}
#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 int16 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
| and 7, and returns the properly rounded 32-bit integer corresponding to the
INLINE bits32 extractFloat32Frac( float32 a )
{
- return a & 0x007FFFFF;
+ return float32_val(a) & 0x007FFFFF;
}
INLINE int16 extractFloat32Exp( float32 a )
{
- return ( a>>23 ) & 0xFF;
+ return ( float32_val(a)>>23 ) & 0xFF;
}
INLINE flag extractFloat32Sign( float32 a )
{
- return a>>31;
+ return float32_val(a)>>31;
+
+}
+/*----------------------------------------------------------------------------
+| 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;
}
/*----------------------------------------------------------------------------
INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
{
- return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
+ return make_float32(
+ ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig);
}
&& ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
- return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
+ return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
+ if ( STATUS(flush_to_zero) ) return packFloat32( zSign, 0, 0 );
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
INLINE bits64 extractFloat64Frac( float64 a )
{
- return a & LIT64( 0x000FFFFFFFFFFFFF );
+ return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF );
}
INLINE int16 extractFloat64Exp( float64 a )
{
- return ( a>>52 ) & 0x7FF;
+ return ( float64_val(a)>>52 ) & 0x7FF;
}
INLINE flag extractFloat64Sign( float64 a )
{
- return a>>63;
+ return float64_val(a)>>63;
+
+}
+/*----------------------------------------------------------------------------
+| 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;
}
/*----------------------------------------------------------------------------
INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
{
- return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig;
+ return make_float64(
+ ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig);
}
&& ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
- return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 );
+ return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
+ if ( STATUS(flush_to_zero) ) return packFloat64( zSign, 0, 0 );
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
goto overflow;
}
if ( zExp <= 0 ) {
+ if ( STATUS(flush_to_zero) ) return packFloatx80( zSign, 0, 0 );
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < 0 )
return packFloat128( zSign, 0x7FFF, 0, 0 );
}
if ( zExp < 0 ) {
+ if ( STATUS(flush_to_zero) ) return packFloat128( zSign, 0, 0, 0 );
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
{
flag zSign;
- if ( a == 0 ) return 0;
+ if ( a == 0 ) return float32_zero;
if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
zSign = ( a < 0 );
return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR );
int8 shiftCount;
bits64 zSig;
- if ( a == 0 ) return 0;
+ if ( a == 0 ) return float64_zero;
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros32( absA ) + 21;
uint64 absA;
int8 shiftCount;
- if ( a == 0 ) return 0;
+ if ( a == 0 ) return float32_zero;
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros64( absA ) - 40;
}
+float32 uint64_to_float32( uint64 a STATUS_PARAM )
+{
+ int8 shiftCount;
+
+ if ( a == 0 ) return float32_zero;
+ shiftCount = countLeadingZeros64( a ) - 40;
+ if ( 0 <= shiftCount ) {
+ return packFloat32( 1 > 0, 0x95 - shiftCount, a<<shiftCount );
+ }
+ else {
+ shiftCount += 7;
+ if ( shiftCount < 0 ) {
+ shift64RightJamming( a, - shiftCount, &a );
+ }
+ else {
+ a <<= shiftCount;
+ }
+ return roundAndPackFloat32( 1 > 0, 0x9C - shiftCount, a STATUS_VAR );
+ }
+}
+
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a'
| to the double-precision floating-point format. The conversion is performed
{
flag zSign;
- if ( a == 0 ) return 0;
+ if ( a == 0 ) return float64_zero;
if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) {
return packFloat64( 1, 0x43E, 0 );
}
}
+float64 uint64_to_float64( uint64 a STATUS_PARAM )
+{
+ if ( a == 0 ) return float64_zero;
+ return normalizeRoundAndPackFloat64( 0, 0x43C, a STATUS_VAR );
+
+}
+
#ifdef FLOATX80
/*----------------------------------------------------------------------------
bits32 aSig;
bits64 aSig64;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
int16 aExp, shiftCount;
bits32 aSig;
int32 z;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
shiftCount = aExp - 0x9E;
if ( 0 <= shiftCount ) {
- if ( a != 0xCF000000 ) {
+ if ( float32_val(a) != 0xCF000000 ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
}
}
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+int16 float32_to_int16_round_to_zero( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits32 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 (sbits32) 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 ( (bits32) ( 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
