root / fpu / softfloat-specialize.h @ b1d8e52e
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/*============================================================================
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This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2b.
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Written by John R. Hauser. This work was made possible in part by the
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International Computer Science Institute, located at Suite 600, 1947 Center
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Street, Berkeley, California 94704. Funding was partially provided by the
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National Science Foundation under grant MIP-9311980. The original version
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of this code was written as part of a project to build a fixed-point vector
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processor in collaboration with the University of California at Berkeley,
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overseen by Profs. Nelson Morgan and John Wawrzynek. More information
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is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
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arithmetic/SoftFloat.html'.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
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been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
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RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
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AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
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COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
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EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
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INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
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OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) the source code for the derivative work includes prominent notice that
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the work is derivative, and (2) the source code includes prominent notice with
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these four paragraphs for those parts of this code that are retained.
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=============================================================================*/
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#if defined(TARGET_MIPS) || defined(TARGET_HPPA)
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#define SNAN_BIT_IS_ONE 1 |
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#else
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#define SNAN_BIT_IS_ONE 0 |
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#endif
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/*----------------------------------------------------------------------------
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| Raises the exceptions specified by `flags'. Floating-point traps can be
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| defined here if desired. It is currently not possible for such a trap
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| to substitute a result value. If traps are not implemented, this routine
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| should be simply `float_exception_flags |= flags;'.
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*----------------------------------------------------------------------------*/
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void float_raise( int8 flags STATUS_PARAM )
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{ |
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STATUS(float_exception_flags) |= flags; |
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} |
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/*----------------------------------------------------------------------------
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| Internal canonical NaN format.
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*----------------------------------------------------------------------------*/
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typedef struct { |
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flag sign; |
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bits64 high, low; |
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} commonNaNT; |
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/*----------------------------------------------------------------------------
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| The pattern for a default generated single-precision NaN.
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*----------------------------------------------------------------------------*/
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#if defined(TARGET_SPARC)
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#define float32_default_nan make_float32(0x7FFFFFFF) |
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#elif defined(TARGET_POWERPC)
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#define float32_default_nan make_float32(0x7FC00000) |
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#elif defined(TARGET_HPPA)
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#define float32_default_nan make_float32(0x7FA00000) |
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#elif SNAN_BIT_IS_ONE
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#define float32_default_nan make_float32(0x7FBFFFFF) |
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#else
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#define float32_default_nan make_float32(0xFFC00000) |
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#endif
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/*----------------------------------------------------------------------------
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| Returns 1 if the single-precision floating-point value `a' is a quiet
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| NaN; otherwise returns 0.
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*----------------------------------------------------------------------------*/
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int float32_is_nan( float32 a_ )
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{ |
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uint32_t a = float32_val(a_); |
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#if SNAN_BIT_IS_ONE
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return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF ); |
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#else
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return ( 0xFF800000 <= (bits32) ( a<<1 ) ); |
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#endif
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} |
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/*----------------------------------------------------------------------------
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| Returns 1 if the single-precision floating-point value `a' is a signaling
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| NaN; otherwise returns 0.
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*----------------------------------------------------------------------------*/
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int float32_is_signaling_nan( float32 a_ )
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{ |
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uint32_t a = float32_val(a_); |
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#if SNAN_BIT_IS_ONE
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return ( 0xFF800000 <= (bits32) ( a<<1 ) ); |
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#else
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return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF ); |
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#endif
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} |
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/*----------------------------------------------------------------------------
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| Returns the result of converting the single-precision floating-point NaN
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| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
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| exception is raised.
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*----------------------------------------------------------------------------*/
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static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM )
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{ |
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commonNaNT z; |
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if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR );
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z.sign = float32_val(a)>>31;
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z.low = 0;
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z.high = ( (bits64) float32_val(a) )<<41;
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return z;
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} |
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/*----------------------------------------------------------------------------
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| Returns the result of converting the canonical NaN `a' to the single-
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| precision floating-point format.
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*----------------------------------------------------------------------------*/
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static float32 commonNaNToFloat32( commonNaNT a )
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{ |
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bits32 mantissa = a.high>>41;
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if ( mantissa )
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return make_float32(
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( ( (bits32) a.sign )<<31 ) | 0x7F800000 | ( a.high>>41 ) ); |
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else
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return float32_default_nan;
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} |
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/*----------------------------------------------------------------------------
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| Takes two single-precision floating-point values `a' and `b', one of which
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| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
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| signaling NaN, the invalid exception is raised.
