cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync/*============================================================================
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncThis C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncPackage, Release 2b.
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncWritten by John R. Hauser. This work was made possible in part by the
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncInternational Computer Science Institute, located at Suite 600, 1947 Center
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncStreet, Berkeley, California 94704. Funding was partially provided by the
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncNational Science Foundation under grant MIP-9311980. The original version
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncof this code was written as part of a project to build a fixed-point vector
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncprocessor in collaboration with the University of California at Berkeley,
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncoverseen by Profs. Nelson Morgan and John Wawrzynek. More information
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncis available through the Web page `http://www.cs.berkeley.edu/~jhauser/
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncarithmetic/SoftFloat.html'.
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncTHIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncbeen made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncRESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncAND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncCOSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncEFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncINSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncOTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncDerivative works are acceptable, even for commercial purposes, so long as
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync(1) the source code for the derivative work includes prominent notice that
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncthe work is derivative, and (2) the source code includes prominent notice with
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsyncthese four paragraphs for those parts of this code that are retained.
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync=============================================================================*/
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync/* FIXME: Flush-To-Zero only effects results. Denormal inputs should also
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync be flushed to zero. */
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync#include "softfloat.h"
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync/*----------------------------------------------------------------------------
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| Primitive arithmetic functions, including multi-word arithmetic, and
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| division and square root approximations. (Can be specialized to target if
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| desired.)
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync*----------------------------------------------------------------------------*/
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync#include "softfloat-macros.h"
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync/*----------------------------------------------------------------------------
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| Functions and definitions to determine: (1) whether tininess for underflow
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| is detected before or after rounding by default, (2) what (if anything)
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| happens when exceptions are raised, (3) how signaling NaNs are distinguished
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| are propagated from function inputs to output. These details are target-
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync| specific.
cabde247f900dcf6e58d009bbdd15099c028c6fcvboxsync*----------------------------------------------------------------------------*/
#include "softfloat-specialize.h"
void set_float_rounding_mode(int val STATUS_PARAM)
{
STATUS(float_rounding_mode) = val;
}
void set_float_exception_flags(int val STATUS_PARAM)
{
STATUS(float_exception_flags) = val;
}
#ifdef FLOATX80
void set_floatx80_rounding_precision(int val STATUS_PARAM)
{
STATUS(floatx80_rounding_precision) = val;
}
#endif
/*----------------------------------------------------------------------------
| 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
| input. If `zSign' is 1, the input is negated before being converted to an
| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input
| is simply rounded to an integer, with the inexact exception raised if the
| input cannot be represented exactly as an integer. However, if the fixed-
| point input is too large, the invalid exception is raised and the largest
| positive or negative integer is returned.
*----------------------------------------------------------------------------*/
static int32 roundAndPackInt32( flag zSign, bits64 absZ STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven;
int8 roundIncrement, roundBits;
int32 z;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
roundIncrement = 0x40;
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
roundIncrement = 0;
}
else {
roundIncrement = 0x7F;
if ( zSign ) {
if ( roundingMode == float_round_up ) roundIncrement = 0;
}
else {
if ( roundingMode == float_round_down ) roundIncrement = 0;
}
}
}
roundBits = absZ & 0x7F;
absZ = ( absZ + roundIncrement )>>7;
absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
z = absZ;
if ( zSign ) z = - z;
if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
float_raise( float_flag_invalid STATUS_VAR);
return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
}
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
return z;
}
/*----------------------------------------------------------------------------
| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
| `absZ1', with binary point between bits 63 and 64 (between the input words),
| and returns the properly rounded 64-bit integer corresponding to the input.
| If `zSign' is 1, the input is negated before being converted to an integer.
| Ordinarily, the fixed-point input is simply rounded to an integer, with
| the inexact exception raised if the input cannot be represented exactly as
| an integer. However, if the fixed-point input is too large, the invalid
| exception is raised and the largest positive or negative integer is
| returned.
*----------------------------------------------------------------------------*/
static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven, increment;
int64 z;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
increment = ( (sbits64) absZ1 < 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
increment = 0;
}
else {
if ( zSign ) {
increment = ( roundingMode == float_round_down ) && absZ1;
}
else {
increment = ( roundingMode == float_round_up ) && absZ1;
}
}
}
if ( increment ) {
++absZ0;
if ( absZ0 == 0 ) goto overflow;
absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven );
}
z = absZ0;
if ( zSign ) z = - z;
if ( z && ( ( z < 0 ) ^ zSign ) ) {
overflow:
float_raise( float_flag_invalid STATUS_VAR);
return
zSign ? (sbits64) LIT64( 0x8000000000000000 )
: LIT64( 0x7FFFFFFFFFFFFFFF );
}
if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact;
return z;
}
/*----------------------------------------------------------------------------
| Returns the fraction bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE bits32 extractFloat32Frac( float32 a )
{
return float32_val(a) & 0x007FFFFF;
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE int16 extractFloat32Exp( float32 a )
{
return ( float32_val(a)>>23 ) & 0xFF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE flag extractFloat32Sign( float32 a )
{
return float32_val(a)>>31;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal single-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
| significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
static void
normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
{
int8 shiftCount;
shiftCount = countLeadingZeros32( aSig ) - 8;
*zSigPtr = aSig<<shiftCount;
*zExpPtr = 1 - shiftCount;
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| single-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.
*----------------------------------------------------------------------------*/
INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
{
return make_float32(
( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig);
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input. Ordinarily, the abstract
| value is simply rounded and packed into the single-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal single-
| precision floating-point number.
| The input significand `zSig' has its binary point between bits 30
| and 29, which is 7 bits to the left of the usual location. This shifted
| significand must be normalized or smaller. If `zSig' is not normalized,
| `zExp' must be 0; in that case, the result returned is a subnormal number,
| and it must not require rounding. In the usual case that `zSig' is
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
| The handling of underflow and overflow follows the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven;
int8 roundIncrement, roundBits;
flag isTiny;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
roundIncrement = 0x40;
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
roundIncrement = 0;
}
else {
roundIncrement = 0x7F;
if ( zSign ) {
if ( roundingMode == float_round_up ) roundIncrement = 0;
}
else {
if ( roundingMode == float_round_down ) roundIncrement = 0;
}
}
}
roundBits = zSig & 0x7F;
if ( 0xFD <= (bits16) zExp ) {
if ( ( 0xFD < zExp )
|| ( ( zExp == 0xFD )
&& ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
if ( STATUS(flush_to_zero) ) return packFloat32( zSign, 0, 0 );
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
|| ( zSig + roundIncrement < 0x80000000 );
shift32RightJamming( zSig, - zExp, &zSig );
zExp = 0;
roundBits = zSig & 0x7F;
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
}
}
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
zSig = ( zSig + roundIncrement )>>7;
zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
if ( zSig == 0 ) zExp = 0;
return packFloat32( zSign, zExp, zSig );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input. This routine is just like
| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/
static float32
normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
{
int8 shiftCount;
shiftCount = countLeadingZeros32( zSig ) - 1;
return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
}
/*----------------------------------------------------------------------------
| Returns the fraction bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE bits64 extractFloat64Frac( float64 a )
{
return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF );
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE int16 extractFloat64Exp( float64 a )
{
return ( float64_val(a)>>52 ) & 0x7FF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE flag extractFloat64Sign( float64 a )
{
return float64_val(a)>>63;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal double-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
| significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
static void
normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr )
{
int8 shiftCount;
shiftCount = countLeadingZeros64( aSig ) - 11;
*zSigPtr = aSig<<shiftCount;
*zExpPtr = 1 - shiftCount;
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| double-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.
