521 lines
19 KiB
C
521 lines
19 KiB
C
|
|
/*============================================================================
|
|
|
|
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.
|
|
|
|
=============================================================================*/
|
|
|
|
#if defined(TARGET_MIPS) || defined(TARGET_HPPA)
|
|
#define SNAN_BIT_IS_ONE 1
|
|
#else
|
|
#define SNAN_BIT_IS_ONE 0
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
#if SNAN_BIT_IS_ONE
|
|
#define float32_default_nan 0x7FBFFFFF
|
|
#else
|
|
#define float32_default_nan 0xFFC00000
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the single-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float32_is_nan( float32 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
|
|
#else
|
|
return ( 0xFF800000 <= (bits32) ( a<<1 ) );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the single-precision floating-point value `a' is a signaling
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float32_is_signaling_nan( float32 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( 0xFF800000 <= (bits32) ( a<<1 ) );
|
|
#else
|
|
return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 );
|
|
#if SNAN_BIT_IS_ONE
|
|
a &= ~0x00400000;
|
|
b &= ~0x00400000;
|
|
#else
|
|
a |= 0x00400000;
|
|
b |= 0x00400000;
|
|
#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 ( (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.
|
|
*----------------------------------------------------------------------------*/
|
|
#if SNAN_BIT_IS_ONE
|
|
#define float64_default_nan LIT64( 0x7FF7FFFFFFFFFFFF )
|
|
#else
|
|
#define float64_default_nan LIT64( 0xFFF8000000000000 )
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the double-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float64_is_nan( float64 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return
|
|
( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
|
|
&& ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
|
|
#else
|
|
return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the double-precision floating-point value `a' is a signaling
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float64_is_signaling_nan( float64 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) );
|
|
#else
|
|
return
|
|
( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
|
|
&& ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 );
|
|
#if SNAN_BIT_IS_ONE
|
|
a &= ~LIT64( 0x0008000000000000 );
|
|
b &= ~LIT64( 0x0008000000000000 );
|
|
#else
|
|
a |= LIT64( 0x0008000000000000 );
|
|
b |= LIT64( 0x0008000000000000 );
|
|
#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 ( (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.
|
|
*----------------------------------------------------------------------------*/
|
|
#if SNAN_BIT_IS_ONE
|
|
#define floatx80_default_nan_high 0x7FFF
|
|
#define floatx80_default_nan_low LIT64( 0xBFFFFFFFFFFFFFFF )
|
|
#else
|
|
#define floatx80_default_nan_high 0xFFFF
|
|
#define floatx80_default_nan_low LIT64( 0xC000000000000000 )
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
|
| quiet NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_is_nan( floatx80 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
bits64 aLow;
|
|
|
|
aLow = a.low & ~ LIT64( 0x4000000000000000 );
|
|
return
|
|
( ( a.high & 0x7FFF ) == 0x7FFF )
|
|
&& (bits64) ( aLow<<1 )
|
|
&& ( a.low == aLow );
|
|
#else
|
|
return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
|
| signaling NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_is_signaling_nan( floatx80 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
|
|
#else
|
|
bits64 aLow;
|
|
|
|
aLow = a.low & ~ LIT64( 0x4000000000000000 );
|
|
return
|
|
( ( a.high & 0x7FFF ) == 0x7FFF )
|
|
&& (bits64) ( aLow<<1 )
|
|
&& ( 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
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 );
|
|
#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( 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 );
|
|
#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
|