Linux-2.6.12-rc2

Initial git repository build. I'm not bothering with the full history,
even though we have it. We can create a separate "historical" git
archive of that later if we want to, and in the meantime it's about
3.2GB when imported into git - space that would just make the early
git days unnecessarily complicated, when we don't have a lot of good
infrastructure for it.

Let it rip!

1 files changed, 3443 insertions, 0 deletions

diff --git a/arch/arm/nwfpe/softfloat.c b/arch/arm/nwfpe/softfloat.c
new file mode 100644
index 00000000000..9d743ae2906
--- /dev/null
+++ b/arch/arm/nwfpe/softfloat.c
@@ -0,0 +1,3443 @@
+/*
+===============================================================================
+
+This C source file is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 2.
+
+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 three paragraphs for those parts of
+this code that are retained.
+
+===============================================================================
+*/
+
+#include "fpa11.h"
+//#include "milieu.h"
+//#include "softfloat.h"
+
+/*
+-------------------------------------------------------------------------------
+Floating-point rounding mode, extended double-precision rounding precision,
+and exception flags.
+-------------------------------------------------------------------------------
+*/
+int8 float_rounding_mode = float_round_nearest_even;
+int8 floatx80_rounding_precision = 80;
+int8 float_exception_flags;
+
+/*
+-------------------------------------------------------------------------------
+Primitive arithmetic functions, including multi-word arithmetic, and
+division and square root approximations.  (Can be specialized to target if
+desired.)
+-------------------------------------------------------------------------------
+*/
+#include "softfloat-macros"
+
+/*
+-------------------------------------------------------------------------------
+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"
+
+/*
+-------------------------------------------------------------------------------
+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 nonzero, 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.  If the fixed-point
+input is too large, however, 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_exception_flags |= float_flag_invalid;
+        return zSign ? 0x80000000 : 0x7FFFFFFF;
+    }
+    if ( roundBits ) float_exception_flags |= float_flag_inexact;
+    return z;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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'.
+-------------------------------------------------------------------------------
+*/
+#if 0   /* in softfloat.h */
+INLINE flag extractFloat32Sign( float32 a )
+{
+
+    return a>>31;
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+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 )
+{
+#if 0
+   float32 f;
+   __asm__("@ packFloat32                               \n\
+            mov %0, %1, asl #31                         \n\
+            orr %0, %2, asl #23                         \n\
+            orr %0, %3"
+            : /* no outputs */
+            : "g" (f), "g" (zSign), "g" (zExp), "g" (zSig)
+            : "cc");
+   return f;
+#else
+    return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
+#endif 
+}
+
+/*
+-------------------------------------------------------------------------------
+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.  If the abstract value is too large, however, 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_exception_flags |= float_flag_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 in
+any way.  In all cases, `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 a & LIT64( 0x000FFFFFFFFFFFFF );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the exponent bits of the double-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE int16 extractFloat64Exp( float64 a )
+{
+
+    return ( a>>52 ) & 0x7FF;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the sign bit of the double-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+#if 0   /* in softfloat.h */
+INLINE flag extractFloat64Sign( float64 a )
+{
+
+    return a>>63;
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+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 ( ( (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.  If the abstract value is too large, however, 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 ) )
+           ) {
+            //register int lr = __builtin_return_address(0);
+            //printk("roundAndPackFloat64 called from 0x%08x\n",lr);
+            float_raise( float_flag_overflow | float_flag_inexact );
+            return 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_exception_flags |= float_flag_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 in