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*----------------------------------------------------------------------------*/
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static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM)
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{ |
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flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; |
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bits32 av, bv, res; |
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aIsNaN = float32_is_nan( a ); |
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aIsSignalingNaN = float32_is_signaling_nan( a ); |
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bIsNaN = float32_is_nan( b ); |
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bIsSignalingNaN = float32_is_signaling_nan( b ); |
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av = float32_val(a); |
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bv = float32_val(b); |
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#if SNAN_BIT_IS_ONE
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av &= ~0x00400000;
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bv &= ~0x00400000;
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#else
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av |= 0x00400000;
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bv |= 0x00400000;
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#endif
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if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
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if ( aIsSignalingNaN ) {
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if ( bIsSignalingNaN ) goto returnLargerSignificand; |
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res = bIsNaN ? bv : av; |
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} |
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else if ( aIsNaN ) { |
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if ( bIsSignalingNaN | ! bIsNaN )
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res = av; |
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else {
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returnLargerSignificand:
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if ( (bits32) ( av<<1 ) < (bits32) ( bv<<1 ) ) |
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res = bv; |
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else if ( (bits32) ( bv<<1 ) < (bits32) ( av<<1 ) ) |
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res = av; |
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else
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res = ( av < bv ) ? av : bv; |
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} |
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} |
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else {
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res = bv; |
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} |
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return make_float32(res);
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} |
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/*----------------------------------------------------------------------------
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| The pattern for a default generated double-precision NaN.
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*----------------------------------------------------------------------------*/
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#if defined(TARGET_SPARC)
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#define float64_default_nan make_float64(LIT64( 0x7FFFFFFFFFFFFFFF )) |
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#elif defined(TARGET_POWERPC)
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#define float64_default_nan make_float64(LIT64( 0x7FF8000000000000 )) |
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#elif defined(TARGET_HPPA)
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#define float64_default_nan make_float64(LIT64( 0x7FF4000000000000 )) |
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#elif SNAN_BIT_IS_ONE
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#define float64_default_nan make_float64(LIT64( 0x7FF7FFFFFFFFFFFF )) |
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#else
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#define float64_default_nan make_float64(LIT64( 0xFFF8000000000000 )) |
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#endif
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/*----------------------------------------------------------------------------
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| Returns 1 if the double-precision floating-point value `a' is a quiet
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| NaN; otherwise returns 0.
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*----------------------------------------------------------------------------*/
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int float64_is_nan( float64 a_ )
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{ |
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bits64 a = float64_val(a_); |
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#if SNAN_BIT_IS_ONE
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return
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( ( ( a>>51 ) & 0xFFF ) == 0xFFE ) |
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&& ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
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#else
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return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) ); |
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#endif
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} |
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/*----------------------------------------------------------------------------
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| Returns 1 if the double-precision floating-point value `a' is a signaling
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| NaN; otherwise returns 0.
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*----------------------------------------------------------------------------*/
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int float64_is_signaling_nan( float64 a_ )
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{ |
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bits64 a = float64_val(a_); |
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#if SNAN_BIT_IS_ONE
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return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) ); |
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#else
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return
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( ( ( a>>51 ) & 0xFFF ) == 0xFFE ) |
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&& ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
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#endif
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} |
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/*----------------------------------------------------------------------------
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| Returns the result of converting the double-precision floating-point NaN
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| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
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| exception is raised.
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*----------------------------------------------------------------------------*/
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static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM)
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{ |
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commonNaNT z; |
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if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
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z.sign = float64_val(a)>>63;
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z.low = 0;
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z.high = float64_val(a)<<12;
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return z;
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} |
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/*----------------------------------------------------------------------------
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| Returns the result of converting the canonical NaN `a' to the double-
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| precision floating-point format.
