+/*
+ * QEMU float support
+ *
+ * Derived from SoftFloat.
+ */
/*============================================================================
=============================================================================*/
+/* softfloat (and in particular the code in softfloat-specialize.h) is
+ * target-dependent and needs the TARGET_* macros.
+ */
+#include "config.h"
+
#include "softfloat.h"
/*----------------------------------------------------------------------------
STATUS(float_exception_flags) = val;
}
-#ifdef FLOATX80
void set_floatx80_rounding_precision(int val STATUS_PARAM)
{
STATUS(floatx80_rounding_precision) = val;
}
-#endif
+
+/*----------------------------------------------------------------------------
+| Returns the fraction bits of the half-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE uint32_t extractFloat16Frac(float16 a)
+{
+ return float16_val(a) & 0x3ff;
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the half-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE int_fast16_t extractFloat16Exp(float16 a)
+{
+ return (float16_val(a) >> 10) & 0x1f;
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the single-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE flag extractFloat16Sign(float16 a)
+{
+ return float16_val(a)>>15;
+}
/*----------------------------------------------------------------------------
| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
| positive or negative integer is returned.
*----------------------------------------------------------------------------*/
-static int32 roundAndPackInt32( flag zSign, bits64 absZ STATUS_PARAM)
+static int32 roundAndPackInt32( flag zSign, uint64_t absZ STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven;
int8 roundIncrement, roundBits;
- int32 z;
+ int32_t z;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
if ( zSign ) z = - z;
if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
float_raise( float_flag_invalid STATUS_VAR);
- return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ return zSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
}
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
return z;
| returned.
*----------------------------------------------------------------------------*/
-static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 STATUS_PARAM)
+static int64 roundAndPackInt64( flag zSign, uint64_t absZ0, uint64_t absZ1 STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven, increment;
- int64 z;
+ int64_t z;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
- increment = ( (sbits64) absZ1 < 0 );
+ increment = ( (int64_t) absZ1 < 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
increment = 0;
if ( increment ) {
++absZ0;
if ( absZ0 == 0 ) goto overflow;
- absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven );
+ absZ0 &= ~ ( ( (uint64_t) ( absZ1<<1 ) == 0 ) & roundNearestEven );
}
z = absZ0;
if ( zSign ) z = - z;
overflow:
float_raise( float_flag_invalid STATUS_VAR);
return
- zSign ? (sbits64) LIT64( 0x8000000000000000 )
+ zSign ? (int64_t) LIT64( 0x8000000000000000 )
: LIT64( 0x7FFFFFFFFFFFFFFF );
}
if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact;
| Returns the fraction bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
-INLINE bits32 extractFloat32Frac( float32 a )
+INLINE uint32_t extractFloat32Frac( float32 a )
{
return float32_val(a) & 0x007FFFFF;
| Returns the exponent bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
-INLINE int16 extractFloat32Exp( float32 a )
+INLINE int_fast16_t extractFloat32Exp(float32 a)
{
return ( float32_val(a)>>23 ) & 0xFF;
}
+/*----------------------------------------------------------------------------
+| If `a' is denormal and we are in flush-to-zero mode then set the
+| input-denormal exception and return zero. Otherwise just return the value.
+*----------------------------------------------------------------------------*/
+static float32 float32_squash_input_denormal(float32 a STATUS_PARAM)
+{
+ if (STATUS(flush_inputs_to_zero)) {
+ if (extractFloat32Exp(a) == 0 && extractFloat32Frac(a) != 0) {
+ float_raise(float_flag_input_denormal STATUS_VAR);
+ return make_float32(float32_val(a) & 0x80000000);
+ }
+ }
+ return a;
+}
+
/*----------------------------------------------------------------------------
| Normalizes the subnormal single-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
*----------------------------------------------------------------------------*/
static void
- normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
+ normalizeFloat32Subnormal(uint32_t aSig, int_fast16_t *zExpPtr, uint32_t *zSigPtr)
{
int8 shiftCount;
| significand.
*----------------------------------------------------------------------------*/
-INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
+INLINE float32 packFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig)
{
return make_float32(
- ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig);
+ ( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) zExp )<<23 ) + zSig);
}
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
+static float32 roundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven;
}
}
roundBits = zSig & 0x7F;
- if ( 0xFD <= (bits16) zExp ) {
+ if ( 0xFD <= (uint16_t) zExp ) {
if ( ( 0xFD < zExp )
|| ( ( zExp == 0xFD )
- && ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
+ && ( (int32_t) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
+ if (STATUS(flush_to_zero)) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ return packFloat32(zSign, 0, 0);
+ }
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
*----------------------------------------------------------------------------*/
static float32
- normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
+ normalizeRoundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM)
{
int8 shiftCount;
| Returns the fraction bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
-INLINE bits64 extractFloat64Frac( float64 a )
+INLINE uint64_t extractFloat64Frac( float64 a )
{
return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF );
| Returns the exponent bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
-INLINE int16 extractFloat64Exp( float64 a )
+INLINE int_fast16_t extractFloat64Exp(float64 a)
{
return ( float64_val(a)>>52 ) & 0x7FF;
}
+/*----------------------------------------------------------------------------
+| If `a' is denormal and we are in flush-to-zero mode then set the
+| input-denormal exception and return zero. Otherwise just return the value.
+*----------------------------------------------------------------------------*/
+static float64 float64_squash_input_denormal(float64 a STATUS_PARAM)
+{
+ if (STATUS(flush_inputs_to_zero)) {
+ if (extractFloat64Exp(a) == 0 && extractFloat64Frac(a) != 0) {
+ float_raise(float_flag_input_denormal STATUS_VAR);
+ return make_float64(float64_val(a) & (1ULL << 63));
+ }
+ }
+ return a;
+}
+
/*----------------------------------------------------------------------------
| Normalizes the subnormal double-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
*----------------------------------------------------------------------------*/
static void
- normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr )
+ normalizeFloat64Subnormal(uint64_t aSig, int_fast16_t *zExpPtr, uint64_t *zSigPtr)
{
int8 shiftCount;
| significand.
*----------------------------------------------------------------------------*/
-INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
+INLINE float64 packFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig)
{
return make_float64(
- ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig);
+ ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig);
}
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
+static float64 roundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven;
- int16 roundIncrement, roundBits;
+ int_fast16_t roundIncrement, roundBits;
flag isTiny;
roundingMode = STATUS(float_rounding_mode);
}
}
roundBits = zSig & 0x3FF;
- if ( 0x7FD <= (bits16) zExp ) {
+ if ( 0x7FD <= (uint16_t) zExp ) {
if ( ( 0x7FD < zExp )
|| ( ( zExp == 0x7FD )
- && ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
+ && ( (int64_t) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
+ if (STATUS(flush_to_zero)) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ return packFloat64(zSign, 0, 0);
+ }
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
*----------------------------------------------------------------------------*/
static float64
- normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
+ normalizeRoundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM)
{
int8 shiftCount;
}
-#ifdef FLOATX80
-
/*----------------------------------------------------------------------------
| Returns the fraction bits of the extended double-precision floating-point
| value `a'.
*----------------------------------------------------------------------------*/
-INLINE bits64 extractFloatx80Frac( floatx80 a )
+INLINE uint64_t extractFloatx80Frac( floatx80 a )
{
return a.low;
*----------------------------------------------------------------------------*/
static void
- normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
+ normalizeFloatx80Subnormal( uint64_t aSig, int32 *zExpPtr, uint64_t *zSigPtr )
{
int8 shiftCount;
| extended double-precision floating-point value, returning the result.
*----------------------------------------------------------------------------*/
-INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
+INLINE floatx80 packFloatx80( flag zSign, int32 zExp, uint64_t zSig )
{
floatx80 z;
z.low = zSig;
- z.high = ( ( (bits16) zSign )<<15 ) + zExp;
+ z.high = ( ( (uint16_t) zSign )<<15 ) + zExp;
return z;
}
static floatx80
roundAndPackFloatx80(
- int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
+ int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1
STATUS_PARAM)
{
int8 roundingMode;
}
}
roundBits = zSig0 & roundMask;
- if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
+ if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) {
if ( ( 0x7FFE < zExp )
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
) {
goto overflow;
}
if ( zExp <= 0 ) {
+ if (STATUS(flush_to_zero)) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ return packFloatx80(zSign, 0, 0);
+ }
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < 0 )
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
zSig0 += roundIncrement;
- if ( (sbits64) zSig0 < 0 ) zExp = 1;
+ if ( (int64_t) zSig0 < 0 ) zExp = 1;
roundIncrement = roundMask + 1;
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
roundMask |= roundIncrement;
if ( zSig0 == 0 ) zExp = 0;
return packFloatx80( zSign, zExp, zSig0 );
precision80:
- increment = ( (sbits64) zSig1 < 0 );
+ increment = ( (int64_t) zSig1 < 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
increment = 0;
}
}
}
- if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
+ if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) {
if ( ( 0x7FFE < zExp )
|| ( ( zExp == 0x7FFE )
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR);
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
if ( roundNearestEven ) {
- increment = ( (sbits64) zSig1 < 0 );
+ increment = ( (int64_t) zSig1 < 0 );
}
else {
if ( zSign ) {
if ( increment ) {
++zSig0;
zSig0 &=
- ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
- if ( (sbits64) zSig0 < 0 ) zExp = 1;
+ ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven );
+ if ( (int64_t) zSig0 < 0 ) zExp = 1;
}
return packFloatx80( zSign, zExp, zSig0 );
}
zSig0 = LIT64( 0x8000000000000000 );
}
else {
- zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
+ zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven );
}
}
else {
static floatx80
normalizeRoundAndPackFloatx80(
- int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
+ int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1
STATUS_PARAM)
{
int8 shiftCount;
}
-#endif
-
-#ifdef FLOAT128
-
/*----------------------------------------------------------------------------
| Returns the least-significant 64 fraction bits of the quadruple-precision
| floating-point value `a'.
*----------------------------------------------------------------------------*/
-INLINE bits64 extractFloat128Frac1( float128 a )
+INLINE uint64_t extractFloat128Frac1( float128 a )
{
return a.low;
| floating-point value `a'.
