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+
+/*============================================================================
+
+This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 2b.
+
+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://www.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 ALL LOSSES,
+COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
+EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
+INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
+OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) the source code for the derivative work includes prominent notice that
+the work is derivative, and (2) the source code includes prominent notice with
+these four paragraphs for those parts of this code that are retained.
+
+=============================================================================*/
+
+/*----------------------------------------------------------------------------
+| Underflow tininess-detection mode, statically initialized to default value.
+| (The declaration in `softfloat.h' must match the `int8' type here.)
+*----------------------------------------------------------------------------*/
+int8 float_detect_tininess = float_tininess_after_rounding;
+
+/*----------------------------------------------------------------------------
+| Raises the exceptions specified by `flags'. Floating-point traps can be
+| defined here if desired. It is currently not possible for such a trap
+| to substitute a result value. If traps are not implemented, this routine
+| should be simply `float_exception_flags |= flags;'.
+*----------------------------------------------------------------------------*/
+
+void float_raise( int8 flags STATUS_PARAM )
+{
+
+ STATUS(float_exception_flags) |= flags;
+
+}
+
+/*----------------------------------------------------------------------------
+| Internal canonical NaN format.
+*----------------------------------------------------------------------------*/
+typedef struct {
+ flag sign;
+ bits64 high, low;
+} commonNaNT;
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated single-precision NaN.
+*----------------------------------------------------------------------------*/
+#define float32_default_nan 0xFFC00000
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is a NaN;
+| otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float32_is_nan( float32 a )
+{
+
+ return ( 0xFF000000 < (bits32) ( a<<1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is a signaling
+| NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float32_is_signaling_nan( float32 a )
+{
+
+ return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point NaN
+| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM )
+{
+ commonNaNT z;
+
+ if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR );
+ z.sign = a>>31;
+ z.low = 0;
+ z.high = ( (bits64) a )<<41;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the single-
+| precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static float32 commonNaNToFloat32( commonNaNT a )
+{
+
+ return ( ( (bits32) a.sign )<<31 ) | 0x7FC00000 | ( a.high>>41 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two single-precision floating-point values `a' and `b', one of which
+| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
+| signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = float32_is_nan( a );
+ aIsSignalingNaN = float32_is_signaling_nan( a );
+ bIsNaN = float32_is_nan( b );
+ bIsSignalingNaN = float32_is_signaling_nan( b );
+ a |= 0x00400000;
+ b |= 0x00400000;
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( (bits32) ( a<<1 ) < (bits32) ( b<<1 ) ) return b;
+ if ( (bits32) ( b<<1 ) < (bits32) ( a<<1 ) ) return a;
+ return ( a < b ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated double-precision NaN.
+*----------------------------------------------------------------------------*/
+#define float64_default_nan LIT64( 0xFFF8000000000000 )
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is a NaN;
+| otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float64_is_nan( float64 a )
+{
+
+ return ( LIT64( 0xFFE0000000000000 ) < (bits64) ( a<<1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is a signaling
+| NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float64_is_signaling_nan( float64 a )
+{
+
+ return
+ ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
+ && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point NaN
+| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM)
+{
+ commonNaNT z;
+
+ if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
+ z.sign = a>>63;
+ z.low = 0;
+ z.high = a<<12;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the double-
+| precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static float64 commonNaNToFloat64( commonNaNT a )
+{
+
+ return
+ ( ( (bits64) a.sign )<<63 )
+ | LIT64( 0x7FF8000000000000 )
+ | ( a.high>>12 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two double-precision floating-point values `a' and `b', one of which
+| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
+| signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = float64_is_nan( a );
+ aIsSignalingNaN = float64_is_signaling_nan( a );
+ bIsNaN = float64_is_nan( b );
+ bIsSignalingNaN = float64_is_signaling_nan( b );
+ a |= LIT64( 0x0008000000000000 );
+ b |= LIT64( 0x0008000000000000 );
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( (bits64) ( a<<1 ) < (bits64) ( b<<1 ) ) return b;
+ if ( (bits64) ( b<<1 ) < (bits64) ( a<<1 ) ) return a;
+ return ( a < b ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated extended double-precision NaN. The
+| `high' and `low' values hold the most- and least-significant bits,
+| respectively.
+*----------------------------------------------------------------------------*/
+#define floatx80_default_nan_high 0xFFFF
+#define floatx80_default_nan_low LIT64( 0xC000000000000000 )
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is a
+| NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_is_nan( floatx80 a )
+{
+
+ return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is a
+| signaling NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_is_signaling_nan( floatx80 a )
+{
+ bits64 aLow;
+
+ aLow = a.low & ~ LIT64( 0x4000000000000000 );
+ return
+ ( ( a.high & 0x7FFF ) == 0x7FFF )
+ && (bits64) ( aLow<<1 )
+ && ( a.low == aLow );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point NaN `a' to the canonical NaN format. If `a' is a signaling NaN, the
+| invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM)
+{
+ commonNaNT z;
+
+ if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
+ z.sign = a.high>>15;
+ z.low = 0;
+ z.high = a.low<<1;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the extended
+| double-precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static floatx80 commonNaNToFloatx80( commonNaNT a )
+{
+ floatx80 z;
+
+ z.low = LIT64( 0xC000000000000000 ) | ( a.high>>1 );
+ z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two extended double-precision floating-point values `a' and `b', one
+| of which is a NaN, and returns the appropriate NaN result. If either `a' or
+| `b' is a signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = floatx80_is_nan( a );
+ aIsSignalingNaN = floatx80_is_signaling_nan( a );
+ bIsNaN = floatx80_is_nan( b );
+ bIsSignalingNaN = floatx80_is_signaling_nan( b );
+ a.low |= LIT64( 0xC000000000000000 );
+ b.low |= LIT64( 0xC000000000000000 );
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( a.low < b.low ) return b;
+ if ( b.low < a.low ) return a;
+ return ( a.high < b.high ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated quadruple-precision NaN. The `high' and
+| `low' values hold the most- and least-significant bits, respectively.
+*----------------------------------------------------------------------------*/
+#define float128_default_nan_high LIT64( 0xFFFF800000000000 )
+#define float128_default_nan_low LIT64( 0x0000000000000000 )
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is a NaN;
+| otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float128_is_nan( float128 a )
+{
+
+ return
+ ( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
+ && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is a
+| signaling NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float128_is_signaling_nan( float128 a )
+{
+
+ return
+ ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
+ && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point NaN
+| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM)
+{
+ commonNaNT z;
+
+ if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
+ z.sign = a.high>>63;
+ shortShift128Left( a.high, a.low, 16, &z.high, &z.low );
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the quadruple-
+| precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static float128 commonNaNToFloat128( commonNaNT a )
+{
+ float128 z;
+
+ shift128Right( a.high, a.low, 16, &z.high, &z.low );
+ z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF800000000000 );
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two quadruple-precision floating-point values `a' and `b', one of
+| which is a NaN, and returns the appropriate NaN result. If either `a' or
+| `b' is a signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = float128_is_nan( a );
+ aIsSignalingNaN = float128_is_signaling_nan( a );
+ bIsNaN = float128_is_nan( b );
+ bIsSignalingNaN = float128_is_signaling_nan( b );
+ a.high |= LIT64( 0x0000800000000000 );
+ b.high |= LIT64( 0x0000800000000000 );
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b;
+ if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a;
+ return ( a.high < b.high ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+#endif
+
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