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*----------------------------------------------------------------------------*/
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static float64 commonNaNToFloat64( commonNaNT a )
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{ |
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bits64 mantissa = a.high>>12;
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if ( mantissa )
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return make_float64(
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( ( (bits64) a.sign )<<63 )
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| LIT64( 0x7FF0000000000000 )
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| ( a.high>>12 ));
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else
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return float64_default_nan;
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} |
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/*----------------------------------------------------------------------------
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| Takes two double-precision floating-point values `a' and `b', one of which
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| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
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| signaling NaN, the invalid exception is raised.
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*----------------------------------------------------------------------------*/
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static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM)
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{ |
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flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; |
277 |
bits64 av, bv, res; |
278 |
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aIsNaN = float64_is_nan( a ); |
280 |
aIsSignalingNaN = float64_is_signaling_nan( a ); |
281 |
bIsNaN = float64_is_nan( b ); |
282 |
bIsSignalingNaN = float64_is_signaling_nan( b ); |
283 |
av = float64_val(a); |
284 |
bv = float64_val(b); |
285 |
#if SNAN_BIT_IS_ONE
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av &= ~LIT64( 0x0008000000000000 );
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bv &= ~LIT64( 0x0008000000000000 );
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#else
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av |= LIT64( 0x0008000000000000 );
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bv |= LIT64( 0x0008000000000000 );
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#endif
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if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
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if ( aIsSignalingNaN ) {
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if ( bIsSignalingNaN ) goto returnLargerSignificand; |
295 |
res = bIsNaN ? bv : av; |
296 |
} |
297 |
else if ( aIsNaN ) { |
298 |
if ( bIsSignalingNaN | ! bIsNaN )
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res = av; |
300 |
else {
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returnLargerSignificand:
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if ( (bits64) ( av<<1 ) < (bits64) ( bv<<1 ) ) |
303 |
res = bv; |
304 |
else if ( (bits64) ( bv<<1 ) < (bits64) ( av<<1 ) ) |
305 |
res = av; |
306 |
else
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res = ( av < bv ) ? av : bv; |
308 |
} |
309 |
} |
310 |
else {
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311 |
res = bv; |
312 |
} |
313 |
return make_float64(res);
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} |
315 |
|
316 |
#ifdef FLOATX80
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317 |
|
318 |
/*----------------------------------------------------------------------------
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| The pattern for a default generated extended double-precision NaN. The
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320 |
| `high' and `low' values hold the most- and least-significant bits,
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321 |
| respectively.
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322 |
*----------------------------------------------------------------------------*/
|
323 |
#if SNAN_BIT_IS_ONE
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324 |
#define floatx80_default_nan_high 0x7FFF |
325 |
#define floatx80_default_nan_low LIT64( 0xBFFFFFFFFFFFFFFF ) |
326 |
#else
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327 |
#define floatx80_default_nan_high 0xFFFF |
328 |
#define floatx80_default_nan_low LIT64( 0xC000000000000000 ) |
329 |
#endif
|
330 |
|
331 |
/*----------------------------------------------------------------------------
|
332 |
| Returns 1 if the extended double-precision floating-point value `a' is a
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333 |
| quiet NaN; otherwise returns 0.
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334 |
*----------------------------------------------------------------------------*/
|
335 |
|
336 |
int floatx80_is_nan( floatx80 a )
|
337 |
{ |
338 |
#if SNAN_BIT_IS_ONE
|
339 |
bits64 aLow; |
340 |
|
341 |
aLow = a.low & ~ LIT64( 0x4000000000000000 );
|
342 |
return
|
343 |
( ( a.high & 0x7FFF ) == 0x7FFF ) |
344 |
&& (bits64) ( aLow<<1 )
|
345 |
&& ( a.low == aLow ); |
346 |
#else
|
347 |
return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 ); |
348 |
#endif
|
349 |
} |
350 |
|
351 |
/*----------------------------------------------------------------------------
|
352 |
| Returns 1 if the extended double-precision floating-point value `a' is a
|
353 |
| signaling NaN; otherwise returns 0.