*----------------------------------------------------------------------------*/
-INLINE bits64 extractFloat128Frac0( float128 a )
+INLINE uint64_t extractFloat128Frac0( float128 a )
{
return a.high & LIT64( 0x0000FFFFFFFFFFFF );
static void
normalizeFloat128Subnormal(
- bits64 aSig0,
- bits64 aSig1,
+ uint64_t aSig0,
+ uint64_t aSig1,
int32 *zExpPtr,
- bits64 *zSig0Ptr,
- bits64 *zSig1Ptr
+ uint64_t *zSig0Ptr,
+ uint64_t *zSig1Ptr
)
{
int8 shiftCount;
*----------------------------------------------------------------------------*/
INLINE float128
- packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
+ packFloat128( flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 )
{
float128 z;
z.low = zSig1;
- z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0;
+ z.high = ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<48 ) + zSig0;
return z;
}
static float128
roundAndPackFloat128(
- flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 STATUS_PARAM)
+ flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1, uint64_t zSig2 STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven, increment, isTiny;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
- increment = ( (sbits64) zSig2 < 0 );
+ increment = ( (int64_t) zSig2 < 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
increment = 0;
}
}
}
- if ( 0x7FFD <= (bits32) zExp ) {
+ if ( 0x7FFD <= (uint32_t) zExp ) {
if ( ( 0x7FFD < zExp )
|| ( ( zExp == 0x7FFD )
&& eq128(
return packFloat128( zSign, 0x7FFF, 0, 0 );
}
if ( zExp < 0 ) {
+ if (STATUS(flush_to_zero)) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ return packFloat128(zSign, 0, 0, 0);
+ }
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
zExp = 0;
if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR);
if ( roundNearestEven ) {
- increment = ( (sbits64) zSig2 < 0 );
+ increment = ( (int64_t) zSig2 < 0 );
}
else {
if ( zSign ) {
static float128
normalizeRoundAndPackFloat128(
- flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 STATUS_PARAM)
+ flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 STATUS_PARAM)
{
int8 shiftCount;
- bits64 zSig2;
+ uint64_t zSig2;
if ( zSig0 == 0 ) {
zSig0 = zSig1;
}
-#endif
-
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a'
| to the single-precision floating-point format. The conversion is performed
flag zSign;
if ( a == 0 ) return float32_zero;
- if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
+ if ( a == (int32_t) 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
zSign = ( a < 0 );
return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR );
flag zSign;
uint32 absA;
int8 shiftCount;
- bits64 zSig;
+ uint64_t zSig;
if ( a == 0 ) return float64_zero;
zSign = ( a < 0 );
}
-#ifdef FLOATX80
-
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a'
| to the extended double-precision floating-point format. The conversion
flag zSign;
uint32 absA;
int8 shiftCount;
- bits64 zSig;
+ uint64_t zSig;
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
zSign = ( a < 0 );
}
-#endif
-
-#ifdef FLOAT128
-
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a' to
| the quadruple-precision floating-point format. The conversion is performed
flag zSign;
uint32 absA;
int8 shiftCount;
- bits64 zSig0;
+ uint64_t zSig0;
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
zSign = ( a < 0 );
}
-#endif
-
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a'
| to the single-precision floating-point format. The conversion is performed
if ( a == 0 ) return float32_zero;
shiftCount = countLeadingZeros64( a ) - 40;
if ( 0 <= shiftCount ) {
- return packFloat32( 1 > 0, 0x95 - shiftCount, a<<shiftCount );
+ return packFloat32(0, 0x95 - shiftCount, a<<shiftCount);
}
else {
shiftCount += 7;
else {
a <<= shiftCount;
}
- return roundAndPackFloat32( 1 > 0, 0x9C - shiftCount, a STATUS_VAR );
+ return roundAndPackFloat32(0, 0x9C - shiftCount, a STATUS_VAR);
}
}
flag zSign;
if ( a == 0 ) return float64_zero;
- if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) {
+ if ( a == (int64_t) LIT64( 0x8000000000000000 ) ) {
return packFloat64( 1, 0x43E, 0 );
}
zSign = ( a < 0 );
}
-#ifdef FLOATX80
-
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a'
| to the extended double-precision floating-point format. The conversion
}
-#endif
-
-#ifdef FLOAT128
-
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a' to
| the quadruple-precision floating-point format. The conversion is performed
uint64 absA;
int8 shiftCount;
int32 zExp;
- bits64 zSig0, zSig1;
+ uint64_t zSig0, zSig1;
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
zSign = ( a < 0 );
}
-#endif
-
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the 32-bit two's complement integer format. The conversion is
int32 float32_to_int32( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits32 aSig;
- bits64 aSig64;
+ int_fast16_t aExp, shiftCount;
+ uint32_t aSig;
+ uint64_t aSig64;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits32 aSig;
- int32 z;
+ int_fast16_t aExp, shiftCount;
+ uint32_t aSig;
+ int32_t z;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
}
- return (sbits32) 0x80000000;
+ return (int32_t) 0x80000000;
}
else if ( aExp <= 0x7E ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
}
aSig = ( aSig | 0x00800000 )<<8;
z = aSig>>( - shiftCount );
- if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
+ if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
if ( aSign ) z = - z;
}
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the 16-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero.
+| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
+| the conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int_fast16_t float32_to_int16_round_to_zero(float32 a STATUS_PARAM)
+{
+ flag aSign;
+ int_fast16_t aExp, shiftCount;
+ uint32_t aSig;
+ int32 z;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ shiftCount = aExp - 0x8E;
+ if ( 0 <= shiftCount ) {
+ if ( float32_val(a) != 0xC7000000 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
+ return 0x7FFF;
+ }
+ }
+ return (int32_t) 0xffff8000;
+ }
+ else if ( aExp <= 0x7E ) {
+ if ( aExp | aSig ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return 0;
+ }
+ shiftCount -= 0x10;
+ aSig = ( aSig | 0x00800000 )<<8;
+ z = aSig>>( - shiftCount );
+ if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ if ( aSign ) {
+ z = - z;
+ }
+ return z;
+
+}
+
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the 64-bit two's complement integer format. The conversion is
int64 float32_to_int64( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits32 aSig;
- bits64 aSig64, aSigExtra;
+ int_fast16_t aExp, shiftCount;
+ uint32_t aSig;
+ uint64_t aSig64, aSigExtra;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
if ( aExp ) aSig |= 0x00800000;
aSig64 = aSig;
int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits32 aSig;
- bits64 aSig64;
+ int_fast16_t aExp, shiftCount;
+ uint32_t aSig;
+ uint64_t aSig64;
int64 z;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
else if ( aExp <= 0x7E ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
aSig64 = aSig | 0x00800000;
aSig64 <<= 40;
z = aSig64>>( - shiftCount );
- if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) {
+ if ( (uint64_t) ( aSig64<<( shiftCount & 63 ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
if ( aSign ) z = - z;
float64 float32_to_float64( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits32 aSig;
+ int_fast16_t aExp;
+ uint32_t aSig;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
- if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ));
+ if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
return packFloat64( aSign, 0x7FF, 0 );
}
if ( aExp == 0 ) {
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
--aExp;
}
- return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );
+ return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 );
}
-#ifdef FLOATX80
-
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the extended double-precision floating-point format. The conversion
floatx80 float32_to_floatx80( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits32 aSig;
+ int_fast16_t aExp;
+ uint32_t aSig;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
- if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) );
+ if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) {
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
aSig |= 0x00800000;
- return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );
+ return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 );
}
-#endif
-
-#ifdef FLOAT128
-
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the double-precision floating-point format. The conversion is
float128 float32_to_float128( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits32 aSig;
+ int_fast16_t aExp;
+ uint32_t aSig;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
- if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) );
+ if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
return packFloat128( aSign, 0x7FFF, 0, 0 );
}
if ( aExp == 0 ) {
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
--aExp;
}
- return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 );
+ return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 );
}
-#endif
-
/*----------------------------------------------------------------------------
| Rounds the single-precision floating-point value `a' to an integer, and
| returns the result as a single-precision floating-point value. The
float32 float32_round_to_int( float32 a STATUS_PARAM)
{
flag aSign;
- int16 aExp;
- bits32 lastBitMask, roundBitsMask;
+ int_fast16_t aExp;
+ uint32_t lastBitMask, roundBitsMask;
int8 roundingMode;
- bits32 z;
+ uint32_t z;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aExp = extractFloat32Exp( a );
if ( 0x96 <= aExp ) {
return a;
}
if ( aExp <= 0x7E ) {
- if ( (bits32) ( float32_val(a)<<1 ) == 0 ) return a;
+ if ( (uint32_t) ( float32_val(a)<<1 ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat32Sign( a );
switch ( STATUS(float_rounding_mode) ) {
static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
{
- int16 aExp, bExp, zExp;
- bits32 aSig, bSig, zSig;
- int16 expDiff;
+ int_fast16_t aExp, bExp, zExp;
+ uint32_t aSig, bSig, zSig;
+ int_fast16_t expDiff;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return a;
}
- if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
+ if ( aExp == 0 ) {
+ if (STATUS(flush_to_zero)) {
+ if (aSig | bSig) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ }
+ return packFloat32(zSign, 0, 0);
+ }
+ return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
+ }
zSig = 0x40000000 + aSig + bSig;
zExp = aExp;
goto roundAndPack;
aSig |= 0x20000000;
zSig = ( aSig + bSig )<<1;
--zExp;
- if ( (sbits32) zSig < 0 ) {
+ if ( (int32_t) zSig < 0 ) {
zSig = aSig + bSig;
++zExp;
}
static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
{
- int16 aExp, bExp, zExp;
- bits32 aSig, bSig, zSig;
- int16 expDiff;
+ int_fast16_t aExp, bExp, zExp;
+ uint32_t aSig, bSig, zSig;
+ int_fast16_t expDiff;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
float32 float32_add( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
float32 float32_sub( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
float32 float32_mul( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
- int16 aExp, bExp, zExp;
- bits32 aSig, bSig;
- bits64 zSig64;
- bits32 zSig;
+ int_fast16_t aExp, bExp, zExp;
+ uint32_t aSig, bSig;
+ uint64_t zSig64;
+ uint32_t zSig;
+
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
zExp = aExp + bExp - 0x7F;
aSig = ( aSig | 0x00800000 )<<7;
bSig = ( bSig | 0x00800000 )<<8;
- shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
+ shift64RightJamming( ( (uint64_t) aSig ) * bSig, 32, &zSig64 );
zSig = zSig64;
- if ( 0 <= (sbits32) ( zSig<<1 ) ) {
+ if ( 0 <= (int32_t) ( zSig<<1 ) ) {
zSig <<= 1;
--zExp;
}
float32 float32_div( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
- int16 aExp, bExp, zExp;
- bits32 aSig, bSig, zSig;
+ int_fast16_t aExp, bExp, zExp;
+ uint32_t aSig, bSig, zSig;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSig >>= 1;
++zExp;
}
- zSig = ( ( (bits64) aSig )<<32 ) / bSig;
+ zSig = ( ( (uint64_t) aSig )<<32 ) / bSig;
if ( ( zSig & 0x3F ) == 0 ) {
- zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 );
+ zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 );
}
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
float32 float32_rem( float32 a, float32 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
- int16 aExp, bExp, expDiff;
- bits32 aSig, bSig;
- bits32 q;
- bits64 aSig64, bSig64, q64;
- bits32 alternateASig;
- sbits32 sigMean;
+ flag aSign, zSign;
+ int_fast16_t aExp, bExp, expDiff;
+ uint32_t aSig, bSig;
+ uint32_t q;
+ uint64_t aSig64, bSig64, q64;
+ uint32_t alternateASig;
+ int32_t sigMean;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
- bSign = extractFloat32Sign( b );
if ( aExp == 0xFF ) {
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
return propagateFloat32NaN( a, b STATUS_VAR );
q = ( bSig <= aSig );
if ( q ) aSig -= bSig;
if ( 0 < expDiff ) {
- q = ( ( (bits64) aSig )<<32 ) / bSig;
+ q = ( ( (uint64_t) aSig )<<32 ) / bSig;
q >>= 32 - expDiff;
bSig >>= 2;
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
}
else {
if ( bSig <= aSig ) aSig -= bSig;
- aSig64 = ( (bits64) aSig )<<40;
- bSig64 = ( (bits64) bSig )<<40;
+ aSig64 = ( (uint64_t) aSig )<<40;
+ bSig64 = ( (uint64_t) bSig )<<40;
expDiff -= 64;
while ( 0 < expDiff ) {
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
alternateASig = aSig;
++q;
aSig -= bSig;
- } while ( 0 <= (sbits32) aSig );
+ } while ( 0 <= (int32_t) aSig );
sigMean = aSig + alternateASig;
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
aSig = alternateASig;
}
- zSign = ( (sbits32) aSig < 0 );
+ zSign = ( (int32_t) aSig < 0 );
if ( zSign ) aSig = - aSig;
return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR );
}
+/*----------------------------------------------------------------------------
+| Returns the result of multiplying the single-precision floating-point values
+| `a' and `b' then adding 'c', with no intermediate rounding step after the
+| multiplication. The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic 754-2008.
+| The flags argument allows the caller to select negation of the
+| addend, the intermediate product, or the final result. (The difference
+| between this and having the caller do a separate negation is that negating
+| externally will flip the sign bit on NaNs.)