*----------------------------------------------------------------------------*/
INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
{
return make_float64(
( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig);
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper double-precision floating-
| point value corresponding to the abstract input. Ordinarily, the abstract
| value is simply rounded and packed into the double-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded
| to a subnormal number, and the underflow and inexact exceptions are raised
| if the abstract input cannot be represented exactly as a subnormal double-
| precision floating-point number.
| The input significand `zSig' has its binary point between bits 62
| and 61, which is 10 bits to the left of the usual location. This shifted
| significand must be normalized or smaller. If `zSig' is not normalized,
| `zExp' must be 0; in that case, the result returned is a subnormal number,
| and it must not require rounding. In the usual case that `zSig' is
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
| The handling of underflow and overflow follows the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven;
int16 roundIncrement, roundBits;
flag isTiny;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
roundIncrement = 0x200;
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
roundIncrement = 0;
}
else {
roundIncrement = 0x3FF;
if ( zSign ) {
if ( roundingMode == float_round_up ) roundIncrement = 0;
}
else {
if ( roundingMode == float_round_down ) roundIncrement = 0;
}
}
}
roundBits = zSig & 0x3FF;
if ( 0x7FD <= (bits16) zExp ) {
if ( ( 0x7FD < zExp )
|| ( ( zExp == 0x7FD )
&& ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
if ( STATUS(flush_to_zero) ) return packFloat64( zSign, 0, 0 );
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < -1 )
|| ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
shift64RightJamming( zSig, - zExp, &zSig );
zExp = 0;
roundBits = zSig & 0x3FF;
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
}
}
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
zSig = ( zSig + roundIncrement )>>10;
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
if ( zSig == 0 ) zExp = 0;
return packFloat64( zSign, zExp, zSig );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper double-precision floating-
| point value corresponding to the abstract input. This routine is just like
| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/
static float64
normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
{
int8 shiftCount;
shiftCount = countLeadingZeros64( zSig ) - 1;
return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
}
#ifdef FLOATX80
/*----------------------------------------------------------------------------
| Returns the fraction bits of the extended double-precision floating-point
| value `a'.
*----------------------------------------------------------------------------*/
INLINE bits64 extractFloatx80Frac( floatx80 a )
{
return a.low;
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the extended double-precision floating-point
| value `a'.
*----------------------------------------------------------------------------*/
INLINE int32 extractFloatx80Exp( floatx80 a )
{
return a.high & 0x7FFF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the extended double-precision floating-point value
| `a'.
*----------------------------------------------------------------------------*/
INLINE flag extractFloatx80Sign( floatx80 a )
{
return a.high>>15;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal extended double-precision floating-point value
| represented by the denormalized significand `aSig'. The normalized exponent
| and significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
static void
normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
{
int8 shiftCount;
shiftCount = countLeadingZeros64( aSig );
*zSigPtr = aSig<<shiftCount;
*zExpPtr = 1 - shiftCount;
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
| extended double-precision floating-point value, returning the result.
*----------------------------------------------------------------------------*/
INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
{
floatx80 z;
z.low = zSig;
z.high = ( ( (bits16) zSign )<<15 ) + zExp;
return z;
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and extended significand formed by the concatenation of `zSig0' and `zSig1',
| and returns the proper extended double-precision floating-point value
| corresponding to the abstract input. Ordinarily, the abstract value is
| rounded and packed into the extended double-precision format, with the
| inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal extended
| double-precision floating-point number.
| If `roundingPrecision' is 32 or 64, the result is rounded to the same
| number of bits as single or double precision, respectively. Otherwise, the
| result is rounded to the full precision of the extended double-precision
| format.
| The input significand must be normalized or smaller. If the input
| significand is not normalized, `zExp' must be 0; in that case, the result
| returned is a subnormal number, and it must not require rounding. The
| handling of underflow and overflow follows the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static floatx80
roundAndPackFloatx80(
int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven, increment, isTiny;
int64 roundIncrement, roundMask, roundBits;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
if ( roundingPrecision == 80 ) goto precision80;
if ( roundingPrecision == 64 ) {
roundIncrement = LIT64( 0x0000000000000400 );
roundMask = LIT64( 0x00000000000007FF );
}
else if ( roundingPrecision == 32 ) {
roundIncrement = LIT64( 0x0000008000000000 );
roundMask = LIT64( 0x000000FFFFFFFFFF );
}
else {
goto precision80;
}
zSig0 |= ( zSig1 != 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
roundIncrement = 0;
}
else {
roundIncrement = roundMask;
if ( zSign ) {
if ( roundingMode == float_round_up ) roundIncrement = 0;
}
else {
if ( roundingMode == float_round_down ) roundIncrement = 0;
}
}
}
roundBits = zSig0 & roundMask;
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
if ( ( 0x7FFE < zExp )
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
) {
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 )
|| ( zSig0 <= zSig0 + roundIncrement );
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
zExp = 0;
roundBits = zSig0 & roundMask;
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
zSig0 += roundIncrement;
if ( (sbits64) zSig0 < 0 ) zExp = 1;
roundIncrement = roundMask + 1;
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
roundMask |= roundIncrement;
}
zSig0 &= ~ roundMask;
return packFloatx80( zSign, zExp, zSig0 );
}
}
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
zSig0 += roundIncrement;
if ( zSig0 < roundIncrement ) {
++zExp;
zSig0 = LIT64( 0x8000000000000000 );
}
roundIncrement = roundMask + 1;
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
roundMask |= roundIncrement;
}
zSig0 &= ~ roundMask;
if ( zSig0 == 0 ) zExp = 0;
return packFloatx80( zSign, zExp, zSig0 );
precision80:
increment = ( (sbits64) zSig1 < 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
increment = 0;
}
else {
if ( zSign ) {
increment = ( roundingMode == float_round_down ) && zSig1;
}
else {
increment = ( roundingMode == float_round_up ) && zSig1;
}
}
}
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
if ( ( 0x7FFE < zExp )
|| ( ( zExp == 0x7FFE )
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
&& increment
)
) {
roundMask = 0;
overflow:
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
if ( ( roundingMode == float_round_to_zero )
|| ( zSign && ( roundingMode == float_round_up ) )
|| ( ! zSign && ( roundingMode == float_round_down ) )
) {
return packFloatx80( zSign, 0x7FFE, ~ roundMask );
}
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( zExp <= 0 ) {
isTiny =
( STATUS(float_detect_tininess) == float_tininess_before_rounding )
|| ( zExp < 0 )
|| ! increment
|| ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
zExp = 0;
if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR);
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
if ( roundNearestEven ) {
increment = ( (sbits64) zSig1 < 0 );
}
else {
if ( zSign ) {
increment = ( roundingMode == float_round_down ) && zSig1;
}
else {
increment = ( roundingMode == float_round_up ) && zSig1;
}
}
if ( increment ) {
++zSig0;
zSig0 &=
~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
if ( (sbits64) zSig0 < 0 ) zExp = 1;
}
return packFloatx80( zSign, zExp, zSig0 );
}
}
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
if ( increment ) {
++zSig0;
if ( zSig0 == 0 ) {
++zExp;
zSig0 = LIT64( 0x8000000000000000 );
}
else {
zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
}
}
else {
if ( zSig0 == 0 ) zExp = 0;
}
return packFloatx80( zSign, zExp, zSig0 );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent
| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
| and returns the proper extended double-precision floating-point value
| corresponding to the abstract input. This routine is just like
| `roundAndPackFloatx80' except that the input significand does not have to be
| normalized.
*----------------------------------------------------------------------------*/
static floatx80
normalizeRoundAndPackFloatx80(
int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
STATUS_PARAM)
{
int8 shiftCount;
if ( zSig0 == 0 ) {
zSig0 = zSig1;
zSig1 = 0;
zExp -= 64;
}
shiftCount = countLeadingZeros64( zSig0 );
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
zExp -= shiftCount;
return
roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR);
}
#endif
#ifdef FLOAT128
/*----------------------------------------------------------------------------
| Returns the least-significant 64 fraction bits of the quadruple-precision
| floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE bits64 extractFloat128Frac1( float128 a )
{
return a.low;
}
/*----------------------------------------------------------------------------
| Returns the most-significant 48 fraction bits of the quadruple-precision
| floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE bits64 extractFloat128Frac0( float128 a )
{
return a.high & LIT64( 0x0000FFFFFFFFFFFF );
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the quadruple-precision floating-point value
| `a'.
*----------------------------------------------------------------------------*/
INLINE int32 extractFloat128Exp( float128 a )
{
return ( a.high>>48 ) & 0x7FFF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the quadruple-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
INLINE flag extractFloat128Sign( float128 a )
{
return a.high>>63;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal quadruple-precision floating-point value
| represented by the denormalized significand formed by the concatenation of
| `aSig0' and `aSig1'. The normalized exponent is stored at the location
| pointed to by `zExpPtr'. The most significant 49 bits of the normalized
| significand are stored at the location pointed to by `zSig0Ptr', and the
| least significant 64 bits of the normalized significand are stored at the
| location pointed to by `zSig1Ptr'.
