExpBigger:
      if ( bExp == 0xFF ) {
          if ( bSig ) return propagateFloat32NaN( a, b );
          return packFloat32( zSign ^ 1, 0xFF, 0 );
      }
      if ( aExp == 0 ) {
          ++expDiff;
      }
      else {
          aSig |= 0x40000000;
      }
      shift32RightJamming( aSig, - expDiff, &aSig );
      bSig |= 0x40000000;
   bBigger:
      zSig = bSig - aSig;
      zExp = bExp;
      zSign ^= 1;
      goto normalizeRoundAndPack;
   aExpBigger:
      if ( aExp == 0xFF ) {
          if ( aSig ) return propagateFloat32NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          --expDiff;
      }
      else {
          bSig |= 0x40000000;
      }
      shift32RightJamming( bSig, expDiff, &bSig );
      aSig |= 0x40000000;
   aBigger:
      zSig = aSig - bSig;
      zExp = aExp;
   normalizeRoundAndPack:
      --zExp;
      return normalizeRoundAndPackFloat32( zSign, zExp, zSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the single-precision floating-point values `a'
  and `b'.  The operation is performed according to the IEC/IEEE Standard for
  Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_add( float32 a, float32 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloat32Sign( a );
      bSign = extractFloat32Sign( b );
      if ( aSign == bSign ) {
          return addFloat32Sigs( a, b, aSign );
      }
      else {
          return subFloat32Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the single-precision floating-point values
  `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
  for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_sub( float32 a, float32 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloat32Sign( a );
      bSign = extractFloat32Sign( b );
      if ( aSign == bSign ) {
          return subFloat32Sigs( a, b, aSign );
      }
      else {
          return addFloat32Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of multiplying the single-precision floating-point values
  `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
  for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_mul( float32 a, float32 b )
  {
      flag aSign, bSign, zSign;
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig;
      bits64 zSig64;
      bits32 zSig;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      bSig = extractFloat32Frac( b );
      bExp = extractFloat32Exp( b );
      bSign = extractFloat32Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0xFF ) {
          if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
              return propagateFloat32NaN( a, b );
          }
          if ( ( bExp | bSig ) == 0 ) {
              float_raise( float_flag_invalid );
              return float32_default_nan;
          }
          return packFloat32( zSign, 0xFF, 0 );
      }
      if ( bExp == 0xFF ) {
          if ( bSig ) return propagateFloat32NaN( a, b );
          if ( ( aExp | aSig ) == 0 ) {
              float_raise( float_flag_invalid );
              return float32_default_nan;
          }
          return packFloat32( zSign, 0xFF, 0 );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) return packFloat32( zSign, 0, 0 );
          normalizeFloat32Subnormal( bSig, &bExp, &bSig );
      }
      zExp = aExp + bExp - 0x7F;
      aSig = ( aSig | 0x00800000 )<<7;
      bSig = ( bSig | 0x00800000 )<<8;
      shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
      zSig = zSig64;
      if ( 0 <= (sbits32) ( zSig<<1 ) ) {
          zSig <<= 1;
          --zExp;
      }
      return roundAndPackFloat32( zSign, zExp, zSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of dividing the single-precision floating-point value `a'
  by the corresponding value `b'.  The operation is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_div( float32 a, float32 b )
  {
      flag aSign, bSign, zSign;
      int16 aExp, bExp, zExp;
      bits32 aSig, bSig, zSig;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      bSig = extractFloat32Frac( b );
      bExp = extractFloat32Exp( b );
      bSign = extractFloat32Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0xFF ) {
          if ( aSig ) return propagateFloat32NaN( a, b );
          if ( bExp == 0xFF ) {
              if ( bSig ) return propagateFloat32NaN( a, b );
              float_raise( float_flag_invalid );
              return float32_default_nan;
          }
          return packFloat32( zSign, 0xFF, 0 );
      }
      if ( bExp == 0xFF ) {
          if ( bSig ) return propagateFloat32NaN( a, b );
          return packFloat32( zSign, 0, 0 );
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) {
              if ( ( aExp | aSig ) == 0 ) {
                  float_raise( float_flag_invalid );
                  return float32_default_nan;
              }
              float_raise( float_flag_divbyzero );
              return packFloat32( zSign, 0xFF, 0 );
          }
          normalizeFloat32Subnormal( bSig, &bExp, &bSig );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
      }
      zExp = aExp - bExp + 0x7D;
      aSig = ( aSig | 0x00800000 )<<7;
      bSig = ( bSig | 0x00800000 )<<8;
      if ( bSig <= ( aSig + aSig ) ) {
          aSig >>= 1;
          ++zExp;
      }
      zSig = ( ( (bits64) aSig )<<32 ) / bSig;
      if ( ( zSig & 0x3F ) == 0 ) {
          zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 );
      }
      return roundAndPackFloat32( zSign, zExp, zSig );
  
  }
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Returns the remainder of the single-precision floating-point value `a'
  with respect to the corresponding value `b'.  The operation is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_rem( float32 a, float32 b )
  {
      flag aSign, bSign, zSign;
      int16 aExp, bExp, expDiff;
      bits32 aSig, bSig;
      bits32 q;
      bits64 aSig64, bSig64, q64;
      bits32 alternateASig;
      sbits32 sigMean;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      bSig = extractFloat32Frac( b );
      bExp = extractFloat32Exp( b );
      bSign = extractFloat32Sign( b );
      if ( aExp == 0xFF ) {
          if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
              return propagateFloat32NaN( a, b );
          }
          float_raise( float_flag_invalid );
          return float32_default_nan;
      }
      if ( bExp == 0xFF ) {
          if ( bSig ) return propagateFloat32NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) {
              float_raise( float_flag_invalid );
              return float32_default_nan;
          }
          normalizeFloat32Subnormal( bSig, &bExp, &bSig );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return a;
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
      }
      expDiff = aExp - bExp;
      aSig |= 0x00800000;
      bSig |= 0x00800000;
      if ( expDiff < 32 ) {
          aSig <<= 8;
          bSig <<= 8;
          if ( expDiff < 0 ) {
              if ( expDiff < -1 ) return a;
              aSig >>= 1;
          }
          q = ( bSig <= aSig );
          if ( q ) aSig -= bSig;
          if ( 0 < expDiff ) {
              q = ( ( (bits64) aSig )<<32 ) / bSig;
              q >>= 32 - expDiff;
              bSig >>= 2;
              aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
          }
          else {
              aSig >>= 2;
              bSig >>= 2;
          }
      }
      else {
          if ( bSig <= aSig ) aSig -= bSig;
          aSig64 = ( (bits64) aSig )<<40;
          bSig64 = ( (bits64) bSig )<<40;
          expDiff -= 64;
          while ( 0 < expDiff ) {
              q64 = estimateDiv128To64( aSig64, 0, bSig64 );
              q64 = ( 2 < q64 ) ? q64 - 2 : 0;
              aSig64 = - ( ( bSig * q64 )<<38 );
              expDiff -= 62;
          }
          expDiff += 64;
          q64 = estimateDiv128To64( aSig64, 0, bSig64 );
          q64 = ( 2 < q64 ) ? q64 - 2 : 0;
          q = q64>>( 64 - expDiff );
          bSig <<= 6;
          aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
      }
      do {
          alternateASig = aSig;
          ++q;
          aSig -= bSig;
      } while ( 0 <= (sbits32) aSig );
      sigMean = aSig + alternateASig;
      if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
          aSig = alternateASig;
      }
      zSign = ( (sbits32) aSig < 0 );
      if ( zSign ) aSig = - aSig;
      return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig );
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Returns the square root of the single-precision floating-point value `a'.
  The operation is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float32_sqrt( float32 a )
  {
      flag aSign;
      int16 aExp, zExp;
      bits32 aSig, zSig;
      bits64 rem, term;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      if ( aExp == 0xFF ) {
          if ( aSig ) return propagateFloat32NaN( a, 0 );
          if ( ! aSign ) return a;
          float_raise( float_flag_invalid );
          return float32_default_nan;
      }
      if ( aSign ) {
          if ( ( aExp | aSig ) == 0 ) return a;
          float_raise( float_flag_invalid );
          return float32_default_nan;
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return 0;
          normalizeFloat32Subnormal( aSig, &aExp, &aSig );
      }
      zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E;
      aSig = ( aSig | 0x00800000 )<<8;
      zSig = estimateSqrt32( aExp, aSig ) + 2;
      if ( ( zSig & 0x7F ) <= 5 ) {
          if ( zSig < 2 ) {
              zSig = 0x7FFFFFFF;
              goto roundAndPack;
          }
          aSig >>= aExp & 1;
          term = ( (bits64) zSig ) * zSig;
          rem = ( ( (bits64) aSig )<<32 ) - term;
          while ( (sbits64) rem < 0 ) {
              --zSig;
              rem += ( ( (bits64) zSig )<<1 ) | 1;
          }
          zSig |= ( rem != 0 );
      }
      shift32RightJamming( zSig, 1, &zSig );
   roundAndPack:
      return roundAndPackFloat32( 0, zExp, zSig );
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the single-precision floating-point value `a' is equal to
  the corresponding value `b', and 0 otherwise.  The comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float32_eq( float32 a, float32 b )
  {
  
      if (    ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
           || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
         ) {
          if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the single-precision floating-point value `a' is less than
  or equal to the corresponding value `b', and 0 otherwise.  The comparison
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float32_le( float32 a, float32 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
           || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloat32Sign( a );
      bSign = extractFloat32Sign( b );
      if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
      return ( a == b ) || ( aSign ^ ( a < b ) );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the single-precision floating-point value `a' is less than
  the corresponding value `b', and 0 otherwise.  The comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float32_lt( float32 a, float32 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
           || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloat32Sign( a );
      bSign = extractFloat32Sign( b );
      if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
      return ( a != b ) && ( aSign ^ ( a < b ) );
  