+*----------------------------------------------------------------------------*/
+
+float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM)
+{
+ flag aSign, bSign, cSign, zSign;
+ int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff;
+ uint32_t aSig, bSig, cSig;
+ flag pInf, pZero, pSign;
+ uint64_t pSig64, cSig64, zSig64;
+ uint32_t pSig;
+ int shiftcount;
+ flag signflip, infzero;
+
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
+ c = float32_squash_input_denormal(c STATUS_VAR);
+ aSig = extractFloat32Frac(a);
+ aExp = extractFloat32Exp(a);
+ aSign = extractFloat32Sign(a);
+ bSig = extractFloat32Frac(b);
+ bExp = extractFloat32Exp(b);
+ bSign = extractFloat32Sign(b);
+ cSig = extractFloat32Frac(c);
+ cExp = extractFloat32Exp(c);
+ cSign = extractFloat32Sign(c);
+
+ infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) ||
+ (aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0));
+
+ /* It is implementation-defined whether the cases of (0,inf,qnan)
+ * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
+ * they return if they do), so we have to hand this information
+ * off to the target-specific pick-a-NaN routine.
+ */
+ if (((aExp == 0xff) && aSig) ||
+ ((bExp == 0xff) && bSig) ||
+ ((cExp == 0xff) && cSig)) {
+ return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR);
+ }
+
+ if (infzero) {
+ float_raise(float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+
+ if (flags & float_muladd_negate_c) {
+ cSign ^= 1;
+ }
+
+ signflip = (flags & float_muladd_negate_result) ? 1 : 0;
+
+ /* Work out the sign and type of the product */
+ pSign = aSign ^ bSign;
+ if (flags & float_muladd_negate_product) {
+ pSign ^= 1;
+ }
+ pInf = (aExp == 0xff) || (bExp == 0xff);
+ pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0);
+
+ if (cExp == 0xff) {
+ if (pInf && (pSign ^ cSign)) {
+ /* addition of opposite-signed infinities => InvalidOperation */
+ float_raise(float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ /* Otherwise generate an infinity of the same sign */
+ return packFloat32(cSign ^ signflip, 0xff, 0);
+ }
+
+ if (pInf) {
+ return packFloat32(pSign ^ signflip, 0xff, 0);
+ }
+
+ if (pZero) {
+ if (cExp == 0) {
+ if (cSig == 0) {
+ /* Adding two exact zeroes */
+ if (pSign == cSign) {
+ zSign = pSign;
+ } else if (STATUS(float_rounding_mode) == float_round_down) {
+ zSign = 1;
+ } else {
+ zSign = 0;
+ }
+ return packFloat32(zSign ^ signflip, 0, 0);
+ }
+ /* Exact zero plus a denorm */
+ if (STATUS(flush_to_zero)) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ return packFloat32(cSign ^ signflip, 0, 0);
+ }
+ }
+ /* Zero plus something non-zero : just return the something */
+ return make_float32(float32_val(c) ^ (signflip << 31));
+ }
+
+ if (aExp == 0) {
+ normalizeFloat32Subnormal(aSig, &aExp, &aSig);
+ }
+ if (bExp == 0) {
+ normalizeFloat32Subnormal(bSig, &bExp, &bSig);
+ }
+
+ /* Calculate the actual result a * b + c */
+
+ /* Multiply first; this is easy. */
+ /* NB: we subtract 0x7e where float32_mul() subtracts 0x7f
+ * because we want the true exponent, not the "one-less-than"
+ * flavour that roundAndPackFloat32() takes.
+ */
+ pExp = aExp + bExp - 0x7e;
+ aSig = (aSig | 0x00800000) << 7;
+ bSig = (bSig | 0x00800000) << 8;
+ pSig64 = (uint64_t)aSig * bSig;
+ if ((int64_t)(pSig64 << 1) >= 0) {
+ pSig64 <<= 1;
+ pExp--;
+ }
+
+ zSign = pSign ^ signflip;
+
+ /* Now pSig64 is the significand of the multiply, with the explicit bit in
+ * position 62.
+ */
+ if (cExp == 0) {
+ if (!cSig) {
+ /* Throw out the special case of c being an exact zero now */
+ shift64RightJamming(pSig64, 32, &pSig64);
+ pSig = pSig64;
+ return roundAndPackFloat32(zSign, pExp - 1,
+ pSig STATUS_VAR);
+ }
+ normalizeFloat32Subnormal(cSig, &cExp, &cSig);
+ }
+
+ cSig64 = (uint64_t)cSig << (62 - 23);
+ cSig64 |= LIT64(0x4000000000000000);
+ expDiff = pExp - cExp;
+
+ if (pSign == cSign) {
+ /* Addition */
+ if (expDiff > 0) {
+ /* scale c to match p */
+ shift64RightJamming(cSig64, expDiff, &cSig64);
+ zExp = pExp;
+ } else if (expDiff < 0) {
+ /* scale p to match c */
+ shift64RightJamming(pSig64, -expDiff, &pSig64);
+ zExp = cExp;
+ } else {
+ /* no scaling needed */
+ zExp = cExp;
+ }
+ /* Add significands and make sure explicit bit ends up in posn 62 */
+ zSig64 = pSig64 + cSig64;
+ if ((int64_t)zSig64 < 0) {
+ shift64RightJamming(zSig64, 1, &zSig64);
+ } else {
+ zExp--;
+ }
+ } else {
+ /* Subtraction */
+ if (expDiff > 0) {
+ shift64RightJamming(cSig64, expDiff, &cSig64);
+ zSig64 = pSig64 - cSig64;
+ zExp = pExp;
+ } else if (expDiff < 0) {
+ shift64RightJamming(pSig64, -expDiff, &pSig64);
+ zSig64 = cSig64 - pSig64;
+ zExp = cExp;
+ zSign ^= 1;
+ } else {
+ zExp = pExp;
+ if (cSig64 < pSig64) {
+ zSig64 = pSig64 - cSig64;
+ } else if (pSig64 < cSig64) {
+ zSig64 = cSig64 - pSig64;
+ zSign ^= 1;
+ } else {
+ /* Exact zero */
+ zSign = signflip;
+ if (STATUS(float_rounding_mode) == float_round_down) {
+ zSign ^= 1;
+ }
+ return packFloat32(zSign, 0, 0);
+ }
+ }
+ --zExp;
+ /* Normalize to put the explicit bit back into bit 62. */
+ shiftcount = countLeadingZeros64(zSig64) - 1;
+ zSig64 <<= shiftcount;
+ zExp -= shiftcount;
+ }
+ shift64RightJamming(zSig64, 32, &zSig64);
+ return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR);
+}
+
+
/*----------------------------------------------------------------------------
| Returns the square root of the single-precision floating-point value `a'.
| The operation is performed according to the IEC/IEEE Standard for Binary
float32 float32_sqrt( float32 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, zExp;
- bits32 aSig, zSig;
- bits64 rem, term;
+ int_fast16_t aExp, zExp;
+ uint32_t aSig, zSig;
+ uint64_t rem, term;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
goto roundAndPack;
}
aSig >>= aExp & 1;
- term = ( (bits64) zSig ) * zSig;
- rem = ( ( (bits64) aSig )<<32 ) - term;
- while ( (sbits64) rem < 0 ) {
+ term = ( (uint64_t) zSig ) * zSig;
+ rem = ( ( (uint64_t) aSig )<<32 ) - term;
+ while ( (int64_t) rem < 0 ) {
--zSig;
- rem += ( ( (bits64) zSig )<<1 ) | 1;
+ rem += ( ( (uint64_t) zSig )<<1 ) | 1;
}
zSig |= ( rem != 0 );
}
}
+/*----------------------------------------------------------------------------
+| Returns the binary exponential of the single-precision floating-point value
+| `a'. The operation is performed according to the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+|
+| Uses the following identities:
+|
+| 1. -------------------------------------------------------------------------
+| x x*ln(2)
+| 2 = e
+|
+| 2. -------------------------------------------------------------------------
+| 2 3 4 5 n
+| x x x x x x x
+| e = 1 + --- + --- + --- + --- + --- + ... + --- + ...
+| 1! 2! 3! 4! 5! n!
+*----------------------------------------------------------------------------*/
+
+static const float64 float32_exp2_coefficients[15] =
+{
+ const_float64( 0x3ff0000000000000ll ), /* 1 */
+ const_float64( 0x3fe0000000000000ll ), /* 2 */
+ const_float64( 0x3fc5555555555555ll ), /* 3 */
+ const_float64( 0x3fa5555555555555ll ), /* 4 */
+ const_float64( 0x3f81111111111111ll ), /* 5 */
+ const_float64( 0x3f56c16c16c16c17ll ), /* 6 */
+ const_float64( 0x3f2a01a01a01a01all ), /* 7 */
+ const_float64( 0x3efa01a01a01a01all ), /* 8 */
+ const_float64( 0x3ec71de3a556c734ll ), /* 9 */
+ const_float64( 0x3e927e4fb7789f5cll ), /* 10 */
+ const_float64( 0x3e5ae64567f544e4ll ), /* 11 */
+ const_float64( 0x3e21eed8eff8d898ll ), /* 12 */
+ const_float64( 0x3de6124613a86d09ll ), /* 13 */
+ const_float64( 0x3da93974a8c07c9dll ), /* 14 */
+ const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */
+};
+
+float32 float32_exp2( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int_fast16_t aExp;
+ uint32_t aSig;
+ float64 r, x, xn;
+ int i;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+
+ if ( aExp == 0xFF) {
+ if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR );
+ return (aSign) ? float32_zero : a;
+ }
+ if (aExp == 0) {
+ if (aSig == 0) return float32_one;
+ }
+
+ float_raise( float_flag_inexact STATUS_VAR);
+
+ /* ******************************* */
+ /* using float64 for approximation */
+ /* ******************************* */
+ x = float32_to_float64(a STATUS_VAR);
+ x = float64_mul(x, float64_ln2 STATUS_VAR);
+
+ xn = x;
+ r = float64_one;
+ for (i = 0 ; i < 15 ; i++) {
+ float64 f;
+
+ f = float64_mul(xn, float32_exp2_coefficients[i] STATUS_VAR);
+ r = float64_add(r, f STATUS_VAR);
+
+ xn = float64_mul(xn, x STATUS_VAR);
+ }
+
+ return float64_to_float32(r, status);
+}
+
+/*----------------------------------------------------------------------------
+| Returns the binary log of the single-precision floating-point value `a'.