int16 aExp, shiftCount;
bits32 aSig;
bits64 aSig64, aSigExtra;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
bits32 aSig;
bits64 aSig64;
int64 z;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
shiftCount = aExp - 0xBE;
if ( 0 <= shiftCount ) {
- if ( a != 0xDF000000 ) {
+ if ( float32_val(a) != 0xDF000000 ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
flag aSign;
int16 aExp;
bits32 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 ) {
int16 aExp;
bits32 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 ) {
int16 aExp;
bits32 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 ) {
int16 aExp;
bits32 lastBitMask, roundBitsMask;
int8 roundingMode;
- float32 z;
+ bits32 z;
+ a = float32_squash_input_denormal(a STATUS_VAR);
aExp = extractFloat32Exp( a );
if ( 0x96 <= aExp ) {
return a;
}
if ( aExp <= 0x7E ) {
- if ( (bits32) ( a<<1 ) == 0 ) return a;
+ if ( (bits32) ( float32_val(a)<<1 ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat32Sign( a );
switch ( STATUS(float_rounding_mode) ) {
}
break;
case float_round_down:
- return aSign ? 0xBF800000 : 0;
+ return make_float32(aSign ? 0xBF800000 : 0);
case float_round_up:
- return aSign ? 0x80000000 : 0x3F800000;
+ return make_float32(aSign ? 0x80000000 : 0x3F800000);
}
return packFloat32( aSign, 0, 0 );
}
lastBitMask = 1;
lastBitMask <<= 0x96 - aExp;
roundBitsMask = lastBitMask - 1;
- z = a;
+ z = float32_val(a);
roundingMode = STATUS(float_rounding_mode);
if ( roundingMode == float_round_nearest_even ) {
z += lastBitMask>>1;
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
}
else if ( roundingMode != float_round_to_zero ) {
- if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
+ if ( extractFloat32Sign( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) {
z += roundBitsMask;
}
}
z &= ~ roundBitsMask;
- if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact;
- return z;
+ if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return make_float32(z);
}
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) ) return packFloat32( zSign, 0, 0 );
+ return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
+ }
zSig = 0x40000000 + aSig + bSig;
zExp = aExp;
goto roundAndPack;
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 );
bits64 zSig64;
bits32 zSig;
+ 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 );
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits32 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 );
float32 float32_rem( float32 a, float32 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int16 aExp, bExp, expDiff;
bits32 aSig, bSig;
bits32 q;
bits64 aSig64, bSig64, q64;
bits32 alternateASig;
sbits32 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 );
int16 aExp, zExp;
bits32 aSig, zSig;
bits64 rem, term;
+ 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, 0 STATUS_VAR );
+ if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR );
if ( ! aSign ) return a;
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
return float32_default_nan;
}
if ( aExp == 0 ) {
- if ( aSig == 0 ) return 0;
+ if ( aSig == 0 ) return float32_zero;
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E;
}
+/*----------------------------------------------------------------------------
+| 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] =
+{
+ make_float64( 0x3ff0000000000000ll ), /* 1 */
+ make_float64( 0x3fe0000000000000ll ), /* 2 */
+ make_float64( 0x3fc5555555555555ll ), /* 3 */
+ make_float64( 0x3fa5555555555555ll ), /* 4 */
+ make_float64( 0x3f81111111111111ll ), /* 5 */
+ make_float64( 0x3f56c16c16c16c17ll ), /* 6 */
+ make_float64( 0x3f2a01a01a01a01all ), /* 7 */
+ make_float64( 0x3efa01a01a01a01all ), /* 8 */
+ make_float64( 0x3ec71de3a556c734ll ), /* 9 */
+ make_float64( 0x3e927e4fb7789f5cll ), /* 10 */
+ make_float64( 0x3e5ae64567f544e4ll ), /* 11 */
+ make_float64( 0x3e21eed8eff8d898ll ), /* 12 */
+ make_float64( 0x3de6124613a86d09ll ), /* 13 */
+ make_float64( 0x3da93974a8c07c9dll ), /* 14 */
+ make_float64( 0x3d6ae7f3e733b81fll ), /* 15 */
+};
+
+float32 float32_exp2( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 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;
+ int16 aExp;
+ bits32 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 = ( (bits64)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
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float32_eq( float32 a, float32 b STATUS_PARAM )
+int float32_eq( 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 ) )
}
return 0;
}
- return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
+ return ( float32_val(a) == float32_val(b) ) ||
+ ( (bits32) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 );
}
| Arithmetic.