  }
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the single-precision floating-point value `a' is equal to
  the corresponding value `b', and 0 otherwise.  The invalid exception is
  raised if either operand is a NaN.  Otherwise, the comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float32_eq_signaling( float32 a, float32 b )
  {
  
      if (    ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
           || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the single-precision floating-point value `a' is less than or
  equal to the corresponding value `b', and 0 otherwise.  Quiet NaNs do not
  cause an exception.  Otherwise, the comparison is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float32_le_quiet( float32 a, float32 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
           || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
         ) {
          if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloat32Sign( a );
      bSign = extractFloat32Sign( b );
      if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
      return ( a == b ) || ( aSign ^ ( a < b ) );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the single-precision floating-point value `a' is less than
  the corresponding value `b', and 0 otherwise.  Quiet NaNs do not cause an
  exception.  Otherwise, the comparison is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float32_lt_quiet( float32 a, float32 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
           || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
         ) {
          if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloat32Sign( a );
      bSign = extractFloat32Sign( b );
      if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
      return ( a != b ) && ( aSign ^ ( a < b ) );
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the 32-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic---which means in particular that the conversion is rounded
  according to the current rounding mode.  If `a' is a NaN, the largest
  positive integer is returned.  Otherwise, if the conversion overflows, the
  largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int32 float64_to_int32( float64 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits64 aSig;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
      if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
      shiftCount = 0x42C - aExp;
      if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
      return roundAndPackInt32( aSign, aSig );
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the 32-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic, except that the conversion is always rounded toward zero.
  If `a' is a NaN, the largest positive integer is returned.  Otherwise, if
  the conversion overflows, the largest integer with the same sign as `a' is
  returned.
  -------------------------------------------------------------------------------
  */
  int32 float64_to_int32_round_to_zero( float64 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits64 aSig, savedASig;
      int32 z;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( 0x41E < aExp ) {
          if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
          goto invalid;
      }
      else if ( aExp < 0x3FF ) {
          if ( aExp || aSig ) float_set_inexact();
          return 0;
      }
      aSig |= LIT64( 0x0010000000000000 );
      shiftCount = 0x433 - aExp;
      savedASig = aSig;
      aSig >>= shiftCount;
      z = aSig;
      if ( aSign ) z = - z;
      if ( ( z < 0 ) ^ aSign ) {
   invalid:
          float_raise( float_flag_invalid );
          return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
      }
      if ( ( aSig<<shiftCount ) != savedASig ) {
          float_set_inexact();
      }
      return z;
  
  }
  
  #ifndef SOFTFLOAT_FOR_GCC /* Not needed */
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the 64-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic---which means in particular that the conversion is rounded
  according to the current rounding mode.  If `a' is a NaN, the largest
  positive integer is returned.  Otherwise, if the conversion overflows, the
  largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int64 float64_to_int64( float64 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits64 aSig, aSigExtra;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
      shiftCount = 0x433 - aExp;
      if ( shiftCount <= 0 ) {
          if ( 0x43E < aExp ) {
              float_raise( float_flag_invalid );
              if (    ! aSign
                   || (    ( aExp == 0x7FF )
                        && ( aSig != LIT64( 0x0010000000000000 ) ) )
                 ) {
                  return LIT64( 0x7FFFFFFFFFFFFFFF );
              }
              return (sbits64) LIT64( 0x8000000000000000 );
          }
          aSigExtra = 0;
          aSig <<= - shiftCount;
      }
      else {
          shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
      }
      return roundAndPackInt64( aSign, aSig, aSigExtra );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the 64-bit two's complement integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic, except that the conversion is always rounded toward zero.
  If `a' is a NaN, the largest positive integer is returned.  Otherwise, if
  the conversion overflows, the largest integer with the same sign as `a' is
  returned.
  -------------------------------------------------------------------------------
  */
  int64 float64_to_int64_round_to_zero( float64 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits64 aSig;
      int64 z;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
      shiftCount = aExp - 0x433;
      if ( 0 <= shiftCount ) {
          if ( 0x43E <= aExp ) {
              if ( a != LIT64( 0xC3E0000000000000 ) ) {
                  float_raise( float_flag_invalid );
                  if (    ! aSign
                       || (    ( aExp == 0x7FF )
                            && ( aSig != LIT64( 0x0010000000000000 ) ) )
                     ) {
                      return LIT64( 0x7FFFFFFFFFFFFFFF );
                  }
              }
              return (sbits64) LIT64( 0x8000000000000000 );
          }
          z = aSig<<shiftCount;
      }
      else {
          if ( aExp < 0x3FE ) {
              if ( aExp | aSig ) float_set_inexact();
              return 0;
          }
          z = aSig>>( - shiftCount );
          if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
              float_set_inexact();
          }
      }
      if ( aSign ) z = - z;
      return z;
  
  }
  #endif /* !SOFTFLOAT_FOR_GCC */
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the single-precision floating-point format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float64_to_float32( float64 a )
  {
      flag aSign;
      int16 aExp;
      bits64 aSig;
      bits32 zSig;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( aExp == 0x7FF ) {
          if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a ) );
          return packFloat32( aSign, 0xFF, 0 );
      }
      shift64RightJamming( aSig, 22, &aSig );
      zSig = aSig;
      if ( aExp || zSig ) {
          zSig |= 0x40000000;
          aExp -= 0x381;
      }
      return roundAndPackFloat32( aSign, aExp, zSig );
  
  }
  
  #ifdef FLOATX80
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the extended double-precision floating-point format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 float64_to_floatx80( float64 a )
  {
      flag aSign;
      int16 aExp;
      bits64 aSig;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( aExp == 0x7FF ) {
          if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a ) );
          return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
          normalizeFloat64Subnormal( aSig, &aExp, &aSig );
      }
      return
          packFloatx80(
              aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 );
  
  }
  
  #endif
  
  #ifdef FLOAT128
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the quadruple-precision floating-point format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float64_to_float128( float64 a )
  {
      flag aSign;
      int16 aExp;
      bits64 aSig, zSig0, zSig1;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( aExp == 0x7FF ) {
          if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a ) );
          return packFloat128( aSign, 0x7FFF, 0, 0 );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
          normalizeFloat64Subnormal( aSig, &aExp, &aSig );
          --aExp;
      }
      shift128Right( aSig, 0, 4, &zSig0, &zSig1 );
      return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 );
  
  }
  
  #endif
  
  #ifndef SOFTFLOAT_FOR_GCC
  /*
  -------------------------------------------------------------------------------
  Rounds the double-precision floating-point value `a' to an integer, and
  returns the result as a double-precision floating-point value.  The
  operation is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_round_to_int( float64 a )
  {
      flag aSign;
      int16 aExp;
      bits64 lastBitMask, roundBitsMask;
      int8 roundingMode;
      float64 z;
  
      aExp = extractFloat64Exp( a );
      if ( 0x433 <= aExp ) {
          if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) {
              return propagateFloat64NaN( a, a );
          }
          return a;
      }
      if ( aExp < 0x3FF ) {
          if ( (bits64) ( a<<1 ) == 0 ) return a;
          float_set_inexact();
          aSign = extractFloat64Sign( a );
          switch ( float_rounding_mode() ) {
           case float_round_nearest_even:
              if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) {
                  return packFloat64( aSign, 0x3FF, 0 );
              }
              break;
           case float_round_down:
              return aSign ? LIT64( 0xBFF0000000000000 ) : 0;
           case float_round_up:
              return
              aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 );
          }
          return packFloat64( aSign, 0, 0 );
      }
      lastBitMask = 1;
      lastBitMask <<= 0x433 - aExp;
      roundBitsMask = lastBitMask - 1;
      z = a;
      roundingMode = float_rounding_mode();
      if ( roundingMode == float_round_nearest_even ) {
          z += lastBitMask>>1;
          if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
      }
      else if ( roundingMode != float_round_to_zero ) {
          if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) {
              z += roundBitsMask;
          }
      }
      z &= ~ roundBitsMask;
      if ( z != a ) float_set_inexact();
      return z;
  
