582 lines
20 KiB
C
582 lines
20 KiB
C
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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) || defined(TARGET_ARM) || defined(TARGET_ALPHA)
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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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if ( STATUS(default_nan_mode) )
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return float32_default_nan;
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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) || defined(TARGET_ARM) || defined(TARGET_ALPHA)
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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;
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bits64 av, bv, res;
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if ( STATUS(default_nan_mode) )
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return float64_default_nan;
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aIsNaN = float64_is_nan( a );
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aIsSignalingNaN = float64_is_signaling_nan( a );
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bIsNaN = float64_is_nan( b );
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bIsSignalingNaN = float64_is_signaling_nan( b );
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av = float64_val(a);
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bv = float64_val(b);
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#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;
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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 ( (bits64) ( av<<1 ) < (bits64) ( bv<<1 ) )
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res = bv;
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else if ( (bits64) ( bv<<1 ) < (bits64) ( 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_float64(res);
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}
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#ifdef FLOATX80
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/*----------------------------------------------------------------------------
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| The pattern for a default generated extended double-precision NaN. The
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| `high' and `low' values hold the most- and least-significant bits,
|
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| respectively.
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*----------------------------------------------------------------------------*/
|
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#if SNAN_BIT_IS_ONE
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#define floatx80_default_nan_high 0x7FFF
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#define floatx80_default_nan_low LIT64( 0xBFFFFFFFFFFFFFFF )
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#else
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#define floatx80_default_nan_high 0xFFFF
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#define floatx80_default_nan_low LIT64( 0xC000000000000000 )
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#endif
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|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
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| quiet NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
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int floatx80_is_nan( floatx80 a )
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|
{
|
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#if SNAN_BIT_IS_ONE
|
|
bits64 aLow;
|
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|
|
aLow = a.low & ~ LIT64( 0x4000000000000000 );
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return
|
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( ( a.high & 0x7FFF ) == 0x7FFF )
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&& (bits64) ( aLow<<1 )
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&& ( a.low == aLow );
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#else
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return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
|
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#endif
|
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}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
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| signaling NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_is_signaling_nan( floatx80 a )
|
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{
|
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#if SNAN_BIT_IS_ONE
|
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return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
|
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#else
|
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bits64 aLow;
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|
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aLow = a.low & ~ LIT64( 0x4000000000000000 );
|
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return
|
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( ( a.high & 0x7FFF ) == 0x7FFF )
|
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&& (bits64) ( aLow<<1 )
|
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&& ( a.low == aLow );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
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static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM)
|
|
{
|
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commonNaNT z;
|
|
|
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if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
|
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z.sign = a.high>>15;
|
|
z.low = 0;
|
|
z.high = a.low;
|
|
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;
|
|
|
|
if (a.high)
|
|
z.low = a.high;
|
|
else
|
|
z.low = floatx80_default_nan_low;
|
|
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;
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
a.low = floatx80_default_nan_low;
|
|
a.high = floatx80_default_nan_high;
|
|
return a;
|
|
}
|
|
|
|
aIsNaN = floatx80_is_nan( a );
|
|
aIsSignalingNaN = floatx80_is_signaling_nan( a );
|
|
bIsNaN = floatx80_is_nan( b );
|
|
bIsSignalingNaN = floatx80_is_signaling_nan( b );
|
|
#if SNAN_BIT_IS_ONE
|
|
a.low &= ~LIT64( 0xC000000000000000 );
|
|
b.low &= ~LIT64( 0xC000000000000000 );
|
|
#else
|
|
a.low |= LIT64( 0xC000000000000000 );
|
|
b.low |= LIT64( 0xC000000000000000 );
|
|
#endif
|
|
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.
|
|
*----------------------------------------------------------------------------*/
|
|
#if SNAN_BIT_IS_ONE
|
|
#define float128_default_nan_high LIT64( 0x7FFF7FFFFFFFFFFF )
|
|
#define float128_default_nan_low LIT64( 0xFFFFFFFFFFFFFFFF )
|
|
#else
|
|
#define float128_default_nan_high LIT64( 0xFFFF800000000000 )
|
|
#define float128_default_nan_low LIT64( 0x0000000000000000 )
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the quadruple-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float128_is_nan( float128 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return
|
|
( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
|
|
&& ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
|
|
#else
|
|
return
|
|
( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
|
|
&& ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the quadruple-precision floating-point value `a' is a
|
|
| signaling NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float128_is_signaling_nan( float128 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return
|
|
( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
|
|
&& ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
|
|
#else
|
|
return
|
|
( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
|
|
&& ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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( 0x7FFF000000000000 );
|
|
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;
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
a.low = float128_default_nan_low;
|
|
a.high = float128_default_nan_high;
|
|
return a;
|
|
}
|
|
|
|
aIsNaN = float128_is_nan( a );
|
|
aIsSignalingNaN = float128_is_signaling_nan( a );
|
|
bIsNaN = float128_is_nan( b );
|
|
bIsSignalingNaN = float128_is_signaling_nan( b );
|
|
#if SNAN_BIT_IS_ONE
|
|
a.high &= ~LIT64( 0x0000800000000000 );
|
|
b.high &= ~LIT64( 0x0000800000000000 );
|
|
#else
|
|
a.high |= LIT64( 0x0000800000000000 );
|
|
b.high |= LIT64( 0x0000800000000000 );
|
|
#endif
|
|
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
|