| Line 3441... |
Line 3441... |
goto shiftRight1;
|
goto shiftRight1;
|
}
|
}
|
zSig0 = aSig + bSig;
|
zSig0 = aSig + bSig;
|
if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
|
if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
|
shiftRight1:
|
shiftRight1:
|
shift64ExtraRightJamming( zSig0, zSig1, 1,
|
No newline at end of file
|
No newline at end of file
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
|
zSig0 |= LIT64( 0x8000000000000000 );
|
|
++zExp;
|
|
roundAndPack:
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the absolute values of the extended
|
|
| double-precision floating-point values `a' and `b'. If `zSign' is 1, the
|
|
| difference is negated before being returned. `zSign' is ignored if the
|
|
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign )
|
|
{
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
int32 expDiff;
|
|
floatx80 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
zSig1 = 0;
|
|
if ( bSig < aSig ) goto aBigger;
|
|
if ( aSig < bSig ) goto bBigger;
|
|
return packFloatx80( float_rounding_mode == float_round_down, 0, 0 );
|
|
bExpBigger:
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) ++expDiff;
|
|
shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
|
bBigger:
|
|
sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) --expDiff;
|
|
shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
|
aBigger:
|
|
sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
return
|
|
normalizeRoundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the extended double-precision floating-point
|
|
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_add( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloatx80Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return subFloatx80Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the extended double-precision floating-
|
|
| point values `a' and `b'. The operation is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_sub( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloatx80Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return addFloatx80Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of multiplying the extended double-precision floating-
|
|
| point values `a' and `b'. The operation is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_mul( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
floatx80 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 )
|
|
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
if ( ( bExp | bSig ) == 0 ) goto invalid;
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
zExp = aExp + bExp - 0x3FFE;
|
|
mul64To128( aSig, bSig, &zSig0, &zSig1 );
|
|
if ( 0 < (sbits64) zSig0 ) {
|
|
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
|
--zExp;
|
|
}
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of dividing the extended double-precision floating-point
|
|
| value `a' by the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_div( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
bits64 rem0, rem1, rem2, term0, term1, term2;
|
|
floatx80 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
goto invalid;
|
|
}
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return packFloatx80( zSign, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
float_raise( float_flag_divbyzero );
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = aExp - bExp + 0x3FFE;
|
|
rem1 = 0;
|
|
if ( bSig <= aSig ) {
|
|
shift128Right( aSig, 0, 1, &aSig, &rem1 );
|
|
++zExp;
|
|
}
|
|
zSig0 = estimateDiv128To64( aSig, rem1, bSig );
|
|
mul64To128( bSig, zSig0, &term0, &term1 );
|
|
sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig0;
|
|
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, bSig );
|
|
if ( (bits64) ( zSig1<<1 ) <= 8 ) {
|
|
mul64To128( bSig, zSig1, &term1, &term2 );
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
|
while ( (sbits64) rem1 < 0 ) {
|
|
--zSig1;
|
|
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 ) != 0 );
|
|
}
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the remainder of the extended double-precision floating-point value
|
|
| `a' with respect to the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_rem( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, expDiff;