  }
  #endif
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the absolute values of the double-precision
  floating-point values `a' and `b'.  If `zSign' is 1, the sum is negated
  before being returned.  `zSign' is ignored if the result is a NaN.
  The addition is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static float64 addFloat64Sigs( float64 a, float64 b, flag zSign )
  {
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig;
      int16 expDiff;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      bSig = extractFloat64Frac( b );
      bExp = extractFloat64Exp( b );
      expDiff = aExp - bExp;
      aSig <<= 9;
      bSig <<= 9;
      if ( 0 < expDiff ) {
          if ( aExp == 0x7FF ) {
              if ( aSig ) return propagateFloat64NaN( a, b );
              return a;
          }
          if ( bExp == 0 ) {
              --expDiff;
          }
          else {
              bSig |= LIT64( 0x2000000000000000 );
          }
          shift64RightJamming( bSig, expDiff, &bSig );
          zExp = aExp;
      }
      else if ( expDiff < 0 ) {
          if ( bExp == 0x7FF ) {
              if ( bSig ) return propagateFloat64NaN( a, b );
              return packFloat64( zSign, 0x7FF, 0 );
          }
          if ( aExp == 0 ) {
              ++expDiff;
          }
          else {
              aSig |= LIT64( 0x2000000000000000 );
          }
          shift64RightJamming( aSig, - expDiff, &aSig );
          zExp = bExp;
      }
      else {
          if ( aExp == 0x7FF ) {
              if ( aSig | bSig ) return propagateFloat64NaN( a, b );
              return a;
          }
          if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
          zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
          zExp = aExp;
          goto roundAndPack;
      }
      aSig |= LIT64( 0x2000000000000000 );
      zSig = ( aSig + bSig )<<1;
      --zExp;
      if ( (sbits64) zSig < 0 ) {
          zSig = aSig + bSig;
          ++zExp;
      }
   roundAndPack:
      return roundAndPackFloat64( zSign, zExp, zSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the absolute values of the double-
  precision floating-point values `a' and `b'.  If `zSign' is 1, the
  difference is negated before being returned.  `zSign' is ignored if the
  result is a NaN.  The subtraction is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static float64 subFloat64Sigs( float64 a, float64 b, flag zSign )
  {
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig;
      int16 expDiff;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      bSig = extractFloat64Frac( b );
      bExp = extractFloat64Exp( b );
      expDiff = aExp - bExp;
      aSig <<= 10;
      bSig <<= 10;
      if ( 0 < expDiff ) goto aExpBigger;
      if ( expDiff < 0 ) goto bExpBigger;
      if ( aExp == 0x7FF ) {
          if ( aSig | bSig ) return propagateFloat64NaN( a, b );
          float_raise( float_flag_invalid );
          return float64_default_nan;
      }
      if ( aExp == 0 ) {
          aExp = 1;
          bExp = 1;
      }
      if ( bSig < aSig ) goto aBigger;
      if ( aSig < bSig ) goto bBigger;
      return packFloat64( float_rounding_mode() == float_round_down, 0, 0 );
   bExpBigger:
      if ( bExp == 0x7FF ) {
          if ( bSig ) return propagateFloat64NaN( a, b );
          return packFloat64( zSign ^ 1, 0x7FF, 0 );
      }
      if ( aExp == 0 ) {
          ++expDiff;
      }
      else {
          aSig |= LIT64( 0x4000000000000000 );
      }
      shift64RightJamming( aSig, - expDiff, &aSig );
      bSig |= LIT64( 0x4000000000000000 );
   bBigger:
      zSig = bSig - aSig;
      zExp = bExp;
      zSign ^= 1;
      goto normalizeRoundAndPack;
   aExpBigger:
      if ( aExp == 0x7FF ) {
          if ( aSig ) return propagateFloat64NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          --expDiff;
      }
      else {
          bSig |= LIT64( 0x4000000000000000 );
      }
      shift64RightJamming( bSig, expDiff, &bSig );
      aSig |= LIT64( 0x4000000000000000 );
   aBigger:
      zSig = aSig - bSig;
      zExp = aExp;
   normalizeRoundAndPack:
      --zExp;
      return normalizeRoundAndPackFloat64( zSign, zExp, zSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the double-precision floating-point values `a'
  and `b'.  The operation is performed according to the IEC/IEEE Standard for
  Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_add( float64 a, float64 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloat64Sign( a );
      bSign = extractFloat64Sign( b );
      if ( aSign == bSign ) {
          return addFloat64Sigs( a, b, aSign );
      }
      else {
          return subFloat64Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the double-precision floating-point values
  `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
  for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_sub( float64 a, float64 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloat64Sign( a );
      bSign = extractFloat64Sign( b );
      if ( aSign == bSign ) {
          return subFloat64Sigs( a, b, aSign );
      }
      else {
          return addFloat64Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of multiplying the double-precision floating-point values
  `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
  for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_mul( float64 a, float64 b )
  {
      flag aSign, bSign, zSign;
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig0, zSig1;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      bSig = extractFloat64Frac( b );
      bExp = extractFloat64Exp( b );
      bSign = extractFloat64Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0x7FF ) {
          if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
              return propagateFloat64NaN( a, b );
          }
          if ( ( bExp | bSig ) == 0 ) {
              float_raise( float_flag_invalid );
              return float64_default_nan;
          }
          return packFloat64( zSign, 0x7FF, 0 );
      }
      if ( bExp == 0x7FF ) {
          if ( bSig ) return propagateFloat64NaN( a, b );
          if ( ( aExp | aSig ) == 0 ) {
              float_raise( float_flag_invalid );
              return float64_default_nan;
          }
          return packFloat64( zSign, 0x7FF, 0 );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
          normalizeFloat64Subnormal( aSig, &aExp, &aSig );
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) return packFloat64( zSign, 0, 0 );
          normalizeFloat64Subnormal( bSig, &bExp, &bSig );
      }
      zExp = aExp + bExp - 0x3FF;
      aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
      bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
      mul64To128( aSig, bSig, &zSig0, &zSig1 );
      zSig0 |= ( zSig1 != 0 );
      if ( 0 <= (sbits64) ( zSig0<<1 ) ) {
          zSig0 <<= 1;
          --zExp;
      }
      return roundAndPackFloat64( zSign, zExp, zSig0 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of dividing the double-precision floating-point value `a'
  by the corresponding value `b'.  The operation is performed according to
  the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_div( float64 a, float64 b )
  {
      flag aSign, bSign, zSign;
      int16 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig;
      bits64 rem0, rem1;
      bits64 term0, term1;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      bSig = extractFloat64Frac( b );
      bExp = extractFloat64Exp( b );
      bSign = extractFloat64Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0x7FF ) {
          if ( aSig ) return propagateFloat64NaN( a, b );
          if ( bExp == 0x7FF ) {
              if ( bSig ) return propagateFloat64NaN( a, b );
              float_raise( float_flag_invalid );
              return float64_default_nan;
          }
          return packFloat64( zSign, 0x7FF, 0 );
      }
      if ( bExp == 0x7FF ) {
          if ( bSig ) return propagateFloat64NaN( a, b );
          return packFloat64( zSign, 0, 0 );
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) {
              if ( ( aExp | aSig ) == 0 ) {
                  float_raise( float_flag_invalid );
                  return float64_default_nan;
              }
              float_raise( float_flag_divbyzero );
              return packFloat64( zSign, 0x7FF, 0 );
          }
          normalizeFloat64Subnormal( bSig, &bExp, &bSig );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
          normalizeFloat64Subnormal( aSig, &aExp, &aSig );
      }
      zExp = aExp - bExp + 0x3FD;
      aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
      bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
      if ( bSig <= ( aSig + aSig ) ) {
          aSig >>= 1;
          ++zExp;
      }
      zSig = estimateDiv128To64( aSig, 0, bSig );
      if ( ( zSig & 0x1FF ) <= 2 ) {
          mul64To128( bSig, zSig, &term0, &term1 );
          sub128( aSig, 0, term0, term1, &rem0, &rem1 );
          while ( (sbits64) rem0 < 0 ) {
              --zSig;
              add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
          }
          zSig |= ( rem1 != 0 );
      }
      return roundAndPackFloat64( zSign, zExp, zSig );
  
  }
  
  #ifndef SOFTFLOAT_FOR_GCC
  /*
  -------------------------------------------------------------------------------
  Returns the remainder of the double-precision floating-point value `a'
  with respect to the corresponding value `b'.  The operation is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_rem( float64 a, float64 b )
  {
      flag aSign, bSign, zSign;
      int16 aExp, bExp, expDiff;
      bits64 aSig, bSig;
      bits64 q, alternateASig;
      sbits64 sigMean;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      bSig = extractFloat64Frac( b );
      bExp = extractFloat64Exp( b );
      bSign = extractFloat64Sign( b );
      if ( aExp == 0x7FF ) {
          if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
              return propagateFloat64NaN( a, b );
          }
          float_raise( float_flag_invalid );
          return float64_default_nan;
      }
      if ( bExp == 0x7FF ) {
          if ( bSig ) return propagateFloat64NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) {
              float_raise( float_flag_invalid );
              return float64_default_nan;
          }
          normalizeFloat64Subnormal( bSig, &bExp, &bSig );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return a;
          normalizeFloat64Subnormal( aSig, &aExp, &aSig );
      }
      expDiff = aExp - bExp;
      aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11;
      bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
      if ( expDiff < 0 ) {
          if ( expDiff < -1 ) return a;
          aSig >>= 1;
      }
      q = ( bSig <= aSig );
      if ( q ) aSig -= bSig;
      expDiff -= 64;
      while ( 0 < expDiff ) {
          q = estimateDiv128To64( aSig, 0, bSig );
          q = ( 2 < q ) ? q - 2 : 0;
          aSig = - ( ( bSig>>2 ) * q );
          expDiff -= 62;
      }
      expDiff += 64;
      if ( 0 < expDiff ) {
          q = estimateDiv128To64( aSig, 0, bSig );
          q = ( 2 < q ) ? q - 2 : 0;
          q >>= 64 - expDiff;
          bSig >>= 2;
          aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
      }
      else {
          aSig >>= 2;
          bSig >>= 2;
      }
      do {
          alternateASig = aSig;
          ++q;
          aSig -= bSig;
      } while ( 0 <= (sbits64) aSig );
      sigMean = aSig + alternateASig;
      if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
          aSig = alternateASig;
      }
      zSign = ( (sbits64) aSig < 0 );
      if ( zSign ) aSig = - aSig;
      return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the square root of the double-precision floating-point value `a'.
  The operation is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float64_sqrt( float64 a )
  {
      flag aSign;
      int16 aExp, zExp;
      bits64 aSig, zSig, doubleZSig;
      bits64 rem0, rem1, term0, term1;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
      if ( aExp == 0x7FF ) {
          if ( aSig ) return propagateFloat64NaN( a, a );
          if ( ! aSign ) return a;
          float_raise( float_flag_invalid );
          return float64_default_nan;
      }
      if ( aSign ) {
          if ( ( aExp | aSig ) == 0 ) return a;
          float_raise( float_flag_invalid );
          return float64_default_nan;
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return 0;
          normalizeFloat64Subnormal( aSig, &aExp, &aSig );
      }
      zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
      aSig |= LIT64( 0x0010000000000000 );
      zSig = estimateSqrt32( aExp, aSig>>21 );
      aSig <<= 9 - ( aExp & 1 );
      zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 );
      if ( ( zSig & 0x1FF ) <= 5 ) {
          doubleZSig = zSig<<1;
          mul64To128( zSig, zSig, &term0, &term1 );
          sub128( aSig, 0, term0, term1, &rem0, &rem1 );
          while ( (sbits64) rem0 < 0 ) {
              --zSig;
              doubleZSig -= 2;
              add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 );
          }
          zSig |= ( ( rem0 | rem1 ) != 0 );
      }
      return roundAndPackFloat64( 0, zExp, zSig );
  
  }
  #endif
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the double-precision floating-point value `a' is equal to the
  corresponding value `b', and 0 otherwise.  The comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float64_eq( float64 a, float64 b )
  {
  
      if (    ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
           || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
         ) {
          if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      return ( a == b ) ||
          ( (bits64) ( ( FLOAT64_DEMANGLE(a) | FLOAT64_DEMANGLE(b) )<<1 ) == 0 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the double-precision floating-point value `a' is less than or
  equal to the corresponding value `b', and 0 otherwise.  The comparison is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float64_le( float64 a, float64 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
           || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloat64Sign( a );
      bSign = extractFloat64Sign( b );
      if ( aSign != bSign )
          return aSign ||
              ( (bits64) ( ( FLOAT64_DEMANGLE(a) | FLOAT64_DEMANGLE(b) )<<1 ) ==
                0 );
      return ( a == b ) ||
          ( aSign ^ ( FLOAT64_DEMANGLE(a) < FLOAT64_DEMANGLE(b) ) );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the double-precision floating-point value `a' is less than
  the corresponding value `b', and 0 otherwise.  The comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float64_lt( float64 a, float64 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
           || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloat64Sign( a );
      bSign = extractFloat64Sign( b );
      if ( aSign != bSign )
          return aSign &&
              ( (bits64) ( ( FLOAT64_DEMANGLE(a) | FLOAT64_DEMANGLE(b) )<<1 ) !=
                0 );
      return ( a != b ) &&
          ( aSign ^ ( FLOAT64_DEMANGLE(a) < FLOAT64_DEMANGLE(b) ) );
  