*----------------------------------------------------------------------------*/
static void
normalizeFloat128Subnormal(
bits64 aSig0,
bits64 aSig1,
int32 *zExpPtr,
bits64 *zSig0Ptr,
bits64 *zSig1Ptr
)
{
int8 shiftCount;
if ( aSig0 == 0 ) {
shiftCount = countLeadingZeros64( aSig1 ) - 15;
if ( shiftCount < 0 ) {
*zSig0Ptr = aSig1>>( - shiftCount );
*zSig1Ptr = aSig1<<( shiftCount & 63 );
}
else {
*zSig0Ptr = aSig1<<shiftCount;
*zSig1Ptr = 0;
}
*zExpPtr = - shiftCount - 63;
}
else {
shiftCount = countLeadingZeros64( aSig0 ) - 15;
shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
*zExpPtr = 1 - shiftCount;
}
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', the exponent `zExp', and the significand formed
| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
| floating-point value, returning the result. After being shifted into the
| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
| added together to form the most significant 32 bits of the result. This
| means that any integer portion of `zSig0' 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 `zSig0' and `zSig1' concatenated form a complete, normalized
| significand.
*----------------------------------------------------------------------------*/
INLINE float128
packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
{
float128 z;
z.low = zSig1;
z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0;
return z;
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and extended significand formed by the concatenation of `zSig0', `zSig1',
| and `zSig2', and returns the proper quadruple-precision floating-point value
| corresponding to the abstract input. Ordinarily, the abstract value is
| simply rounded and packed into the quadruple-precision format, with the
| inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal quadruple-
| precision floating-point number.
| The input significand must be normalized or smaller. If the input
| significand is not normalized, `zExp' must be 0; in that case, the result
| returned is a subnormal number, and it must not require rounding. In the
| usual case that the input significand is normalized, `zExp' must be 1 less
| than the ``true'' floating-point exponent. The handling of underflow and
| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static float128
roundAndPackFloat128(
flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 STATUS_PARAM)
{
int8 roundingMode;
flag roundNearestEven, increment, isTiny;
roundingMode = STATUS(float_rounding_mode);
roundNearestEven = ( roundingMode == float_round_nearest_even );
increment = ( (sbits64) zSig2 < 0 );
if ( ! roundNearestEven ) {
if ( roundingMode == float_round_to_zero ) {
increment = 0;
}
else {
if ( zSign ) {
increment = ( roundingMode == float_round_down ) && zSig2;
}
else {
increment = ( roundingMode == float_round_up ) && zSig2;
}
}
}
if ( 0x7FFD <= (bits32) zExp ) {
if ( ( 0x7FFD < zExp )
|| ( ( zExp == 0x7FFD )
&& eq128(
LIT64( 0x0001FFFFFFFFFFFF ),
LIT64( 0xFFFFFFFFFFFFFFFF ),
zSig0,
zSig1
)
&& increment
)
) {
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
if ( ( roundingMode == float_round_to_zero )
|| ( zSign && ( roundingMode == float_round_up ) )
|| ( ! zSign && ( roundingMode == float_round_down ) )
) {
return
packFloat128(
zSign,
0x7FFE,
LIT64( 0x0000FFFFFFFFFFFF ),
LIT64( 0xFFFFFFFFFFFFFFFF )
);
}
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 )
|| ! increment
|| lt128(
zSig0,
zSig1,
LIT64( 0x0001FFFFFFFFFFFF ),
LIT64( 0xFFFFFFFFFFFFFFFF )
);
shift128ExtraRightJamming(
zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
zExp = 0;
if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR);
if ( roundNearestEven ) {
increment = ( (sbits64) zSig2 < 0 );
}
else {
if ( zSign ) {
increment = ( roundingMode == float_round_down ) && zSig2;
}
else {
increment = ( roundingMode == float_round_up ) && zSig2;
}
}
}
}
if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact;
if ( increment ) {
add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
}
else {
if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
}
return packFloat128( zSign, zExp, zSig0, zSig1 );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand formed by the concatenation of `zSig0' and `zSig1', and
| returns the proper quadruple-precision floating-point value corresponding
| to the abstract input. This routine is just like `roundAndPackFloat128'
| except that the input significand has fewer bits and does not have to be
| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
| point exponent.
*----------------------------------------------------------------------------*/
static float128
normalizeRoundAndPackFloat128(
flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 STATUS_PARAM)
{
int8 shiftCount;
bits64 zSig2;
if ( zSig0 == 0 ) {
zSig0 = zSig1;
zSig1 = 0;
zExp -= 64;
}
shiftCount = countLeadingZeros64( zSig0 ) - 15;
if ( 0 <= shiftCount ) {
zSig2 = 0;
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
}
else {
shift128ExtraRightJamming(
zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
}
zExp -= shiftCount;
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR);
}
#endif
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a'
| to the single-precision floating-point format. The conversion is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 int32_to_float32( int32 a STATUS_PARAM )
{
flag zSign;
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 );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a'
| to the double-precision floating-point format. The conversion is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 int32_to_float64( int32 a STATUS_PARAM )
{
flag zSign;
uint32 absA;
int8 shiftCount;
bits64 zSig;
if ( a == 0 ) return float64_zero;
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros32( absA ) + 21;
zSig = absA;
return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount );
}
#ifdef FLOATX80
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a'
| to the extended double-precision floating-point format. The conversion
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
floatx80 int32_to_floatx80( int32 a STATUS_PARAM )
{
flag zSign;
uint32 absA;
int8 shiftCount;
bits64 zSig;
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros32( absA ) + 32;
zSig = absA;
return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
}
#endif
#ifdef FLOAT128
/*----------------------------------------------------------------------------
| Returns the result of converting the 32-bit two's complement integer `a' to
| the quadruple-precision floating-point format. The conversion is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float128 int32_to_float128( int32 a STATUS_PARAM )
{
flag zSign;
uint32 absA;
int8 shiftCount;
bits64 zSig0;
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros32( absA ) + 17;
zSig0 = absA;
return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 );
}
#endif
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a'
| to the single-precision floating-point format. The conversion is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 int64_to_float32( int64 a STATUS_PARAM )
{
flag zSign;
uint64 absA;
int8 shiftCount;
if ( a == 0 ) return float32_zero;
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros64( absA ) - 40;
if ( 0 <= shiftCount ) {
return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount );
}
else {
shiftCount += 7;
if ( shiftCount < 0 ) {
shift64RightJamming( absA, - shiftCount, &absA );
}
else {
absA <<= shiftCount;
}
return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR );
}
}
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
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 int64_to_float64( int64 a STATUS_PARAM )
{
flag zSign;
if ( a == 0 ) return float64_zero;
if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) {
return packFloat64( 1, 0x43E, 0 );
}
zSign = ( a < 0 );
return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR );
}
float64 uint64_to_float64( uint64 a STATUS_PARAM )
{
if ( a == 0 ) return float64_zero;
return normalizeRoundAndPackFloat64( 0, 0x43C, a STATUS_VAR );
}
#ifdef FLOATX80
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a'
| to the extended double-precision floating-point format. The conversion
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
floatx80 int64_to_floatx80( int64 a STATUS_PARAM )
{
flag zSign;
uint64 absA;
int8 shiftCount;
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros64( absA );
return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount );
}
#endif
#ifdef FLOAT128
/*----------------------------------------------------------------------------
| Returns the result of converting the 64-bit two's complement integer `a' to
| the quadruple-precision floating-point format. The conversion is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float128 int64_to_float128( int64 a STATUS_PARAM )
{
flag zSign;
uint64 absA;
int8 shiftCount;
int32 zExp;
bits64 zSig0, zSig1;
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
zSign = ( a < 0 );
absA = zSign ? - a : a;
shiftCount = countLeadingZeros64( absA ) + 49;
zExp = 0x406E - shiftCount;
if ( 64 <= shiftCount ) {
zSig1 = 0;
zSig0 = absA;
shiftCount -= 64;
}
else {
zSig1 = absA;
zSig0 = 0;
}
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
return packFloat128( zSign, zExp, zSig0, zSig1 );
}
#endif
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the 32-bit two's complement integer format. The conversion is
| 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 float32_to_int32( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp, shiftCount;
bits32 aSig;
bits64 aSig64;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( ( aExp == 0xFF ) && aSig ) aSign = 0;
if ( aExp ) aSig |= 0x00800000;
shiftCount = 0xAF - aExp;
aSig64 = aSig;
aSig64 <<= 32;
if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 );
return roundAndPackInt32( aSign, aSig64 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the single-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 float32_to_int32_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 - 0x9E;
if ( 0 <= shiftCount ) {
if ( float32_val(a) != 0xCF000000 ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