+| The operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+float32 float32_log2( float32 a STATUS_PARAM )
+{
+ flag aSign, zSign;
+ int_fast16_t aExp;
+ uint32_t aSig, zSig, i;
+
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ }
+ if ( aSign ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR );
+ return a;
+ }
+
+ aExp -= 0x7F;
+ aSig |= 0x00800000;
+ zSign = aExp < 0;
+ zSig = aExp << 23;
+
+ for (i = 1 << 22; i > 0; i >>= 1) {
+ aSig = ( (uint64_t)aSig * aSig ) >> 23;
+ if ( aSig & 0x01000000 ) {
+ aSig >>= 1;
+ zSig |= i;
+ }
+ }
+
+ if ( zSign )
+ zSig = -zSig;
+
+ return normalizeRoundAndPackFloat32( zSign, 0x85, zSig STATUS_VAR );
+}
+
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is equal to
-| the corresponding value `b', and 0 otherwise. The comparison is performed
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. Otherwise, the comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float32_eq( float32 a, float32 b STATUS_PARAM )
{
+ uint32_t av, bv;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
- if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
- float_raise( float_flag_invalid STATUS_VAR);
- }
+ float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
- return ( float32_val(a) == float32_val(b) ) ||
- ( (bits32) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 );
-
+ av = float32_val(a);
+ bv = float32_val(b);
+ return ( av == bv ) || ( (uint32_t) ( ( av | bv )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is less than
-| or equal to the corresponding value `b', and 0 otherwise. The comparison
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
+| or equal to the corresponding value `b', and 0 otherwise. The invalid
+| exception is raised if either operand is a NaN. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float32_le( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
- bits32 av, bv;
+ uint32_t av, bv;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
bSign = extractFloat32Sign( b );
av = float32_val(a);
bv = float32_val(b);
- if ( aSign != bSign ) return aSign || ( (bits32) ( ( av | bv )<<1 ) == 0 );
+ if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 );
return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is less than
-| the corresponding value `b', and 0 otherwise. The comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. The comparison is performed according
+| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float32_lt( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
- bits32 av, bv;
+ uint32_t av, bv;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
bSign = extractFloat32Sign( b );
av = float32_val(a);
bv = float32_val(b);
- if ( aSign != bSign ) return aSign && ( (bits32) ( ( av | bv )<<1 ) != 0 );
+ if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 );
return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
/*----------------------------------------------------------------------------
-| Returns 1 if the single-precision floating-point value `a' is equal to
-| the corresponding value `b', and 0 otherwise. The invalid exception is
-| raised if either operand is a NaN. Otherwise, the comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| Returns 1 if the single-precision floating-point values `a' and `b' cannot
+| be compared, and 0 otherwise. The invalid exception is raised if either
+| operand is a NaN. The comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-int float32_eq_signaling( float32 a, float32 b STATUS_PARAM )
+int float32_unordered( float32 a, float32 b STATUS_PARAM )
{
- bits32 av, bv;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
- return 0;
+ return 1;
}
- av = float32_val(a);
- bv = float32_val(b);
- return ( av == bv ) || ( (bits32) ( ( av | bv )<<1 ) == 0 );
+ return 0;
+}
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is equal to
+| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
+| exception. The comparison is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+int float32_eq_quiet( float32 a, float32 b STATUS_PARAM )
+{
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ return ( float32_val(a) == float32_val(b) ) ||
+ ( (uint32_t) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
int float32_le_quiet( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
- bits32 av, bv;
+ uint32_t av, bv;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
bSign = extractFloat32Sign( b );
av = float32_val(a);
bv = float32_val(b);
- if ( aSign != bSign ) return aSign || ( (bits32) ( ( av | bv )<<1 ) == 0 );
+ if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 );
return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
int float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
- bits32 av, bv;
+ uint32_t av, bv;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
bSign = extractFloat32Sign( b );
av = float32_val(a);
bv = float32_val(b);
- if ( aSign != bSign ) return aSign && ( (bits32) ( ( av | bv )<<1 ) != 0 );
+ if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 );
return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point values `a' and `b' cannot
+| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The
+| comparison is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+int float32_unordered_quiet( float32 a, float32 b STATUS_PARAM )
+{
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ b = float32_squash_input_denormal(b STATUS_VAR);
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 1;
+ }
+ return 0;
+}
+
/*----------------------------------------------------------------------------
| Returns the result of converting the double-precision floating-point value
| `a' to the 32-bit two's complement integer format. The conversion is
int32 float64_to_int32( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig;
+ int_fast16_t aExp, shiftCount;
+ uint64_t aSig;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig, savedASig;
- int32 z;
+ int_fast16_t aExp, shiftCount;
+ uint64_t aSig, savedASig;
+ int32_t z;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
if ( ( z < 0 ) ^ aSign ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
- return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
}
if ( ( aSig<<shiftCount ) != savedASig ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the 16-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero.
+| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
+| the conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int_fast16_t float64_to_int16_round_to_zero(float64 a STATUS_PARAM)
+{
+ flag aSign;
+ int_fast16_t aExp, shiftCount;
+ uint64_t aSig, savedASig;
+ int32 z;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( 0x40E < aExp ) {
+ if ( ( aExp == 0x7FF ) && aSig ) {
+ aSign = 0;
+ }
+ goto invalid;
+ }
+ else if ( aExp < 0x3FF ) {
+ if ( aExp || aSig ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return 0;
+ }
+ aSig |= LIT64( 0x0010000000000000 );
+ shiftCount = 0x433 - aExp;
+ savedASig = aSig;
+ aSig >>= shiftCount;
+ z = aSig;
+ if ( aSign ) {
+ z = - z;
+ }
+ if ( ( (int16_t)z < 0 ) ^ aSign ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ return aSign ? (int32_t) 0xffff8000 : 0x7FFF;
+ }
+ if ( ( aSig<<shiftCount ) != savedASig ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return z;
+}
+
/*----------------------------------------------------------------------------
| Returns the result of converting the double-precision floating-point value
| `a' to the 64-bit two's complement integer format. The conversion is
int64 float64_to_int64( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig, aSigExtra;
+ int_fast16_t aExp, shiftCount;
+ uint64_t aSig, aSigExtra;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
aSigExtra = 0;
aSig <<= - shiftCount;
int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig;
+ int_fast16_t aExp, shiftCount;
+ uint64_t aSig;
int64 z;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
z = aSig<<shiftCount;
}
return 0;
}
z = aSig>>( - shiftCount );
- if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
+ if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
}
float32 float64_to_float32( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 aSig;
- bits32 zSig;
+ int_fast16_t aExp;
+ uint64_t aSig;
+ uint32_t zSig;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
- if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) );
+ if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
return packFloat32( aSign, 0xFF, 0 );
}
shift64RightJamming( aSig, 22, &aSig );
}
-#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
+| half-precision floating-point value, returning the result. After being
+| shifted into the proper positions, the three fields are simply added
+| together to form the result. This means that any integer portion of `zSig'
+| will be added into the exponent. Since a properly normalized significand
+| will have an integer portion equal to 1, the `zExp' input should be 1 less
+| than the desired result exponent whenever `zSig' is a complete, normalized
+| significand.
+*----------------------------------------------------------------------------*/
+static float16 packFloat16(flag zSign, int_fast16_t zExp, uint16_t zSig)
+{
+ return make_float16(
+ (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig);
+}
+
+/* Half precision floats come in two formats: standard IEEE and "ARM" format.
+ The latter gains extra exponent range by omitting the NaN/Inf encodings. */
+
+float32 float16_to_float32(float16 a, flag ieee STATUS_PARAM)
+{
+ flag aSign;
+ int_fast16_t aExp;
+ uint32_t aSig;
+
+ aSign = extractFloat16Sign(a);
+ aExp = extractFloat16Exp(a);
+ aSig = extractFloat16Frac(a);
+
+ if (aExp == 0x1f && ieee) {
+ if (aSig) {
+ return commonNaNToFloat32(float16ToCommonNaN(a STATUS_VAR) STATUS_VAR);
+ }
+ return packFloat32(aSign, 0xff, 0);
+ }
+ if (aExp == 0) {
+ int8 shiftCount;
+
+ if (aSig == 0) {
+ return packFloat32(aSign, 0, 0);
+ }
+
+ shiftCount = countLeadingZeros32( aSig ) - 21;
+ aSig = aSig << shiftCount;
+ aExp = -shiftCount;
+ }
+ return packFloat32( aSign, aExp + 0x70, aSig << 13);
+}
+
+float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM)
+{
+ flag aSign;
+ int_fast16_t aExp;
+ uint32_t aSig;
+ uint32_t mask;
+ uint32_t increment;
+ int8 roundingMode;
+ a = float32_squash_input_denormal(a STATUS_VAR);
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if (aSig) {
+ /* Input is a NaN */
+ float16 r = commonNaNToFloat16( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
+ if (!ieee) {
+ return packFloat16(aSign, 0, 0);
+ }
+ return r;
+ }
+ /* Infinity */
+ if (!ieee) {
+ float_raise(float_flag_invalid STATUS_VAR);
+ return packFloat16(aSign, 0x1f, 0x3ff);
+ }
+ return packFloat16(aSign, 0x1f, 0);
+ }
+ if (aExp == 0 && aSig == 0) {
+ return packFloat16(aSign, 0, 0);
+ }
+ /* Decimal point between bits 22 and 23. */
+ aSig |= 0x00800000;
+ aExp -= 0x7f;
+ if (aExp < -14) {
+ mask = 0x00ffffff;
+ if (aExp >= -24) {
+ mask >>= 25 + aExp;
+ }
+ } else {
+ mask = 0x00001fff;
+ }
+ if (aSig & mask) {
+ float_raise( float_flag_underflow STATUS_VAR );
+ roundingMode = STATUS(float_rounding_mode);
+ switch (roundingMode) {
+ case float_round_nearest_even:
+ increment = (mask + 1) >> 1;
+ if ((aSig & mask) == increment) {
+ increment = aSig & (increment << 1);
+ }
+ break;
+ case float_round_up:
+ increment = aSign ? 0 : mask;
+ break;
+ case float_round_down:
+ increment = aSign ? mask : 0;
+ break;
+ default: /* round_to_zero */
+ increment = 0;
+ break;
+ }
+ aSig += increment;
+ if (aSig >= 0x01000000) {
+ aSig >>= 1;
+ aExp++;
+ }
+ } else if (aExp < -14
+ && STATUS(float_detect_tininess) == float_tininess_before_rounding) {
+ float_raise( float_flag_underflow STATUS_VAR);
+ }
+
+ if (ieee) {
+ if (aExp > 15) {
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ return packFloat16(aSign, 0x1f, 0);
+ }
+ } else {
+ if (aExp > 16) {
+ float_raise(float_flag_invalid | float_flag_inexact STATUS_VAR);
+ return packFloat16(aSign, 0x1f, 0x3ff);
+ }
+ }
+ if (aExp < -24) {
+ return packFloat16(aSign, 0, 0);
+ }
+ if (aExp < -14) {
+ aSig >>= -14 - aExp;
+ aExp = -14;
+ }
+ return packFloat16(aSign, aExp + 14, aSig >> 13);
+}
/*----------------------------------------------------------------------------
| Returns the result of converting the double-precision floating-point value
floatx80 float64_to_floatx80( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 aSig;
+ int_fast16_t aExp;
+ uint64_t aSig;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
- if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) );
+ if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) {
}
-#endif
-
-#ifdef FLOAT128
-
/*----------------------------------------------------------------------------
| Returns the result of converting the double-precision floating-point value
| `a' to the quadruple-precision floating-point format. The conversion is
float128 float64_to_float128( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 aSig, zSig0, zSig1;
+ int_fast16_t aExp;
+ uint64_t aSig, zSig0, zSig1;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
- if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) );
+ if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
return packFloat128( aSign, 0x7FFF, 0, 0 );
}
if ( aExp == 0 ) {
}
-#endif
-
/*----------------------------------------------------------------------------
| Rounds the double-precision floating-point value `a' to an integer, and
| returns the result as a double-precision floating-point value. The
float64 float64_round_to_int( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 lastBitMask, roundBitsMask;
+ int_fast16_t aExp;
+ uint64_t lastBitMask, roundBitsMask;
int8 roundingMode;
- bits64 z;
+ uint64_t z;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aExp = extractFloat64Exp( a );
if ( 0x433 <= aExp ) {
return a;
}
if ( aExp < 0x3FF ) {
- if ( (bits64) ( float64_val(a)<<1 ) == 0 ) return a;
+ if ( (uint64_t) ( float64_val(a)<<1 ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat64Sign( a );
switch ( STATUS(float_rounding_mode) ) {
static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
{
- int16 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig;
- int16 expDiff;
+ int_fast16_t aExp, bExp, zExp;
+ uint64_t aSig, bSig, zSig;
+ int_fast16_t expDiff;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return a;
}
- if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
+ if ( aExp == 0 ) {
+ if (STATUS(flush_to_zero)) {
+ if (aSig | bSig) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ }
+ return packFloat64(zSign, 0, 0);
+ }
+ return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
+ }
zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
zExp = aExp;
goto roundAndPack;
aSig |= LIT64( 0x2000000000000000 );
zSig = ( aSig + bSig )<<1;
--zExp;
- if ( (sbits64) zSig < 0 ) {
+ if ( (int64_t) zSig < 0 ) {
zSig = aSig + bSig;
++zExp;
}
static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
{
- int16 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig;
- int16 expDiff;
+ int_fast16_t aExp, bExp, zExp;
+ uint64_t aSig, bSig, zSig;
+ int_fast16_t expDiff;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
float64 float64_add( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
float64 float64_sub( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
float64 float64_mul( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
- int16 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig0, zSig1;
+ int_fast16_t aExp, bExp, zExp;
+ uint64_t aSig, bSig, zSig0, zSig1;
+
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
mul64To128( aSig, bSig, &zSig0, &zSig1 );
zSig0 |= ( zSig1 != 0 );
- if ( 0 <= (sbits64) ( zSig0<<1 ) ) {
+ if ( 0 <= (int64_t) ( zSig0<<1 ) ) {
zSig0 <<= 1;
--zExp;
}
float64 float64_div( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
- int16 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig;
- bits64 rem0, rem1;
- bits64 term0, term1;
+ int_fast16_t aExp, bExp, zExp;
+ uint64_t aSig, bSig, zSig;
+ uint64_t rem0, rem1;
+ uint64_t term0, term1;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
if ( ( zSig & 0x1FF ) <= 2 ) {
mul64To128( bSig, zSig, &term0, &term1 );
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
+ while ( (int64_t) rem0 < 0 ) {
--zSig;
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
}
float64 float64_rem( float64 a, float64 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
- int16 aExp, bExp, expDiff;
- bits64 aSig, bSig;
- bits64 q, alternateASig;
- sbits64 sigMean;
+ flag aSign, zSign;
+ int_fast16_t aExp, bExp, expDiff;
+ uint64_t aSig, bSig;
+ uint64_t q, alternateASig;
+ int64_t sigMean;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
- bSign = extractFloat64Sign( b );
if ( aExp == 0x7FF ) {
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
return propagateFloat64NaN( a, b STATUS_VAR );
alternateASig = aSig;
++q;
aSig -= bSig;
- } while ( 0 <= (sbits64) aSig );
+ } while ( 0 <= (int64_t) aSig );
sigMean = aSig + alternateASig;
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
aSig = alternateASig;
}
- zSign = ( (sbits64) aSig < 0 );
+ zSign = ( (int64_t) aSig < 0 );
if ( zSign ) aSig = - aSig;
return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR );
}
+/*----------------------------------------------------------------------------
+| Returns the result of multiplying the double-precision floating-point values
+| `a' and `b' then adding 'c', with no intermediate rounding step after the
+| multiplication. The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic 754-2008.