  }
  
  #ifndef SOFTFLOAT_FOR_GCC
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the double-precision floating-point value `a' is equal to the
  corresponding value `b', and 0 otherwise.  The invalid exception is raised
  if either operand is a NaN.  Otherwise, the comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float64_eq_signaling( float64 a, float64 b )
  {
  
      if (    ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
           || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the double-precision floating-point value `a' is less than or
  equal to the corresponding value `b', and 0 otherwise.  Quiet NaNs do not
  cause an exception.  Otherwise, the comparison is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float64_le_quiet( float64 a, float64 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
           || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
         ) {
          if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloat64Sign( a );
      bSign = extractFloat64Sign( b );
      if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
      return ( a == b ) || ( aSign ^ ( a < b ) );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the double-precision floating-point value `a' is less than
  the corresponding value `b', and 0 otherwise.  Quiet NaNs do not cause an
  exception.  Otherwise, the comparison is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float64_lt_quiet( float64 a, float64 b )
  {
      flag aSign, bSign;
  
      if (    ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
           || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
         ) {
          if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloat64Sign( a );
      bSign = extractFloat64Sign( b );
      if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
      return ( a != b ) && ( aSign ^ ( a < b ) );
  
  }
  #endif
  
  #ifdef FLOATX80
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the 32-bit two's complement integer format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic---which means in particular that the conversion
  is rounded according to the current rounding mode.  If `a' is a NaN, the
  largest positive integer is returned.  Otherwise, if the conversion
  overflows, the largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int32 floatx80_to_int32( floatx80 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
      shiftCount = 0x4037 - aExp;
      if ( shiftCount <= 0 ) shiftCount = 1;
      shift64RightJamming( aSig, shiftCount, &aSig );
      return roundAndPackInt32( aSign, aSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the 32-bit two's complement integer format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic, except that the conversion is always rounded
  toward zero.  If `a' is a NaN, the largest positive integer is returned.
  Otherwise, if the conversion overflows, the largest integer with the same
  sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int32 floatx80_to_int32_round_to_zero( floatx80 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig, savedASig;
      int32 z;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      if ( 0x401E < aExp ) {
          if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
          goto invalid;
      }
      else if ( aExp < 0x3FFF ) {
          if ( aExp || aSig ) float_set_inexact();
          return 0;
      }
      shiftCount = 0x403E - aExp;
      savedASig = aSig;
      aSig >>= shiftCount;
      z = aSig;
      if ( aSign ) z = - z;
      if ( ( z < 0 ) ^ aSign ) {
   invalid:
          float_raise( float_flag_invalid );
          return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
      }
      if ( ( aSig<<shiftCount ) != savedASig ) {
          float_set_inexact();
      }
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the 64-bit two's complement integer format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic---which means in particular that the conversion
  is rounded according to the current rounding mode.  If `a' is a NaN,
  the largest positive integer is returned.  Otherwise, if the conversion
  overflows, the largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int64 floatx80_to_int64( floatx80 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig, aSigExtra;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      shiftCount = 0x403E - aExp;
      if ( shiftCount <= 0 ) {
          if ( shiftCount ) {
              float_raise( float_flag_invalid );
              if (    ! aSign
                   || (    ( aExp == 0x7FFF )
                        && ( aSig != LIT64( 0x8000000000000000 ) ) )
                 ) {
                  return LIT64( 0x7FFFFFFFFFFFFFFF );
              }
              return (sbits64) LIT64( 0x8000000000000000 );
          }
          aSigExtra = 0;
      }
      else {
          shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
      }
      return roundAndPackInt64( aSign, aSig, aSigExtra );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the 64-bit two's complement integer format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic, except that the conversion is always rounded
  toward zero.  If `a' is a NaN, the largest positive integer is returned.
  Otherwise, if the conversion overflows, the largest integer with the same
  sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int64 floatx80_to_int64_round_to_zero( floatx80 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig;
      int64 z;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      shiftCount = aExp - 0x403E;
      if ( 0 <= shiftCount ) {
          aSig &= LIT64( 0x7FFFFFFFFFFFFFFF );
          if ( ( a.high != 0xC03E ) || aSig ) {
              float_raise( float_flag_invalid );
              if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) {
                  return LIT64( 0x7FFFFFFFFFFFFFFF );
              }
          }
          return (sbits64) LIT64( 0x8000000000000000 );
      }
      else if ( aExp < 0x3FFF ) {
          if ( aExp | aSig ) float_set_inexact();
          return 0;
      }
      z = aSig>>( - shiftCount );
      if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
          float_set_inexact();
      }
      if ( aSign ) z = - z;
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the single-precision floating-point format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 floatx80_to_float32( floatx80 a )
  {
      flag aSign;
      int32 aExp;
      bits64 aSig;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( (bits64) ( aSig<<1 ) ) {
              return commonNaNToFloat32( floatx80ToCommonNaN( a ) );
          }
          return packFloat32( aSign, 0xFF, 0 );
      }
      shift64RightJamming( aSig, 33, &aSig );
      if ( aExp || aSig ) aExp -= 0x3F81;
      return roundAndPackFloat32( aSign, aExp, aSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the double-precision floating-point format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 floatx80_to_float64( floatx80 a )
  {
      flag aSign;
      int32 aExp;
      bits64 aSig, zSig;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( (bits64) ( aSig<<1 ) ) {
              return commonNaNToFloat64( floatx80ToCommonNaN( a ) );
          }
          return packFloat64( aSign, 0x7FF, 0 );
      }
      shift64RightJamming( aSig, 1, &zSig );
      if ( aExp || aSig ) aExp -= 0x3C01;
      return roundAndPackFloat64( aSign, aExp, zSig );
  
  }
  
  #ifdef FLOAT128
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the extended double-precision floating-
  point value `a' to the quadruple-precision floating-point format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 floatx80_to_float128( floatx80 a )
  {
      flag aSign;
      int16 aExp;
      bits64 aSig, zSig0, zSig1;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) {
          return commonNaNToFloat128( floatx80ToCommonNaN( a ) );
      }
      shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
      return packFloat128( aSign, aExp, zSig0, zSig1 );
  
  }
  
  #endif
  
  /*
  -------------------------------------------------------------------------------
  Rounds the extended double-precision floating-point value `a' to an integer,
  and returns the result as an extended quadruple-precision floating-point
  value.  The operation is performed according to the IEC/IEEE Standard for
  Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_round_to_int( floatx80 a )
  {
      flag aSign;
      int32 aExp;
      bits64 lastBitMask, roundBitsMask;
      int8 roundingMode;
      floatx80 z;
  
      aExp = extractFloatx80Exp( a );
      if ( 0x403E <= aExp ) {
          if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) {
              return propagateFloatx80NaN( a, a );
          }
          return a;
      }
      if ( aExp < 0x3FFF ) {
          if (    ( aExp == 0 )
               && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
              return a;
          }
          float_set_inexact();
          aSign = extractFloatx80Sign( a );
          switch ( float_rounding_mode() ) {
           case float_round_nearest_even:
              if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 )
                 ) {
                  return
                      packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) );
              }
              break;
           case float_round_down:
              return
                    aSign ?
                        packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) )
                  : packFloatx80( 0, 0, 0 );
           case float_round_up:
              return
                    aSign ? packFloatx80( 1, 0, 0 )
                  : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) );
          }
          return packFloatx80( aSign, 0, 0 );
      }
      lastBitMask = 1;
      lastBitMask <<= 0x403E - aExp;
      roundBitsMask = lastBitMask - 1;
      z = a;
      roundingMode = float_rounding_mode();
      if ( roundingMode == float_round_nearest_even ) {
          z.low += lastBitMask>>1;
          if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
      }
      else if ( roundingMode != float_round_to_zero ) {
          if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
              z.low += roundBitsMask;
          }
      }
      z.low &= ~ roundBitsMask;
      if ( z.low == 0 ) {
          ++z.high;
          z.low = LIT64( 0x8000000000000000 );
      }
      if ( z.low != a.low ) float_set_inexact();
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the absolute values of the extended double-
  precision floating-point values `a' and `b'.  If `zSign' is 1, the sum is
  negated before being returned.  `zSign' is ignored if the result is a NaN.
  The addition is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign )
  {
      int32 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig0, zSig1;
      int32 expDiff;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      bSig = extractFloatx80Frac( b );
      bExp = extractFloatx80Exp( b );
      expDiff = aExp - bExp;
      if ( 0 < expDiff ) {
          if ( aExp == 0x7FFF ) {
              if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
              return a;
          }
          if ( bExp == 0 ) --expDiff;
          shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
          zExp = aExp;
      }
      else if ( expDiff < 0 ) {
          if ( bExp == 0x7FFF ) {
              if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
              return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
          }
          if ( aExp == 0 ) ++expDiff;
          shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
          zExp = bExp;
      }
      else {
          if ( aExp == 0x7FFF ) {
              if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
                  return propagateFloatx80NaN( a, b );
              }
              return a;
          }
          zSig1 = 0;
          zSig0 = aSig + bSig;
          if ( aExp == 0 ) {
              normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
              goto roundAndPack;
          }
          zExp = aExp;
          goto shiftRight1;
      }
      zSig0 = aSig + bSig;
      if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
   shiftRight1:
      shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
      zSig0 |= LIT64( 0x8000000000000000 );
      ++zExp;
   roundAndPack:
      return
          roundAndPackFloatx80(
              floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the absolute values of the extended
  double-precision floating-point values `a' and `b'.  If `zSign' is 1, the
  difference is negated before being returned.  `zSign' is ignored if the
  result is a NaN.  The subtraction is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign )
  {
      int32 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig0, zSig1;
      int32 expDiff;
      floatx80 z;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      bSig = extractFloatx80Frac( b );
      bExp = extractFloatx80Exp( b );
      expDiff = aExp - bExp;
      if ( 0 < expDiff ) goto aExpBigger;
      if ( expDiff < 0 ) goto bExpBigger;
      if ( aExp == 0x7FFF ) {
          if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
              return propagateFloatx80NaN( a, b );
          }
          float_raise( float_flag_invalid );
          z.low = floatx80_default_nan_low;
          z.high = floatx80_default_nan_high;
          return z;
      }
      if ( aExp == 0 ) {
          aExp = 1;
          bExp = 1;
      }
      zSig1 = 0;
      if ( bSig < aSig ) goto aBigger;
      if ( aSig < bSig ) goto bBigger;
      return packFloatx80( float_rounding_mode() == float_round_down, 0, 0 );
   bExpBigger:
      if ( bExp == 0x7FFF ) {
          if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
          return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( aExp == 0 ) ++expDiff;
      shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
   bBigger:
      sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
      zExp = bExp;
      zSign ^= 1;
      goto normalizeRoundAndPack;
   aExpBigger:
      if ( aExp == 0x7FFF ) {
          if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) --expDiff;
      shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
   aBigger:
      sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
      zExp = aExp;
   normalizeRoundAndPack:
      return
          normalizeRoundAndPackFloatx80(
              floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the extended double-precision floating-point
  values `a' and `b'.  The operation is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_add( floatx80 a, floatx80 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloatx80Sign( a );
      bSign = extractFloatx80Sign( b );
      if ( aSign == bSign ) {
          return addFloatx80Sigs( a, b, aSign );
      }
      else {
          return subFloatx80Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the extended double-precision floating-
  point values `a' and `b'.  The operation is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_sub( floatx80 a, floatx80 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloatx80Sign( a );
      bSign = extractFloatx80Sign( b );
      if ( aSign == bSign ) {
          return subFloatx80Sigs( a, b, aSign );
      }
      else {
          return addFloatx80Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of multiplying the extended double-precision floating-
  point values `a' and `b'.  The operation is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_mul( floatx80 a, floatx80 b )
  {
      flag aSign, bSign, zSign;
      int32 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig0, zSig1;
      floatx80 z;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      bSig = extractFloatx80Frac( b );
      bExp = extractFloatx80Exp( b );
      bSign = extractFloatx80Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0x7FFF ) {
          if (    (bits64) ( aSig<<1 )
               || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
              return propagateFloatx80NaN( a, b );
          }
          if ( ( bExp | bSig ) == 0 ) goto invalid;
          return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( bExp == 0x7FFF ) {
          if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
          if ( ( aExp | aSig ) == 0 ) {
   invalid:
              float_raise( float_flag_invalid );
              z.low = floatx80_default_nan_low;
              z.high = floatx80_default_nan_high;
              return z;
          }
          return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
          normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
          normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
      }
      zExp = aExp + bExp - 0x3FFE;
      mul64To128( aSig, bSig, &zSig0, &zSig1 );
      if ( 0 < (sbits64) zSig0 ) {
          shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
          --zExp;
      }
      return
          roundAndPackFloatx80(
              floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of dividing the extended double-precision floating-point
  value `a' by the corresponding value `b'.  The operation is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_div( floatx80 a, floatx80 b )
  {
      flag aSign, bSign, zSign;
      int32 aExp, bExp, zExp;
      bits64 aSig, bSig, zSig0, zSig1;
      bits64 rem0, rem1, rem2, term0, term1, term2;
      floatx80 z;
  