}
return (sbits32) 0x80000000;
}
else if ( aExp <= 0x7E ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
return 0;
}
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
| 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 float32_to_int64( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp, shiftCount;
bits32 aSig;
bits64 aSig64, aSigExtra;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
shiftCount = 0xBE - aExp;
if ( shiftCount < 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
return (sbits64) LIT64( 0x8000000000000000 );
}
if ( aExp ) aSig |= 0x00800000;
aSig64 = aSig;
aSig64 <<= 40;
shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra );
return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the single-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 float32_to_int64_round_to_zero( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp, shiftCount;
bits32 aSig;
bits64 aSig64;
int64 z;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
shiftCount = aExp - 0xBE;
if ( 0 <= shiftCount ) {
if ( float32_val(a) != 0xDF000000 ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
return (sbits64) LIT64( 0x8000000000000000 );
}
else if ( aExp <= 0x7E ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
return 0;
}
aSig64 = aSig | 0x00800000;
aSig64 <<= 40;
z = aSig64>>( - shiftCount );
if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) {
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 double-precision floating-point format. The conversion is
| performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
float64 float32_to_float64( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits32 aSig;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ));
return packFloat64( aSign, 0x7FF, 0 );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat64( aSign, 0, 0 );
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
--aExp;
}
return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );
}
#ifdef FLOATX80
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the extended double-precision floating-point format. The conversion
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
floatx80 float32_to_floatx80( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits32 aSig;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) );
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
aSig |= 0x00800000;
return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );
}
#endif
#ifdef FLOAT128
/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the double-precision floating-point format. The conversion is
| performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
float128 float32_to_float128( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits32 aSig;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) );
return packFloat128( aSign, 0x7FFF, 0, 0 );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
--aExp;
}
return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 );
}
#endif
/*----------------------------------------------------------------------------
| Rounds the single-precision floating-point value `a' to an integer, and
| returns the result as a single-precision floating-point value. The
| operation is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 float32_round_to_int( float32 a STATUS_PARAM)
{
flag aSign;
int16 aExp;
bits32 lastBitMask, roundBitsMask;
int8 roundingMode;
bits32 z;
aExp = extractFloat32Exp( a );
if ( 0x96 <= aExp ) {
if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
return propagateFloat32NaN( a, a STATUS_VAR );
}
return a;
}
if ( aExp <= 0x7E ) {
if ( (bits32) ( float32_val(a)<<1 ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat32Sign( a );
switch ( STATUS(float_rounding_mode) ) {
case float_round_nearest_even:
if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
return packFloat32( aSign, 0x7F, 0 );
}
break;
case float_round_down:
return make_float32(aSign ? 0xBF800000 : 0);
case float_round_up:
return make_float32(aSign ? 0x80000000 : 0x3F800000);
}
return packFloat32( aSign, 0, 0 );
}
lastBitMask = 1;
lastBitMask <<= 0x96 - aExp;
roundBitsMask = lastBitMask - 1;
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( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) {
z += roundBitsMask;
}
}
z &= ~ roundBitsMask;
if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact;
return make_float32(z);
}
/*----------------------------------------------------------------------------
| Returns the result of adding the absolute values of the single-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 float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
{
int16 aExp, bExp, zExp;
bits32 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
expDiff = aExp - bExp;
aSig <<= 6;
bSig <<= 6;
if ( 0 < expDiff ) {
if ( aExp == 0xFF ) {
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
--expDiff;
}
else {
bSig |= 0x20000000;
}
shift32RightJamming( bSig, expDiff, &bSig );
zExp = aExp;
}
else if ( expDiff < 0 ) {
if ( bExp == 0xFF ) {
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return packFloat32( zSign, 0xFF, 0 );
}
if ( aExp == 0 ) {
++expDiff;
}
else {
aSig |= 0x20000000;
}
shift32RightJamming( aSig, - expDiff, &aSig );
zExp = bExp;
}
else {
if ( aExp == 0xFF ) {
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return a;
}
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;
}
aSig |= 0x20000000;
zSig = ( aSig + bSig )<<1;
--zExp;
if ( (sbits32) zSig < 0 ) {
zSig = aSig + bSig;
++zExp;
}
roundAndPack:
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of subtracting the absolute values of the single-
| 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 float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
{
int16 aExp, bExp, zExp;
bits32 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
expDiff = aExp - bExp;
aSig <<= 7;
bSig <<= 7;
if ( 0 < expDiff ) goto aExpBigger;
if ( expDiff < 0 ) goto bExpBigger;
if ( aExp == 0xFF ) {
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
if ( aExp == 0 ) {
aExp = 1;
bExp = 1;
}
if ( bSig < aSig ) goto aBigger;
if ( aSig < bSig ) goto bBigger;
return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
bExpBigger:
if ( bExp == 0xFF ) {
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return packFloat32( zSign ^ 1, 0xFF, 0 );
}
if ( aExp == 0 ) {
++expDiff;
}
else {
aSig |= 0x40000000;
}
shift32RightJamming( aSig, - expDiff, &aSig );
bSig |= 0x40000000;
bBigger:
zSig = bSig - aSig;
zExp = bExp;
zSign ^= 1;
goto normalizeRoundAndPack;
aExpBigger:
if ( aExp == 0xFF ) {
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
--expDiff;
}
else {
bSig |= 0x40000000;
}
shift32RightJamming( bSig, expDiff, &bSig );
aSig |= 0x40000000;
aBigger:
zSig = aSig - bSig;
zExp = aExp;
normalizeRoundAndPack:
--zExp;
return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of adding the single-precision floating-point values `a'
| and `b'. The operation is performed according to the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 float32_add( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
if ( aSign == bSign ) {
return addFloat32Sigs( a, b, aSign STATUS_VAR);
}
else {
return subFloat32Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| Returns the result of subtracting the single-precision floating-point values
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 float32_sub( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( b );
if ( aSign == bSign ) {
return subFloat32Sigs( a, b, aSign STATUS_VAR );
}
else {
return addFloat32Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| Returns the result of multiplying the single-precision floating-point values
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 float32_mul( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits32 aSig, bSig;
bits64 zSig64;
bits32 zSig;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
bSign = extractFloat32Sign( b );
zSign = aSign ^ bSign;
if ( aExp == 0xFF ) {
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
return propagateFloat32NaN( a, b STATUS_VAR );
}
if ( ( bExp | bSig ) == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
return packFloat32( zSign, 0xFF, 0 );
}
if ( bExp == 0xFF ) {
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
if ( ( aExp | aSig ) == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
return packFloat32( zSign, 0xFF, 0 );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
if ( bExp == 0 ) {
if ( bSig == 0 ) return packFloat32( zSign, 0, 0 );
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
}
zExp = aExp + bExp - 0x7F;
aSig = ( aSig | 0x00800000 )<<7;
bSig = ( bSig | 0x00800000 )<<8;
shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
zSig = zSig64;
if ( 0 <= (sbits32) ( zSig<<1 ) ) {
zSig <<= 1;
--zExp;
}
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of dividing the single-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.
*----------------------------------------------------------------------------*/
float32 float32_div( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits32 aSig, bSig, zSig;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
bSign = extractFloat32Sign( b );
zSign = aSign ^ bSign;
if ( aExp == 0xFF ) {
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR );
if ( bExp == 0xFF ) {
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
return packFloat32( zSign, 0xFF, 0 );
}
if ( bExp == 0xFF ) {
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return packFloat32( zSign, 0, 0 );
}
if ( bExp == 0 ) {
if ( bSig == 0 ) {
if ( ( aExp | aSig ) == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
float_raise( float_flag_divbyzero STATUS_VAR);
return packFloat32( zSign, 0xFF, 0 );
}
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
zExp = aExp - bExp + 0x7D;
aSig = ( aSig | 0x00800000 )<<7;
bSig = ( bSig | 0x00800000 )<<8;
if ( bSig <= ( aSig + aSig ) ) {
aSig >>= 1;
++zExp;
}
zSig = ( ( (bits64) aSig )<<32 ) / bSig;
if ( ( zSig & 0x3F ) == 0 ) {
zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 );
}
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the remainder of the single-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.