+| The flags argument allows the caller to select negation of the
+| addend, the intermediate product, or the final result. (The difference
+| between this and having the caller do a separate negation is that negating
+| externally will flip the sign bit on NaNs.)
+*----------------------------------------------------------------------------*/
+
+float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM)
+{
+ flag aSign, bSign, cSign, zSign;
+ int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff;
+ uint64_t aSig, bSig, cSig;
+ flag pInf, pZero, pSign;
+ uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1;
+ int shiftcount;
+ flag signflip, infzero;
+
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
+ c = float64_squash_input_denormal(c STATUS_VAR);
+ aSig = extractFloat64Frac(a);
+ aExp = extractFloat64Exp(a);
+ aSign = extractFloat64Sign(a);
+ bSig = extractFloat64Frac(b);
+ bExp = extractFloat64Exp(b);
+ bSign = extractFloat64Sign(b);
+ cSig = extractFloat64Frac(c);
+ cExp = extractFloat64Exp(c);
+ cSign = extractFloat64Sign(c);
+
+ infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) ||
+ (aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0));
+
+ /* It is implementation-defined whether the cases of (0,inf,qnan)
+ * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
+ * they return if they do), so we have to hand this information
+ * off to the target-specific pick-a-NaN routine.
+ */
+ if (((aExp == 0x7ff) && aSig) ||
+ ((bExp == 0x7ff) && bSig) ||
+ ((cExp == 0x7ff) && cSig)) {
+ return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR);
+ }
+
+ if (infzero) {
+ float_raise(float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+
+ if (flags & float_muladd_negate_c) {
+ cSign ^= 1;
+ }
+
+ signflip = (flags & float_muladd_negate_result) ? 1 : 0;
+
+ /* Work out the sign and type of the product */
+ pSign = aSign ^ bSign;
+ if (flags & float_muladd_negate_product) {
+ pSign ^= 1;
+ }
+ pInf = (aExp == 0x7ff) || (bExp == 0x7ff);
+ pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0);
+
+ if (cExp == 0x7ff) {
+ if (pInf && (pSign ^ cSign)) {
+ /* addition of opposite-signed infinities => InvalidOperation */
+ float_raise(float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ /* Otherwise generate an infinity of the same sign */
+ return packFloat64(cSign ^ signflip, 0x7ff, 0);
+ }
+
+ if (pInf) {
+ return packFloat64(pSign ^ signflip, 0x7ff, 0);
+ }
+
+ if (pZero) {
+ if (cExp == 0) {
+ if (cSig == 0) {
+ /* Adding two exact zeroes */
+ if (pSign == cSign) {
+ zSign = pSign;
+ } else if (STATUS(float_rounding_mode) == float_round_down) {
+ zSign = 1;
+ } else {
+ zSign = 0;
+ }
+ return packFloat64(zSign ^ signflip, 0, 0);
+ }
+ /* Exact zero plus a denorm */
+ if (STATUS(flush_to_zero)) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ return packFloat64(cSign ^ signflip, 0, 0);
+ }
+ }
+ /* Zero plus something non-zero : just return the something */
+ return make_float64(float64_val(c) ^ ((uint64_t)signflip << 63));
+ }
+
+ if (aExp == 0) {
+ normalizeFloat64Subnormal(aSig, &aExp, &aSig);
+ }
+ if (bExp == 0) {
+ normalizeFloat64Subnormal(bSig, &bExp, &bSig);
+ }
+
+ /* Calculate the actual result a * b + c */
+
+ /* Multiply first; this is easy. */
+ /* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff
+ * because we want the true exponent, not the "one-less-than"
+ * flavour that roundAndPackFloat64() takes.
+ */
+ pExp = aExp + bExp - 0x3fe;
+ aSig = (aSig | LIT64(0x0010000000000000))<<10;
+ bSig = (bSig | LIT64(0x0010000000000000))<<11;
+ mul64To128(aSig, bSig, &pSig0, &pSig1);
+ if ((int64_t)(pSig0 << 1) >= 0) {
+ shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1);
+ pExp--;
+ }
+
+ zSign = pSign ^ signflip;
+
+ /* Now [pSig0:pSig1] is the significand of the multiply, with the explicit
+ * bit in position 126.
+ */
+ if (cExp == 0) {
+ if (!cSig) {
+ /* Throw out the special case of c being an exact zero now */
+ shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1);
+ return roundAndPackFloat64(zSign, pExp - 1,
+ pSig1 STATUS_VAR);
+ }
+ normalizeFloat64Subnormal(cSig, &cExp, &cSig);
+ }
+
+ /* Shift cSig and add the explicit bit so [cSig0:cSig1] is the
+ * significand of the addend, with the explicit bit in position 126.
+ */
+ cSig0 = cSig << (126 - 64 - 52);
+ cSig1 = 0;
+ cSig0 |= LIT64(0x4000000000000000);
+ expDiff = pExp - cExp;
+
+ if (pSign == cSign) {
+ /* Addition */
+ if (expDiff > 0) {
+ /* scale c to match p */
+ shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1);
+ zExp = pExp;
+ } else if (expDiff < 0) {
+ /* scale p to match c */
+ shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1);
+ zExp = cExp;
+ } else {
+ /* no scaling needed */
+ zExp = cExp;
+ }
+ /* Add significands and make sure explicit bit ends up in posn 126 */
+ add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
+ if ((int64_t)zSig0 < 0) {
+ shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1);
+ } else {
+ zExp--;
+ }
+ shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1);
+ return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR);
+ } else {
+ /* Subtraction */
+ if (expDiff > 0) {
+ shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1);
+ sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
+ zExp = pExp;
+ } else if (expDiff < 0) {
+ shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1);
+ sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1);
+ zExp = cExp;
+ zSign ^= 1;
+ } else {
+ zExp = pExp;
+ if (lt128(cSig0, cSig1, pSig0, pSig1)) {
+ sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
+ } else if (lt128(pSig0, pSig1, cSig0, cSig1)) {
+ sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1);
+ zSign ^= 1;
+ } else {
+ /* Exact zero */
+ zSign = signflip;
+ if (STATUS(float_rounding_mode) == float_round_down) {
+ zSign ^= 1;
+ }
+ return packFloat64(zSign, 0, 0);
+ }
+ }
+ --zExp;
+ /* Do the equivalent of normalizeRoundAndPackFloat64() but
+ * starting with the significand in a pair of uint64_t.
+ */
+ if (zSig0) {
+ shiftcount = countLeadingZeros64(zSig0) - 1;
+ shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1);
+ if (zSig1) {
+ zSig0 |= 1;
+ }
+ zExp -= shiftcount;
+ } else {
+ shiftcount = countLeadingZeros64(zSig1) - 1;
+ zSig0 = zSig1 << shiftcount;
+ zExp -= (shiftcount + 64);
+ }
+ return roundAndPackFloat64(zSign, zExp, zSig0 STATUS_VAR);
+ }
+}
+
/*----------------------------------------------------------------------------
| Returns the square root of the double-precision floating-point value `a'.
| The operation is performed according to the IEC/IEEE Standard for Binary
float64 float64_sqrt( float64 a STATUS_PARAM )
{
flag aSign;
- int16 aExp, zExp;
- bits64 aSig, zSig, doubleZSig;
- bits64 rem0, rem1, term0, term1;
+ int_fast16_t aExp, zExp;
+ uint64_t aSig, zSig, doubleZSig;
+ uint64_t rem0, rem1, term0, term1;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
doubleZSig = zSig<<1;
mul64To128( zSig, zSig, &term0, &term1 );
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
+ while ( (int64_t) rem0 < 0 ) {
--zSig;
doubleZSig -= 2;
add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 );
}
+/*----------------------------------------------------------------------------
+| Returns the binary log of the double-precision floating-point value `a'.