      aSig = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      bSig = extractFloatx80Frac( b );
      bExp = extractFloatx80Exp( b );
      bSign = extractFloatx80Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0x7FFF ) {
          if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
          if ( bExp == 0x7FFF ) {
              if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
              goto invalid;
          }
          return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( bExp == 0x7FFF ) {
          if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
          return packFloatx80( zSign, 0, 0 );
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) {
              if ( ( aExp | aSig ) == 0 ) {
   invalid:
                  float_raise( float_flag_invalid );
                  z.low = floatx80_default_nan_low;
                  z.high = floatx80_default_nan_high;
                  return z;
              }
              float_raise( float_flag_divbyzero );
              return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
          }
          normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
      }
      if ( aExp == 0 ) {
          if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
          normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
      }
      zExp = aExp - bExp + 0x3FFE;
      rem1 = 0;
      if ( bSig <= aSig ) {
          shift128Right( aSig, 0, 1, &aSig, &rem1 );
          ++zExp;
      }
      zSig0 = estimateDiv128To64( aSig, rem1, bSig );
      mul64To128( bSig, zSig0, &term0, &term1 );
      sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
      while ( (sbits64) rem0 < 0 ) {
          --zSig0;
          add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
      }
      zSig1 = estimateDiv128To64( rem1, 0, bSig );
      if ( (bits64) ( zSig1<<1 ) <= 8 ) {
          mul64To128( bSig, zSig1, &term1, &term2 );
          sub128( rem1, 0, term1, term2, &rem1, &rem2 );
          while ( (sbits64) rem1 < 0 ) {
              --zSig1;
              add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
          }
          zSig1 |= ( ( rem1 | rem2 ) != 0 );
      }
      return
          roundAndPackFloatx80(
              floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the remainder of the extended double-precision floating-point value
  `a' with respect to the corresponding value `b'.  The operation is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_rem( floatx80 a, floatx80 b )
  {
      flag aSign, bSign, zSign;
      int32 aExp, bExp, expDiff;
      bits64 aSig0, aSig1, bSig;
      bits64 q, term0, term1, alternateASig0, alternateASig1;
      floatx80 z;
  
      aSig0 = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      bSig = extractFloatx80Frac( b );
      bExp = extractFloatx80Exp( b );
      bSign = extractFloatx80Sign( b );
      if ( aExp == 0x7FFF ) {
          if (    (bits64) ( aSig0<<1 )
               || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
              return propagateFloatx80NaN( a, b );
          }
          goto invalid;
      }
      if ( bExp == 0x7FFF ) {
          if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          if ( bSig == 0 ) {
   invalid:
              float_raise( float_flag_invalid );
              z.low = floatx80_default_nan_low;
              z.high = floatx80_default_nan_high;
              return z;
          }
          normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
      }
      if ( aExp == 0 ) {
          if ( (bits64) ( aSig0<<1 ) == 0 ) return a;
          normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
      }
      bSig |= LIT64( 0x8000000000000000 );
      zSign = aSign;
      expDiff = aExp - bExp;
      aSig1 = 0;
      if ( expDiff < 0 ) {
          if ( expDiff < -1 ) return a;
          shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
          expDiff = 0;
      }
      q = ( bSig <= aSig0 );
      if ( q ) aSig0 -= bSig;
      expDiff -= 64;
      while ( 0 < expDiff ) {
          q = estimateDiv128To64( aSig0, aSig1, bSig );
          q = ( 2 < q ) ? q - 2 : 0;
          mul64To128( bSig, q, &term0, &term1 );
          sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
          shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
          expDiff -= 62;
      }
      expDiff += 64;
      if ( 0 < expDiff ) {
          q = estimateDiv128To64( aSig0, aSig1, bSig );
          q = ( 2 < q ) ? q - 2 : 0;
          q >>= 64 - expDiff;
          mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
          sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
          shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
          while ( le128( term0, term1, aSig0, aSig1 ) ) {
              ++q;
              sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
          }
      }
      else {
          term1 = 0;
          term0 = bSig;
      }
      sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
      if (    lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
           || (    eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
                && ( q & 1 ) )
         ) {
          aSig0 = alternateASig0;
          aSig1 = alternateASig1;
          zSign = ! zSign;
      }
      return
          normalizeRoundAndPackFloatx80(
              80, zSign, bExp + expDiff, aSig0, aSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the square root of the extended double-precision floating-point
  value `a'.  The operation is performed according to the IEC/IEEE Standard
  for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 floatx80_sqrt( floatx80 a )
  {
      flag aSign;
      int32 aExp, zExp;
      bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0;
      bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
      floatx80 z;
  
      aSig0 = extractFloatx80Frac( a );
      aExp = extractFloatx80Exp( a );
      aSign = extractFloatx80Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a );
          if ( ! aSign ) return a;
          goto invalid;
      }
      if ( aSign ) {
          if ( ( aExp | aSig0 ) == 0 ) return a;
   invalid:
          float_raise( float_flag_invalid );
          z.low = floatx80_default_nan_low;
          z.high = floatx80_default_nan_high;
          return z;
      }
      if ( aExp == 0 ) {
          if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
          normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
      }
      zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
      zSig0 = estimateSqrt32( aExp, aSig0>>32 );
      shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 );
      zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
      doubleZSig0 = zSig0<<1;
      mul64To128( zSig0, zSig0, &term0, &term1 );
      sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
      while ( (sbits64) rem0 < 0 ) {
          --zSig0;
          doubleZSig0 -= 2;
          add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
      }
      zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
      if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) {
          if ( zSig1 == 0 ) zSig1 = 1;
          mul64To128( doubleZSig0, zSig1, &term1, &term2 );
          sub128( rem1, 0, term1, term2, &rem1, &rem2 );
          mul64To128( zSig1, zSig1, &term2, &term3 );
          sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
          while ( (sbits64) rem1 < 0 ) {
              --zSig1;
              shortShift128Left( 0, zSig1, 1, &term2, &term3 );
              term3 |= 1;
              term2 |= doubleZSig0;
              add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
          }
          zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
      }
      shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 );
      zSig0 |= doubleZSig0;
      return
          roundAndPackFloatx80(
              floatx80_rounding_precision, 0, zExp, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the extended double-precision floating-point value `a' is
  equal to the corresponding value `b', and 0 otherwise.  The comparison is
  performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag floatx80_eq( floatx80 a, floatx80 b )
  {
  
      if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( a )<<1 ) )
           || (    ( extractFloatx80Exp( b ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( b )<<1 ) )
         ) {
          if (    floatx80_is_signaling_nan( a )
               || floatx80_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      return
             ( a.low == b.low )
          && (    ( a.high == b.high )
               || (    ( a.low == 0 )
                    && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
             );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the extended double-precision floating-point value `a' is
  less than or equal to the corresponding value `b', and 0 otherwise.  The
  comparison is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag floatx80_le( floatx80 a, floatx80 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( a )<<1 ) )
           || (    ( extractFloatx80Exp( b ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( b )<<1 ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloatx80Sign( a );
      bSign = extractFloatx80Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              || (    ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   == 0 );
      }
      return
            aSign ? le128( b.high, b.low, a.high, a.low )
          : le128( a.high, a.low, b.high, b.low );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the extended double-precision floating-point value `a' is
  less than the corresponding value `b', and 0 otherwise.  The comparison
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag floatx80_lt( floatx80 a, floatx80 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( a )<<1 ) )
           || (    ( extractFloatx80Exp( b ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( b )<<1 ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloatx80Sign( a );
      bSign = extractFloatx80Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              && (    ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   != 0 );
      }
      return
            aSign ? lt128( b.high, b.low, a.high, a.low )
          : lt128( a.high, a.low, b.high, b.low );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the extended double-precision floating-point value `a' is equal
  to the corresponding value `b', and 0 otherwise.  The invalid exception is
  raised if either operand is a NaN.  Otherwise, the comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag floatx80_eq_signaling( floatx80 a, floatx80 b )
  {
  