*----------------------------------------------------------------------------*/
float32 float32_rem( float32 a, float32 b STATUS_PARAM )
{
flag aSign, zSign;
int16 aExp, bExp, expDiff;
bits32 aSig, bSig;
bits32 q;
bits64 aSig64, bSig64, q64;
bits32 alternateASig;
sbits32 sigMean;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
bSig = extractFloat32Frac( b );
bExp = extractFloat32Exp( b );
if ( aExp == 0xFF ) {
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
return propagateFloat32NaN( a, b STATUS_VAR );
}
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
if ( bExp == 0xFF ) {
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
if ( bSig == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return a;
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
expDiff = aExp - bExp;
aSig |= 0x00800000;
bSig |= 0x00800000;
if ( expDiff < 32 ) {
aSig <<= 8;
bSig <<= 8;
if ( expDiff < 0 ) {
if ( expDiff < -1 ) return a;
aSig >>= 1;
}
q = ( bSig <= aSig );
if ( q ) aSig -= bSig;
if ( 0 < expDiff ) {
q = ( ( (bits64) aSig )<<32 ) / bSig;
q >>= 32 - expDiff;
bSig >>= 2;
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
}
else {
aSig >>= 2;
bSig >>= 2;
}
}
else {
if ( bSig <= aSig ) aSig -= bSig;
aSig64 = ( (bits64) aSig )<<40;
bSig64 = ( (bits64) bSig )<<40;
expDiff -= 64;
while ( 0 < expDiff ) {
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
aSig64 = - ( ( bSig * q64 )<<38 );
expDiff -= 62;
}
expDiff += 64;
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
q = q64>>( 64 - expDiff );
bSig <<= 6;
aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
}
do {
alternateASig = aSig;
++q;
aSig -= bSig;
} while ( 0 <= (sbits32) aSig );
sigMean = aSig + alternateASig;
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
aSig = alternateASig;
}
zSign = ( (sbits32) aSig < 0 );
if ( zSign ) aSig = - aSig;
return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the square root of the single-precision floating-point value `a'.
| The operation is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float32 float32_sqrt( float32 a STATUS_PARAM )
{
flag aSign;
int16 aExp, zExp;
bits32 aSig, zSig;
bits64 rem, term;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR );
if ( ! aSign ) return a;
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
if ( aSign ) {
if ( ( aExp | aSig ) == 0 ) return a;
float_raise( float_flag_invalid STATUS_VAR);
return float32_default_nan;
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return float32_zero;
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
}
zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E;
aSig = ( aSig | 0x00800000 )<<8;
zSig = estimateSqrt32( aExp, aSig ) + 2;
if ( ( zSig & 0x7F ) <= 5 ) {
if ( zSig < 2 ) {
zSig = 0x7FFFFFFF;
goto roundAndPack;
}
aSig >>= aExp & 1;
term = ( (bits64) zSig ) * zSig;
rem = ( ( (bits64) aSig )<<32 ) - term;
while ( (sbits64) rem < 0 ) {
--zSig;
rem += ( ( (bits64) zSig )<<1 ) | 1;
}
zSig |= ( rem != 0 );
}
shift32RightJamming( zSig, 1, &zSig );
roundAndPack:
return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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;
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;
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.
*----------------------------------------------------------------------------*/
int float32_eq( float32 a, float32 b STATUS_PARAM )
{
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 0;
}
return ( float32_val(a) == float32_val(b) ) ||
( (bits32) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is less than
| or equal to the corresponding value `b', and 0 otherwise. The comparison
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
int float32_le( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
bits32 av, bv;
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( 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 ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is less than
| the corresponding value `b', and 0 otherwise. The comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float32_lt( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
bits32 av, bv;
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( 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 ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is equal to
| the corresponding value `b', and 0 otherwise. The invalid exception is
| raised if either operand is a NaN. Otherwise, the comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float32_eq_signaling( float32 a, float32 b STATUS_PARAM )
{
bits32 av, bv;
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
av = float32_val(a);
bv = float32_val(b);
return ( av == bv ) || ( (bits32) ( ( av | bv )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-precision floating-point value `a' is less than or
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
| cause an exception. Otherwise, the comparison is performed according to the
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float32_le_quiet( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
bits32 av, bv;
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 0;
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( 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 ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the single-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.
*----------------------------------------------------------------------------*/
int float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
{
flag aSign, bSign;
bits32 av, bv;
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
) {
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 0;
}
aSign = extractFloat32Sign( a );
bSign = extractFloat32Sign( 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 ) );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the double-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 float64_to_int32( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp, shiftCount;
bits64 aSig;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
shiftCount = 0x42C - aExp;
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
return roundAndPackInt32( aSign, aSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the double-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 float64_to_int32_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 ( 0x41E < 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 ( ( z < 0 ) ^ aSign ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
}
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
| 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 float64_to_int64( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp, shiftCount;
bits64 aSig, aSigExtra;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
shiftCount = 0x433 - aExp;
if ( shiftCount <= 0 ) {
if ( 0x43E < aExp ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign
|| ( ( aExp == 0x7FF )
&& ( aSig != LIT64( 0x0010000000000000 ) ) )
) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
return (sbits64) LIT64( 0x8000000000000000 );
}
aSigExtra = 0;
aSig <<= - shiftCount;
}
else {
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
}
return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the double-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 float64_to_int64_round_to_zero( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp, shiftCount;
bits64 aSig;
int64 z;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
shiftCount = aExp - 0x433;
if ( 0 <= shiftCount ) {
if ( 0x43E <= aExp ) {
if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign
|| ( ( aExp == 0x7FF )
&& ( aSig != LIT64( 0x0010000000000000 ) ) )
) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
return (sbits64) LIT64( 0x8000000000000000 );
}
z = aSig<<shiftCount;
}
else {
if ( aExp < 0x3FE ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
return 0;
}
z = aSig>>( - shiftCount );
if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
}
if ( aSign ) z = - z;
return z;
}
/*----------------------------------------------------------------------------
| Returns the result of converting the double-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 float64_to_float32( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits64 aSig;
bits32 zSig;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) );
return packFloat32( aSign, 0xFF, 0 );
}
shift64RightJamming( aSig, 22, &aSig );
zSig = aSig;
if ( aExp || zSig ) {
zSig |= 0x40000000;
aExp -= 0x381;
}
return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 bits16 packFloat16(flag zSign, int16 zExp, bits16 zSig)
{
return (((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( bits16 a, flag ieee STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits32 aSig;
aSign = a >> 15;
aExp = (a >> 10) & 0x1f;
aSig = a & 0x3ff;
if (aExp == 0x1f && ieee) {
if (aSig) {
/* Make sure correct exceptions are raised. */
float32ToCommonNaN(a STATUS_VAR);
aSig |= 0x200;
}
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);
}
bits16 float32_to_float16( float32 a, flag ieee STATUS_PARAM)
{
flag aSign;
int16 aExp;
bits32 aSig;
bits32 mask;
bits32 increment;
int8 roundingMode;
aSig = extractFloat32Frac( a );
aExp = extractFloat32Exp( a );
aSign = extractFloat32Sign( a );
if ( aExp == 0xFF ) {
if (aSig) {
/* Make sure correct exceptions are raised. */
float32ToCommonNaN(a STATUS_VAR);
aSig |= 0x00400000;
}
return packFloat16(aSign, 0x1f, aSig >> 13);
}
if (aExp == 0 && aSign == 0) {
return packFloat16(aSign, 0, 0);
}
/* Decimal point between bits 22 and 23. */
aSig |= 0x00800000;
aExp -= 0x7f;
if (aExp < -14) {
mask = 0x007fffff;
if (aExp < -24) {
aExp = -25;
} else {
mask >>= 24 + 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_overflow | 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
/*----------------------------------------------------------------------------
| Returns the result of converting the double-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 float64_to_floatx80( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits64 aSig;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) );
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
}
return
packFloatx80(
aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 );
}
#endif
#ifdef FLOAT128
/*----------------------------------------------------------------------------
| Returns the result of converting the double-precision floating-point value
| `a' to the quadruple-precision floating-point format. The conversion is
| performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
float128 float64_to_float128( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits64 aSig, zSig0, zSig1;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) );
