8559666ddb
These special values are needed to implement some helper functions, which return/use these values in some cases. Signed-off-by: Christophe Lyon <christophe.lyon@st.com> Reviewed-by: Peter Maydell <peter.maydell@linaro.org> Signed-off-by: Aurelien Jarno <aurelien@aurel32.net>
810 lines
27 KiB
C
810 lines
27 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.
|
|
|
|
=============================================================================*/
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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;
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the half-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float16_is_quiet_nan(float16 a_)
|
|
{
|
|
uint16_t a = float16_val(a_);
|
|
#if SNAN_BIT_IS_ONE
|
|
return (((a >> 9) & 0x3F) == 0x3E) && (a & 0x1FF);
|
|
#else
|
|
return ((a & ~0x8000) >= 0x7c80);
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the half-precision floating-point value `a' is a signaling
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float16_is_signaling_nan(float16 a_)
|
|
{
|
|
uint16_t a = float16_val(a_);
|
|
#if SNAN_BIT_IS_ONE
|
|
return ((a & ~0x8000) >= 0x7c80);
|
|
#else
|
|
return (((a >> 9) & 0x3F) == 0x3E) && (a & 0x1FF);
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns a quiet NaN if the half-precision floating point value `a' is a
|
|
| signaling NaN; otherwise returns `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
float16 float16_maybe_silence_nan(float16 a_)
|
|
{
|
|
if (float16_is_signaling_nan(a_)) {
|
|
#if SNAN_BIT_IS_ONE
|
|
# if defined(TARGET_MIPS) || defined(TARGET_SH4)
|
|
return float16_default_nan;
|
|
# else
|
|
# error Rules for silencing a signaling NaN are target-specific
|
|
# endif
|
|
#else
|
|
uint16_t a = float16_val(a_);
|
|
a |= (1 << 9);
|
|
return make_float16(a);
|
|
#endif
|
|
}
|
|
return a_;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the half-precision floating-point NaN
|
|
| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
|
|
| exception is raised.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static commonNaNT float16ToCommonNaN( float16 a STATUS_PARAM )
|
|
{
|
|
commonNaNT z;
|
|
|
|
if ( float16_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR );
|
|
z.sign = float16_val(a) >> 15;
|
|
z.low = 0;
|
|
z.high = ((bits64) float16_val(a))<<54;
|
|
return z;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the canonical NaN `a' to the half-
|
|
| precision floating-point format.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float16 commonNaNToFloat16(commonNaNT a STATUS_PARAM)
|
|
{
|
|
uint16_t mantissa = a.high>>54;
|
|
|
|
if (STATUS(default_nan_mode)) {
|
|
return float16_default_nan;
|
|
}
|
|
|
|
if (mantissa) {
|
|
return make_float16(((((uint16_t) a.sign) << 15)
|
|
| (0x1F << 10) | mantissa));
|
|
} else {
|
|
return float16_default_nan;
|
|
}
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the single-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float32_is_quiet_nan( float32 a_ )
|
|
{
|
|
uint32_t a = float32_val(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_ )
|
|
{
|
|
uint32_t a = float32_val(a_);
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( 0xFF800000 <= (bits32) ( a<<1 ) );
|
|
#else
|
|
return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns a quiet NaN if the single-precision floating point value `a' is a
|
|
| signaling NaN; otherwise returns `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float32 float32_maybe_silence_nan( float32 a_ )
|
|
{
|
|
if (float32_is_signaling_nan(a_)) {
|
|
#if SNAN_BIT_IS_ONE
|
|
# if defined(TARGET_MIPS) || defined(TARGET_SH4)
|
|
return float32_default_nan;
|
|
# else
|
|
# error Rules for silencing a signaling NaN are target-specific
|
|
# endif
|
|
#else
|
|
bits32 a = float32_val(a_);
|
|
a |= (1 << 22);
|
|
return make_float32(a);
|
|
#endif
|
|
}
|
|
return a_;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 = float32_val(a)>>31;
|
|
z.low = 0;
|
|
z.high = ( (bits64) float32_val(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 STATUS_PARAM)
|
|
{
|
|
bits32 mantissa = a.high>>41;
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
return float32_default_nan;
|
|
}
|
|
|
|
if ( mantissa )
|
|
return make_float32(
|
|
( ( (bits32) a.sign )<<31 ) | 0x7F800000 | ( a.high>>41 ) );
|
|
else
|
|
return float32_default_nan;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Select which NaN to propagate for a two-input operation.