*----------------------------------------------------------------------------*/
-flag float32_le( float32 a, float32 b STATUS_PARAM )
+int float32_le( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
+ 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 ) )
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
- if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
- return ( a == b ) || ( aSign ^ ( a < b ) );
+ av = float32_val(a);
+ bv = float32_val(b);
+ if ( aSign != bSign ) return aSign || ( (bits32) ( ( av | bv )<<1 ) == 0 );
+ return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float32_lt( float32 a, float32 b STATUS_PARAM )
+int float32_lt( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
+ 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 ) )
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
- if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
- return ( a != b ) && ( aSign ^ ( a < b ) );
+ av = float32_val(a);
+ bv = float32_val(b);
+ if ( aSign != bSign ) return aSign && ( (bits32) ( ( av | bv )<<1 ) != 0 );
+ return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float32_eq_signaling( float32 a, float32 b STATUS_PARAM )
+int float32_eq_signaling( 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 ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
+ av = float32_val(a);
+ bv = float32_val(b);
+ return ( av == bv ) || ( (bits32) ( ( av | bv )<<1 ) == 0 );
}
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float32_le_quiet( float32 a, float32 b STATUS_PARAM )
+int float32_le_quiet( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
+ 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 ) )
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
- if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
- return ( a == b ) || ( aSign ^ ( a < b ) );
+ av = float32_val(a);
+ bv = float32_val(b);
+ if ( aSign != bSign ) return aSign || ( (bits32) ( ( av | bv )<<1 ) == 0 );
+ return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
+int float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
+ 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 ) )
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
- if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
- return ( a != b ) && ( aSign ^ ( a < b ) );
+ av = float32_val(a);
+ bv = float32_val(b);
+ if ( aSign != bSign ) return aSign && ( (bits32) ( ( av | bv )<<1 ) != 0 );
+ return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
flag aSign;
int16 aExp, shiftCount;
bits64 aSig;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
int16 aExp, shiftCount;
bits64 aSig, savedASig;
int32 z;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
}
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+int16 float64_to_int16_round_to_zero( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits64 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 ? (sbits32) 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
flag aSign;
int16 aExp, shiftCount;
bits64 aSig, aSigExtra;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
int16 aExp, shiftCount;
bits64 aSig;
int64 z;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
shiftCount = aExp - 0x433;
if ( 0 <= shiftCount ) {
if ( 0x43E <= aExp ) {
- if ( a != LIT64( 0xC3E0000000000000 ) ) {
+ if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign
|| ( ( aExp == 0x7FF )
int16 aExp;
bits64 aSig;
bits32 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 );
}
+
+/*----------------------------------------------------------------------------
+| 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, int16 zExp, bits16 zSig)
+{
+ return make_float16(
+ (((bits32)zSign) << 15) + (((bits32)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;
+ int16 aExp;
+ bits32 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, aSig << 13);
+ }
+ 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;
+ int16 aExp;
+ bits32 aSig;
+ bits32 mask;
+ bits32 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);
+}
+
#ifdef FLOATX80
/*----------------------------------------------------------------------------
int16 aExp;
bits64 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 ) {
int16 aExp;
bits64 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 ) {
int16 aExp;
bits64 lastBitMask, roundBitsMask;
int8 roundingMode;
- float64 z;
+ bits64 z;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aExp = extractFloat64Exp( a );
if ( 0x433 <= aExp ) {
return a;
}
if ( aExp < 0x3FF ) {
- if ( (bits64) ( a<<1 ) == 0 ) return a;
+ if ( (bits64) ( float64_val(a)<<1 ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat64Sign( a );
switch ( STATUS(float_rounding_mode) ) {
}
break;
case float_round_down:
- return aSign ? LIT64( 0xBFF0000000000000 ) : 0;
+ return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0);
case float_round_up:
- return
- aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 );
+ return make_float64(
+ aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 ));
}
return packFloat64( aSign, 0, 0 );
}
lastBitMask = 1;
lastBitMask <<= 0x433 - aExp;
roundBitsMask = lastBitMask - 1;
- z = a;
+ z = float64_val(a);
roundingMode = STATUS(float_rounding_mode);
if ( roundingMode == float_round_nearest_even ) {
z += lastBitMask>>1;
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
}
else if ( roundingMode != float_round_to_zero ) {
- if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) {
+ if ( extractFloat64Sign( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) {
z += roundBitsMask;
}
}
z &= ~ roundBitsMask;
- if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact;
- return z;
+ if ( z != float64_val(a) )
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ return make_float64(z);
}
+float64 float64_trunc_to_int( float64 a STATUS_PARAM)
+{
+ int oldmode;
+ float64 res;
+ oldmode = STATUS(float_rounding_mode);
+ STATUS(float_rounding_mode) = float_round_to_zero;
+ res = float64_round_to_int(a STATUS_VAR);
+ STATUS(float_rounding_mode) = oldmode;
+ return res;
+}
+
/*----------------------------------------------------------------------------
| Returns the result of adding the absolute values of the double-precision
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
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) ) return packFloat64( zSign, 0, 0 );
+ return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
+ }
zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
zExp = aExp;
goto roundAndPack;
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 );
int16 aExp, bExp, zExp;