return packFloat128( aSign, 0x7FFF, 0, 0 );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
--aExp;
}
shift128Right( aSig, 0, 4, &zSig0, &zSig1 );
return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 );
}
#endif
/*----------------------------------------------------------------------------
| Rounds the double-precision floating-point value `a' to an integer, and
| returns the result as a double-precision floating-point value. The
| operation is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 float64_round_to_int( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits64 lastBitMask, roundBitsMask;
int8 roundingMode;
bits64 z;
aExp = extractFloat64Exp( a );
if ( 0x433 <= aExp ) {
if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) {
return propagateFloat64NaN( a, a STATUS_VAR );
}
return a;
}
if ( aExp < 0x3FF ) {
if ( (bits64) ( float64_val(a)<<1 ) == 0 ) return a;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat64Sign( a );
switch ( STATUS(float_rounding_mode) ) {
case float_round_nearest_even:
if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) {
return packFloat64( aSign, 0x3FF, 0 );
}
break;
case float_round_down:
return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0);
case float_round_up:
return make_float64(
aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 ));
}
return packFloat64( aSign, 0, 0 );
}
lastBitMask = 1;
lastBitMask <<= 0x433 - aExp;
roundBitsMask = lastBitMask - 1;
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( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) {
z += roundBitsMask;
}
}
z &= ~ roundBitsMask;
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
| 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 float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
{
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
expDiff = aExp - bExp;
aSig <<= 9;
bSig <<= 9;
if ( 0 < expDiff ) {
if ( aExp == 0x7FF ) {
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
--expDiff;
}
else {
bSig |= LIT64( 0x2000000000000000 );
}
shift64RightJamming( bSig, expDiff, &bSig );
zExp = aExp;
}
else if ( expDiff < 0 ) {
if ( bExp == 0x7FF ) {
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return packFloat64( zSign, 0x7FF, 0 );
}
if ( aExp == 0 ) {
++expDiff;
}
else {
aSig |= LIT64( 0x2000000000000000 );
}
shift64RightJamming( aSig, - expDiff, &aSig );
zExp = bExp;
}
else {
if ( aExp == 0x7FF ) {
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return a;
}
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;
}
aSig |= LIT64( 0x2000000000000000 );
zSig = ( aSig + bSig )<<1;
--zExp;
if ( (sbits64) zSig < 0 ) {
zSig = aSig + bSig;
++zExp;
}
roundAndPack:
return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of subtracting the absolute values of the 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 float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
{
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig;
int16 expDiff;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
expDiff = aExp - bExp;
aSig <<= 10;
bSig <<= 10;
if ( 0 < expDiff ) goto aExpBigger;
if ( expDiff < 0 ) goto bExpBigger;
if ( aExp == 0x7FF ) {
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
if ( aExp == 0 ) {
aExp = 1;
bExp = 1;
}
if ( bSig < aSig ) goto aBigger;
if ( aSig < bSig ) goto bBigger;
return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
bExpBigger:
if ( bExp == 0x7FF ) {
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return packFloat64( zSign ^ 1, 0x7FF, 0 );
}
if ( aExp == 0 ) {
++expDiff;
}
else {
aSig |= LIT64( 0x4000000000000000 );
}
shift64RightJamming( aSig, - expDiff, &aSig );
bSig |= LIT64( 0x4000000000000000 );
bBigger:
zSig = bSig - aSig;
zExp = bExp;
zSign ^= 1;
goto normalizeRoundAndPack;
aExpBigger:
if ( aExp == 0x7FF ) {
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
--expDiff;
}
else {
bSig |= LIT64( 0x4000000000000000 );
}
shift64RightJamming( bSig, expDiff, &bSig );
aSig |= LIT64( 0x4000000000000000 );
aBigger:
zSig = aSig - bSig;
zExp = aExp;
normalizeRoundAndPack:
--zExp;
return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of adding the double-precision floating-point values `a'
| and `b'. The operation is performed according to the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 float64_add( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
if ( aSign == bSign ) {
return addFloat64Sigs( a, b, aSign STATUS_VAR );
}
else {
return subFloat64Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| Returns the result of subtracting the double-precision floating-point values
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 float64_sub( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
if ( aSign == bSign ) {
return subFloat64Sigs( a, b, aSign STATUS_VAR );
}
else {
return addFloat64Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| Returns the result of multiplying the double-precision floating-point values
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 float64_mul( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig0, zSig1;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
bSign = extractFloat64Sign( b );
zSign = aSign ^ bSign;
if ( aExp == 0x7FF ) {
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
return propagateFloat64NaN( a, b STATUS_VAR );
}
if ( ( bExp | bSig ) == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
return packFloat64( zSign, 0x7FF, 0 );
}
if ( bExp == 0x7FF ) {
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
if ( ( aExp | aSig ) == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
return packFloat64( zSign, 0x7FF, 0 );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
}
if ( bExp == 0 ) {
if ( bSig == 0 ) return packFloat64( zSign, 0, 0 );
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
}
zExp = aExp + bExp - 0x3FF;
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
mul64To128( aSig, bSig, &zSig0, &zSig1 );
zSig0 |= ( zSig1 != 0 );
if ( 0 <= (sbits64) ( zSig0<<1 ) ) {
zSig0 <<= 1;
--zExp;
}
return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of dividing the 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.
*----------------------------------------------------------------------------*/
float64 float64_div( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign, zSign;
int16 aExp, bExp, zExp;
bits64 aSig, bSig, zSig;
bits64 rem0, rem1;
bits64 term0, term1;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
bSign = extractFloat64Sign( b );
zSign = aSign ^ bSign;
if ( aExp == 0x7FF ) {
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR );
if ( bExp == 0x7FF ) {
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
return packFloat64( zSign, 0x7FF, 0 );
}
if ( bExp == 0x7FF ) {
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return packFloat64( zSign, 0, 0 );
}
if ( bExp == 0 ) {
if ( bSig == 0 ) {
if ( ( aExp | aSig ) == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
float_raise( float_flag_divbyzero STATUS_VAR);
return packFloat64( zSign, 0x7FF, 0 );
}
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
}
zExp = aExp - bExp + 0x3FD;
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
if ( bSig <= ( aSig + aSig ) ) {
aSig >>= 1;
++zExp;
}
zSig = estimateDiv128To64( aSig, 0, bSig );
if ( ( zSig & 0x1FF ) <= 2 ) {
mul64To128( bSig, zSig, &term0, &term1 );
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
while ( (sbits64) rem0 < 0 ) {
--zSig;
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
}
zSig |= ( rem1 != 0 );
}
return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the remainder of the 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.
*----------------------------------------------------------------------------*/
float64 float64_rem( float64 a, float64 b STATUS_PARAM )
{
flag aSign, zSign;
int16 aExp, bExp, expDiff;
bits64 aSig, bSig;
bits64 q, alternateASig;
sbits64 sigMean;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
bSig = extractFloat64Frac( b );
bExp = extractFloat64Exp( b );
if ( aExp == 0x7FF ) {
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
return propagateFloat64NaN( a, b STATUS_VAR );
}
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
if ( bExp == 0x7FF ) {
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
if ( bSig == 0 ) {
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return a;
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
}
expDiff = aExp - bExp;
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11;
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
if ( expDiff < 0 ) {
if ( expDiff < -1 ) return a;
aSig >>= 1;
}
q = ( bSig <= aSig );
if ( q ) aSig -= bSig;
expDiff -= 64;
while ( 0 < expDiff ) {
q = estimateDiv128To64( aSig, 0, bSig );
q = ( 2 < q ) ? q - 2 : 0;
aSig = - ( ( bSig>>2 ) * q );
expDiff -= 62;
}
expDiff += 64;
if ( 0 < expDiff ) {
q = estimateDiv128To64( aSig, 0, bSig );
q = ( 2 < q ) ? q - 2 : 0;
q >>= 64 - expDiff;
bSig >>= 2;
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
}
else {
aSig >>= 2;
bSig >>= 2;
}
do {
alternateASig = aSig;
++q;
aSig -= bSig;
} while ( 0 <= (sbits64) aSig );
sigMean = aSig + alternateASig;
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
aSig = alternateASig;
}
zSign = ( (sbits64) aSig < 0 );
if ( zSign ) aSig = - aSig;
return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the square root of the double-precision floating-point value `a'.
| The operation is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float64 float64_sqrt( float64 a STATUS_PARAM )
{
flag aSign;
int16 aExp, zExp;
bits64 aSig, zSig, doubleZSig;
bits64 rem0, rem1, term0, term1;
aSig = extractFloat64Frac( a );
aExp = extractFloat64Exp( a );
aSign = extractFloat64Sign( a );
if ( aExp == 0x7FF ) {
if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR );
if ( ! aSign ) return a;
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
if ( aSign ) {
if ( ( aExp | aSig ) == 0 ) return a;
float_raise( float_flag_invalid STATUS_VAR);
return float64_default_nan;
}
if ( aExp == 0 ) {
if ( aSig == 0 ) return float64_zero;
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
}
zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
aSig |= LIT64( 0x0010000000000000 );
zSig = estimateSqrt32( aExp, aSig>>21 );
aSig <<= 9 - ( aExp & 1 );
zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 );
if ( ( zSig & 0x1FF ) <= 5 ) {
doubleZSig = zSig<<1;
mul64To128( zSig, zSig, &term0, &term1 );
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
while ( (sbits64) rem0 < 0 ) {
--zSig;
doubleZSig -= 2;
add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 );
}
zSig |= ( ( rem0 | rem1 ) != 0 );
}
return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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;
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.
