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Diffstat (limited to 'src/lib/softfloat/softfloat.c')
-rw-r--r-- | src/lib/softfloat/softfloat.c | 4941 |
1 files changed, 0 insertions, 4941 deletions
diff --git a/src/lib/softfloat/softfloat.c b/src/lib/softfloat/softfloat.c deleted file mode 100644 index edd4def337b..00000000000 --- a/src/lib/softfloat/softfloat.c +++ /dev/null @@ -1,4941 +0,0 @@ - -/*============================================================================ - -This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic -Package, Release 2b. - -Written by John R. Hauser. This work was made possible in part by the -International Computer Science Institute, located at Suite 600, 1947 Center -Street, Berkeley, California 94704. Funding was partially provided by the -National Science Foundation under grant MIP-9311980. The original version -of this code was written as part of a project to build a fixed-point vector -processor in collaboration with the University of California at Berkeley, -overseen by Profs. Nelson Morgan and John Wawrzynek. More information -is available through the Web page `http://www.cs.berkeley.edu/~jhauser/ -arithmetic/SoftFloat.html'. - -THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has -been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES -RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS -AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES, -COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE -EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE -INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR -OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. - -Derivative works are acceptable, even for commercial purposes, so long as -(1) the source code for the derivative work includes prominent notice that -the work is derivative, and (2) the source code includes prominent notice with -these four paragraphs for those parts of this code that are retained. - -=============================================================================*/ - -#include "milieu.h" -#include "softfloat.h" - -/*---------------------------------------------------------------------------- -| Floating-point rounding mode, extended double-precision rounding precision, -| and exception flags. -*----------------------------------------------------------------------------*/ -int8 float_exception_flags = 0; -#ifdef FLOATX80 -int8 floatx80_rounding_precision = 80; -#endif - -int8 float_rounding_mode = float_round_nearest_even; - -/*---------------------------------------------------------------------------- -| Functions and definitions to determine: (1) whether tininess for underflow -| is detected before or after rounding by default, (2) what (if anything) -| happens when exceptions are raised, (3) how signaling NaNs are distinguished -| from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs -| are propagated from function inputs to output. These details are target- -| specific. -*----------------------------------------------------------------------------*/ -#include "softfloat-specialize" - -/*---------------------------------------------------------------------------- -| 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 ) -{ - int8 roundingMode; - flag roundNearestEven; - int8 roundIncrement, roundBits; - int32 z; - - roundingMode = 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 ); - return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; - } - if ( roundBits ) 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 ) -{ - int8 roundingMode; - flag roundNearestEven, increment; - int64 z; - - roundingMode = 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 ); - return - zSign ? (sbits64) LIT64( 0x8000000000000000 ) - : LIT64( 0x7FFFFFFFFFFFFFFF ); - } - if ( absZ1 ) 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 a & 0x007FFFFF; - -} - -/*---------------------------------------------------------------------------- -| Returns the exponent bits of the single-precision floating-point value `a'. -*----------------------------------------------------------------------------*/ - -INLINE int16 extractFloat32Exp( float32 a ) -{ - return ( a>>23 ) & 0xFF; - -} - -/*---------------------------------------------------------------------------- -| Returns the sign bit of the single-precision floating-point value `a'. -*----------------------------------------------------------------------------*/ - -INLINE flag extractFloat32Sign( float32 a ) -{ - return 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 ( ( (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 ) -{ - int8 roundingMode; - flag roundNearestEven; - int8 roundIncrement, roundBits; - flag isTiny; - - roundingMode = 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 ); - return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 ); - } - if ( zExp < 0 ) { - isTiny = - ( 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 ); - } - } - if ( roundBits ) 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 ) -{ - int8 shiftCount; - - shiftCount = countLeadingZeros32( zSig ) - 1; - return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount ); - -} - -/*---------------------------------------------------------------------------- -| Returns the fraction bits of the double-precision floating-point value `a'. -*----------------------------------------------------------------------------*/ - -INLINE bits64 extractFloat64Frac( float64 a ) -{ - return a & LIT64( 0x000FFFFFFFFFFFFF ); - -} - -/*---------------------------------------------------------------------------- -| Returns the exponent bits of the double-precision floating-point value `a'. -*----------------------------------------------------------------------------*/ - -INLINE int16 extractFloat64Exp( float64 a ) -{ - return ( a>>52 ) & 0x7FF; - -} - -/*---------------------------------------------------------------------------- -| Returns the sign bit of the double-precision floating-point value `a'. -*----------------------------------------------------------------------------*/ - -INLINE flag extractFloat64Sign( float64 a ) -{ - return 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 ( ( (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 ) -{ - int8 roundingMode; - flag roundNearestEven; - int16 roundIncrement, roundBits; - flag isTiny; - - roundingMode = 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 ); - return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 ); - } - if ( zExp < 0 ) { - isTiny = - ( 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 ); - } - } - if ( roundBits ) 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 ) -{ - int8 shiftCount; - - shiftCount = countLeadingZeros64( zSig ) - 1; - return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount ); - -} - -#ifdef FLOATX80 - -/*---------------------------------------------------------------------------- -| 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; - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -// roundAndPackFloatx80 is now also used in fyl2x.c - -/* static */ floatx80 - roundAndPackFloatx80( - int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 - ) -{ - int8 roundingMode; - flag roundNearestEven, increment, isTiny; - int64 roundIncrement, roundMask, roundBits; - - roundingMode = 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 ) { - isTiny = - ( 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 ); - if ( roundBits ) 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 ) 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 ); - 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 = - ( 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 ); - if ( zSig1 ) 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 ) 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 - ) -{ - 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 ); - -} - -#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; - } - -} - -#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 ) -{ - flag zSign; - - if ( a == 0 ) return 0; - if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); - zSign = ( a < 0 ); - return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag zSign; - uint32 absA; - int8 shiftCount; - bits64 zSig; - - if ( a == 0 ) return 0; - 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 ) -{ - 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 ) -{ - 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 ) -{ - flag zSign; - uint64 absA; - int8 shiftCount; -// bits32 zSig; - - if ( a == 0 ) return 0; - 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 ); - } - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag zSign; - - if ( a == 0 ) return 0; - if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) { - return packFloat64( 1, 0x43E, 0 ); - } - zSign = ( a < 0 ); - return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a ); - -} - -#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 ) -{ - 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 ) -{ - 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 ) -{ - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ( a != 0xCF000000 ) { - float_raise( float_flag_invalid ); - if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; - } - return (sbits32) 0x80000000; - } - else if ( aExp <= 0x7E ) { - if ( aExp | aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - aSig = ( aSig | 0x00800000 )<<8; - z = aSig>>( - shiftCount ); - if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) { - 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 ) -{ - 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 ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ( a != 0xDF000000 ) { - float_raise( float_flag_invalid ); - if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { - return LIT64( 0x7FFFFFFFFFFFFFFF ); - } - } - return (sbits64) LIT64( 0x8000000000000000 ); - } - else if ( aExp <= 0x7E ) { - if ( aExp | aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - aSig64 = aSig | 0x00800000; - aSig64 <<= 40; - z = aSig64>>( - shiftCount ); - if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) { - 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 ) -{ - flag aSign; - int16 aExp; - bits32 aSig; - - aSig = extractFloat32Frac( a ); - aExp = extractFloat32Exp( a ); - aSign = extractFloat32Sign( a ); - if ( aExp == 0xFF ) { - if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) ); - 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 ) -{ - flag aSign; - int16 aExp; - bits32 aSig; - - aSig = extractFloat32Frac( a ); - aExp = extractFloat32Exp( a ); - aSign = extractFloat32Sign( a ); - if ( aExp == 0xFF ) { - if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) ); - 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 ) -{ - flag aSign; - int16 aExp; - bits32 aSig; - - aSig = extractFloat32Frac( a ); - aExp = extractFloat32Exp( a ); - aSign = extractFloat32Sign( a ); - if ( aExp == 0xFF ) { - if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a ) ); - 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 ) -{ - flag aSign; - int16 aExp; - bits32 lastBitMask, roundBitsMask; - int8 roundingMode; - float32 z; - - aExp = extractFloat32Exp( a ); - if ( 0x96 <= aExp ) { - if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { - return propagateFloat32NaN( a, a ); - } - return a; - } - if ( aExp <= 0x7E ) { - if ( (bits32) ( a<<1 ) == 0 ) return a; - float_exception_flags |= float_flag_inexact; - aSign = extractFloat32Sign( a ); - switch ( float_rounding_mode ) { - case float_round_nearest_even: - if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { - return packFloat32( aSign, 0x7F, 0 ); - } - break; - case float_round_down: - return aSign ? 0xBF800000 : 0; - case float_round_up: - return aSign ? 0x80000000 : 0x3F800000; - } - return packFloat32( aSign, 0, 0 ); - } - lastBitMask = 1; - lastBitMask <<= 0x96 - aExp; - roundBitsMask = lastBitMask - 1; - z = a; - roundingMode = float_rounding_mode; - if ( roundingMode == float_round_nearest_even ) { - z += lastBitMask>>1; - if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; - } - else if ( roundingMode != float_round_to_zero ) { - if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) { - z += roundBitsMask; - } - } - z &= ~ roundBitsMask; - if ( z != a ) float_exception_flags |= float_flag_inexact; - return 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 ) -{ - 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 ); - 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 ); - 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 ); - return a; - } - if ( aExp == 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - float_raise( float_flag_invalid ); - return float32_default_nan; - } - if ( aExp == 0 ) { - aExp = 1; - bExp = 1; - } - if ( bSig < aSig ) goto aBigger; - if ( aSig < bSig ) goto bBigger; - return packFloat32( float_rounding_mode == float_round_down, 0, 0 ); - bExpBigger: - if ( bExp == 0xFF ) { - if ( bSig ) return propagateFloat32NaN( a, b ); - 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 ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag aSign, bSign; - - aSign = extractFloat32Sign( a ); - bSign = extractFloat32Sign( b ); - if ( aSign == bSign ) { - return addFloat32Sigs( a, b, aSign ); - } - else { - return subFloat32Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag aSign, bSign; - - aSign = extractFloat32Sign( a ); - bSign = extractFloat32Sign( b ); - if ( aSign == bSign ) { - return subFloat32Sigs( a, b, aSign ); - } - else { - return addFloat32Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - } - if ( ( bExp | bSig ) == 0 ) { - float_raise( float_flag_invalid ); - return float32_default_nan; - } - return packFloat32( zSign, 0xFF, 0 ); - } - if ( bExp == 0xFF ) { - if ( bSig ) return propagateFloat32NaN( a, b ); - if ( ( aExp | aSig ) == 0 ) { - float_raise( float_flag_invalid ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - if ( bExp == 0xFF ) { - if ( bSig ) return propagateFloat32NaN( a, b ); - float_raise( float_flag_invalid ); - return float32_default_nan; - } - return packFloat32( zSign, 0xFF, 0 ); - } - if ( bExp == 0xFF ) { - if ( bSig ) return propagateFloat32NaN( a, b ); - return packFloat32( zSign, 0, 0 ); - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - if ( ( aExp | aSig ) == 0 ) { - float_raise( float_flag_invalid ); - return float32_default_nan; - } - float_raise( float_flag_divbyzero ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); -// bSign = extractFloat32Sign( b ); - if ( aExp == 0xFF ) { - if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { - return propagateFloat32NaN( a, b ); - } - float_raise( float_flag_invalid ); - return float32_default_nan; - } - if ( bExp == 0xFF ) { - if ( bSig ) return propagateFloat32NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - float_raise( float_flag_invalid ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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, 0 ); - if ( ! aSign ) return a; - float_raise( float_flag_invalid ); - return float32_default_nan; - } - if ( aSign ) { - if ( ( aExp | aSig ) == 0 ) return a; - float_raise( float_flag_invalid ); - return float32_default_nan; - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return 0; - 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 ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the single-precision floating-point value `a' is equal to -| the corresponding value `b', and 0 otherwise. The comparison is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float32_eq( float32 a, float32 b ) -{ - 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 ); - } - return 0; - } - return ( a == b ) || ( (bits32) ( ( a | 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. -*----------------------------------------------------------------------------*/ - -flag float32_le( float32 a, float32 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) - || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloat32Sign( a ); - bSign = extractFloat32Sign( b ); - if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); - return ( a == b ) || ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -flag float32_lt( float32 a, float32 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) - || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloat32Sign( a ); - bSign = extractFloat32Sign( b ); - if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); - return ( a != b ) && ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -flag float32_eq_signaling( float32 a, float32 b ) -{ - if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) - || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - return ( a == b ) || ( (bits32) ( ( a | 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. Quiet NaNs do not -| cause an exception. Otherwise, the comparison is performed according to the -| IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float32_le_quiet( float32 a, float32 b ) -{ - flag aSign, bSign; -// int16 aExp, bExp; - - 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 ); - } - return 0; - } - aSign = extractFloat32Sign( a ); - bSign = extractFloat32Sign( b ); - if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); - return ( a == b ) || ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -flag float32_lt_quiet( float32 a, float32 b ) -{ - flag aSign, bSign; - - 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 ); - } - return 0; - } - aSign = extractFloat32Sign( a ); - bSign = extractFloat32Sign( b ); - if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); - return ( a != b ) && ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ) 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 ); - return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; - } - if ( ( aSig<<shiftCount ) != savedASig ) { - 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 ) -{ - 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 ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ( a != LIT64( 0xC3E0000000000000 ) ) { - float_raise( float_flag_invalid ); - if ( ! aSign - || ( ( aExp == 0x7FF ) - && ( aSig != LIT64( 0x0010000000000000 ) ) ) - ) { - return LIT64( 0x7FFFFFFFFFFFFFFF ); - } - } - return (sbits64) LIT64( 0x8000000000000000 ); - } - z = aSig<<shiftCount; - } - else { - if ( aExp < 0x3FE ) { - if ( aExp | aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - z = aSig>>( - shiftCount ); - if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { - 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 ) -{ - 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 ) ); - return packFloat32( aSign, 0xFF, 0 ); - } - shift64RightJamming( aSig, 22, &aSig ); - zSig = aSig; - if ( aExp || zSig ) { - zSig |= 0x40000000; - aExp -= 0x381; - } - return roundAndPackFloat32( aSign, aExp, zSig ); - -} - -#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 ) -{ - flag aSign; - int16 aExp; - bits64 aSig; - - aSig = extractFloat64Frac( a ); - aExp = extractFloat64Exp( a ); - aSign = extractFloat64Sign( a ); - if ( aExp == 0x7FF ) { - if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a ) ); - 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 ) -{ - 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 ) ); - 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 ) -{ - flag aSign; - int16 aExp; - bits64 lastBitMask, roundBitsMask; - int8 roundingMode; - float64 z; - - aExp = extractFloat64Exp( a ); - if ( 0x433 <= aExp ) { - if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { - return propagateFloat64NaN( a, a ); - } - return a; - } - if ( aExp < 0x3FF ) { - if ( (bits64) ( a<<1 ) == 0 ) return a; - float_exception_flags |= float_flag_inexact; - aSign = extractFloat64Sign( a ); - switch ( float_rounding_mode ) { - case float_round_nearest_even: - if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { - return packFloat64( aSign, 0x3FF, 0 ); - } - break; - case float_round_down: - return aSign ? LIT64( 0xBFF0000000000000 ) : 0; - case float_round_up: - return - aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 ); - } - return packFloat64( aSign, 0, 0 ); - } - lastBitMask = 1; - lastBitMask <<= 0x433 - aExp; - roundBitsMask = lastBitMask - 1; - z = a; - roundingMode = float_rounding_mode; - if ( roundingMode == float_round_nearest_even ) { - z += lastBitMask>>1; - if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; - } - else if ( roundingMode != float_round_to_zero ) { - if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) { - z += roundBitsMask; - } - } - z &= ~ roundBitsMask; - if ( z != a ) float_exception_flags |= float_flag_inexact; - return z; - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - 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 ); - 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 ); - return a; - } - if ( aExp == 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - float_raise( float_flag_invalid ); - return float64_default_nan; - } - if ( aExp == 0 ) { - aExp = 1; - bExp = 1; - } - if ( bSig < aSig ) goto aBigger; - if ( aSig < bSig ) goto bBigger; - return packFloat64( float_rounding_mode == float_round_down, 0, 0 ); - bExpBigger: - if ( bExp == 0x7FF ) { - if ( bSig ) return propagateFloat64NaN( a, b ); - 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 ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag aSign, bSign; - - aSign = extractFloat64Sign( a ); - bSign = extractFloat64Sign( b ); - if ( aSign == bSign ) { - return addFloat64Sigs( a, b, aSign ); - } - else { - return subFloat64Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag aSign, bSign; - - aSign = extractFloat64Sign( a ); - bSign = extractFloat64Sign( b ); - if ( aSign == bSign ) { - return subFloat64Sigs( a, b, aSign ); - } - else { - return addFloat64Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - } - if ( ( bExp | bSig ) == 0 ) { - float_raise( float_flag_invalid ); - return float64_default_nan; - } - return packFloat64( zSign, 0x7FF, 0 ); - } - if ( bExp == 0x7FF ) { - if ( bSig ) return propagateFloat64NaN( a, b ); - if ( ( aExp | aSig ) == 0 ) { - float_raise( float_flag_invalid ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - if ( bExp == 0x7FF ) { - if ( bSig ) return propagateFloat64NaN( a, b ); - float_raise( float_flag_invalid ); - return float64_default_nan; - } - return packFloat64( zSign, 0x7FF, 0 ); - } - if ( bExp == 0x7FF ) { - if ( bSig ) return propagateFloat64NaN( a, b ); - return packFloat64( zSign, 0, 0 ); - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - if ( ( aExp | aSig ) == 0 ) { - float_raise( float_flag_invalid ); - return float64_default_nan; - } - float_raise( float_flag_divbyzero ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); -// bSign = extractFloat64Sign( b ); - if ( aExp == 0x7FF ) { - if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { - return propagateFloat64NaN( a, b ); - } - float_raise( float_flag_invalid ); - return float64_default_nan; - } - if ( bExp == 0x7FF ) { - if ( bSig ) return propagateFloat64NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - float_raise( float_flag_invalid ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - flag aSign; - int16 aExp, zExp; - bits64 aSig, zSig, doubleZSig; - bits64 rem0, rem1, term0, term1; -// float64 z; - - aSig = extractFloat64Frac( a ); - aExp = extractFloat64Exp( a ); - aSign = extractFloat64Sign( a ); - if ( aExp == 0x7FF ) { - if ( aSig ) return propagateFloat64NaN( a, a ); - if ( ! aSign ) return a; - float_raise( float_flag_invalid ); - return float64_default_nan; - } - if ( aSign ) { - if ( ( aExp | aSig ) == 0 ) return a; - float_raise( float_flag_invalid ); - return float64_default_nan; - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return 0; - 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 ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the double-precision floating-point value `a' is equal to the -| corresponding value `b', and 0 otherwise. The comparison