      if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( a )<<1 ) )
           || (    ( extractFloatx80Exp( b ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( b )<<1 ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      return
             ( a.low == b.low )
          && (    ( a.high == b.high )
               || (    ( a.low == 0 )
                    && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
             );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the extended double-precision floating-point value `a' is less
  than or equal to the corresponding value `b', and 0 otherwise.  Quiet NaNs
  do not cause an exception.  Otherwise, the comparison is performed according
  to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag floatx80_le_quiet( floatx80 a, floatx80 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( a )<<1 ) )
           || (    ( extractFloatx80Exp( b ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( b )<<1 ) )
         ) {
          if (    floatx80_is_signaling_nan( a )
               || floatx80_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloatx80Sign( a );
      bSign = extractFloatx80Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              || (    ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   == 0 );
      }
      return
            aSign ? le128( b.high, b.low, a.high, a.low )
          : le128( a.high, a.low, b.high, b.low );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the extended double-precision floating-point value `a' is less
  than the corresponding value `b', and 0 otherwise.  Quiet NaNs do not cause
  an exception.  Otherwise, the comparison is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag floatx80_lt_quiet( floatx80 a, floatx80 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( a )<<1 ) )
           || (    ( extractFloatx80Exp( b ) == 0x7FFF )
                && (bits64) ( extractFloatx80Frac( b )<<1 ) )
         ) {
          if (    floatx80_is_signaling_nan( a )
               || floatx80_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloatx80Sign( a );
      bSign = extractFloatx80Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              && (    ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   != 0 );
      }
      return
            aSign ? lt128( b.high, b.low, a.high, a.low )
          : lt128( a.high, a.low, b.high, b.low );
  
  }
  
  #endif
  
  #ifdef FLOAT128
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the 32-bit two's complement integer format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic---which means in particular that the conversion is rounded
  according to the current rounding mode.  If `a' is a NaN, the largest
  positive integer is returned.  Otherwise, if the conversion overflows, the
  largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int32 float128_to_int32( float128 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig0, aSig1;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0;
      if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
      aSig0 |= ( aSig1 != 0 );
      shiftCount = 0x4028 - aExp;
      if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 );
      return roundAndPackInt32( aSign, aSig0 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the 32-bit two's complement integer format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic, except that the conversion is always rounded toward zero.  If
  `a' is a NaN, the largest positive integer is returned.  Otherwise, if the
  conversion overflows, the largest integer with the same sign as `a' is
  returned.
  -------------------------------------------------------------------------------
  */
  int32 float128_to_int32_round_to_zero( float128 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig0, aSig1, savedASig;
      int32 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      aSig0 |= ( aSig1 != 0 );
      if ( 0x401E < aExp ) {
          if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0;
          goto invalid;
      }
      else if ( aExp < 0x3FFF ) {
          if ( aExp || aSig0 ) float_set_inexact();
          return 0;
      }
      aSig0 |= LIT64( 0x0001000000000000 );
      shiftCount = 0x402F - aExp;
      savedASig = aSig0;
      aSig0 >>= shiftCount;
      z = aSig0;
      if ( aSign ) z = - z;
      if ( ( z < 0 ) ^ aSign ) {
   invalid:
          float_raise( float_flag_invalid );
          return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
      }
      if ( ( aSig0<<shiftCount ) != savedASig ) {
          float_set_inexact();
      }
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the 64-bit two's complement integer format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic---which means in particular that the conversion is rounded
  according to the current rounding mode.  If `a' is a NaN, the largest
  positive integer is returned.  Otherwise, if the conversion overflows, the
  largest integer with the same sign as `a' is returned.
  -------------------------------------------------------------------------------
  */
  int64 float128_to_int64( float128 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig0, aSig1;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
      shiftCount = 0x402F - aExp;
      if ( shiftCount <= 0 ) {
          if ( 0x403E < aExp ) {
              float_raise( float_flag_invalid );
              if (    ! aSign
                   || (    ( aExp == 0x7FFF )
                        && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) )
                      )
                 ) {
                  return LIT64( 0x7FFFFFFFFFFFFFFF );
              }
              return (sbits64) LIT64( 0x8000000000000000 );
          }
          shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 );
      }
      else {
          shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 );
      }
      return roundAndPackInt64( aSign, aSig0, aSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the 64-bit two's complement integer format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic, except that the conversion is always rounded toward zero.
  If `a' is a NaN, the largest positive integer is returned.  Otherwise, if
  the conversion overflows, the largest integer with the same sign as `a' is
  returned.
  -------------------------------------------------------------------------------
  */
  int64 float128_to_int64_round_to_zero( float128 a )
  {
      flag aSign;
      int32 aExp, shiftCount;
      bits64 aSig0, aSig1;
      int64 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
      shiftCount = aExp - 0x402F;
      if ( 0 < shiftCount ) {
          if ( 0x403E <= aExp ) {
              aSig0 &= LIT64( 0x0000FFFFFFFFFFFF );
              if (    ( a.high == LIT64( 0xC03E000000000000 ) )
                   && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) {
                  if ( aSig1 ) float_set_inexact();
              }
              else {
                  float_raise( float_flag_invalid );
                  if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) {
                      return LIT64( 0x7FFFFFFFFFFFFFFF );
                  }
              }
              return (sbits64) LIT64( 0x8000000000000000 );
          }
          z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
          if ( (bits64) ( aSig1<<shiftCount ) ) {
              float_set_inexact();
          }
      }
      else {
          if ( aExp < 0x3FFF ) {
              if ( aExp | aSig0 | aSig1 ) {
                  float_set_inexact();
              }
              return 0;
          }
          z = aSig0>>( - shiftCount );
          if (    aSig1
               || ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) {
              float_set_inexact();
          }
      }
      if ( aSign ) z = - z;
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the single-precision floating-point format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  float32 float128_to_float32( float128 a )
  {
      flag aSign;
      int32 aExp;
      bits64 aSig0, aSig1;
      bits32 zSig;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 ) {
              return commonNaNToFloat32( float128ToCommonNaN( a ) );
          }
          return packFloat32( aSign, 0xFF, 0 );
      }
      aSig0 |= ( aSig1 != 0 );
      shift64RightJamming( aSig0, 18, &aSig0 );
      zSig = aSig0;
      if ( aExp || zSig ) {
          zSig |= 0x40000000;
          aExp -= 0x3F81;
      }
      return roundAndPackFloat32( aSign, aExp, zSig );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the double-precision floating-point format.  The conversion
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  float64 float128_to_float64( float128 a )
  {
      flag aSign;
      int32 aExp;
      bits64 aSig0, aSig1;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 ) {
              return commonNaNToFloat64( float128ToCommonNaN( a ) );
          }
          return packFloat64( aSign, 0x7FF, 0 );
      }
      shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
      aSig0 |= ( aSig1 != 0 );
      if ( aExp || aSig0 ) {
          aSig0 |= LIT64( 0x4000000000000000 );
          aExp -= 0x3C01;
      }
      return roundAndPackFloat64( aSign, aExp, aSig0 );
  
  }
  
  #ifdef FLOATX80
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the quadruple-precision floating-point
  value `a' to the extended double-precision floating-point format.  The
  conversion is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  floatx80 float128_to_floatx80( float128 a )
  {
      flag aSign;
      int32 aExp;
      bits64 aSig0, aSig1;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 ) {
              return commonNaNToFloatx80( float128ToCommonNaN( a ) );
          }
          return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
      }
      if ( aExp == 0 ) {
          if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 );
          normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
      }
      else {
          aSig0 |= LIT64( 0x0001000000000000 );
      }
      shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
      return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 );
  
  }
  
  #endif
  
  /*
  -------------------------------------------------------------------------------
  Rounds the quadruple-precision floating-point value `a' to an integer, and
  returns the result as a quadruple-precision floating-point value.  The
  operation is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_round_to_int( float128 a )
  {
      flag aSign;
      int32 aExp;
      bits64 lastBitMask, roundBitsMask;
      int8 roundingMode;
      float128 z;
  