*----------------------------------------------------------------------------*/
int float64_eq( float64 a, float64 b STATUS_PARAM )
{
bits64 av, bv;
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 0;
}
av = float64_val(a);
bv = float64_val(b);
return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is less than or
| equal to the corresponding value `b', and 0 otherwise. The comparison is
| performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/
int float64_le( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
bits64 av, bv;
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
if ( aSign != bSign ) return aSign || ( (bits64) ( ( av | bv )<<1 ) == 0 );
return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is less than
| the corresponding value `b', and 0 otherwise. The comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float64_lt( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
bits64 av, bv;
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
if ( aSign != bSign ) return aSign && ( (bits64) ( ( av | bv )<<1 ) != 0 );
return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the double-precision floating-point value `a' is equal to the
| corresponding value `b', and 0 otherwise. The invalid exception is raised
| if either operand is a NaN. Otherwise, the comparison is performed
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
int float64_eq_signaling( float64 a, float64 b STATUS_PARAM )
{
bits64 av, bv;
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
av = float64_val(a);
bv = float64_val(b);
return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 );
}
/*----------------------------------------------------------------------------
| Returns 1 if the 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.
*----------------------------------------------------------------------------*/
int float64_le_quiet( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
bits64 av, bv;
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 0;
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
if ( aSign != bSign ) return aSign || ( (bits64) ( ( av | bv )<<1 ) == 0 );
return ( av == bv ) || ( aSign ^ ( av < bv ) );
}
/*----------------------------------------------------------------------------
| Returns 1 if the 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.
*----------------------------------------------------------------------------*/
int float64_lt_quiet( float64 a, float64 b STATUS_PARAM )
{
flag aSign, bSign;
bits64 av, bv;
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
) {
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 0;
}
aSign = extractFloat64Sign( a );
bSign = extractFloat64Sign( b );
av = float64_val(a);
bv = float64_val(b);
if ( aSign != bSign ) return aSign && ( (bits64) ( ( av | bv )<<1 ) != 0 );
return ( av != bv ) && ( aSign ^ ( av < bv ) );
}
#ifdef FLOATX80
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-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 floatx80_to_int32( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp, shiftCount;
bits64 aSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
shiftCount = 0x4037 - aExp;
if ( shiftCount <= 0 ) shiftCount = 1;
shift64RightJamming( aSig, shiftCount, &aSig );
return roundAndPackInt32( aSign, aSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-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 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp, shiftCount;
bits64 aSig, savedASig;
int32 z;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( 0x401E < aExp ) {
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
goto invalid;
}
else if ( aExp < 0x3FFF ) {
if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
return 0;
}
shiftCount = 0x403E - aExp;
savedASig = aSig;
aSig >>= shiftCount;
z = aSig;
if ( aSign ) z = - z;
if ( ( z < 0 ) ^ aSign ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
}
if ( ( aSig<<shiftCount ) != savedASig ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
return z;
}
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-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 floatx80_to_int64( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp, shiftCount;
bits64 aSig, aSigExtra;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
shiftCount = 0x403E - aExp;
if ( shiftCount <= 0 ) {
if ( shiftCount ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign
|| ( ( aExp == 0x7FFF )
&& ( aSig != LIT64( 0x8000000000000000 ) ) )
) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
return (sbits64) LIT64( 0x8000000000000000 );
}
aSigExtra = 0;
}
else {
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
}
return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-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 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp, shiftCount;
bits64 aSig;
int64 z;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
shiftCount = aExp - 0x403E;
if ( 0 <= shiftCount ) {
aSig &= LIT64( 0x7FFFFFFFFFFFFFFF );
if ( ( a.high != 0xC03E ) || aSig ) {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
return (sbits64) LIT64( 0x8000000000000000 );
}
else if ( aExp < 0x3FFF ) {
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
return 0;
}
z = aSig>>( - shiftCount );
if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
if ( aSign ) z = - z;
return z;
}
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-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 floatx80_to_float32( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp;
bits64 aSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig<<1 ) ) {
return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) );
}
return packFloat32( aSign, 0xFF, 0 );
}
shift64RightJamming( aSig, 33, &aSig );
if ( aExp || aSig ) aExp -= 0x3F81;
return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
}
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-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 floatx80_to_float64( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp;
bits64 aSig, zSig;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig<<1 ) ) {
return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) );
}
return packFloat64( aSign, 0x7FF, 0 );
}
shift64RightJamming( aSig, 1, &zSig );
if ( aExp || aSig ) aExp -= 0x3C01;
return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR );
}
#ifdef FLOAT128
/*----------------------------------------------------------------------------
| Returns the result of converting the extended double-precision floating-
| point value `a' to the quadruple-precision floating-point format. The
| conversion is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
float128 floatx80_to_float128( floatx80 a STATUS_PARAM )
{
flag aSign;
int16 aExp;
bits64 aSig, zSig0, zSig1;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
aSign = extractFloatx80Sign( a );
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) {
return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) );
}
shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
return packFloat128( aSign, aExp, zSig0, zSig1 );
}
#endif
/*----------------------------------------------------------------------------
| Rounds the extended double-precision floating-point value `a' to an integer,
| and returns the result as an extended quadruple-precision floating-point
| value. The operation is performed according to the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM )
{
flag aSign;
int32 aExp;
bits64 lastBitMask, roundBitsMask;
int8 roundingMode;
floatx80 z;
aExp = extractFloatx80Exp( a );
if ( 0x403E <= aExp ) {
if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) {
return propagateFloatx80NaN( a, a STATUS_VAR );
}
return a;
}
if ( aExp < 0x3FFF ) {
if ( ( aExp == 0 )
&& ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
return a;
}
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloatx80Sign( a );
switch ( STATUS(float_rounding_mode) ) {
case float_round_nearest_even:
if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 )
) {
return
packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) );
}
break;
case float_round_down:
return
aSign ?
packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) )
: packFloatx80( 0, 0, 0 );
case float_round_up:
return
aSign ? packFloatx80( 1, 0, 0 )
: packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) );
}
return packFloatx80( aSign, 0, 0 );
}
lastBitMask = 1;
lastBitMask <<= 0x403E - aExp;
roundBitsMask = lastBitMask - 1;
z = a;
roundingMode = STATUS(float_rounding_mode);
if ( roundingMode == float_round_nearest_even ) {
z.low += lastBitMask>>1;
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
}
else if ( roundingMode != float_round_to_zero ) {
if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
z.low += roundBitsMask;
}
}
z.low &= ~ roundBitsMask;
if ( z.low == 0 ) {
++z.high;
z.low = LIT64( 0x8000000000000000 );
}
if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact;
return z;
}
/*----------------------------------------------------------------------------
| Returns the result of adding the absolute values of the extended double-
| 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 floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM)
{
int32 aExp, bExp, zExp;
bits64 aSig, bSig, zSig0, zSig1;
int32 expDiff;
aSig = extractFloatx80Frac( a );
aExp = extractFloatx80Exp( a );
bSig = extractFloatx80Frac( b );
bExp = extractFloatx80Exp( b );
expDiff = aExp - bExp;
if ( 0 < expDiff ) {
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) --expDiff;
shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
zExp = aExp;
}
else if ( expDiff < 0 ) {
if ( bExp == 0x7FFF ) {
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( aExp == 0 ) ++expDiff;
shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
zExp = bExp;
}
else {
if ( aExp == 0x7FFF ) {
if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
return propagateFloatx80NaN( a, b STATUS_VAR );
}
return a;
}
zSig1 = 0;
zSig0 = aSig + bSig;
if ( aExp == 0 ) {
normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
goto roundAndPack;
}
zExp = aExp;
goto shiftRight1;
}
zSig0 = aSig + bSig;
if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
shiftRight1:
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
zSig0 |= LIT64( 0x8000000000000000 );
++zExp;
roundAndPack:
return
roundAndPackFloatx80(
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
}
float_raise( float_flag_invalid STATUS_VAR);
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( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
bExpBigger:
if ( bExp == 0x7FFF ) {
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
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 STATUS_VAR );
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(
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloatx80Sign( a );
bSign = extractFloatx80Sign( b );
if ( aSign == bSign ) {
return addFloatx80Sigs( a, b, aSign STATUS_VAR );
}
else {
return subFloatx80Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloatx80Sign( a );
bSign = extractFloatx80Sign( b );
if ( aSign == bSign ) {
return subFloatx80Sigs( a, b, aSign STATUS_VAR );
}
else {
return addFloatx80Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
}
if ( ( bExp | bSig ) == 0 ) goto invalid;
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( bExp == 0x7FFF ) {
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
if ( ( aExp | aSig ) == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
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(
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
if ( bExp == 0x7FFF ) {
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
goto invalid;
}
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( bExp == 0x7FFF ) {
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return packFloatx80( zSign, 0, 0 );
}
if ( bExp == 0 ) {
if ( bSig == 0 ) {
if ( ( aExp | aSig ) == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
z.low = floatx80_default_nan_low;
z.high = floatx80_default_nan_high;
return z;
}
float_raise( float_flag_divbyzero STATUS_VAR);
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(
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
flag aSign, 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 );
if ( aExp == 0x7FFF ) {
if ( (bits64) ( aSig0<<1 )
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
return propagateFloatx80NaN( a, b STATUS_VAR );
}
goto invalid;
}
if ( bExp == 0x7FFF ) {
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
if ( bSig == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
if ( ! aSign ) return a;
goto invalid;
}
if ( aSign ) {
if ( ( aExp | aSig0 ) == 0 ) return a;
invalid:
float_raise( float_flag_invalid STATUS_VAR);
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(
STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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.