bits64 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 );
aSign = extractFloat64Sign( a );
bits64 aSig, bSig, zSig;
bits64 rem0, rem1;
bits64 term0, term1;
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ b = float64_squash_input_denormal(b STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
float64 float64_rem( float64 a, float64 b STATUS_PARAM )
{
- flag aSign, bSign, zSign;
+ flag aSign, zSign;
int16 aExp, bExp, expDiff;
bits64 aSig, bSig;
bits64 q, alternateASig;
sbits64 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 );
int16 aExp, zExp;
bits64 aSig, zSig, doubleZSig;
bits64 rem0, rem1, term0, term1;
+ a = float64_squash_input_denormal(a STATUS_VAR);
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
return float64_default_nan;
}
if ( aExp == 0 ) {
- if ( aSig == 0 ) return 0;
+ if ( aSig == 0 ) return float64_zero;
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
}
zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
}
+/*----------------------------------------------------------------------------
+| 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;
+ int16 aExp;
+ bits64 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 = (bits64)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
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float64_eq( float64 a, float64 b STATUS_PARAM )
+int float64_eq( float64 a, float64 b STATUS_PARAM )
{
+ 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 ) )
}
return 0;
}
- return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
+ av = float64_val(a);
+ bv = float64_val(b);
+ return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 );
}
| Arithmetic.
*----------------------------------------------------------------------------*/
-flag float64_le( float64 a, float64 b STATUS_PARAM )
+int float64_le( 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 ) )
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
- if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
- return ( a == b ) || ( aSign ^ ( a < 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 ) );
}
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float64_lt( float64 a, float64 b STATUS_PARAM )
+int float64_lt( 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 ) )
) {
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
- if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
- return ( a != b ) && ( aSign ^ ( a < 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 ) );
}
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float64_eq_signaling( float64 a, float64 b STATUS_PARAM )
+int float64_eq_signaling( float64 a, float64 b STATUS_PARAM )
{
+ 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 ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
+ av = float64_val(a);
+ bv = float64_val(b);
+ return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 );
}
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float64_le_quiet( float64 a, float64 b STATUS_PARAM )
+int float64_le_quiet( 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 ) )
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
- if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
- return ( a == b ) || ( aSign ^ ( a < 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 ) );
}
| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float64_lt_quiet( float64 a, float64 b STATUS_PARAM )
+int float64_lt_quiet( 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 ) )
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
- if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
- return ( a != b ) && ( aSign ^ ( a < 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 ) );
}
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig<<1 ) ) {
- return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) );
+ return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloat32( aSign, 0xFF, 0 );
}
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig<<1 ) ) {
- return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) );
+ return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
return packFloat64( aSign, 0x7FF, 0 );
}
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) {
- return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) );
+ return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
}
shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
return packFloat128( aSign, aExp, zSig0, zSig1 );
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;
aSign = extractFloatx80Sign( a );
bSig = extractFloatx80Frac( b );
bExp = extractFloatx80Exp( b );
- bSign = extractFloatx80Sign( b );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig0<<1 )
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
| Arithmetic.
*----------------------------------------------------------------------------*/
-flag floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
{
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
{
flag aSign, bSign;
| Arithmetic.
*----------------------------------------------------------------------------*/
-flag floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
{
flag aSign, bSign;
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM )
{
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM )
{
flag aSign, bSign;
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM )
+int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM )
{
flag aSign, bSign;
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 );
}
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 );
}
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 ) );
}
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) ) return packFloat128( zSign, 0, 0, 0 );
+ return packFloat128( zSign, 0, zSig0, zSig1 );
+ }
zSig2 = 0;
zSig0 |= LIT64( 0x0002000000000000 );
zExp = aExp;
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;
bSig1 = extractFloat128Frac1( b );
bSig0 = extractFloat128Frac0( b );
bExp = extractFloat128Exp( b );
- bSign = extractFloat128Sign( b );
if ( aExp == 0x7FFF ) {
if ( ( aSig0 | aSig1 )
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
} while ( 0 <= (sbits64) aSig0 );
add128(
- aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 );
+ aSig0, aSig1, alternateASig0, alternateASig1, (bits64 *)&sigMean0, &sigMean1 );
if ( ( sigMean0 < 0 )
|| ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
aSig0 = alternateASig0;
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float128_eq( float128 a, float128 b STATUS_PARAM )
+int float128_eq( float128 a, float128 b STATUS_PARAM )
{
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
| Arithmetic.