+any way.  In all cases, `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.  If the abstract value is too large, however, 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_exception_flags |= float_flag_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_exception_flags |= float_flag_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_exception_flags |= float_flag_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 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
+                if ( (sbits64) zSig0 < 0 ) zExp = 1;
+            }
+            return packFloatx80( zSign, zExp, zSig0 );
+        }
+    }
+    if ( zSig1 ) float_exception_flags |= float_flag_inexact;
+    if ( increment ) {
+        ++zSig0;
+        if ( zSig0 == 0 ) {
+            ++zExp;
+            zSig0 = LIT64( 0x8000000000000000 );
+        }
+        else {
+            zSig0 &= ~ ( ( zSig1 + zSig1 == 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
+
+/*
+-------------------------------------------------------------------------------
+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 == 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 aSign;
+    uint32 absA;
+    int8 shiftCount;
+    bits64 zSig;
+
+    if ( a == 0 ) return 0;
+    aSign = ( a < 0 );
+    absA = aSign ? - a : a;
+    shiftCount = countLeadingZeros32( absA ) + 21;
+    zSig = absA;
+    return packFloat64( aSign, 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
+
+/*
+-------------------------------------------------------------------------------
+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 zSig;
+
+    aSig = extractFloat32Frac( a );
+    aExp = extractFloat32Exp( a );
+    aSign = extractFloat32Sign( a );
+    if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
+    if ( aExp ) aSig |= 0x00800000;
+    shiftCount = 0xAF - aExp;
+    zSig = aSig;
+    zSig <<= 32;
+    if ( 0 < shiftCount ) shift64RightJamming( zSig, shiftCount, &zSig );
+    return roundAndPackInt32( aSign, zSig );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 ) return 0x80000000;
+        float_raise( float_flag_invalid );
+        if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
+        return 0x80000000;
+    }
+    else if ( aExp <= 0x7E ) {
+        if ( aExp | aSig ) float_exception_flags |= float_flag_inexact;
+        return 0;
+    }
+    aSig = ( aSig | 0x00800000 )<<8;
+    z = aSig>>( - shiftCount );
+    if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
+        float_exception_flags |= float_flag_inexact;
+    }
+    return aSign ? - z : z;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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
+
+/*
+-------------------------------------------------------------------------------
+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_exception_flags |= float_flag_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_exception_flags |= float_flag_inexact;
+    return z;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of adding the absolute values of the single-precision
+floating-point values `a' and `b'.  If `zSign' is true, 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 true, 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 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 = 0xFFFFFFFF;
+        }
+        else {
+            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 );
+    return roundAndPackFloat32( 0, zExp, zSig );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 ) );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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;
+    //int16 aExp, bExp;
+
+    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 ) );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 );
+    shiftCount = 0x433 - aExp;
+    if ( shiftCount < 21 ) {
+        if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
+        goto invalid;
+    }
+    else if ( 52 < shiftCount ) {
+        if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
+        return 0;
+    }
+    aSig |= LIT64( 0x0010000000000000 );
+    savedASig = aSig;
+    aSig >>= shiftCount;
+    z = aSig;
+    if ( aSign ) z = - z;
+    if ( ( z < 0 ) ^ aSign ) {
+ invalid:
+        float_exception_flags |= float_flag_invalid;
+        return aSign ? 0x80000000 : 0x7FFFFFFF;
+    }
+    if ( ( aSig<<shiftCount ) != savedASig ) {
+        float_exception_flags |= float_flag_inexact;
+    }
+    return z;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of converting the double-precision floating-point value
+`a' to the 32-bit two's complement unsigned 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 positive integer is returned.
+-------------------------------------------------------------------------------
+*/
+int32 float64_to_uint32( float64 a )
+{
+    flag aSign;
+    int16 aExp, shiftCount;
+    bits64 aSig;
+
+    aSig = extractFloat64Frac( a );
+    aExp = extractFloat64Exp( a );
+    aSign = 0; //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 );
+}
+
+/*
+-------------------------------------------------------------------------------
+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 positive integer is returned.