+| The operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+float64 float64_log2( float64 a STATUS_PARAM )
+{
+ flag aSign, zSign;
+ int_fast16_t aExp;
+ uint64_t aSig, aSig0, aSig1, zSig, i;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 );
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ }
+ if ( aSign ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return propagateFloat64NaN( a, float64_zero STATUS_VAR );
+ return a;
+ }
+
+ aExp -= 0x3FF;
+ aSig |= LIT64( 0x0010000000000000 );
+ zSign = aExp < 0;
+ zSig = (uint64_t)aExp << 52;
+ for (i = 1LL << 51; i > 0; i >>= 1) {
+ mul64To128( aSig, aSig, &aSig0, &aSig1 );
+ aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 );
+ if ( aSig & LIT64( 0x0020000000000000 ) ) {
+ aSig >>= 1;
+ zSig |= i;
+ }
+ }
+
+ if ( zSign )
+ zSig = -zSig;
+ return normalizeRoundAndPackFloat64( zSign, 0x408, zSig STATUS_VAR );
+}
+
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is equal to the
-| corresponding value `b', and 0 otherwise. The comparison is performed
+| corresponding value `b', and 0 otherwise. The invalid exception is raised
+| if either operand is a NaN. Otherwise, the comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float64_eq( float64 a, float64 b STATUS_PARAM )
{
- bits64 av, bv;
+ uint64_t av, bv;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
- if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
- float_raise( float_flag_invalid STATUS_VAR);
- }
+ float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
av = float64_val(a);
bv = float64_val(b);
- return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 );
+ return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is less than or
-| equal to the corresponding value `b', and 0 otherwise. The comparison is
-| performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
+| equal to the corresponding value `b', and 0 otherwise. The invalid
+| exception is raised if either operand is a NaN. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float64_le( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
- bits64 av, bv;
+ uint64_t av, bv;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
- if ( aSign != bSign ) return aSign || ( (bits64) ( ( av | bv )<<1 ) == 0 );
+ if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 );
return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is less than
-| the corresponding value `b', and 0 otherwise. The comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. The comparison is performed according
+| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+int float64_lt( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+ uint64_t av, bv;
+
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ av = float64_val(a);
+ bv = float64_val(b);
+ if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 );
+ return ( av != bv ) && ( aSign ^ ( av < bv ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point values `a' and `b' cannot
+| be compared, and 0 otherwise. The invalid exception is raised if either
+| operand is a NaN. The comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-int float64_lt( float64 a, float64 b STATUS_PARAM )
+int float64_unordered( float64 a, float64 b STATUS_PARAM )
{
- flag aSign, bSign;
- bits64 av, bv;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
- return 0;
+ return 1;
}
- aSign = extractFloat64Sign( a );
- bSign = extractFloat64Sign( b );
- av = float64_val(a);
- bv = float64_val(b);
- if ( aSign != bSign ) return aSign && ( (bits64) ( ( av | bv )<<1 ) != 0 );
- return ( av != bv ) && ( aSign ^ ( av < bv ) );
-
+ return 0;
}
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is equal to the
-| corresponding value `b', and 0 otherwise. The invalid exception is raised
-| if either operand is a NaN. Otherwise, the comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
+| exception.The comparison is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-int float64_eq_signaling( float64 a, float64 b STATUS_PARAM )
+int float64_eq_quiet( float64 a, float64 b STATUS_PARAM )
{
- bits64 av, bv;
+ uint64_t av, bv;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
- float_raise( float_flag_invalid STATUS_VAR);
+ if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
return 0;
}
av = float64_val(a);
bv = float64_val(b);
- return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 );
+ return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 );
}
int float64_le_quiet( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
- bits64 av, bv;
+ uint64_t av, bv;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
- if ( aSign != bSign ) return aSign || ( (bits64) ( ( av | bv )<<1 ) == 0 );
+ if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 );
return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
int float64_lt_quiet( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
- bits64 av, bv;
+ uint64_t av, bv;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
- if ( aSign != bSign ) return aSign && ( (bits64) ( ( av | bv )<<1 ) != 0 );
+ if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 );
return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
-#ifdef FLOATX80
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point values `a' and `b' cannot
+| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The
+| comparison is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+int float64_unordered_quiet( float64 a, float64 b STATUS_PARAM )
+{
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 1;
+ }
+ return 0;
+}
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-precision floating-
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig;
+ uint64_t aSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
- if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
+ if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0;
shiftCount = 0x4037 - aExp;
if ( shiftCount <= 0 ) shiftCount = 1;
shift64RightJamming( aSig, shiftCount, &aSig );
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig, savedASig;
- int32 z;
+ uint64_t aSig, savedASig;
+ int32_t z;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( 0x401E < aExp ) {
- if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
+ if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0;
goto invalid;
}
else if ( aExp < 0x3FFF ) {
if ( ( z < 0 ) ^ aSign ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
- return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
}
if ( ( aSig<<shiftCount ) != savedASig ) {
STATUS(float_exception_flags) |= float_flag_inexact;
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig, aSigExtra;
+ uint64_t aSig, aSigExtra;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
aSigExtra = 0;
}
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig;
+ uint64_t aSig;
int64 z;
aSig = extractFloatx80Frac( a );
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
else if ( aExp < 0x3FFF ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
return 0;
}
z = aSig>>( - shiftCount );
- if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
+ if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
if ( aSign ) z = - z;
{
flag aSign;
int32 aExp;
- bits64 aSig;
+ uint64_t aSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig<<1 ) ) {
- return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) );
+ if ( (uint64_t) ( aSig<<1 ) ) {
+ return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloat32( aSign, 0xFF, 0 );
}
{
flag aSign;
int32 aExp;
- bits64 aSig, zSig;
+ uint64_t aSig, zSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig<<1 ) ) {
- return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) );
+ if ( (uint64_t) ( aSig<<1 ) ) {
+ return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloat64( aSign, 0x7FF, 0 );
}
}
-#ifdef FLOAT128
-
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-precision floating-
| point value `a' to the quadruple-precision floating-point format. The
float128 floatx80_to_float128( floatx80 a STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 aSig, zSig0, zSig1;
+ int_fast16_t aExp;
+ uint64_t aSig, zSig0, zSig1;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
- if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) {
- return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) );
+ if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) {
+ return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
return packFloat128( aSign, aExp, zSig0, zSig1 );
}
-#endif
-
/*----------------------------------------------------------------------------
| Rounds the extended double-precision floating-point value `a' to an integer,
| and returns the result as an extended quadruple-precision floating-point
{
flag aSign;
int32 aExp;
- bits64 lastBitMask, roundBitsMask;
+ uint64_t lastBitMask, roundBitsMask;
int8 roundingMode;
floatx80 z;
aExp = extractFloatx80Exp( a );
if ( 0x403E <= aExp ) {
- if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) {
+ if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) {
return propagateFloatx80NaN( a, a STATUS_VAR );
}
return a;
}
if ( aExp < 0x3FFF ) {
if ( ( aExp == 0 )
- && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
+ && ( (uint64_t) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
return a;
}
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloatx80Sign( a );
switch ( STATUS(float_rounding_mode) ) {
case float_round_nearest_even:
- if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 )
+ if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 )
) {
return
packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) );
static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM)
{
int32 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig0, zSig1;
+ uint64_t aSig, bSig, zSig0, zSig1;
int32 expDiff;
aSig = extractFloatx80Frac( a );
expDiff = aExp - bExp;
if ( 0 < expDiff ) {
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) --expDiff;
}
else if ( expDiff < 0 ) {
if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) ++expDiff;
}
else {
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
+ if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) {
return propagateFloatx80NaN( a, b STATUS_VAR );
}
return a;
goto shiftRight1;
}
zSig0 = aSig + bSig;
- if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
+ if ( (int64_t) zSig0 < 0 ) goto roundAndPack;
shiftRight1:
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
zSig0 |= LIT64( 0x8000000000000000 );
static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM )
{
int32 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig0, zSig1;
+ uint64_t aSig, bSig, zSig0, zSig1;
int32 expDiff;
floatx80 z;
if ( 0 < expDiff ) goto aExpBigger;
if ( expDiff < 0 ) goto bExpBigger;
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
+ if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) {
return propagateFloatx80NaN( a, b STATUS_VAR );
}
float_raise( float_flag_invalid STATUS_VAR);
return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
bExpBigger:
if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) ++expDiff;
goto normalizeRoundAndPack;
aExpBigger:
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) --expDiff;
{
flag aSign, bSign, zSign;
int32 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig0, zSig1;
+ uint64_t aSig, bSig, zSig0, zSig1;
floatx80 z;
aSig = extractFloatx80Frac( a );
bSign = extractFloatx80Sign( b );
zSign = aSign ^ bSign;
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig<<1 )
- || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
+ if ( (uint64_t) ( aSig<<1 )
+ || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) {
return propagateFloatx80NaN( a, b STATUS_VAR );
}
if ( ( bExp | bSig ) == 0 ) goto invalid;
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
if ( ( aExp | aSig ) == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
}
zExp = aExp + bExp - 0x3FFE;
mul64To128( aSig, bSig, &zSig0, &zSig1 );
- if ( 0 < (sbits64) zSig0 ) {
+ if ( 0 < (int64_t) zSig0 ) {
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
--zExp;
}
{
flag aSign, bSign, zSign;
int32 aExp, bExp, zExp;
- bits64 aSig, bSig, zSig0, zSig1;
- bits64 rem0, rem1, rem2, term0, term1, term2;
+ uint64_t aSig, bSig, zSig0, zSig1;
+ uint64_t rem0, rem1, rem2, term0, term1, term2;
floatx80 z;
aSig = extractFloatx80Frac( a );
bSign = extractFloatx80Sign( b );
zSign = aSign ^ bSign;
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
goto invalid;
}
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return packFloatx80( zSign, 0, 0 );
}
if ( bExp == 0 ) {
zSig0 = estimateDiv128To64( aSig, rem1, bSig );
mul64To128( bSig, zSig0, &term0, &term1 );
sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
+ while ( (int64_t) rem0 < 0 ) {
--zSig0;
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
}
zSig1 = estimateDiv128To64( rem1, 0, bSig );
- if ( (bits64) ( zSig1<<1 ) <= 8 ) {
+ if ( (uint64_t) ( zSig1<<1 ) <= 8 ) {
mul64To128( bSig, zSig1, &term1, &term2 );
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
- while ( (sbits64) rem1 < 0 ) {
+ while ( (int64_t) rem1 < 0 ) {
--zSig1;
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
}
floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int32 aExp, bExp, expDiff;
- bits64 aSig0, aSig1, bSig;
- bits64 q, term0, term1, alternateASig0, alternateASig1;
+ uint64_t aSig0, aSig1, bSig;
+ uint64_t q, term0, term1, alternateASig0, alternateASig1;
floatx80 z;
aSig0 = extractFloatx80Frac( a );
aSign = extractFloatx80Sign( a );
bSig = extractFloatx80Frac( b );
bExp = extractFloatx80Exp( b );
- bSign = extractFloatx80Sign( b );
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig0<<1 )
- || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
+ if ( (uint64_t) ( aSig0<<1 )
+ || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) {
return propagateFloatx80NaN( a, b STATUS_VAR );
}
goto invalid;
}
if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
}
if ( aExp == 0 ) {
- if ( (bits64) ( aSig0<<1 ) == 0 ) return a;
+ if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a;
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
}
bSig |= LIT64( 0x8000000000000000 );
{
flag aSign;
int32 aExp, zExp;
- bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0;
- bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0;
+ uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
floatx80 z;
aSig0 = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR );
+ if ( (uint64_t) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR );
if ( ! aSign ) return a;
goto invalid;
}
doubleZSig0 = zSig0<<1;
mul64To128( zSig0, zSig0, &term0, &term1 );
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
+ while ( (int64_t) rem0 < 0 ) {
--zSig0;
doubleZSig0 -= 2;
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
mul64To128( zSig1, zSig1, &term2, &term3 );
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
- while ( (sbits64) rem1 < 0 ) {
+ while ( (int64_t) rem1 < 0 ) {
--zSig1;
shortShift128Left( 0, zSig1, 1, &term2, &term3 );
term3 |= 1;
}
/*----------------------------------------------------------------------------
-| Returns 1 if the extended double-precision floating-point value `a' is
-| equal to the corresponding value `b', and 0 otherwise. The comparison is
-| performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
+| Returns 1 if the extended double-precision floating-point value `a' is equal
+| to the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. Otherwise, the comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
{
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
) {
- if ( floatx80_is_signaling_nan( a )
- || floatx80_is_signaling_nan( b ) ) {
- float_raise( float_flag_invalid STATUS_VAR);
- }
+ float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
return
( a.low == b.low )
&& ( ( a.high == b.high )
|| ( ( a.low == 0 )
- && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
+ && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) )
);
}
/*----------------------------------------------------------------------------
| Returns 1 if the extended double-precision floating-point value `a' is
| less than or equal to the corresponding value `b', and 0 otherwise. The
-| comparison is performed according to the IEC/IEEE Standard for Binary
-| Floating-Point Arithmetic.