      aExp = extractFloat128Exp( a );
      if ( 0x402F <= aExp ) {
          if ( 0x406F <= aExp ) {
              if (    ( aExp == 0x7FFF )
                   && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) )
                 ) {
                  return propagateFloat128NaN( a, a );
              }
              return a;
          }
          lastBitMask = 1;
          lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1;
          roundBitsMask = lastBitMask - 1;
          z = a;
          roundingMode = float_rounding_mode();
          if ( roundingMode == float_round_nearest_even ) {
              if ( lastBitMask ) {
                  add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low );
                  if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
              }
              else {
                  if ( (sbits64) z.low < 0 ) {
                      ++z.high;
                      if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1;
                  }
              }
          }
          else if ( roundingMode != float_round_to_zero ) {
              if (   extractFloat128Sign( z )
                   ^ ( roundingMode == float_round_up ) ) {
                  add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low );
              }
          }
          z.low &= ~ roundBitsMask;
      }
      else {
          if ( aExp < 0x3FFF ) {
              if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
              float_set_inexact();
              aSign = extractFloat128Sign( a );
              switch ( float_rounding_mode() ) {
               case float_round_nearest_even:
                  if (    ( aExp == 0x3FFE )
                       && (   extractFloat128Frac0( a )
                            | extractFloat128Frac1( a ) )
                     ) {
                      return packFloat128( aSign, 0x3FFF, 0, 0 );
                  }
                  break;
               case float_round_down:
                  return
                        aSign ? packFloat128( 1, 0x3FFF, 0, 0 )
                      : packFloat128( 0, 0, 0, 0 );
               case float_round_up:
                  return
                        aSign ? packFloat128( 1, 0, 0, 0 )
                      : packFloat128( 0, 0x3FFF, 0, 0 );
              }
              return packFloat128( aSign, 0, 0, 0 );
          }
          lastBitMask = 1;
          lastBitMask <<= 0x402F - aExp;
          roundBitsMask = lastBitMask - 1;
          z.low = 0;
          z.high = a.high;
          roundingMode = float_rounding_mode();
          if ( roundingMode == float_round_nearest_even ) {
              z.high += lastBitMask>>1;
              if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) {
                  z.high &= ~ lastBitMask;
              }
          }
          else if ( roundingMode != float_round_to_zero ) {
              if (   extractFloat128Sign( z )
                   ^ ( roundingMode == float_round_up ) ) {
                  z.high |= ( a.low != 0 );
                  z.high += roundBitsMask;
              }
          }
          z.high &= ~ roundBitsMask;
      }
      if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
          float_set_inexact();
      }
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the absolute values of the quadruple-precision
  floating-point values `a' and `b'.  If `zSign' is 1, the sum is negated
  before being returned.  `zSign' is ignored if the result is a NaN.
  The addition is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static float128 addFloat128Sigs( float128 a, float128 b, flag zSign )
  {
      int32 aExp, bExp, zExp;
      bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
      int32 expDiff;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      bSig1 = extractFloat128Frac1( b );
      bSig0 = extractFloat128Frac0( b );
      bExp = extractFloat128Exp( b );
      expDiff = aExp - bExp;
      if ( 0 < expDiff ) {
          if ( aExp == 0x7FFF ) {
              if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b );
              return a;
          }
          if ( bExp == 0 ) {
              --expDiff;
          }
          else {
              bSig0 |= LIT64( 0x0001000000000000 );
          }
          shift128ExtraRightJamming(
              bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
          zExp = aExp;
      }
      else if ( expDiff < 0 ) {
          if ( bExp == 0x7FFF ) {
              if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
              return packFloat128( zSign, 0x7FFF, 0, 0 );
          }
          if ( aExp == 0 ) {
              ++expDiff;
          }
          else {
              aSig0 |= LIT64( 0x0001000000000000 );
          }
          shift128ExtraRightJamming(
              aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
          zExp = bExp;
      }
      else {
          if ( aExp == 0x7FFF ) {
              if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
                  return propagateFloat128NaN( a, b );
              }
              return a;
          }
          add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
          if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 );
          zSig2 = 0;
          zSig0 |= LIT64( 0x0002000000000000 );
          zExp = aExp;
          goto shiftRight1;
      }
      aSig0 |= LIT64( 0x0001000000000000 );
      add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
      --zExp;
      if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack;
      ++zExp;
   shiftRight1:
      shift128ExtraRightJamming(
          zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
   roundAndPack:
      return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the absolute values of the quadruple-
  precision floating-point values `a' and `b'.  If `zSign' is 1, the
  difference is negated before being returned.  `zSign' is ignored if the
  result is a NaN.  The subtraction is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  static float128 subFloat128Sigs( float128 a, float128 b, flag zSign )
  {
      int32 aExp, bExp, zExp;
      bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
      int32 expDiff;
      float128 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      bSig1 = extractFloat128Frac1( b );
      bSig0 = extractFloat128Frac0( b );
      bExp = extractFloat128Exp( b );
      expDiff = aExp - bExp;
      shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
      shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 );
      if ( 0 < expDiff ) goto aExpBigger;
      if ( expDiff < 0 ) goto bExpBigger;
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
              return propagateFloat128NaN( a, b );
          }
          float_raise( float_flag_invalid );
          z.low = float128_default_nan_low;
          z.high = float128_default_nan_high;
          return z;
      }
      if ( aExp == 0 ) {
          aExp = 1;
          bExp = 1;
      }
      if ( bSig0 < aSig0 ) goto aBigger;
      if ( aSig0 < bSig0 ) goto bBigger;
      if ( bSig1 < aSig1 ) goto aBigger;
      if ( aSig1 < bSig1 ) goto bBigger;
      return packFloat128( float_rounding_mode() == float_round_down, 0, 0, 0 );
   bExpBigger:
      if ( bExp == 0x7FFF ) {
          if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
          return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 );
      }
      if ( aExp == 0 ) {
          ++expDiff;
      }
      else {
          aSig0 |= LIT64( 0x4000000000000000 );
      }
      shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
      bSig0 |= LIT64( 0x4000000000000000 );
   bBigger:
      sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 );
      zExp = bExp;
      zSign ^= 1;
      goto normalizeRoundAndPack;
   aExpBigger:
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          --expDiff;
      }
      else {
          bSig0 |= LIT64( 0x4000000000000000 );
      }
      shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 );
      aSig0 |= LIT64( 0x4000000000000000 );
   aBigger:
      sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
      zExp = aExp;
   normalizeRoundAndPack:
      --zExp;
      return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of adding the quadruple-precision floating-point values
  `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
  for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_add( float128 a, float128 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloat128Sign( a );
      bSign = extractFloat128Sign( b );
      if ( aSign == bSign ) {
          return addFloat128Sigs( a, b, aSign );
      }
      else {
          return subFloat128Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of subtracting the quadruple-precision floating-point
  values `a' and `b'.  The operation is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_sub( float128 a, float128 b )
  {
      flag aSign, bSign;
  
      aSign = extractFloat128Sign( a );
      bSign = extractFloat128Sign( b );
      if ( aSign == bSign ) {
          return subFloat128Sigs( a, b, aSign );
      }
      else {
          return addFloat128Sigs( a, b, aSign );
      }
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of multiplying the quadruple-precision floating-point
  values `a' and `b'.  The operation is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_mul( float128 a, float128 b )
  {
      flag aSign, bSign, zSign;
      int32 aExp, bExp, zExp;
      bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
      float128 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      bSig1 = extractFloat128Frac1( b );
      bSig0 = extractFloat128Frac0( b );
      bExp = extractFloat128Exp( b );
      bSign = extractFloat128Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0x7FFF ) {
          if (    ( aSig0 | aSig1 )
               || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
              return propagateFloat128NaN( a, b );
          }
          if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid;
          return packFloat128( zSign, 0x7FFF, 0, 0 );
      }
      if ( bExp == 0x7FFF ) {
          if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
          if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
   invalid:
              float_raise( float_flag_invalid );
              z.low = float128_default_nan_low;
              z.high = float128_default_nan_high;
              return z;
          }
          return packFloat128( zSign, 0x7FFF, 0, 0 );
      }
      if ( aExp == 0 ) {
          if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
          normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
      }
      if ( bExp == 0 ) {
          if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
          normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
      }
      zExp = aExp + bExp - 0x4000;
      aSig0 |= LIT64( 0x0001000000000000 );
      shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 );
      mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 );
      add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 );
      zSig2 |= ( zSig3 != 0 );
      if ( LIT64( 0x0002000000000000 ) <= zSig0 ) {
          shift128ExtraRightJamming(
              zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
          ++zExp;
      }
      return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of dividing the quadruple-precision floating-point value
  `a' by the corresponding value `b'.  The operation is performed according to
  the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_div( float128 a, float128 b )
  {
      flag aSign, bSign, zSign;
      int32 aExp, bExp, zExp;
      bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
      bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
      float128 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      bSig1 = extractFloat128Frac1( b );
      bSig0 = extractFloat128Frac0( b );
      bExp = extractFloat128Exp( b );
      bSign = extractFloat128Sign( b );
      zSign = aSign ^ bSign;
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b );
          if ( bExp == 0x7FFF ) {
              if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
              goto invalid;
          }
          return packFloat128( zSign, 0x7FFF, 0, 0 );
      }
      if ( bExp == 0x7FFF ) {
          if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
          return packFloat128( zSign, 0, 0, 0 );
      }
      if ( bExp == 0 ) {
          if ( ( bSig0 | bSig1 ) == 0 ) {
              if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
   invalid:
                  float_raise( float_flag_invalid );
                  z.low = float128_default_nan_low;
                  z.high = float128_default_nan_high;
                  return z;
              }
              float_raise( float_flag_divbyzero );
              return packFloat128( zSign, 0x7FFF, 0, 0 );
          }
          normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
      }
      if ( aExp == 0 ) {
          if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
          normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
      }
      zExp = aExp - bExp + 0x3FFD;
      shortShift128Left(
          aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 );
      shortShift128Left(
          bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 );
      if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) {
          shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
          ++zExp;
      }
      zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 );
      mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 );
      sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
      while ( (sbits64) rem0 < 0 ) {
          --zSig0;
          add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
      }
      zSig1 = estimateDiv128To64( rem1, rem2, bSig0 );
      if ( ( zSig1 & 0x3FFF ) <= 4 ) {
          mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 );
          sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
          while ( (sbits64) rem1 < 0 ) {
              --zSig1;
              add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
          }
          zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
      }
      shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 );
      return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the remainder of the quadruple-precision floating-point value `a'
  with respect to the corresponding value `b'.  The operation is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_rem( float128 a, float128 b )
  {
      flag aSign, bSign, zSign;
      int32 aExp, bExp, expDiff;
      bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
      bits64 allZero, alternateASig0, alternateASig1, sigMean1;
      sbits64 sigMean0;
      float128 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      bSig1 = extractFloat128Frac1( b );
      bSig0 = extractFloat128Frac0( b );
      bExp = extractFloat128Exp( b );
      bSign = extractFloat128Sign( b );
      if ( aExp == 0x7FFF ) {
          if (    ( aSig0 | aSig1 )
               || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
              return propagateFloat128NaN( a, b );
          }
          goto invalid;
      }
      if ( bExp == 0x7FFF ) {
          if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
          return a;
      }
      if ( bExp == 0 ) {
          if ( ( bSig0 | bSig1 ) == 0 ) {
   invalid:
              float_raise( float_flag_invalid );
              z.low = float128_default_nan_low;
              z.high = float128_default_nan_high;
              return z;
          }
          normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
      }
      if ( aExp == 0 ) {
          if ( ( aSig0 | aSig1 ) == 0 ) return a;
          normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
      }
      expDiff = aExp - bExp;
      if ( expDiff < -1 ) return a;
      shortShift128Left(
          aSig0 | LIT64( 0x0001000000000000 ),
          aSig1,
          15 - ( expDiff < 0 ),
          &aSig0,
          &aSig1
      );
      shortShift128Left(
          bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 );
      q = le128( bSig0, bSig1, aSig0, aSig1 );
      if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
      expDiff -= 64;
      while ( 0 < expDiff ) {
          q = estimateDiv128To64( aSig0, aSig1, bSig0 );
          q = ( 4 < q ) ? q - 4 : 0;
          mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
          shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
          shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
          sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
          expDiff -= 61;
      }
      if ( -64 < expDiff ) {
          q = estimateDiv128To64( aSig0, aSig1, bSig0 );
          q = ( 4 < q ) ? q - 4 : 0;
          q >>= - expDiff;
          shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
          expDiff += 52;
          if ( expDiff < 0 ) {
              shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
          }
          else {
              shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 );
          }
          mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
          sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 );
      }
      else {
          shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
          shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
      }
      do {
          alternateASig0 = aSig0;
          alternateASig1 = aSig1;
          ++q;
          sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
      } while ( 0 <= (sbits64) aSig0 );
      add128(
          aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 );
      if (    ( sigMean0 < 0 )
           || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
          aSig0 = alternateASig0;
          aSig1 = alternateASig1;
      }
      zSign = ( (sbits64) aSig0 < 0 );
      if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
      return
          normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the square root of the quadruple-precision floating-point value `a'.
  The operation is performed according to the IEC/IEEE Standard for Binary
  Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  float128 float128_sqrt( float128 a )
  {
      flag aSign;
      int32 aExp, zExp;
      bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
      bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
      float128 z;
  