|
|
| IEEE754 doesn't specify all the details of this, so the
|
|
| algorithm is target-specific.
|
|
| The routine is passed various bits of information about the
|
|
| two NaNs and should return 0 to select NaN a and 1 for NaN b.
|
|
| Note that signalling NaNs are always squashed to quiet NaNs
|
|
| by the caller, by calling floatXX_maybe_silence_nan() before
|
|
| returning them.
|
|
|
|
|
| aIsLargerSignificand is only valid if both a and b are NaNs
|
|
| of some kind, and is true if a has the larger significand,
|
|
| or if both a and b have the same significand but a is
|
|
| positive but b is negative. It is only needed for the x87
|
|
| tie-break rule.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
#if defined(TARGET_ARM)
|
|
static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN,
|
|
flag aIsLargerSignificand)
|
|
{
|
|
/* ARM mandated NaN propagation rules: take the first of:
|
|
* 1. A if it is signaling
|
|
* 2. B if it is signaling
|
|
* 3. A (quiet)
|
|
* 4. B (quiet)
|
|
* A signaling NaN is always quietened before returning it.
|
|
*/
|
|
if (aIsSNaN) {
|
|
return 0;
|
|
} else if (bIsSNaN) {
|
|
return 1;
|
|
} else if (aIsQNaN) {
|
|
return 0;
|
|
} else {
|
|
return 1;
|
|
}
|
|
}
|
|
#elif defined(TARGET_MIPS)
|
|
static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN,
|
|
flag aIsLargerSignificand)
|
|
{
|
|
/* According to MIPS specifications, if one of the two operands is
|
|
* a sNaN, a new qNaN has to be generated. This is done in
|
|
* floatXX_maybe_silence_nan(). For qNaN inputs the specifications
|
|
* says: "When possible, this QNaN result is one of the operand QNaN
|
|
* values." In practice it seems that most implementations choose
|
|
* the first operand if both operands are qNaN. In short this gives
|
|
* the following rules:
|
|
* 1. A if it is signaling
|
|
* 2. B if it is signaling
|
|
* 3. A (quiet)
|
|
* 4. B (quiet)
|
|
* A signaling NaN is always silenced before returning it.
|
|
*/
|
|
if (aIsSNaN) {
|
|
return 0;
|
|
} else if (bIsSNaN) {
|
|
return 1;
|
|
} else if (aIsQNaN) {
|
|
return 0;
|
|
} else {
|
|
return 1;
|
|
}
|
|
}
|
|
#elif defined(TARGET_PPC)
|
|
static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN,
|
|
flag aIsLargerSignificand)
|
|
{
|
|
/* PowerPC propagation rules:
|
|
* 1. A if it sNaN or qNaN
|
|
* 2. B if it sNaN or qNaN
|
|
* A signaling NaN is always silenced before returning it.
|
|
*/
|
|
if (aIsSNaN || aIsQNaN) {
|
|
return 0;
|
|
} else {
|
|
return 1;
|
|
}
|
|
}
|
|
#else
|
|
static int pickNaN(flag aIsQNaN, flag aIsSNaN, flag bIsQNaN, flag bIsSNaN,
|
|
flag aIsLargerSignificand)
|
|
{
|
|
/* This implements x87 NaN propagation rules:
|
|
* SNaN + QNaN => return the QNaN
|
|
* two SNaNs => return the one with the larger significand, silenced
|
|
* two QNaNs => return the one with the larger significand
|
|
* SNaN and a non-NaN => return the SNaN, silenced
|
|
* QNaN and a non-NaN => return the QNaN
|
|
*
|
|
* If we get down to comparing significands and they are the same,
|
|
* return the NaN with the positive sign bit (if any).