+-------------------------------------------------------------------------------
+*/
+int32 float64_to_uint32_round_to_zero( float64 a )
+{
+    flag aSign;
+    int16 aExp, shiftCount;
+    bits64 aSig, savedASig;
+    int32 z;
+
+    aSig = extractFloat64Frac( a );
+    aExp = extractFloat64Exp( a );
+    aSign = extractFloat64Sign( a );
+    shiftCount = 0x433 - aExp;
+    if ( shiftCount < 21 ) {
+        if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
+        goto invalid;
+    }
+    else if ( 52 < shiftCount ) {
+        if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
+        return 0;
+    }
+    aSig |= LIT64( 0x0010000000000000 );
+    savedASig = aSig;
+    aSig >>= shiftCount;
+    z = aSig;
+    if ( aSign ) z = - z;
+    if ( ( z < 0 ) ^ aSign ) {
+ invalid:
+        float_exception_flags |= float_flag_invalid;
+        return aSign ? 0x80000000 : 0x7FFFFFFF;
+    }
+    if ( ( aSig<<shiftCount ) != savedASig ) {
+        float_exception_flags |= float_flag_inexact;
+    }
+    return z;
+}
+
+/*
+-------------------------------------------------------------------------------
+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
+
+/*
+-------------------------------------------------------------------------------
+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 <= 0x3FE ) {
+        if ( (bits64) ( a<<1 ) == 0 ) return a;
+        float_exception_flags |= float_flag_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_exception_flags |= float_flag_inexact;
+    return z;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of adding the absolute values of the double-precision
+floating-point values `a' and `b'.  If `zSign' is true, 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 true, 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 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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;
+    bits64 rem0, rem1, term0, term1; //, shiftedRem;
+    //float64 z;
+
+    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 );
+    zSig <<= 31;
+    aSig <<= 9 - ( aExp & 1 );
+    zSig = estimateDiv128To64( aSig, 0, zSig ) + zSig + 2;
+    if ( ( zSig & 0x3FF ) <= 5 ) {
+        if ( zSig < 2 ) {
+            zSig = LIT64( 0xFFFFFFFFFFFFFFFF );
+        }
+        else {
+            aSig <<= 2;
+            mul64To128( zSig, zSig, &term0, &term1 );
+            sub128( aSig, 0, term0, term1, &rem0, &rem1 );
+            while ( (sbits64) rem0 < 0 ) {
+                --zSig;
+                shortShift128Left( 0, zSig, 1, &term0, &term1 );
+                term1 |= 1;
+                add128( rem0, rem1, term0, term1, &rem0, &rem1 );
+            }
+            zSig |= ( ( rem0 | rem1 ) != 0 );
+        }
+    }
+    shift64RightJamming( zSig, 1, &zSig );
+    return roundAndPackFloat64( 0, zExp, zSig );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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) ( ( 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.  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) ( ( 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.  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) ( ( a | b )<<1 ) != 0 );
+    return ( a != b ) && ( aSign ^ ( a < b ) );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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;
+    //int16 aExp, bExp;
+
+    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 ) );
+
+}
+
+#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 );
+    shiftCount = 0x403E - aExp;
+    if ( shiftCount < 32 ) {
+        if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
+        goto invalid;
+    }
+    else if ( 63 < shiftCount ) {
+        if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
+        return 0;
+    }
+    savedASig = aSig;
+    aSig >>= shiftCount;
+    z = aSig;
+    if ( aSign ) z = - z;
+    if ( ( z < 0 ) ^ aSign ) {
+ invalid:
+        float_exception_flags |= float_flag_invalid;
+        return aSign ? 0x80000000 : 0x7FFFFFFF;
+    }
+    if ( ( aSig<<shiftCount ) != savedASig ) {
+        float_exception_flags |= float_flag_inexact;
+    }
+    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 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 <= 0x3FFE ) {
+        if (    ( aExp == 0 )
+             && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
+            return a;
+        }
+        float_exception_flags |= float_flag_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_exception_flags |= float_flag_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 true, 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 true,
+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;
+    bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+    bits64 shiftedRem0, shiftedRem1;
+    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 );
+    zSig0 <<= 31;
+    aSig1 = 0;
+    shift128Right( aSig0, 0, ( aExp & 1 ) + 2, &aSig0, &aSig1 );
+    zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0 ) + zSig0 + 4;
+    if ( 0 <= (sbits64) zSig0 ) zSig0 = LIT64( 0xFFFFFFFFFFFFFFFF );
+    shortShift128Left( aSig0, aSig1, 2, &aSig0, &aSig1 );
+    mul64To128( zSig0, zSig0, &term0, &term1 );
+    sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
+    while ( (sbits64) rem0 < 0 ) {
+        --zSig0;
+        shortShift128Left( 0, zSig0, 1, &term0, &term1 );
+        term1 |= 1;
+        add128( rem0, rem1, term0, term1, &rem0, &rem1 );
+    }
+    shortShift128Left( rem0, rem1, 63, &shiftedRem0, &shiftedRem1 );
+    zSig1 = estimateDiv128To64( shiftedRem0, shiftedRem1, zSig0 );
+    if ( (bits64) ( zSig1<<1 ) <= 10 ) {
+        if ( zSig1 == 0 ) zSig1 = 1;
+        mul64To128( zSig0, zSig1, &term1, &term2 );
+        shortShift128Left( term1, term2, 1, &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;
+            shortShift192Left( 0, zSig0, zSig1, 1, &term1, &term2, &term3 );
+            term3 |= 1;
+            add192(
+                rem1, rem2, rem3, term1, term2, term3, &rem1, &rem2, &rem3 );
+        }
+        zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
+    }
+    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
+