*----------------------------------------------------------------------------*/
int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
{
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 STATUS_VAR);
}
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.
*----------------------------------------------------------------------------*/
int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
{
flag aSign, bSign;
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
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.
*----------------------------------------------------------------------------*/
int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
{
flag aSign, bSign;
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
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.
*----------------------------------------------------------------------------*/
int floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM )
{
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 0;
}
return
( a.low == b.low )
&& ( ( a.high == b.high )
|| ( ( a.low == 0 )
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
);
}
/*----------------------------------------------------------------------------
| 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.
*----------------------------------------------------------------------------*/
int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM )
{
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 STATUS_VAR);
}
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.
*----------------------------------------------------------------------------*/
int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM )
{
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 STATUS_VAR);
}
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 STATUS_PARAM )
{
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 ) STATUS(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 STATUS_VAR);
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
}
if ( ( aSig0<<shiftCount ) != savedASig ) {
STATUS(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 STATUS_PARAM )
{
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 STATUS_VAR);
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 ) STATUS(float_exception_flags) |= float_flag_inexact;
}
else {
float_raise( float_flag_invalid STATUS_VAR);
if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) {
return LIT64( 0x7FFFFFFFFFFFFFFF );
}
}
return (sbits64) LIT64( 0x8000000000000000 );
}
z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
if ( (bits64) ( aSig1<<shiftCount ) ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
}
else {
if ( aExp < 0x3FFF ) {
if ( aExp | aSig0 | aSig1 ) {
STATUS(float_exception_flags) |= float_flag_inexact;
}
return 0;
}
z = aSig0>>( - shiftCount );
if ( aSig1
|| ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) {
STATUS(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 STATUS_PARAM )
{
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 STATUS_VAR ) );
}
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR ) );
}
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 STATUS_VAR );
}
#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 STATUS_PARAM )
{
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 STATUS_VAR ) );
}
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 STATUS_VAR );
}
#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 STATUS_PARAM )
{
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 STATUS_VAR );
}
return a;
}
lastBitMask = 1;
lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1;
roundBitsMask = lastBitMask - 1;
z = a;
roundingMode = STATUS(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;
STATUS(float_exception_flags) |= float_flag_inexact;
aSign = extractFloat128Sign( a );
switch ( STATUS(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 = STATUS(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 ) ) {
STATUS(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 STATUS_PARAM)
{
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 STATUS_VAR );
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 STATUS_VAR );
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 STATUS_VAR );
}
return a;
}
add128( aSig0, aSig1, bSig0, bSig1, &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;
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM)
{
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 STATUS_VAR );
}
float_raise( float_flag_invalid STATUS_VAR);
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( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 );
bExpBigger:
if ( bExp == 0x7FFF ) {
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
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 STATUS_VAR );
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloat128Sign( a );
bSign = extractFloat128Sign( b );
if ( aSign == bSign ) {
return addFloat128Sigs( a, b, aSign STATUS_VAR );
}
else {
return subFloat128Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
flag aSign, bSign;
aSign = extractFloat128Sign( a );
bSign = extractFloat128Sign( b );
if ( aSign == bSign ) {
return subFloat128Sigs( a, b, aSign STATUS_VAR );
}
else {
return addFloat128Sigs( a, b, aSign STATUS_VAR );
}
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
}
if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid;
return packFloat128( zSign, 0x7FFF, 0, 0 );
}
if ( bExp == 0x7FFF ) {
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
if ( bExp == 0x7FFF ) {
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
goto invalid;
}
return packFloat128( zSign, 0x7FFF, 0, 0 );
}
if ( bExp == 0x7FFF ) {
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
return packFloat128( zSign, 0, 0, 0 );
}
if ( bExp == 0 ) {
if ( ( bSig0 | bSig1 ) == 0 ) {
if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
z.low = float128_default_nan_low;
z.high = float128_default_nan_high;
return z;
}
float_raise( float_flag_divbyzero STATUS_VAR);
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
flag aSign, 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 );
if ( aExp == 0x7FFF ) {
if ( ( aSig0 | aSig1 )
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
return propagateFloat128NaN( a, b STATUS_VAR );
}
goto invalid;
}
if ( bExp == 0x7FFF ) {
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
return a;
}
if ( bExp == 0 ) {
if ( ( bSig0 | bSig1 ) == 0 ) {
invalid:
float_raise( float_flag_invalid STATUS_VAR);
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, (bits64 *)&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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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 STATUS_PARAM )
{
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 STATUS_VAR );
if ( ! aSign ) return a;
goto invalid;
}
if ( aSign ) {
if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
invalid:
float_raise( float_flag_invalid STATUS_VAR);
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 STATUS_VAR );
}
/*----------------------------------------------------------------------------
| 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.
*----------------------------------------------------------------------------*/
int float128_eq( float128 a, float128 b STATUS_PARAM )
{
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
) {
if ( float128_is_signaling_nan( a )
|| float128_is_signaling_nan( b ) ) {
float_raise( float_flag_invalid STATUS_VAR);
}
return 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.
*----------------------------------------------------------------------------*/
int float128_le( float128 a, float128 b STATUS_PARAM )
{
flag aSign, bSign;
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
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.
*----------------------------------------------------------------------------*/
int float128_lt( float128 a, float128 b STATUS_PARAM )
{
flag aSign, bSign;
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
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.
*----------------------------------------------------------------------------*/
int float128_eq_signaling( float128 a, float128 b STATUS_PARAM )
{
if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
) {
float_raise( float_flag_invalid STATUS_VAR);
return 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.
*----------------------------------------------------------------------------*/
int float128_le_quiet( float128 a, float128 b STATUS_PARAM )
{
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 STATUS_VAR);
}
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.
*----------------------------------------------------------------------------*/
int float128_lt_quiet( float128 a, float128 b STATUS_PARAM )
{
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 STATUS_VAR);
}
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
/* misc functions */
float32 uint32_to_float32( unsigned int a STATUS_PARAM )
{
return int64_to_float32(a STATUS_VAR);
}
float64 uint32_to_float64( unsigned int a STATUS_PARAM )
{
return int64_to_float64(a STATUS_VAR);
}
unsigned int float32_to_uint32( float32 a STATUS_PARAM )
{
int64_t v;
unsigned int res;
v = float32_to_int64(a STATUS_VAR);
if (v < 0) {
res = 0;
float_raise( float_flag_invalid STATUS_VAR);
} else if (v > 0xffffffff) {
res = 0xffffffff;
float_raise( float_flag_invalid STATUS_VAR);
} else {
res = v;
}
return res;
}
unsigned int float32_to_uint32_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 > 0xffffffff) {
res = 0xffffffff;
float_raise( float_flag_invalid STATUS_VAR);
} else {
res = v;
}
return res;
}
unsigned int float64_to_uint32( float64 a STATUS_PARAM )
{
int64_t v;
unsigned int res;
v = float64_to_int64(a STATUS_VAR);
if (v < 0) {
res = 0;
float_raise( float_flag_invalid STATUS_VAR);
} else if (v > 0xffffffff) {
res = 0xffffffff;
float_raise( float_flag_invalid STATUS_VAR);
} else {
res = v;
}
return res;
}
unsigned int float64_to_uint32_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 > 0xffffffff) {
res = 0xffffffff;
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 int float ## s ## _compare_internal( float ## s a, float ## s b, \
int is_quiet STATUS_PARAM ) \
{ \
flag aSign, bSign; \
bits ## s av, bv; \
\
if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \
extractFloat ## s ## Frac( a ) ) || \
( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \
extractFloat ## s ## Frac( b ) )) { \
if (!is_quiet || \
float ## s ## _is_signaling_nan( a ) || \
float ## s ## _is_signaling_nan( b ) ) { \
float_raise( float_flag_invalid STATUS_VAR); \
} \
return float_relation_unordered; \
} \
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) ( ( av | bv )<<1 ) == 0 ) { \
/* zero case */ \
return float_relation_equal; \
} else { \
return 1 - (2 * aSign); \
} \
} else { \
if (av == bv) { \
return float_relation_equal; \
} else { \
return 1 - 2 * (aSign ^ ( av < bv )); \
} \
} \
} \
\
int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \
{ \
return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \
} \
\
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;
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;
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