is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float64_eq( float64 a, float64 b ) -{ - 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 ); - } - return 0; - } - return ( a == b ) || ( (bits64) ( ( a | b )<<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. -*----------------------------------------------------------------------------*/ - -flag float64_le( float64 a, float64 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) - || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloat64Sign( a ); - bSign = extractFloat64Sign( b ); - if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); - return ( a == b ) || ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -flag float64_lt( float64 a, float64 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) - || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloat64Sign( a ); - bSign = extractFloat64Sign( b ); - if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); - return ( a != b ) && ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -flag float64_eq_signaling( float64 a, float64 b ) -{ - if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) - || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - return ( a == b ) || ( (bits64) ( ( a | b )<<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. -*----------------------------------------------------------------------------*/ - -flag float64_le_quiet( float64 a, float64 b ) -{ - flag aSign, bSign; -// int16 aExp, bExp; - - 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 ); - } - return 0; - } - aSign = extractFloat64Sign( a ); - bSign = extractFloat64Sign( b ); - if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); - return ( a == b ) || ( aSign ^ ( a < b ) ); - -} - -/*---------------------------------------------------------------------------- -| 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. -*----------------------------------------------------------------------------*/ - -flag float64_lt_quiet( float64 a, float64 b ) -{ - flag aSign, bSign; - - 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 ); - } - return 0; - } - aSign = extractFloat64Sign( a ); - bSign = extractFloat64Sign( b ); - if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); - return ( a != b ) && ( aSign ^ ( a < b ) ); - -} - -#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 ) -{ - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ) 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 ); - return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; - } - if ( ( aSig<<shiftCount ) != savedASig ) { - 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 ) -{ - 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 ); - 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 ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ); - if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { - return LIT64( 0x7FFFFFFFFFFFFFFF ); - } - } - return (sbits64) LIT64( 0x8000000000000000 ); - } - else if ( aExp < 0x3FFF ) { - if ( aExp | aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - z = aSig>>( - shiftCount ); - if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { - 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 ) -{ - 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 ) ); - } - return packFloat32( aSign, 0xFF, 0 ); - } - shift64RightJamming( aSig, 33, &aSig ); - if ( aExp || aSig ) aExp -= 0x3F81; - return roundAndPackFloat32( aSign, aExp, aSig ); - -} - -/*---------------------------------------------------------------------------- -| 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 ) -{ - 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 ) ); - } - return packFloat64( aSign, 0x7FF, 0 ); - } - shift64RightJamming( aSig, 1, &zSig ); - if ( aExp || aSig ) aExp -= 0x3C01; - return roundAndPackFloat64( aSign, aExp, zSig ); - -} - -#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 ) -{ - 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 ) ); - } - 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 ) -{ - 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 ); - } - return a; - } - if ( aExp < 0x3FFF ) { - if ( ( aExp == 0 ) - && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { - return a; - } - float_exception_flags |= float_flag_inexact; - aSign = extractFloatx80Sign( a ); - switch ( 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 = 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 ) 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 ) -{ - 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 ); - 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 ); - 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 ); - } - 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( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of subtracting the absolute values of the extended -| double-precision floating-point values `a' and `b'. If `zSign' is 1, the -| difference is negated before being returned. `zSign' is ignored if the -| result is a NaN. The subtraction is performed according to the IEC/IEEE -| Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign ) -{ - int32 aExp, bExp, zExp; - bits64 aSig, bSig, zSig0, zSig1; - int32 expDiff; - floatx80 z; - - aSig = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - expDiff = aExp - bExp; - if ( 0 < expDiff ) goto aExpBigger; - if ( expDiff < 0 ) goto bExpBigger; - if ( aExp == 0x7FFF ) { - if ( (bits64) ( ( aSig | bSig )<<1 ) ) { - return propagateFloatx80NaN( a, b ); - } - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - if ( aExp == 0 ) { - aExp = 1; - bExp = 1; - } - zSig1 = 0; - if ( bSig < aSig ) goto aBigger; - if ( aSig < bSig ) goto bBigger; - return packFloatx80( float_rounding_mode == float_round_down, 0, 0 ); - bExpBigger: - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( aExp == 0 ) ++expDiff; - shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); - bBigger: - sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); - zExp = bExp; - zSign ^= 1; - goto normalizeRoundAndPack; - aExpBigger: - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return a; - } - if ( bExp == 0 ) --expDiff; - shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); - aBigger: - sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); - zExp = aExp; - normalizeRoundAndPack: - return - normalizeRoundAndPackFloatx80( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of adding the extended double-precision floating-point -| values `a' and `b'. The operation is performed according to the IEC/IEEE -| Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 floatx80_add( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign == bSign ) { - return addFloatx80Sigs( a, b, aSign ); - } - else { - return subFloatx80Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| Returns the result of subtracting the extended double-precision floating- -| point values `a' and `b'. The operation is performed according to the -| IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 floatx80_sub( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign == bSign ) { - return subFloatx80Sigs( a, b, aSign ); - } - else { - return addFloatx80Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| Returns the result of multiplying the extended double-precision floating- -| point values `a' and `b'. The operation is performed according to the -| IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 floatx80_mul( floatx80 a, floatx80 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, zExp; - bits64 aSig, bSig, zSig0, zSig1; - floatx80 z; - - aSig = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - bSign = extractFloatx80Sign( b ); - zSign = aSign ^ bSign; - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig<<1 ) - || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { - return propagateFloatx80NaN( a, b ); - } - if ( ( bExp | bSig ) == 0 ) goto invalid; - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - if ( ( aExp | aSig ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); - normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); - } - if ( bExp == 0 ) { - if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); - normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); - } - zExp = aExp + bExp - 0x3FFE; - mul64To128( aSig, bSig, &zSig0, &zSig1 ); - if ( 0 < (sbits64) zSig0 ) { - shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); - --zExp; - } - return - roundAndPackFloatx80( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of dividing the extended double-precision floating-point -| value `a' by the corresponding value `b'. The operation is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 floatx80_div( floatx80 a, floatx80 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, zExp; - bits64 aSig, bSig, zSig0, zSig1; - bits64 rem0, rem1, rem2, term0, term1, term2; - floatx80 z; - - aSig = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - bSign = extractFloatx80Sign( b ); - zSign = aSign ^ bSign; - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - goto invalid; - } - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return packFloatx80( zSign, 0, 0 ); - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - if ( ( aExp | aSig ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - float_raise( float_flag_divbyzero ); - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); - normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); - } - zExp = aExp - bExp + 0x3FFE; - rem1 = 0; - if ( bSig <= aSig ) { - shift128Right( aSig, 0, 1, &aSig, &rem1 ); - ++zExp; - } - zSig0 = estimateDiv128To64( aSig, rem1, bSig ); - mul64To128( bSig, zSig0, &term0, &term1 ); - sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); - while ( (sbits64) rem0 < 0 ) { - --zSig0; - add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); - } - zSig1 = estimateDiv128To64( rem1, 0, bSig ); - if ( (bits64) ( zSig1<<1 ) <= 8 ) { - mul64To128( bSig, zSig1, &term1, &term2 ); - sub128( rem1, 0, term1, term2, &rem1, &rem2 ); - while ( (sbits64) rem1 < 0 ) { - --zSig1; - add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); - } - zSig1 |= ( ( rem1 | rem2 ) != 0 ); - } - return - roundAndPackFloatx80( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the remainder of the extended double-precision floating-point value -| `a' with respect to the corresponding value `b'. The operation is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 floatx80_rem( floatx80 a, floatx80 b ) -{ - flag aSign, zSign; - int32 aExp, bExp, expDiff; - bits64 aSig0, aSig1, bSig; - bits64 q, term0, term1, alternateASig0, alternateASig1; - floatx80 z; - - aSig0 = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); -// bSign = extractFloatx80Sign( b ); - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig0<<1 ) - || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { - return propagateFloatx80NaN( a, b ); - } - goto invalid; - } - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); - } - if ( aExp == 0 ) { - if ( (bits64) ( aSig0<<1 ) == 0 ) return a; - normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); - } - bSig |= LIT64( 0x8000000000000000 ); - zSign = aSign; - expDiff = aExp - bExp; - aSig1 = 0; - if ( expDiff < 0 ) { - if ( expDiff < -1 ) return a; - shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); - expDiff = 0; - } - q = ( bSig <= aSig0 ); - if ( q ) aSig0 -= bSig; - expDiff -= 64; - while ( 0 < expDiff ) { - q = estimateDiv128To64( aSig0, aSig1, bSig ); - q = ( 2 < q ) ? q - 2 : 0; - mul64To128( bSig, q, &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); - shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); - expDiff -= 62; - } - expDiff += 64; - if ( 0 < expDiff ) { - q = estimateDiv128To64( aSig0, aSig1, bSig ); - q = ( 2 < q ) ? q - 2 : 0; - q >>= 64 - expDiff; - mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); - shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); - while ( le128( term0, term1, aSig0, aSig1 ) ) { - ++q; - sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); - } - } - else { - term1 = 0; - term0 = bSig; - } - sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); - if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) - || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) - && ( q & 1 ) ) - ) { - aSig0 = alternateASig0; - aSig1 = alternateASig1; - zSign = ! zSign; - } - return - normalizeRoundAndPackFloatx80( - 80, zSign, bExp + expDiff, aSig0, aSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the square root of the extended double-precision floating-point -| value `a'. The operation is performed according to the IEC/IEEE Standard -| for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 floatx80_sqrt( floatx80 a ) -{ - flag aSign; - int32 aExp, zExp; - bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0; - bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; - floatx80 z; - - aSig0 = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a ); - if ( ! aSign ) return a; - goto invalid; - } - if ( aSign ) { - if ( ( aExp | aSig0 ) == 0 ) return a; - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - if ( aExp == 0 ) { - if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); - normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); - } - zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; - zSig0 = estimateSqrt32( aExp, aSig0>>32 ); - shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); - zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); - doubleZSig0 = zSig0<<1; - mul64To128( zSig0, zSig0, &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); - while ( (sbits64) rem0 < 0 ) { - --zSig0; - doubleZSig0 -= 2; - add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); - } - zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); - if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { - if ( zSig1 == 0 ) zSig1 = 1; - mul64To128( doubleZSig0, zSig1, &term1, &term2 ); - sub128( rem1, 0, term1, term2, &rem1, &rem2 ); - mul64To128( zSig1, zSig1, &term2, &term3 ); - sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); - while ( (sbits64) rem1 < 0 ) { - --zSig1; - shortShift128Left( 0, zSig1, 1, &term2, &term3 ); - term3 |= 1; - term2 |= doubleZSig0; - add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); - } - zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); - } - shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); - zSig0 |= doubleZSig0; - return - roundAndPackFloatx80( - floatx80_rounding_precision, 0, zExp, zSig0, zSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the extended double-precision floating-point value `a' is -| equal to the corresponding value `b', and 0 otherwise. The comparison is -| performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic. -*----------------------------------------------------------------------------*/ - -flag floatx80_eq( floatx80 a, floatx80 b ) -{ - if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( a )<<1 ) ) - || ( ( extractFloatx80Exp( b ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( b )<<1 ) ) - ) { - if ( floatx80_is_signaling_nan( a ) - || floatx80_is_signaling_nan( b ) ) { - float_raise( float_flag_invalid ); - } - return 0; - } - return - ( a.low == b.low ) - && ( ( a.high == b.high ) - || ( ( a.low == 0 ) - && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) - ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the extended double-precision floating-point value `a' is -| less than or equal to the corresponding value `b', and 0 otherwise. The -| comparison is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag floatx80_le( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( a )<<1 ) ) - || ( ( extractFloatx80Exp( b ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( b )<<1 ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign != bSign ) { - return - aSign - || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - == 0 ); - } - return - aSign ? le128( b.high, b.low, a.high, a.low ) - : le128( a.high, a.low, b.high, b.low ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the extended double-precision floating-point value `a' is -| less than the corresponding value `b', and 0 otherwise. The comparison -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic. -*----------------------------------------------------------------------------*/ - -flag floatx80_lt( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( a )<<1 ) ) - || ( ( extractFloatx80Exp( b ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( b )<<1 ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign != bSign ) { - return - aSign - && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - != 0 ); - } - return - aSign ? lt128( b.high, b.low, a.high, a.low ) - : lt128( a.high, a.low, b.high, b.low ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the extended double-precision floating-point value `a' is equal -| to the corresponding value `b', and 0 otherwise. The invalid exception is -| raised if either operand is a NaN. Otherwise, the comparison is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag floatx80_eq_signaling( floatx80 a, floatx80 b ) -{ - if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( a )<<1 ) ) - || ( ( extractFloatx80Exp( b ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( b )<<1 ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - return - ( a.low == b.low ) - && ( ( a.high == b.high ) - || ( ( a.low == 0 ) - && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) - ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the extended double-precision floating-point value `a' is less -| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs -| do not cause an exception. Otherwise, the comparison is performed according -| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag floatx80_le_quiet( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( a )<<1 ) ) - || ( ( extractFloatx80Exp( b ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( b )<<1 ) ) - ) { - if ( floatx80_is_signaling_nan( a ) - || floatx80_is_signaling_nan( b ) ) { - float_raise( float_flag_invalid ); - } - return 0; - } - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign != bSign ) { - return - aSign - || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - == 0 ); - } - return - aSign ? le128( b.high, b.low, a.high, a.low ) - : le128( a.high, a.low, b.high, b.low ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the extended double-precision floating-point value `a' is less -| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause -| an exception. Otherwise, the comparison is performed according to the -| IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag floatx80_lt_quiet( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( a )<<1 ) ) - || ( ( extractFloatx80Exp( b ) == 0x7FFF ) - && (bits64) ( extractFloatx80Frac( b )<<1 ) ) - ) { - if ( floatx80_is_signaling_nan( a ) - || floatx80_is_signaling_nan( b ) ) { - float_raise( float_flag_invalid ); - } - return 0; - } - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign != bSign ) { - return - aSign - && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - != 0 ); - } - return - aSign ? lt128( b.high, b.low, a.high, a.low ) - : lt128( a.high, a.low, b.high, b.low ); - -} - -#endif - -#ifdef FLOAT128 - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the 32-bit two's complement integer format. The conversion -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic---which means in particular that the conversion is rounded -| according to the current rounding mode. If `a' is a NaN, the largest -| positive integer is returned. Otherwise, if the conversion overflows, the -| largest integer with the same sign as `a' is returned. -*----------------------------------------------------------------------------*/ - -int32 float128_to_int32( float128 a ) -{ - flag aSign; - int32 aExp, shiftCount; - bits64 aSig0, aSig1; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; - if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); - aSig0 |= ( aSig1 != 0 ); - shiftCount = 0x4028 - aExp; - if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); - return roundAndPackInt32( aSign, aSig0 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the 32-bit two's complement integer format. The conversion -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic, except that the conversion is always rounded toward zero. If -| `a' is a NaN, the largest positive integer is returned. Otherwise, if the -| conversion overflows, the largest integer with the same sign as `a' is -| returned. -*----------------------------------------------------------------------------*/ - -int32 float128_to_int32_round_to_zero( float128 a ) -{ - flag aSign; - int32 aExp, shiftCount; - bits64 aSig0, aSig1, savedASig; - int32 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - aSig0 |= ( aSig1 != 0 ); - if ( 0x401E < aExp ) { - if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; - goto invalid; - } - else if ( aExp < 0x3FFF ) { - if ( aExp || aSig0 ) float_exception_flags |= float_flag_inexact; - return 0; - } - aSig0 |= LIT64( 0x0001000000000000 ); - shiftCount = 0x402F - aExp; - savedASig = aSig0; - aSig0 >>= shiftCount; - z = aSig0; - if ( aSign ) z = - z; - if ( ( z < 0 ) ^ aSign ) { - invalid: - float_raise( float_flag_invalid ); - return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; - } - if ( ( aSig0<<shiftCount ) != savedASig ) { - float_exception_flags |= float_flag_inexact; - } - return z; - -} - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the 64-bit two's complement integer format. The conversion -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic---which means in particular that the conversion is rounded -| according to the current rounding mode. If `a' is a NaN, the largest -| positive integer is returned. Otherwise, if the conversion overflows, the -| largest integer with the same sign as `a' is returned. -*----------------------------------------------------------------------------*/ - -int64 float128_to_int64( float128 a ) -{ - flag aSign; - int32 aExp, shiftCount; - bits64 aSig0, aSig1; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); - shiftCount = 0x402F - aExp; - if ( shiftCount <= 0 ) { - if ( 0x403E < aExp ) { - float_raise( float_flag_invalid ); - if ( ! aSign - || ( ( aExp == 0x7FFF ) - && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) - ) - ) { - return LIT64( 0x7FFFFFFFFFFFFFFF ); - } - return (sbits64) LIT64( 0x8000000000000000 ); - } - shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); - } - else { - shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); - } - return roundAndPackInt64( aSign, aSig0, aSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the 64-bit two's complement integer format. The conversion -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic, except that the conversion is always rounded toward zero. -| If `a' is a NaN, the largest positive integer is returned. Otherwise, if -| the conversion overflows, the largest integer with the same sign as `a' is -| returned. -*----------------------------------------------------------------------------*/ - -int64 float128_to_int64_round_to_zero( float128 a ) -{ - flag aSign; - int32 aExp, shiftCount; - bits64 aSig0, aSig1; - int64 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); - shiftCount = aExp - 0x402F; - if ( 0 < shiftCount ) { - if ( 0x403E <= aExp ) { - aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); - if ( ( a.high == LIT64( 0xC03E000000000000 ) ) - && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { - if ( aSig1 ) float_exception_flags |= float_flag_inexact; - } - else { - float_raise( float_flag_invalid ); - if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { - return LIT64( 0x7FFFFFFFFFFFFFFF ); - } - } - return (sbits64) LIT64( 0x8000000000000000 ); - } - z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); - if ( (bits64) ( aSig1<<shiftCount ) ) { - float_exception_flags |= float_flag_inexact; - } - } - else { - if ( aExp < 0x3FFF ) { - if ( aExp | aSig0 | aSig1 ) { - float_exception_flags |= float_flag_inexact; - } - return 0; - } - z = aSig0>>( - shiftCount ); - if ( aSig1 - || ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) { - float_exception_flags |= float_flag_inexact; - } - } - if ( aSign ) z = - z; - return z; - -} - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the single-precision floating-point format. The conversion -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic. -*----------------------------------------------------------------------------*/ - -float32 float128_to_float32( float128 a ) -{ - flag aSign; - int32 aExp; - bits64 aSig0, aSig1; - bits32 zSig; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) { - return commonNaNToFloat32( float128ToCommonNaN( a ) ); - } - return packFloat32( aSign, 0xFF, 0 ); - } - aSig0 |= ( aSig1 != 0 ); - shift64RightJamming( aSig0, 18, &aSig0 ); - zSig = aSig0; - if ( aExp || zSig ) { - zSig |= 0x40000000; - aExp -= 0x3F81; - } - return roundAndPackFloat32( aSign, aExp, zSig ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the double-precision floating-point format. The conversion -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic. -*----------------------------------------------------------------------------*/ - -float64 float128_to_float64( float128 a ) -{ - flag aSign; - int32 aExp; - bits64 aSig0, aSig1; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) { - return commonNaNToFloat64( float128ToCommonNaN( a ) ); - } - return packFloat64( aSign, 0x7FF, 0 ); - } - shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); - aSig0 |= ( aSig1 != 0 ); - if ( aExp || aSig0 ) { - aSig0 |= LIT64( 0x4000000000000000 ); - aExp -= 0x3C01; - } - return roundAndPackFloat64( aSign, aExp, aSig0 ); - -} - -#ifdef FLOATX80 - -/*---------------------------------------------------------------------------- -| Returns the result of converting the quadruple-precision floating-point -| value `a' to the extended double-precision floating-point format. The -| conversion is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -floatx80 float128_to_floatx80( float128 a ) -{ - flag aSign; - int32 aExp; - bits64 aSig0, aSig1; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) { - return commonNaNToFloatx80( float128ToCommonNaN( a ) ); - } - return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( aExp == 0 ) { - if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); - normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); - } - else { - aSig0 |= LIT64( 0x0001000000000000 ); - } - shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); - return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 ); - -} - -#endif - -/*---------------------------------------------------------------------------- -| Rounds the quadruple-precision floating-point value `a' to an integer, and -| returns the result as a quadruple-precision floating-point value. The -| operation is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_round_to_int( float128 a ) -{ - flag aSign; - int32 aExp; - bits64 lastBitMask, roundBitsMask; - int8 roundingMode; - float128 z; - - aExp = extractFloat128Exp( a ); - if ( 0x402F <= aExp ) { - if ( 0x406F <= aExp ) { - if ( ( aExp == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) - ) { - return propagateFloat128NaN( a, a ); - } - return a; - } - lastBitMask = 1; - lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; - roundBitsMask = lastBitMask - 1; - z = a; - roundingMode = float_rounding_mode; - if ( roundingMode == float_round_nearest_even ) { - if ( lastBitMask ) { - add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); - if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; - } - else { - if ( (sbits64) z.low < 0 ) { - ++z.high; - if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1; - } - } - } - else if ( roundingMode != float_round_to_zero ) { - if ( extractFloat128Sign( z ) - ^ ( roundingMode == float_round_up ) ) { - add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low ); - } - } - z.low &= ~ roundBitsMask; - } - else { - if ( aExp < 0x3FFF ) { - if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a; - float_exception_flags |= float_flag_inexact; - aSign = extractFloat128Sign( a ); - switch ( float_rounding_mode ) { - case float_round_nearest_even: - if ( ( aExp == 0x3FFE ) - && ( extractFloat128Frac0( a ) - | extractFloat128Frac1( a ) ) - ) { - return packFloat128( aSign, 0x3FFF, 0, 0 ); - } - break; - case float_round_down: - return - aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) - : packFloat128( 0, 0, 0, 0 ); - case float_round_up: - return - aSign ? packFloat128( 1, 0, 0, 0 ) - : packFloat128( 0, 0x3FFF, 0, 0 ); - } - return packFloat128( aSign, 0, 0, 0 ); - } - lastBitMask = 1; - lastBitMask <<= 0x402F - aExp; - roundBitsMask = lastBitMask - 1; - z.low = 0; - z.high = a.high; - roundingMode = float_rounding_mode; - if ( roundingMode == float_round_nearest_even ) { - z.high += lastBitMask>>1; - if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { - z.high &= ~ lastBitMask; - } - } - else if ( roundingMode != float_round_to_zero ) { - if ( extractFloat128Sign( z ) - ^ ( roundingMode == float_round_up ) ) { - z.high |= ( a.low != 0 ); - z.high += roundBitsMask; - } - } - z.high &= ~ roundBitsMask; - } - if ( ( z.low != a.low ) || ( z.high != a.high ) ) { - float_exception_flags |= float_flag_inexact; - } - return z; - -} - -/*---------------------------------------------------------------------------- -| Returns the result of adding the absolute values of the quadruple-precision -| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated -| before being returned. `zSign' is ignored if the result is a NaN. -| The addition is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -static float128 addFloat128Sigs( float128 a, float128 b, flag zSign ) -{ - int32 aExp, bExp, zExp; - bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; - int32 expDiff; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - bSig1 = extractFloat128Frac1( b ); - bSig0 = extractFloat128Frac0( b ); - bExp = extractFloat128Exp( b ); - expDiff = aExp - bExp; - if ( 0 < expDiff ) { - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - --expDiff; - } - else { - bSig0 |= LIT64( 0x0001000000000000 ); - } - shift128ExtraRightJamming( - bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); - zExp = aExp; - } - else if ( expDiff < 0 ) { - if ( bExp == 0x7FFF ) { - if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b ); - return packFloat128( zSign, 0x7FFF, 0, 0 ); - } - if ( aExp == 0 ) { - ++expDiff; - } - else { - aSig0 |= LIT64( 0x0001000000000000 ); - } - shift128ExtraRightJamming( - aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); - zExp = bExp; - } - else { - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 | bSig0 | bSig1 ) { - return propagateFloat128NaN( a, b ); - } - return a; - } - add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); - if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 ); - zSig2 = 0; - zSig0 |= LIT64( 0x0002000000000000 ); - zExp = aExp; - goto shiftRight1; - } - aSig0 |= LIT64( 0x0001000000000000 ); - add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); - --zExp; - if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; - ++zExp; - shiftRight1: - shift128ExtraRightJamming( - zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); - roundAndPack: - return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of subtracting the absolute values of the quadruple- -| precision floating-point values `a' and `b'. If `zSign' is 1, the -| difference is negated before being returned. `zSign' is ignored if the -| result is a NaN. The subtraction is performed according to the IEC/IEEE -| Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -static float128 subFloat128Sigs( float128 a, float128 b, flag zSign ) -{ - int32 aExp, bExp, zExp; - bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; - int32 