*----------------------------------------------------------------------------*/
-flag float128_le( float128 a, float128 b STATUS_PARAM )
+int float128_le( float128 a, float128 b STATUS_PARAM )
{
flag aSign, bSign;
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float128_lt( float128 a, float128 b STATUS_PARAM )
+int float128_lt( float128 a, float128 b STATUS_PARAM )
{
flag aSign, bSign;
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float128_eq_signaling( float128 a, float128 b STATUS_PARAM )
+int float128_eq_signaling( float128 a, float128 b STATUS_PARAM )
{
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float128_le_quiet( float128 a, float128 b STATUS_PARAM )
+int float128_le_quiet( float128 a, float128 b STATUS_PARAM )
{
flag aSign, bSign;
| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-flag float128_lt_quiet( float128 a, float128 b STATUS_PARAM )
+int float128_lt_quiet( float128 a, float128 b STATUS_PARAM )
{
flag aSign, bSign;
return res;
}
+unsigned int float32_to_uint16_round_to_zero( float32 a STATUS_PARAM )
+{
+ int64_t v;
+ unsigned int 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;
+}
+
unsigned int float64_to_uint32( float64 a STATUS_PARAM )
{
int64_t v;
return res;
}
+unsigned int float64_to_uint16_round_to_zero( float64 a STATUS_PARAM )
+{
+ int64_t v;
+ unsigned int 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)
+{
+ int64_t v;
+
+ v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR));
+ v += float64_val(a);
+ v = float64_to_int64(make_float64(v) STATUS_VAR);
+
+ return v - INT64_MIN;
+}
+
+uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM)
+{
+ int64_t v;
+
+ v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR));
+ v += float64_val(a);
+ v = float64_to_int64_round_to_zero(make_float64(v) STATUS_VAR);
+
+ return v - INT64_MIN;
+}
+
#define COMPARE(s, nan_exp) \
-INLINE char float ## s ## _compare_internal( float ## s a, float ## s b, \
+INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \
int is_quiet STATUS_PARAM ) \
{ \
flag aSign, bSign; \
+ bits ## s 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(b); \
if ( aSign != bSign ) { \
- if ( (bits ## s) ( ( a | b )<<1 ) == 0 ) { \
+ if ( (bits ## s) ( ( av | bv )<<1 ) == 0 ) { \
/* zero case */ \
return float_relation_equal; \
} else { \
return 1 - (2 * aSign); \
} \
} else { \
- if (a == b) { \
+ if (av == bv) { \
return float_relation_equal; \
} else { \
- return 1 - 2 * (aSign ^ ( a < b )); \
+ return 1 - 2 * (aSign ^ ( av < bv )); \
} \
} \
} \
\
-char float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \
+int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \
{ \
return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \
} \
\
-char float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \
+int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \
{ \
return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \
}
COMPARE(32, 0xff)
COMPARE(64, 0x7ff)
+
+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);
+}
+
+/* Multiply A by 2 raised to the power N. */
+float32 float32_scalbn( float32 a, int n STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+
+ a = float32_squash_input_denormal(a STATUS_VAR);
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+
+ if ( aExp == 0xFF ) {
+ return a;
+ }
+ if ( aExp != 0 )
+ aSig |= 0x00800000;
+ else if ( aSig == 0 )
+ return a;
+
+ 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;
+
+ a = float64_squash_input_denormal(a STATUS_VAR);
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+
+ if ( aExp == 0x7FF ) {
+ return a;
+ }
+ if ( aExp != 0 )
+ aSig |= LIT64( 0x0010000000000000 );
+ else if ( aSig == 0 )
+ return a;
+
+ 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;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+
+ if ( aExp == 0x7FF ) {
+ return a;
+ }
+ if (aExp == 0 && aSig == 0)
+ return a;
+
+ aExp += n;
+ 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;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp == 0x7FFF ) {
+ return a;
+ }
+ if ( aExp != 0 )
+ aSig0 |= LIT64( 0x0001000000000000 );
+ else if ( aSig0 == 0 && aSig1 == 0 )
+ return a;
+
+ aExp += n - 1;
+ return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
+ STATUS_VAR );
+
+}
+#endif
projects / qemu.git / blobdiff