+| invalid exception is raised if either operand is a NaN. The comparison is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
*----------------------------------------------------------------------------*/
int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
flag aSign, bSign;
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
if ( aSign != bSign ) {
return
aSign
- || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
== 0 );
}
return
/*----------------------------------------------------------------------------
| Returns 1 if the extended double-precision floating-point value `a' is
-| less than the corresponding value `b', and 0 otherwise. The comparison
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
+| less than the corresponding value `b', and 0 otherwise. The invalid
+| exception is raised if either operand is a NaN. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
flag aSign, bSign;
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
if ( aSign != bSign ) {
return
aSign
- && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
!= 0 );
}
return
}
/*----------------------------------------------------------------------------
-| Returns 1 if the extended double-precision floating-point value `a' is equal
-| to the corresponding value `b', and 0 otherwise. The invalid exception is
-| raised if either operand is a NaN. Otherwise, the comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| Returns 1 if the extended double-precision floating-point values `a' and `b'
+| cannot be compared, and 0 otherwise. The invalid exception is raised if
+| either operand is a NaN. The comparison is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+int floatx80_unordered( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 1;
+ }
+ return 0;
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is
+| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
+| cause an exception. The comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-int floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_eq_quiet( floatx80 a, floatx80 b STATUS_PARAM )
{
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
) {
- float_raise( float_flag_invalid STATUS_VAR);
+ if ( floatx80_is_signaling_nan( a )
+ || floatx80_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
return 0;
}
return
( a.low == b.low )
&& ( ( a.high == b.high )
|| ( ( a.low == 0 )
- && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
+ && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) )
);
}
flag aSign, bSign;
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
) {
if ( floatx80_is_signaling_nan( a )
|| floatx80_is_signaling_nan( b ) ) {
if ( aSign != bSign ) {
return
aSign
- || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
== 0 );
}
return
flag aSign, bSign;
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
) {
if ( floatx80_is_signaling_nan( a )
|| floatx80_is_signaling_nan( b ) ) {
if ( aSign != bSign ) {
return
aSign
- && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
!= 0 );
}
return
}
-#endif
-
-#ifdef FLOAT128
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point values `a' and `b'
+| cannot be compared, and 0 otherwise. Quiet NaNs do not cause an exception.
+| The comparison is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+int floatx80_unordered_quiet( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ if ( floatx80_is_signaling_nan( a )
+ || floatx80_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 1;
+ }
+ return 0;
+}
/*----------------------------------------------------------------------------
| Returns the result of converting the quadruple-precision floating-point
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig0, aSig1;
+ uint64_t aSig0, aSig1;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig0, aSig1, savedASig;
- int32 z;
+ uint64_t aSig0, aSig1, savedASig;
+ int32_t z;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
if ( ( z < 0 ) ^ aSign ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
- return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
}
if ( ( aSig0<<shiftCount ) != savedASig ) {
STATUS(float_exception_flags) |= float_flag_inexact;
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig0, aSig1;
+ uint64_t aSig0, aSig1;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 );
}
{
flag aSign;
int32 aExp, shiftCount;
- bits64 aSig0, aSig1;
+ uint64_t aSig0, aSig1;
int64 z;
aSig1 = extractFloat128Frac1( a );
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
- return (sbits64) LIT64( 0x8000000000000000 );
+ return (int64_t) LIT64( 0x8000000000000000 );
}
z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
- if ( (bits64) ( aSig1<<shiftCount ) ) {
+ if ( (uint64_t) ( aSig1<<shiftCount ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
}
}
z = aSig0>>( - shiftCount );
if ( aSig1
- || ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) {
+ || ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
}
{
flag aSign;
int32 aExp;
- bits64 aSig0, aSig1;
- bits32 zSig;
+ uint64_t aSig0, aSig1;
+ uint32_t zSig;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
aSign = extractFloat128Sign( a );
if ( aExp == 0x7FFF ) {
if ( aSig0 | aSig1 ) {
- return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) );
+ return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloat32( aSign, 0xFF, 0 );
}
{
flag aSign;
int32 aExp;
- bits64 aSig0, aSig1;
+ uint64_t aSig0, aSig1;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
aSign = extractFloat128Sign( a );
if ( aExp == 0x7FFF ) {
if ( aSig0 | aSig1 ) {
- return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) );
+ return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloat64( aSign, 0x7FF, 0 );
}
}
-#ifdef FLOATX80
-
/*----------------------------------------------------------------------------
| Returns the result of converting the quadruple-precision floating-point
| value `a' to the extended double-precision floating-point format. The
{
flag aSign;
int32 aExp;
- bits64 aSig0, aSig1;
+ uint64_t aSig0, aSig1;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
aSign = extractFloat128Sign( a );
if ( aExp == 0x7FFF ) {
if ( aSig0 | aSig1 ) {
- return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) );
+ return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
}
-#endif
-
/*----------------------------------------------------------------------------
| Rounds the quadruple-precision floating-point value `a' to an integer, and
| returns the result as a quadruple-precision floating-point value. The
{
flag aSign;
int32 aExp;
- bits64 lastBitMask, roundBitsMask;
+ uint64_t lastBitMask, roundBitsMask;
int8 roundingMode;
float128 z;
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
}
else {
- if ( (sbits64) z.low < 0 ) {
+ if ( (int64_t) z.low < 0 ) {
++z.high;
- if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1;
+ if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1;
}
}
}
}
else {
if ( aExp < 0x3FFF ) {
- if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
+ if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat128Sign( a );
switch ( STATUS(float_rounding_mode) ) {
static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
{
int32 aExp, bExp, zExp;
- bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
+ uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
int32 expDiff;
aSig1 = extractFloat128Frac1( a );
return a;
}
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
- if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 );
+ if ( aExp == 0 ) {
+ if (STATUS(flush_to_zero)) {
+ if (zSig0 | zSig1) {
+ float_raise(float_flag_output_denormal STATUS_VAR);
+ }
+ return packFloat128(zSign, 0, 0, 0);
+ }
+ return packFloat128( zSign, 0, zSig0, zSig1 );
+ }
zSig2 = 0;
zSig0 |= LIT64( 0x0002000000000000 );
zExp = aExp;
static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
{
int32 aExp, bExp, zExp;
- bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
+ uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
int32 expDiff;
float128 z;
{
flag aSign, bSign, zSign;
int32 aExp, bExp, zExp;
- bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
+ uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
float128 z;
aSig1 = extractFloat128Frac1( a );
{
flag aSign, bSign, zSign;
int32 aExp, bExp, zExp;
- bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
- bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
+ uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
float128 z;
aSig1 = extractFloat128Frac1( a );
zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 );
mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 );
sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
- while ( (sbits64) rem0 < 0 ) {
+ while ( (int64_t) rem0 < 0 ) {
--zSig0;
add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
}
if ( ( zSig1 & 0x3FFF ) <= 4 ) {
mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 );
sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
- while ( (sbits64) rem1 < 0 ) {
+ while ( (int64_t) rem1 < 0 ) {
--zSig1;
add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
}
float128 float128_rem( float128 a, float128 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int32 aExp, bExp, expDiff;
- bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
- bits64 allZero, alternateASig0, alternateASig1, sigMean1;
- sbits64 sigMean0;
+ uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
+ uint64_t allZero, alternateASig0, alternateASig1, sigMean1;
+ int64_t sigMean0;
float128 z;
aSig1 = extractFloat128Frac1( a );
bSig1 = extractFloat128Frac1( b );
bSig0 = extractFloat128Frac0( b );
bExp = extractFloat128Exp( b );
- bSign = extractFloat128Sign( b );
if ( aExp == 0x7FFF ) {
if ( ( aSig0 | aSig1 )
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
alternateASig1 = aSig1;
++q;
sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
- } while ( 0 <= (sbits64) aSig0 );
+ } while ( 0 <= (int64_t) aSig0 );
add128(
- aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 );
+ aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 );
if ( ( sigMean0 < 0 )
|| ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
aSig0 = alternateASig0;
aSig1 = alternateASig1;
}
- zSign = ( (sbits64) aSig0 < 0 );
+ zSign = ( (int64_t) aSig0 < 0 );
if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
return
normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR );
{
flag aSign;
int32 aExp, zExp;
- bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
- bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
+ uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
float128 z;
aSig1 = extractFloat128Frac1( a );
doubleZSig0 = zSig0<<1;
mul64To128( zSig0, zSig0, &term0, &term1 );
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
+ while ( (int64_t) rem0 < 0 ) {
--zSig0;
doubleZSig0 -= 2;
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
mul64To128( zSig1, zSig1, &term2, &term3 );
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
- while ( (sbits64) rem1 < 0 ) {
+ while ( (int64_t) rem1 < 0 ) {
--zSig1;
shortShift128Left( 0, zSig1, 1, &term2, &term3 );
term3 |= 1;
/*----------------------------------------------------------------------------
| Returns 1 if the quadruple-precision floating-point value `a' is equal to
-| the corresponding value `b', and 0 otherwise. The comparison is performed
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. Otherwise, the comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
) {
- if ( float128_is_signaling_nan( a )
- || float128_is_signaling_nan( b ) ) {
- float_raise( float_flag_invalid STATUS_VAR);
- }
+ float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
return
( a.low == b.low )
&& ( ( a.high == b.high )
|| ( ( a.low == 0 )
- && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) )
+ && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) )
);
}
/*----------------------------------------------------------------------------
| Returns 1 if the quadruple-precision floating-point value `a' is less than
-| or equal to the corresponding value `b', and 0 otherwise. The comparison
-| is performed according to the IEC/IEEE Standard for Binary Floating-Point
-| Arithmetic.