      aSig1 = extractFloat128Frac1( a );
      aSig0 = extractFloat128Frac0( a );
      aExp = extractFloat128Exp( a );
      aSign = extractFloat128Sign( a );
      if ( aExp == 0x7FFF ) {
          if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a );
          if ( ! aSign ) return a;
          goto invalid;
      }
      if ( aSign ) {
          if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
   invalid:
          float_raise( float_flag_invalid );
          z.low = float128_default_nan_low;
          z.high = float128_default_nan_high;
          return z;
      }
      if ( aExp == 0 ) {
          if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 );
          normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
      }
      zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE;
      aSig0 |= LIT64( 0x0001000000000000 );
      zSig0 = estimateSqrt32( aExp, aSig0>>17 );
      shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 );
      zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
      doubleZSig0 = zSig0<<1;
      mul64To128( zSig0, zSig0, &term0, &term1 );
      sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
      while ( (sbits64) rem0 < 0 ) {
          --zSig0;
          doubleZSig0 -= 2;
          add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
      }
      zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
      if ( ( zSig1 & 0x1FFF ) <= 5 ) {
          if ( zSig1 == 0 ) zSig1 = 1;
          mul64To128( doubleZSig0, zSig1, &term1, &term2 );
          sub128( rem1, 0, term1, term2, &rem1, &rem2 );
          mul64To128( zSig1, zSig1, &term2, &term3 );
          sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
          while ( (sbits64) rem1 < 0 ) {
              --zSig1;
              shortShift128Left( 0, zSig1, 1, &term2, &term3 );
              term3 |= 1;
              term2 |= doubleZSig0;
              add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
          }
          zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
      }
      shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 );
      return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the quadruple-precision floating-point value `a' is equal to
  the corresponding value `b', and 0 otherwise.  The comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float128_eq( float128 a, float128 b )
  {
  
      if (    (    ( extractFloat128Exp( a ) == 0x7FFF )
                && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
           || (    ( extractFloat128Exp( b ) == 0x7FFF )
                && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
         ) {
          if (    float128_is_signaling_nan( a )
               || float128_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      return
             ( a.low == b.low )
          && (    ( a.high == b.high )
               || (    ( a.low == 0 )
                    && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) )
             );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the quadruple-precision floating-point value `a' is less than
  or equal to the corresponding value `b', and 0 otherwise.  The comparison
  is performed according to the IEC/IEEE Standard for Binary Floating-Point
  Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float128_le( float128 a, float128 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloat128Exp( a ) == 0x7FFF )
                && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
           || (    ( extractFloat128Exp( b ) == 0x7FFF )
                && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloat128Sign( a );
      bSign = extractFloat128Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              || (    ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   == 0 );
      }
      return
            aSign ? le128( b.high, b.low, a.high, a.low )
          : le128( a.high, a.low, b.high, b.low );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the quadruple-precision floating-point value `a' is less than
  the corresponding value `b', and 0 otherwise.  The comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float128_lt( float128 a, float128 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloat128Exp( a ) == 0x7FFF )
                && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
           || (    ( extractFloat128Exp( b ) == 0x7FFF )
                && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      aSign = extractFloat128Sign( a );
      bSign = extractFloat128Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              && (    ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   != 0 );
      }
      return
            aSign ? lt128( b.high, b.low, a.high, a.low )
          : lt128( a.high, a.low, b.high, b.low );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the quadruple-precision floating-point value `a' is equal to
  the corresponding value `b', and 0 otherwise.  The invalid exception is
  raised if either operand is a NaN.  Otherwise, the comparison is performed
  according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float128_eq_signaling( float128 a, float128 b )
  {
  
      if (    (    ( extractFloat128Exp( a ) == 0x7FFF )
                && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
           || (    ( extractFloat128Exp( b ) == 0x7FFF )
                && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
         ) {
          float_raise( float_flag_invalid );
          return 0;
      }
      return
             ( a.low == b.low )
          && (    ( a.high == b.high )
               || (    ( a.low == 0 )
                    && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) )
             );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the quadruple-precision floating-point value `a' is less than
  or equal to the corresponding value `b', and 0 otherwise.  Quiet NaNs do not
  cause an exception.  Otherwise, the comparison is performed according to the
  IEC/IEEE Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float128_le_quiet( float128 a, float128 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloat128Exp( a ) == 0x7FFF )
                && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
           || (    ( extractFloat128Exp( b ) == 0x7FFF )
                && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
         ) {
          if (    float128_is_signaling_nan( a )
               || float128_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloat128Sign( a );
      bSign = extractFloat128Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              || (    ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   == 0 );
      }
      return
            aSign ? le128( b.high, b.low, a.high, a.low )
          : le128( a.high, a.low, b.high, b.low );
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns 1 if the quadruple-precision floating-point value `a' is less than
  the corresponding value `b', and 0 otherwise.  Quiet NaNs do not cause an
  exception.  Otherwise, the comparison is performed according to the IEC/IEEE
  Standard for Binary Floating-Point Arithmetic.
  -------------------------------------------------------------------------------
  */
  flag float128_lt_quiet( float128 a, float128 b )
  {
      flag aSign, bSign;
  
      if (    (    ( extractFloat128Exp( a ) == 0x7FFF )
                && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
           || (    ( extractFloat128Exp( b ) == 0x7FFF )
                && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
         ) {
          if (    float128_is_signaling_nan( a )
               || float128_is_signaling_nan( b ) ) {
              float_raise( float_flag_invalid );
          }
          return 0;
      }
      aSign = extractFloat128Sign( a );
      bSign = extractFloat128Sign( b );
      if ( aSign != bSign ) {
          return
                 aSign
              && (    ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
                   != 0 );
      }
      return
            aSign ? lt128( b.high, b.low, a.high, a.low )
          : lt128( a.high, a.low, b.high, b.low );
  
  }
  
  #endif
  
  
  #if defined(SOFTFLOAT_FOR_GCC) && defined(SOFTFLOAT_NEED_FIXUNS)
  
  /*
   * These two routines are not part of the original softfloat distribution.
   *
   * They are based on the corresponding conversions to integer but return
   * unsigned numbers instead since these functions are required by GCC.
   *
   * Added by Mark Brinicombe <mark@NetBSD.org>   27/09/97
   *
   * float64 version overhauled for SoftFloat 2a [bjh21 2000-07-15]
   */
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the double-precision floating-point value
  `a' to the 32-bit unsigned integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-point
  Arithmetic, except that the conversion is always rounded toward zero.  If
  `a' is a NaN, the largest positive integer is returned.  If the conversion
  overflows, the largest integer positive is returned.
  -------------------------------------------------------------------------------
  */
  uint32 float64_to_uint32_round_to_zero( float64 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits64 aSig, savedASig;
      uint32 z;
  
      aSig = extractFloat64Frac( a );
      aExp = extractFloat64Exp( a );
      aSign = extractFloat64Sign( a );
  
      if (aSign) {
          float_raise( float_flag_invalid );
          return(0);
      }
  
      if ( 0x41E < aExp ) {
          float_raise( float_flag_invalid );
          return 0xffffffff;
      }
      else if ( aExp < 0x3FF ) {
          if ( aExp || aSig ) float_set_inexact();
          return 0;
      }
      aSig |= LIT64( 0x0010000000000000 );
      shiftCount = 0x433 - aExp;
      savedASig = aSig;
      aSig >>= shiftCount;
      z = aSig;
      if ( ( aSig<<shiftCount ) != savedASig ) {
          float_set_inexact();
      }
      return z;
  
  }
  
  /*
  -------------------------------------------------------------------------------
  Returns the result of converting the single-precision floating-point value
  `a' to the 32-bit unsigned integer format.  The conversion is
  performed according to the IEC/IEEE Standard for Binary Floating-point
  Arithmetic, except that the conversion is always rounded toward zero.  If
  `a' is a NaN, the largest positive integer is returned.  If the conversion
  overflows, the largest positive integer is returned.
  -------------------------------------------------------------------------------
  */
  uint32 float32_to_uint32_round_to_zero( float32 a )
  {
      flag aSign;
      int16 aExp, shiftCount;
      bits32 aSig;
      uint32 z;
  
      aSig = extractFloat32Frac( a );
      aExp = extractFloat32Exp( a );
      aSign = extractFloat32Sign( a );
      shiftCount = aExp - 0x9E;
  
      if (aSign) {
          float_raise( float_flag_invalid );
          return(0);
      }
      if ( 0 < shiftCount ) {
          float_raise( float_flag_invalid );
          return 0xFFFFFFFF;
      }
      else if ( aExp <= 0x7E ) {
          if ( aExp | aSig ) float_set_inexact();
          return 0;
      }
      aSig = ( aSig | 0x800000 )<<8;
      z = aSig>>( - shiftCount );
      if ( aSig<<( shiftCount & 31 ) ) {
          float_set_inexact();
      }
      return z;
  
  }
  
  #endif
  
  #endif /* _STANDALONE */