|
|
bits64 aSig0, aSig1, bSig;
|
|
bits64 q, term0, term1, alternateASig0, alternateASig1;
|
|
floatx80 z;
|
|
|
|
aSig0 = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( 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 ) ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
goto invalid;
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( (bits64) ( aSig0<<1 ) == 0 ) return a;
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
|
}
|
|
bSig |= LIT64( 0x8000000000000000 );
|
|
zSign = aSign;
|
|
expDiff = aExp - bExp;
|
|
aSig1 = 0;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
|
|
expDiff = 0;
|
|
}
|
|
q = ( bSig <= aSig0 );
|
|
if ( q ) aSig0 -= bSig;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
mul64To128( bSig, q, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
if ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
q >>= 64 - expDiff;
|
|
mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
|
|
while ( le128( term0, term1, aSig0, aSig1 ) ) {
|
|
++q;
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
}
|
|
}
|
|
else {
|
|
term1 = 0;
|
|
term0 = bSig;
|
|
}
|
|
sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
|
|
if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
|
|| ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
|
&& ( q & 1 ) )
|
|
) {
|
|
aSig0 = alternateASig0;
|
|
aSig1 = alternateASig1;
|
|
zSign = ! zSign;
|
|
}
|
|
return
|
|
normalizeRoundAndPackFloatx80(
|
|
80, zSign, bExp + expDiff, aSig0, aSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the square root of the extended double-precision floating-point
|
|
| value `a'. The operation is performed according to the IEC/IEEE Standard
|
|
| for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_sqrt( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, zExp;
|
|
bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0;
|
|
bits64 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 );
|
|
if ( ! aSign ) return a;
|
|
goto invalid;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig0 ) == 0 ) return a;
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
|
}
|
|
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
|
|
zSig0 = estimateSqrt32( aExp, aSig0>>32 );
|
|
shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 );
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
|
|
doubleZSig0 = zSig0<<1;
|
|
mul64To128( zSig0, zSig0, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig0;
|
|
doubleZSig0 -= 2;
|
|
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
|
if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) {
|
|
if ( zSig1 == 0 ) zSig1 = 1;
|
|
mul64To128( doubleZSig0, zSig1, &term1, &term2 );
|
|
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 ) {
|
|
--zSig1;
|
|
shortShift128Left( 0, zSig1, 1, &term2, &term3 );
|
|
term3 |= 1;
|
|
term2 |= doubleZSig0;
|
|
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 );
|
|
zSig0 |= doubleZSig0;
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, 0, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag floatx80_eq( floatx80 a, floatx80 b )
|
|
{
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if ( floatx80_is_signaling_nan( a )
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (bits16) ( ( 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag floatx80_le( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag floatx80_lt( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag floatx80_eq_signaling( floatx80 a, floatx80 b )
|
|
{
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (bits16) ( ( 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. Quiet NaNs
|
|
| do not cause an exception. Otherwise, the comparison is performed according
|
|
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag floatx80_le_quiet( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if ( floatx80_is_signaling_nan( a )
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is less
|
|
| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
|
|
| an exception. Otherwise, the comparison is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag floatx80_lt_quiet( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if ( floatx80_is_signaling_nan( a )