+| or equal to the corresponding value `b', and 0 otherwise. The invalid
+| exception is raised if either operand is a NaN. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float128_le( float128 a, float128 b STATUS_PARAM )
if ( aSign != bSign ) {
return
aSign
- || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
== 0 );
}
return
/*----------------------------------------------------------------------------
| Returns 1 if the quadruple-precision floating-point value `a' is less than
-| the corresponding value `b', and 0 otherwise. The comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. The comparison is performed according
+| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float128_lt( float128 a, float128 b STATUS_PARAM )
if ( aSign != bSign ) {
return
aSign
- && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
!= 0 );
}
return
}
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot
+| be compared, and 0 otherwise. The invalid exception is raised if either
+| operand is a NaN. The comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+int float128_unordered( float128 a, float128 b STATUS_PARAM )
+{
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 1;
+ }
+ return 0;
+}
+
/*----------------------------------------------------------------------------
| Returns 1 if the quadruple-precision floating-point value `a' is equal to
-| the corresponding value `b', and 0 otherwise. The invalid exception is
-| raised if either operand is a NaN. Otherwise, the comparison is performed
-| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
+| exception. The comparison is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-int float128_eq_signaling( float128 a, float128 b STATUS_PARAM )
+int float128_eq_quiet( float128 a, float128 b STATUS_PARAM )
{
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
) {
- float_raise( float_flag_invalid STATUS_VAR);
+ if ( float128_is_signaling_nan( a )
+ || float128_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
return 0;
}
return
( a.low == b.low )
&& ( ( a.high == b.high )
|| ( ( a.low == 0 )
- && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) )
+ && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) )
);
}
if ( aSign != bSign ) {
return
aSign
- || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
== 0 );
}
return
if ( aSign != bSign ) {
return
aSign
- && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
!= 0 );
}
return
}
-#endif
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot
+| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The
+| comparison is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+int float128_unordered_quiet( float128 a, float128 b STATUS_PARAM )
+{
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ if ( float128_is_signaling_nan( a )
+ || float128_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 1;
+ }
+ return 0;
+}
/* misc functions */
-float32 uint32_to_float32( unsigned int a STATUS_PARAM )
+float32 uint32_to_float32( uint32 a STATUS_PARAM )
{
return int64_to_float32(a STATUS_VAR);
}
-float64 uint32_to_float64( unsigned int a STATUS_PARAM )
+float64 uint32_to_float64( uint32 a STATUS_PARAM )
{
return int64_to_float64(a STATUS_VAR);
}
-unsigned int float32_to_uint32( float32 a STATUS_PARAM )
+uint32 float32_to_uint32( float32 a STATUS_PARAM )
{
int64_t v;
- unsigned int res;
+ uint32 res;
v = float32_to_int64(a STATUS_VAR);
if (v < 0) {
return res;
}
-unsigned int float32_to_uint32_round_to_zero( float32 a STATUS_PARAM )
+uint32 float32_to_uint32_round_to_zero( float32 a STATUS_PARAM )
{
int64_t v;
- unsigned int res;
+ uint32 res;
v = float32_to_int64_round_to_zero(a STATUS_VAR);
if (v < 0) {
return res;
}
-unsigned int float64_to_uint32( float64 a STATUS_PARAM )
+uint_fast16_t float32_to_uint16_round_to_zero(float32 a STATUS_PARAM)
+{
+ int64_t v;
+ uint_fast16_t res;
+
+ v = float32_to_int64_round_to_zero(a STATUS_VAR);
+ if (v < 0) {
+ res = 0;
+ float_raise( float_flag_invalid STATUS_VAR);
+ } else if (v > 0xffff) {
+ res = 0xffff;
+ float_raise( float_flag_invalid STATUS_VAR);
+ } else {
+ res = v;
+ }
+ return res;
+}
+
+uint32 float64_to_uint32( float64 a STATUS_PARAM )
{
int64_t v;
- unsigned int res;
+ uint32 res;
v = float64_to_int64(a STATUS_VAR);
if (v < 0) {
return res;
}
-unsigned int float64_to_uint32_round_to_zero( float64 a STATUS_PARAM )
+uint32 float64_to_uint32_round_to_zero( float64 a STATUS_PARAM )
{
int64_t v;
- unsigned int res;
+ uint32 res;
v = float64_to_int64_round_to_zero(a STATUS_VAR);
if (v < 0) {
return res;
}
+uint_fast16_t float64_to_uint16_round_to_zero(float64 a STATUS_PARAM)
+{
+ int64_t v;
+ uint_fast16_t res;
+
+ v = float64_to_int64_round_to_zero(a STATUS_VAR);
+ if (v < 0) {
+ res = 0;
+ float_raise( float_flag_invalid STATUS_VAR);
+ } else if (v > 0xffff) {
+ res = 0xffff;
+ float_raise( float_flag_invalid STATUS_VAR);
+ } else {
+ res = v;
+ }
+ return res;
+}
+
/* FIXME: This looks broken. */
uint64_t float64_to_uint64 (float64 a STATUS_PARAM)
{
int is_quiet STATUS_PARAM ) \
{ \
flag aSign, bSign; \
- bits ## s av, bv; \
+ uint ## s ## _t av, bv; \
+ a = float ## s ## _squash_input_denormal(a STATUS_VAR); \
+ b = float ## s ## _squash_input_denormal(b STATUS_VAR); \
\
if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \
extractFloat ## s ## Frac( a ) ) || \
aSign = extractFloat ## s ## Sign( a ); \
bSign = extractFloat ## s ## Sign( b ); \
av = float ## s ## _val(a); \
- bv = float ## s ## _val(a); \
+ bv = float ## s ## _val(b); \
if ( aSign != bSign ) { \
- if ( (bits ## s) ( ( av | bv )<<1 ) == 0 ) { \
+ if ( (uint ## s ## _t) ( ( av | bv )<<1 ) == 0 ) { \
/* zero case */ \
return float_relation_equal; \
} else { \
COMPARE(32, 0xff)
COMPARE(64, 0x7ff)
+INLINE int floatx80_compare_internal( floatx80 a, floatx80 b,
+ int is_quiet STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if (( ( extractFloatx80Exp( a ) == 0x7fff ) &&
+ ( extractFloatx80Frac( a )<<1 ) ) ||
+ ( ( extractFloatx80Exp( b ) == 0x7fff ) &&
+ ( extractFloatx80Frac( b )<<1 ) )) {
+ if (!is_quiet ||
+ floatx80_is_signaling_nan( a ) ||
+ floatx80_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return float_relation_unordered;
+ }
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign != bSign ) {
+
+ if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) &&
+ ( ( a.low | b.low ) == 0 ) ) {
+ /* zero case */
+ return float_relation_equal;
+ } else {
+ return 1 - (2 * aSign);
+ }
+ } else {
+ if (a.low == b.low && a.high == b.high) {
+ return float_relation_equal;
+ } else {
+ return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) ));
+ }
+ }
+}
+
+int floatx80_compare( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ return floatx80_compare_internal(a, b, 0 STATUS_VAR);
+}
+
+int floatx80_compare_quiet( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ return floatx80_compare_internal(a, b, 1 STATUS_VAR);
+}
+
+INLINE int float128_compare_internal( float128 a, float128 b,
+ int is_quiet STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if (( ( extractFloat128Exp( a ) == 0x7fff ) &&
+ ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) ||
+ ( ( extractFloat128Exp( b ) == 0x7fff ) &&
+ ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) {
+ if (!is_quiet ||
+ float128_is_signaling_nan( a ) ||
+ float128_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return float_relation_unordered;
+ }
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign != bSign ) {
+ if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) {
+ /* zero case */
+ return float_relation_equal;
+ } else {
+ return 1 - (2 * aSign);
+ }
+ } else {
+ if (a.low == b.low && a.high == b.high) {
+ return float_relation_equal;
+ } else {
+ return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) ));
+ }
+ }
+}
+
+int float128_compare( float128 a, float128 b STATUS_PARAM )
+{
+ return float128_compare_internal(a, b, 0 STATUS_VAR);
+}
+
+int float128_compare_quiet( float128 a, float128 b STATUS_PARAM )
+{
+ return float128_compare_internal(a, b, 1 STATUS_VAR);
+}
+
+/* min() and max() functions. These can't be implemented as
+ * 'compare and pick one input' because that would mishandle
+ * NaNs and +0 vs -0.
+ */
+#define MINMAX(s, nan_exp) \
+INLINE float ## s float ## s ## _minmax(float ## s a, float ## s b, \
+ int ismin STATUS_PARAM ) \
+{ \
+ flag aSign, bSign; \
+ uint ## s ## _t av, bv; \
+ a = float ## s ## _squash_input_denormal(a STATUS_VAR); \
+ b = float ## s ## _squash_input_denormal(b STATUS_VAR); \
+ if (float ## s ## _is_any_nan(a) || \
+ float ## s ## _is_any_nan(b)) { \
+ return propagateFloat ## s ## NaN(a, b STATUS_VAR); \
+ } \
+ aSign = extractFloat ## s ## Sign(a); \
+ bSign = extractFloat ## s ## Sign(b); \
+ av = float ## s ## _val(a); \
+ bv = float ## s ## _val(b); \
+ if (aSign != bSign) { \
+ if (ismin) { \
+ return aSign ? a : b; \
+ } else { \
+ return aSign ? b : a; \
+ } \
+ } else { \
+ if (ismin) { \
+ return (aSign ^ (av < bv)) ? a : b; \
+ } else { \
+ return (aSign ^ (av < bv)) ? b : a; \
+ } \
+ } \
+} \
+ \
+float ## s float ## s ## _min(float ## s a, float ## s b STATUS_PARAM) \
+{ \
+ return float ## s ## _minmax(a, b, 1 STATUS_VAR); \
+} \
+ \
+float ## s float ## s ## _max(float ## s a, float ## s b STATUS_PARAM) \
+{ \
+ return float ## s ## _minmax(a, b, 0 STATUS_VAR); \
+}
+
+MINMAX(32, 0xff)
+MINMAX(64, 0x7ff)
+
+
/* Multiply A by 2 raised to the power N. */
float32 float32_scalbn( float32 a, int n STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits32 aSig;
+ int16_t aExp;
+ uint32_t aSig;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
+ if ( aSig ) {
+ return propagateFloat32NaN( a, a STATUS_VAR );
+ }
return a;
}
- aExp += n;
- return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
+ if ( aExp != 0 )
+ aSig |= 0x00800000;
+ else if ( aSig == 0 )
+ return a;
+
+ if (n > 0x200) {
+ n = 0x200;
+ } else if (n < -0x200) {
+ n = -0x200;
+ }
+
+ aExp += n - 1;
+ aSig <<= 7;
+ return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
}
float64 float64_scalbn( float64 a, int n STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 aSig;
+ int16_t aExp;
+ uint64_t aSig;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
+ if ( aSig ) {
+ return propagateFloat64NaN( a, a STATUS_VAR );
+ }
return a;
}
- aExp += n;
- return roundAndPackFloat64( aSign, aExp, aSig STATUS_VAR );
+ if ( aExp != 0 )
+ aSig |= LIT64( 0x0010000000000000 );
+ else if ( aSig == 0 )
+ return a;
+
+ if (n > 0x1000) {
+ n = 0x1000;
+ } else if (n < -0x1000) {
+ n = -0x1000;
+ }
+
+ aExp += n - 1;
+ aSig <<= 10;
+ return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR );
}
-#ifdef FLOATX80
floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM )
{
flag aSign;
- int16 aExp;
- bits64 aSig;
+ int32_t aExp;
+ uint64_t aSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
- if ( aExp == 0x7FF ) {
+ if ( aExp == 0x7FFF ) {
+ if ( aSig<<1 ) {
+ return propagateFloatx80NaN( a, a STATUS_VAR );
+ }
+ return a;
+ }
+
+ if (aExp == 0 && aSig == 0)
return a;
+
+ if (n > 0x10000) {
+ n = 0x10000;
+ } else if (n < -0x10000) {
+ n = -0x10000;
}
+
aExp += n;
- return roundAndPackFloatx80( STATUS(floatx80_rounding_precision),
- aSign, aExp, aSig, 0 STATUS_VAR );
+ return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision),
+ aSign, aExp, aSig, 0 STATUS_VAR );
}
-#endif
-#ifdef FLOAT128
float128 float128_scalbn( float128 a, int n STATUS_PARAM )
{
flag aSign;
- int32 aExp;
- bits64 aSig0, aSig1;
+ int32_t aExp;
+ uint64_t aSig0, aSig1;
aSig1 = extractFloat128Frac1( a );
aSig0 = extractFloat128Frac0( a );
aExp = extractFloat128Exp( a );
aSign = extractFloat128Sign( a );
if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) {
+ return propagateFloat128NaN( a, a STATUS_VAR );
+ }
return a;
}
- aExp += n;
- return roundAndPackFloat128( aSign, aExp, aSig0, aSig1, 0 STATUS_VAR );
+ if ( aExp != 0 )
+ aSig0 |= LIT64( 0x0001000000000000 );
+ else if ( aSig0 == 0 && aSig1 == 0 )
+ return a;
+
+ if (n > 0x10000) {
+ n = 0x10000;
+ } else if (n < -0x10000) {
+ n = -0x10000;
+ }
+
+ aExp += n - 1;
+ return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
+ STATUS_VAR );
}
-#endif
projects / qemu.git / blobdiff