|
|
*/
|
|
if (aIsSNaN) {
|
|
if (bIsSNaN) {
|
|
return aIsLargerSignificand ? 0 : 1;
|
|
}
|
|
return bIsQNaN ? 1 : 0;
|
|
}
|
|
else if (aIsQNaN) {
|
|
if (bIsSNaN || !bIsQNaN)
|
|
return 0;
|
|
else {
|
|
return aIsLargerSignificand ? 0 : 1;
|
|
}
|
|
} else {
|
|
return 1;
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN;
|
|
flag aIsLargerSignificand;
|
|
bits32 av, bv;
|
|
|
|
aIsQuietNaN = float32_is_quiet_nan( a );
|
|
aIsSignalingNaN = float32_is_signaling_nan( a );
|
|
bIsQuietNaN = float32_is_quiet_nan( b );
|
|
bIsSignalingNaN = float32_is_signaling_nan( b );
|
|
av = float32_val(a);
|
|
bv = float32_val(b);
|
|
|
|
if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
|
|
|
|
if ( STATUS(default_nan_mode) )
|
|
return float32_default_nan;
|
|
|
|
if ((bits32)(av<<1) < (bits32)(bv<<1)) {
|
|
aIsLargerSignificand = 0;
|
|
} else if ((bits32)(bv<<1) < (bits32)(av<<1)) {
|
|
aIsLargerSignificand = 1;
|
|
} else {
|
|
aIsLargerSignificand = (av < bv) ? 1 : 0;
|
|
}
|
|
|
|
if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN,
|
|
aIsLargerSignificand)) {
|
|
return float32_maybe_silence_nan(b);
|
|
} else {
|
|
return float32_maybe_silence_nan(a);
|
|
}
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the double-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float64_is_quiet_nan( float64 a_ )
|
|
{
|
|
bits64 a = float64_val(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_ )
|
|
{
|
|
bits64 a = float64_val(a_);
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( LIT64( 0xFFF0000000000000 ) <= (bits64) ( a<<1 ) );
|
|
#else
|
|
return
|
|
( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
|
|
&& ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns a quiet NaN if the double-precision floating point value `a' is a
|
|
| signaling NaN; otherwise returns `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float64 float64_maybe_silence_nan( float64 a_ )
|
|
{
|
|
if (float64_is_signaling_nan(a_)) {
|
|
#if SNAN_BIT_IS_ONE
|
|
# if defined(TARGET_MIPS) || defined(TARGET_SH4)
|
|
return float64_default_nan;
|
|
# else
|
|
# error Rules for silencing a signaling NaN are target-specific
|
|
# endif
|
|
#else
|
|
bits64 a = float64_val(a_);
|
|
a |= LIT64( 0x0008000000000000 );
|
|
return make_float64(a);
|
|
#endif
|
|
}
|
|
return a_;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 = float64_val(a)>>63;
|
|
z.low = 0;
|
|
z.high = float64_val(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 STATUS_PARAM)
|
|
{
|
|
bits64 mantissa = a.high>>12;
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
return float64_default_nan;
|
|
}
|
|
|
|
if ( mantissa )
|
|
return make_float64(
|
|
( ( (bits64) a.sign )<<63 )
|
|
| LIT64( 0x7FF0000000000000 )
|
|
| ( a.high>>12 ));
|
|
else
|
|
return float64_default_nan;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN;
|
|
flag aIsLargerSignificand;
|
|
bits64 av, bv;
|
|
|
|
aIsQuietNaN = float64_is_quiet_nan( a );
|
|
aIsSignalingNaN = float64_is_signaling_nan( a );
|
|
bIsQuietNaN = float64_is_quiet_nan( b );
|
|
bIsSignalingNaN = float64_is_signaling_nan( b );
|
|
av = float64_val(a);
|
|
bv = float64_val(b);
|
|
|
|
if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
|
|
|
|
if ( STATUS(default_nan_mode) )
|
|
return float64_default_nan;
|
|
|
|
if ((bits64)(av<<1) < (bits64)(bv<<1)) {
|
|
aIsLargerSignificand = 0;
|
|
} else if ((bits64)(bv<<1) < (bits64)(av<<1)) {
|
|
aIsLargerSignificand = 1;
|
|
} else {
|
|
aIsLargerSignificand = (av < bv) ? 1 : 0;
|
|
}
|
|
|
|
if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN,
|
|
aIsLargerSignificand)) {
|
|
return float64_maybe_silence_nan(b);
|
|
} else {
|
|
return float64_maybe_silence_nan(a);
|
|
}
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
|
| quiet NaN; otherwise returns 0. This slightly differs from the same
|
|
| function for other types as floatx80 has an explicit bit.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_is_quiet_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 )
|
|
&& (LIT64( 0x8000000000000000 ) <= ((bits64) ( a.low<<1 )));
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is a
|
|
| signaling NaN; otherwise returns 0. This slightly differs from the same
|
|
| function for other types as floatx80 has an explicit bit.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_is_signaling_nan( floatx80 a )