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
#ifdef FLOAT128
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 32-bit two's complement integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic---which means in particular that the conversion is rounded
|
|
| according to the current rounding mode. 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int32 float128_to_int32( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, shiftCount;
|
|
bits64 aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0;
|
|
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
|
|
aSig0 |= ( aSig1 != 0 );
|
|
shiftCount = 0x4028 - aExp;
|
|
if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 );
|
|
return roundAndPackInt32( aSign, aSig0 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 32-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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int32 float128_to_int32_round_to_zero( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, shiftCount;
|
|
bits64 aSig0, aSig1, savedASig;
|
|
int32 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
aSig0 |= ( aSig1 != 0 );
|
|
if ( 0x401E < aExp ) {
|
|
if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0;
|
|
goto invalid;
|
|
}
|
|
else if ( aExp < 0x3FFF ) {
|
|
if ( aExp || aSig0 ) float_exception_flags |= float_flag_inexact;
|
|
return 0;
|
|
}
|
|
aSig0 |= LIT64( 0x0001000000000000 );
|
|
shiftCount = 0x402F - aExp;
|
|
savedASig = aSig0;
|
|
aSig0 >>= shiftCount;
|
|
z = aSig0;
|
|
if ( aSign ) z = - z;
|
|
if ( ( z < 0 ) ^ aSign ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
|
|
}
|
|
if ( ( aSig0<<shiftCount ) != savedASig ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 64-bit two's complement integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic---which means in particular that the conversion is rounded
|
|
| according to the current rounding mode. 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int64 float128_to_int64( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, shiftCount;
|
|
bits64 aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
|
|
shiftCount = 0x402F - aExp;
|
|
if ( shiftCount <= 0 ) {
|
|
if ( 0x403E < aExp ) {
|
|
float_raise( float_flag_invalid );
|
|
if ( ! aSign
|
|
|| ( ( aExp == 0x7FFF )
|
|
&& ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) )
|
|
)
|
|
) {
|
|
return LIT64( 0x7FFFFFFFFFFFFFFF );
|
|
}
|
|
return (sbits64) LIT64( 0x8000000000000000 );
|
|
}
|
|
shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 );
|
|
}
|
|
return roundAndPackInt64( aSign, aSig0, aSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 64-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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int64 float128_to_int64_round_to_zero( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, shiftCount;
|
|
bits64 aSig0, aSig1;
|
|
int64 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
|
|
shiftCount = aExp - 0x402F;
|
|
if ( 0 < shiftCount ) {
|
|
if ( 0x403E <= aExp ) {
|
|
aSig0 &= LIT64( 0x0000FFFFFFFFFFFF );
|
|
if ( ( a.high == LIT64( 0xC03E000000000000 ) )
|
|
&& ( aSig1 < LIT64( 0x0002000000000000 ) ) ) {
|
|
if ( aSig1 ) float_exception_flags |= float_flag_inexact;
|
|
}
|
|
else {
|
|
float_raise( float_flag_invalid );
|
|
if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) {
|
|
return LIT64( 0x7FFFFFFFFFFFFFFF );
|
|
}
|
|
}
|
|
return (sbits64) LIT64( 0x8000000000000000 );
|
|
}
|
|
z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
|
|
if ( (bits64) ( aSig1<<shiftCount ) ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
}
|
|
else {
|
|
if ( aExp < 0x3FFF ) {
|
|
if ( aExp | aSig0 | aSig1 ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return 0;
|
|
}
|
|
z = aSig0>>( - shiftCount );
|
|
if ( aSig1
|
|
|| ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
}
|
|
if ( aSign ) z = - z;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the single-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float32 float128_to_float32( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 aSig0, aSig1;
|
|
bits32 zSig;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
return commonNaNToFloat32( float128ToCommonNaN( a ) );