|
354 |
*----------------------------------------------------------------------------*/
|
355 |
|
356 |
int floatx80_is_signaling_nan( floatx80 a )
|
357 |
{ |
358 |
#if SNAN_BIT_IS_ONE
|
359 |
return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 ); |
360 |
#else
|
361 |
bits64 aLow; |
362 |
|
363 |
aLow = a.low & ~ LIT64( 0x4000000000000000 );
|
364 |
return
|
365 |
( ( a.high & 0x7FFF ) == 0x7FFF ) |
366 |
&& (bits64) ( aLow<<1 )
|
367 |
&& ( a.low == aLow ); |
368 |
#endif
|
369 |
} |
370 |
|
371 |
/*----------------------------------------------------------------------------
|
372 |
| Returns the result of converting the extended double-precision floating-
|
373 |
| point NaN `a' to the canonical NaN format. If `a' is a signaling NaN, the
|
374 |
| invalid exception is raised.
|
375 |
*----------------------------------------------------------------------------*/
|
376 |
|
377 |
static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM)
|
378 |
{ |
379 |
commonNaNT z; |
380 |
|
381 |
if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
|
382 |
z.sign = a.high>>15;
|
383 |
z.low = 0;
|
384 |
z.high = a.low; |
385 |
return z;
|
386 |
} |
387 |
|
388 |
/*----------------------------------------------------------------------------
|
389 |
| Returns the result of converting the canonical NaN `a' to the extended
|
390 |
| double-precision floating-point format.
|
391 |
*----------------------------------------------------------------------------*/
|
392 |
|
393 |
static floatx80 commonNaNToFloatx80( commonNaNT a )
|
394 |
{ |
395 |
floatx80 z; |
396 |
|
397 |
if (a.high)
|
398 |
z.low = a.high; |
399 |
else
|
400 |
z.low = floatx80_default_nan_low; |
401 |
z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF; |
402 |
return z;
|
403 |
} |
404 |
|
405 |
/*----------------------------------------------------------------------------
|
406 |
| Takes two extended double-precision floating-point values `a' and `b', one
|
407 |
| of which is a NaN, and returns the appropriate NaN result. If either `a' or
|
408 |
| `b' is a signaling NaN, the invalid exception is raised.
|
409 |
*----------------------------------------------------------------------------*/
|
410 |
|
411 |
static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM)
|
412 |
{ |
413 |
flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; |
414 |
|
415 |
aIsNaN = floatx80_is_nan( a ); |
416 |
aIsSignalingNaN = floatx80_is_signaling_nan( a ); |
417 |
bIsNaN = floatx80_is_nan( b ); |
418 |
bIsSignalingNaN = floatx80_is_signaling_nan( b ); |
419 |
#if SNAN_BIT_IS_ONE
|
420 |
a.low &= ~LIT64( 0xC000000000000000 );
|
421 |
b.low &= ~LIT64( 0xC000000000000000 );
|
422 |
#else
|
423 |
a.low |= LIT64( 0xC000000000000000 );
|
424 |
b.low |= LIT64( 0xC000000000000000 );
|
425 |
#endif
|
426 |
if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
|
427 |
if ( aIsSignalingNaN ) {
|
428 |
if ( bIsSignalingNaN ) goto returnLargerSignificand; |
429 |
return bIsNaN ? b : a;
|
430 |
} |
431 |
else if ( aIsNaN ) { |
432 |
if ( bIsSignalingNaN | ! bIsNaN ) return a; |
433 |
returnLargerSignificand:
|
434 |
if ( a.low < b.low ) return b; |
435 |
if ( b.low < a.low ) return a; |
436 |
return ( a.high < b.high ) ? a : b;
|
437 |
} |
438 |
else {
|
439 |
return b;
|
440 |
} |
441 |
} |
442 |
|
443 |
#endif
|
444 |
|
445 |
#ifdef FLOAT128
|
446 |
|
447 |
/*----------------------------------------------------------------------------
|
448 |
| The pattern for a default generated quadruple-precision NaN. The `high' and
|
449 |
| `low' values hold the most- and least-significant bits, respectively.
|
450 |
*----------------------------------------------------------------------------*/
|
451 |
#if SNAN_BIT_IS_ONE
|
452 |
#define float128_default_nan_high LIT64( 0x7FFF7FFFFFFFFFFF ) |
453 |
#define float128_default_nan_low LIT64( 0xFFFFFFFFFFFFFFFF ) |
454 |
#else
|
455 |
#define float128_default_nan_high LIT64( 0xFFFF800000000000 ) |
456 |
#define float128_default_nan_low LIT64( 0x0000000000000000 ) |
457 |
#endif
|
458 |
|
459 |
/*----------------------------------------------------------------------------
|
460 |
| Returns 1 if the quadruple-precision floating-point value `a' is a quiet
|
461 |
| NaN; otherwise returns 0.