|
|
{
|
|
#if SNAN_BIT_IS_ONE
|
|
return ( ( a.high & 0x7FFF ) == 0x7FFF )
|
|
&& (LIT64( 0x8000000000000000 ) <= ((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 a quiet NaN if the extended double-precision floating point value
|
|
| `a' is a signaling NaN; otherwise returns `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_maybe_silence_nan( floatx80 a )
|
|
{
|
|
if (floatx80_is_signaling_nan(a)) {
|
|
#if SNAN_BIT_IS_ONE
|
|
# if defined(TARGET_MIPS) || defined(TARGET_SH4)
|
|
a.low = floatx80_default_nan_low;
|
|
a.high = floatx80_default_nan_high;
|
|
# else
|
|
# error Rules for silencing a signaling NaN are target-specific
|
|
# endif
|
|
#else
|
|
a.low |= LIT64( 0xC000000000000000 );
|
|
return a;
|
|
#endif
|
|
}
|
|
return a;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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;
|
|
return z;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the canonical NaN `a' to the extended
|
|
| double-precision floating-point format.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static floatx80 commonNaNToFloatx80( commonNaNT a STATUS_PARAM)
|
|
{
|
|
floatx80 z;
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return 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 aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN;
|
|
flag aIsLargerSignificand;
|
|
|
|
aIsQuietNaN = floatx80_is_quiet_nan( a );
|
|
aIsSignalingNaN = floatx80_is_signaling_nan( a );
|
|
bIsQuietNaN = floatx80_is_quiet_nan( b );
|
|
bIsSignalingNaN = floatx80_is_signaling_nan( b );
|
|
|
|
if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
a.low = floatx80_default_nan_low;
|
|
a.high = floatx80_default_nan_high;
|
|
return a;
|
|
}
|
|
|
|
if (a.low < b.low) {
|
|
aIsLargerSignificand = 0;
|
|
} else if (b.low < a.low) {
|
|
aIsLargerSignificand = 1;
|
|
} else {
|
|
aIsLargerSignificand = (a.high < b.high) ? 1 : 0;
|
|
}
|
|
|
|
if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN,
|
|
aIsLargerSignificand)) {
|
|
return floatx80_maybe_silence_nan(b);
|
|
} else {
|
|
return floatx80_maybe_silence_nan(a);
|
|
}
|
|
}
|
|
|
|
#endif
|
|
|
|
#ifdef FLOAT128
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the quadruple-precision floating-point value `a' is a quiet
|
|
| NaN; otherwise returns 0.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int float128_is_quiet_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 a quiet NaN if the quadruple-precision floating point value `a' is
|
|
| a signaling NaN; otherwise returns `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_maybe_silence_nan( float128 a )
|
|
{
|
|
if (float128_is_signaling_nan(a)) {
|
|
#if SNAN_BIT_IS_ONE
|
|
# if defined(TARGET_MIPS) || defined(TARGET_SH4)
|
|
a.low = float128_default_nan_low;
|
|
a.high = float128_default_nan_high;
|
|
# else
|
|
# error Rules for silencing a signaling NaN are target-specific
|
|
# endif
|
|
#else
|
|
a.high |= LIT64( 0x0000800000000000 );
|
|
return a;
|
|
#endif
|
|
}
|
|
return a;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 STATUS_PARAM)
|
|
{
|
|
float128 z;
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
z.low = float128_default_nan_low;
|
|
z.high = float128_default_nan_high;
|
|
return 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 aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN;
|
|
flag aIsLargerSignificand;
|
|
|
|
aIsQuietNaN = float128_is_quiet_nan( a );
|
|
aIsSignalingNaN = float128_is_signaling_nan( a );
|
|
bIsQuietNaN = float128_is_quiet_nan( b );
|
|
bIsSignalingNaN = float128_is_signaling_nan( b );
|
|
|
|
if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
|
|
|
|
if ( STATUS(default_nan_mode) ) {
|
|
a.low = float128_default_nan_low;
|
|
a.high = float128_default_nan_high;
|
|
return a;
|
|
}
|
|
|
|
if (lt128(a.high<<1, a.low, b.high<<1, b.low)) {
|
|
aIsLargerSignificand = 0;
|
|
} else if (lt128(b.high<<1, b.low, a.high<<1, a.low)) {
|
|
aIsLargerSignificand = 1;
|
|
} else {
|
|
aIsLargerSignificand = (a.high < b.high) ? 1 : 0;
|
|
}
|
|
|
|
if (pickNaN(aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN,
|
|
aIsLargerSignificand)) {
|
|
return float128_maybe_silence_nan(b);
|
|
} else {
|
|
return float128_maybe_silence_nan(a);
|
|
}
|
|
}
|
|
|
|
#endif
|