|
|
}
|
|
return packFloat32( aSign, 0xFF, 0 );
|
|
}
|
|
aSig0 |= ( aSig1 != 0 );
|
|
shift64RightJamming( aSig0, 18, &aSig0 );
|
|
zSig = aSig0;
|
|
if ( aExp || zSig ) {
|
|
zSig |= 0x40000000;
|
|
aExp -= 0x3F81;
|
|
}
|
|
return roundAndPackFloat32( aSign, aExp, zSig );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the double-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float64 float128_to_float64( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
return commonNaNToFloat64( float128ToCommonNaN( a ) );
|
|
}
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
|
}
|
|
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
|
aSig0 |= ( aSig1 != 0 );
|
|
if ( aExp || aSig0 ) {
|
|
aSig0 |= LIT64( 0x4000000000000000 );
|
|
aExp -= 0x3C01;
|
|
}
|
|
return roundAndPackFloat64( aSign, aExp, aSig0 );
|
|
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the extended double-precision floating-point format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 float128_to_floatx80( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
return commonNaNToFloatx80( float128ToCommonNaN( a ) );
|
|
}
|
|
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
aSig0 |= LIT64( 0x0001000000000000 );
|
|
}
|
|
shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
|
|
return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Rounds the quadruple-precision floating-point value `a' to an integer, and
|
|
| returns the result as a quadruple-precision floating-point value. The
|
|
| operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_round_to_int( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 lastBitMask, roundBitsMask;
|
|
int8 roundingMode;
|
|
float128 z;
|
|
|
|
aExp = extractFloat128Exp( a );
|
|
if ( 0x402F <= aExp ) {
|
|
if ( 0x406F <= aExp ) {
|
|
if ( ( aExp == 0x7FFF )
|
|
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) )
|
|
) {
|
|
return propagateFloat128NaN( a, a );
|
|
}
|
|
return a;
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z = a;
|
|
roundingMode = float_rounding_mode;
|
|
if ( roundingMode == float_round_nearest_even ) {
|
|
if ( lastBitMask ) {
|
|
add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low );
|
|
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
|
|
}
|
|
else {
|
|
if ( (sbits64) z.low < 0 ) {
|
|
++z.high;
|
|
if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1;
|
|
}
|
|
}
|
|
}
|
|
else if ( roundingMode != float_round_to_zero ) {
|
|
if ( extractFloat128Sign( z )
|
|
^ ( roundingMode == float_round_up ) ) {
|
|
add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low );
|
|
}
|
|
}
|
|
z.low &= ~ roundBitsMask;
|
|
}
|
|
else {
|
|
if ( aExp < 0x3FFF ) {
|
|
if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
|
|
float_exception_flags |= float_flag_inexact;
|
|
aSign = extractFloat128Sign( a );
|
|
switch ( float_rounding_mode ) {
|
|
case float_round_nearest_even:
|
|
if ( ( aExp == 0x3FFE )
|
|
&& ( extractFloat128Frac0( a )
|
|
| extractFloat128Frac1( a ) )
|
|
) {
|
|
return packFloat128( aSign, 0x3FFF, 0, 0 );
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
return
|
|
aSign ? packFloat128( 1, 0x3FFF, 0, 0 )
|
|
: packFloat128( 0, 0, 0, 0 );
|
|
case float_round_up:
|
|
return
|
|
aSign ? packFloat128( 1, 0, 0, 0 )
|
|
: packFloat128( 0, 0x3FFF, 0, 0 );
|
|
}
|
|
return packFloat128( aSign, 0, 0, 0 );
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask <<= 0x402F - aExp;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z.low = 0;
|
|
z.high = a.high;
|
|
roundingMode = float_rounding_mode;
|
|
if ( roundingMode == float_round_nearest_even ) {
|
|
z.high += lastBitMask>>1;
|
|
if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) {
|
|
z.high &= ~ lastBitMask;
|
|
}
|
|
}
|
|
else if ( roundingMode != float_round_to_zero ) {
|
|
if ( extractFloat128Sign( z )
|
|
^ ( roundingMode == float_round_up ) ) {
|
|
z.high |= ( a.low != 0 );
|
|
z.high += roundBitsMask;
|
|
}
|
|
}
|
|
z.high &= ~ roundBitsMask;
|
|
}
|
|
if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the absolute values of the quadruple-precision
|
|
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
|
| before being returned. `zSign' is ignored if the result is a NaN.