|
462 |
*----------------------------------------------------------------------------*/
|
463 |
|
464 |
int float128_is_nan( float128 a )
|
465 |
{ |
466 |
#if SNAN_BIT_IS_ONE
|
467 |
return
|
468 |
( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE ) |
469 |
&& ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
|
470 |
#else
|
471 |
return
|
472 |
( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) ) |
473 |
&& ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
|
474 |
#endif
|
475 |
} |
476 |
|
477 |
/*----------------------------------------------------------------------------
|
478 |
| Returns 1 if the quadruple-precision floating-point value `a' is a
|
479 |
| signaling NaN; otherwise returns 0.
|
480 |
*----------------------------------------------------------------------------*/
|
481 |
|
482 |
int float128_is_signaling_nan( float128 a )
|
483 |
{ |
484 |
#if SNAN_BIT_IS_ONE
|
485 |
return
|
486 |
( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) ) |
487 |
&& ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
|
488 |
#else
|
489 |
return
|
490 |
( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE ) |
491 |
&& ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
|
492 |
#endif
|
493 |
} |
494 |
|
495 |
/*----------------------------------------------------------------------------
|
496 |
| Returns the result of converting the quadruple-precision floating-point NaN
|
497 |
| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
|
498 |
| exception is raised.
|
499 |
*----------------------------------------------------------------------------*/
|
500 |
|
501 |
static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM)
|
502 |
{ |
503 |
commonNaNT z; |
504 |
|
505 |
if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
|
506 |
z.sign = a.high>>63;
|
507 |
shortShift128Left( a.high, a.low, 16, &z.high, &z.low );
|
508 |
return z;
|
509 |
} |
510 |
|
511 |
/*----------------------------------------------------------------------------
|
512 |
| Returns the result of converting the canonical NaN `a' to the quadruple-
|
513 |
| precision floating-point format.
|
514 |
*----------------------------------------------------------------------------*/
|
515 |
|
516 |
static float128 commonNaNToFloat128( commonNaNT a )
|
517 |
{ |
518 |
float128 z; |
519 |
|
520 |
shift128Right( a.high, a.low, 16, &z.high, &z.low );
|
521 |
z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF000000000000 ); |
522 |
return z;
|
523 |
} |
524 |
|
525 |
/*----------------------------------------------------------------------------
|
526 |
| Takes two quadruple-precision floating-point values `a' and `b', one of
|
527 |
| which is a NaN, and returns the appropriate NaN result. If either `a' or
|
528 |
| `b' is a signaling NaN, the invalid exception is raised.
|
529 |
*----------------------------------------------------------------------------*/
|
530 |
|
531 |
static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM)
|
532 |
{ |
533 |
flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; |
534 |
|
535 |
aIsNaN = float128_is_nan( a ); |
536 |
aIsSignalingNaN = float128_is_signaling_nan( a ); |
537 |
bIsNaN = float128_is_nan( b ); |
538 |
bIsSignalingNaN = float128_is_signaling_nan( b ); |
539 |
#if SNAN_BIT_IS_ONE
|
540 |
a.high &= ~LIT64( 0x0000800000000000 );
|
541 |
b.high &= ~LIT64( 0x0000800000000000 );
|
542 |
#else
|
543 |
a.high |= LIT64( 0x0000800000000000 );
|
544 |
b.high |= LIT64( 0x0000800000000000 );
|
545 |
#endif
|
546 |
if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
|
547 |
if ( aIsSignalingNaN ) {
|
548 |
if ( bIsSignalingNaN ) goto returnLargerSignificand; |
549 |
return bIsNaN ? b : a;
|
550 |
} |
551 |
else if ( aIsNaN ) { |
552 |
if ( bIsSignalingNaN | ! bIsNaN ) return a; |
553 |
returnLargerSignificand:
|
554 |
if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b; |
555 |
if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a; |
556 |
return ( a.high < b.high ) ? a : b;
|
557 |
} |
558 |
else {
|
559 |
return b;
|
560 |
} |
561 |
} |
562 |
|
563 |
#endif
|