|
|
| The addition is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float128 addFloat128Sigs( float128 a, float128 b, flag zSign )
|
|
{
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
|
|
int32 expDiff;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig0 |= LIT64( 0x0001000000000000 );
|
|
}
|
|
shift128ExtraRightJamming(
|
|
bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
|
|
zExp = aExp;
|
|
}
|
|
else if ( expDiff < 0 ) {
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig0 |= LIT64( 0x0001000000000000 );
|
|
}
|
|
shift128ExtraRightJamming(
|
|
aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
|
|
zExp = bExp;
|
|
}
|
|
else {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
|
return propagateFloat128NaN( a, b );
|
|
}
|
|
return a;
|
|
}
|
|
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
|
|
if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 );
|
|
zSig2 = 0;
|
|
zSig0 |= LIT64( 0x0002000000000000 );
|
|
zExp = aExp;
|
|
goto shiftRight1;
|
|
}
|
|
aSig0 |= LIT64( 0x0001000000000000 );
|
|
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
|
|
--zExp;
|
|
if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack;
|
|
++zExp;
|
|
shiftRight1:
|
|
shift128ExtraRightJamming(
|
|
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
|
roundAndPack:
|
|
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the absolute values of the quadruple-
|
|
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
|
| difference is negated before being returned. `zSign' is ignored if the
|
|
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float128 subFloat128Sigs( float128 a, float128 b, flag zSign )
|
|
{
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
|
|
int32 expDiff;
|
|
float128 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
expDiff = aExp - bExp;
|
|
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
|
shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 );
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
|
return propagateFloat128NaN( a, b );
|
|
}
|
|
float_raise( float_flag_invalid );
|
|
z.low = float128_default_nan_low;
|
|
z.high = float128_default_nan_high;
|
|
return z;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
if ( bSig0 < aSig0 ) goto aBigger;
|
|
if ( aSig0 < bSig0 ) goto bBigger;
|
|
if ( bSig1 < aSig1 ) goto aBigger;
|
|
if ( aSig1 < bSig1 ) goto bBigger;
|
|
return packFloat128( float_rounding_mode == float_round_down, 0, 0, 0 );
|
|
bExpBigger:
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
|
|
return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig0 |= LIT64( 0x4000000000000000 );
|
|
}
|
|
shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
|
|
bSig0 |= LIT64( 0x4000000000000000 );
|
|
bBigger:
|
|
sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 );
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig0 |= LIT64( 0x4000000000000000 );
|
|
}
|
|
shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 );
|
|
aSig0 |= LIT64( 0x4000000000000000 );
|
|
aBigger:
|
|
sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
--zExp;
|
|
return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the quadruple-precision floating-point values
|
|
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
|
| for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_add( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloat128Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return subFloat128Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the quadruple-precision floating-point
|
|
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_sub( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloat128Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return addFloat128Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of multiplying the quadruple-precision floating-point
|
|
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_mul( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
|
|
float128 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
bSign = extractFloat128Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( ( aSig0 | aSig1 )
|
|
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
|
return propagateFloat128NaN( a, b );
|
|
}
|
|
if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid;
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
|
|
if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = float128_default_nan_low;
|
|
z.high = float128_default_nan_high;
|
|
return z;
|
|
}
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
|
|
}
|
|
zExp = aExp + bExp - 0x4000;
|
|
aSig0 |= LIT64( 0x0001000000000000 );
|
|
shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 );
|
|
mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 );
|
|
add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 );
|
|
zSig2 |= ( zSig3 != 0 );
|
|
if ( LIT64( 0x0002000000000000 ) <= zSig0 ) {
|
|
shift128ExtraRightJamming(
|
|
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
|
++zExp;
|
|
}
|
|
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of dividing the quadruple-precision floating-point value
|
|
| `a' by the corresponding value `b'. The operation is performed according to
|
|
| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_div( float128 a, float128 b )
|
|
{
|
|
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;
|
|
float128 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
bSign = extractFloat128Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b );
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
|
|
goto invalid;
|
|
}
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
|
|
return packFloat128( zSign, 0, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( ( bSig0 | bSig1 ) == 0 ) {
|
|
if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = float128_default_nan_low;
|
|
z.high = float128_default_nan_high;
|
|
return z;
|
|
}
|
|
float_raise( float_flag_divbyzero );
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
zExp = aExp - bExp + 0x3FFD;
|
|
shortShift128Left(
|
|
aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 );
|
|
shortShift128Left(
|
|
bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 );
|
|
if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) {
|
|
shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
|
|
++zExp;
|
|
}
|
|
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 ) {
|
|
--zSig0;
|
|
add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, rem2, bSig0 );
|
|
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 ) {
|
|
--zSig1;
|
|
add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 );
|
|
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the remainder of the quadruple-precision floating-point value `a'
|
|
| with respect to the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_rem( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, expDiff;
|
|
bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
|
|
bits64 allZero, alternateASig0, alternateASig1, sigMean1;
|
|
sbits64 sigMean0;
|
|
float128 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( ( aSig0 | aSig1 )
|
|
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
|
return propagateFloat128NaN( a, b );
|
|
}
|
|
goto invalid;
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( ( bSig0 | bSig1 ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = float128_default_nan_low;
|
|
z.high = float128_default_nan_high;
|
|
return z;
|
|
}
|
|
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return a;
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
expDiff = aExp - bExp;
|
|
if ( expDiff < -1 ) return a;
|
|
shortShift128Left(
|
|
aSig0 | LIT64( 0x0001000000000000 ),
|
|
aSig1,
|
|
15 - ( expDiff < 0 ),
|
|
&aSig0,
|
|
&aSig1
|
|
);
|
|
shortShift128Left(
|
|
bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 );
|
|
q = le128( bSig0, bSig1, aSig0, aSig1 );
|
|
if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig0 );
|
|
q = ( 4 < q ) ? q - 4 : 0;
|
|
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
|
|
shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
|
|
shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
|
|
sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
|
|
expDiff -= 61;
|
|
}
|
|
if ( -64 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig0 );
|
|
q = ( 4 < q ) ? q - 4 : 0;
|
|
q >>= - expDiff;
|
|
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
|
expDiff += 52;
|
|
if ( expDiff < 0 ) {
|
|
shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 );
|
|
}
|
|
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
|
|
sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
|
|
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
|
}
|
|
do {
|
|
alternateASig0 = aSig0;
|
|
alternateASig1 = aSig1;
|
|
++q;
|
|
sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
|
|
} while ( 0 <= (sbits64) aSig0 );
|
|
add128(
|
|
aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 );
|
|
if ( ( sigMean0 < 0 )
|
|
|| ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
|
|
aSig0 = alternateASig0;
|
|
aSig1 = alternateASig1;
|
|
}
|
|
zSign = ( (sbits64) aSig0 < 0 );
|
|
if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
|
|
return
|
|
normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the square root of the quadruple-precision floating-point value `a'.
|
|
| The operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_sqrt( float128 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, zExp;
|
|
bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
|
|
bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
|
|
float128 z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a );
|
|
if ( ! aSign ) return a;
|
|
goto invalid;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = float128_default_nan_low;
|
|
z.high = float128_default_nan_high;
|
|
return z;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE;
|
|
aSig0 |= LIT64( 0x0001000000000000 );
|
|
zSig0 = estimateSqrt32( aExp, aSig0>>17 );
|
|
shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 );
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
|
|
doubleZSig0 = zSig0<<1;
|
|
mul64To128( zSig0, zSig0, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig0;
|
|
doubleZSig0 -= 2;
|
|
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
|
if ( ( zSig1 & 0x1FFF ) <= 5 ) {
|
|
if ( zSig1 == 0 ) zSig1 = 1;
|
|
mul64To128( doubleZSig0, zSig1, &term1, &term2 );
|
|
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 ) {
|
|
--zSig1;
|
|
shortShift128Left( 0, zSig1, 1, &term2, &term3 );
|
|
term3 |= 1;
|
|
term2 |= doubleZSig0;
|
|
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 );
|
|
return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the quadruple-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 float128_eq( float128 a, float128 b )
|
|
{
|
|
|
|
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 );
|
|
}
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (bits64) ( ( 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag float128_le( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
|
|
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|
|
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
|
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag float128_lt( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
|
|
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|
|
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
|
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag float128_eq_signaling( float128 a, float128 b )
|
|
{
|
|
|
|
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
|
|
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|
|
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
|
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (bits64) ( ( 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. Quiet NaNs do not
|
|
| cause an exception. Otherwise, the comparison is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag float128_le_quiet( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
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 );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
|
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
|
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
flag float128_lt_quiet( float128 a, float128 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
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 );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
|
No newline at end of file
|
No newline at end of file
|