expDiff; - float128 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - bSig1 = extractFloat128Frac1( b ); - bSig0 = extractFloat128Frac0( b ); - bExp = extractFloat128Exp( b ); - expDiff = aExp - bExp; - shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); - shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); - if ( 0 < expDiff ) goto aExpBigger; - if ( expDiff < 0 ) goto bExpBigger; - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 | bSig0 | bSig1 ) { - return propagateFloat128NaN( a, b ); - } - float_raise( float_flag_invalid ); - z.low = float128_default_nan_low; - z.high = float128_default_nan_high; - return z; - } - if ( aExp == 0 ) { - aExp = 1; - bExp = 1; - } - if ( bSig0 < aSig0 ) goto aBigger; - if ( aSig0 < bSig0 ) goto bBigger; - if ( bSig1 < aSig1 ) goto aBigger; - if ( aSig1 < bSig1 ) goto bBigger; - return packFloat128( float_rounding_mode == float_round_down, 0, 0, 0 ); - bExpBigger: - if ( bExp == 0x7FFF ) { - if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b ); - return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); - } - if ( aExp == 0 ) { - ++expDiff; - } - else { - aSig0 |= LIT64( 0x4000000000000000 ); - } - shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); - bSig0 |= LIT64( 0x4000000000000000 ); - bBigger: - sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); - zExp = bExp; - zSign ^= 1; - goto normalizeRoundAndPack; - aExpBigger: - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - --expDiff; - } - else { - bSig0 |= LIT64( 0x4000000000000000 ); - } - shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); - aSig0 |= LIT64( 0x4000000000000000 ); - aBigger: - sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); - zExp = aExp; - normalizeRoundAndPack: - --zExp; - return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of adding the quadruple-precision floating-point values -| `a' and `b'. The operation is performed according to the IEC/IEEE Standard -| for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_add( float128 a, float128 b ) -{ - flag aSign, bSign; - - aSign = extractFloat128Sign( a ); - bSign = extractFloat128Sign( b ); - if ( aSign == bSign ) { - return addFloat128Sigs( a, b, aSign ); - } - else { - return subFloat128Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| Returns the result of subtracting the quadruple-precision floating-point -| values `a' and `b'. The operation is performed according to the IEC/IEEE -| Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_sub( float128 a, float128 b ) -{ - flag aSign, bSign; - - aSign = extractFloat128Sign( a ); - bSign = extractFloat128Sign( b ); - if ( aSign == bSign ) { - return subFloat128Sigs( a, b, aSign ); - } - else { - return addFloat128Sigs( a, b, aSign ); - } - -} - -/*---------------------------------------------------------------------------- -| Returns the result of multiplying the quadruple-precision floating-point -| values `a' and `b'. The operation is performed according to the IEC/IEEE -| Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_mul( float128 a, float128 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, zExp; - bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; - float128 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - bSig1 = extractFloat128Frac1( b ); - bSig0 = extractFloat128Frac0( b ); - bExp = extractFloat128Exp( b ); - bSign = extractFloat128Sign( b ); - zSign = aSign ^ bSign; - if ( aExp == 0x7FFF ) { - if ( ( aSig0 | aSig1 ) - || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { - return propagateFloat128NaN( a, b ); - } - if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; - return packFloat128( zSign, 0x7FFF, 0, 0 ); - } - if ( bExp == 0x7FFF ) { - if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b ); - if ( ( aExp | aSig0 | aSig1 ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = float128_default_nan_low; - z.high = float128_default_nan_high; - return z; - } - return packFloat128( zSign, 0x7FFF, 0, 0 ); - } - if ( aExp == 0 ) { - if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); - normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); - } - if ( bExp == 0 ) { - if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); - normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); - } - zExp = aExp + bExp - 0x4000; - aSig0 |= LIT64( 0x0001000000000000 ); - shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); - mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); - add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); - zSig2 |= ( zSig3 != 0 ); - if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { - shift128ExtraRightJamming( - zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); - ++zExp; - } - return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the result of dividing the quadruple-precision floating-point value -| `a' by the corresponding value `b'. The operation is performed according to -| the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_div( float128 a, float128 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, zExp; - bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; - bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; - float128 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - bSig1 = extractFloat128Frac1( b ); - bSig0 = extractFloat128Frac0( b ); - bExp = extractFloat128Exp( b ); - bSign = extractFloat128Sign( b ); - zSign = aSign ^ bSign; - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b ); - if ( bExp == 0x7FFF ) { - if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b ); - goto invalid; - } - return packFloat128( zSign, 0x7FFF, 0, 0 ); - } - if ( bExp == 0x7FFF ) { - if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b ); - return packFloat128( zSign, 0, 0, 0 ); - } - if ( bExp == 0 ) { - if ( ( bSig0 | bSig1 ) == 0 ) { - if ( ( aExp | aSig0 | aSig1 ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = float128_default_nan_low; - z.high = float128_default_nan_high; - return z; - } - float_raise( float_flag_divbyzero ); - return packFloat128( zSign, 0x7FFF, 0, 0 ); - } - normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); - } - if ( aExp == 0 ) { - if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); - normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); - } - zExp = aExp - bExp + 0x3FFD; - shortShift128Left( - aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); - shortShift128Left( - bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); - if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { - shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); - ++zExp; - } - zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); - mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); - sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); - while ( (sbits64) rem0 < 0 ) { - --zSig0; - add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); - } - zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); - if ( ( zSig1 & 0x3FFF ) <= 4 ) { - mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); - sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); - while ( (sbits64) rem1 < 0 ) { - --zSig1; - add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); - } - zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); - } - shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); - return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the remainder of the quadruple-precision floating-point value `a' -| with respect to the corresponding value `b'. The operation is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_rem( float128 a, float128 b ) -{ - flag aSign, zSign; - int32 aExp, bExp, expDiff; - bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; - bits64 allZero, alternateASig0, alternateASig1, sigMean1; - sbits64 sigMean0; - float128 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - bSig1 = extractFloat128Frac1( b ); - bSig0 = extractFloat128Frac0( b ); - bExp = extractFloat128Exp( b ); -// bSign = extractFloat128Sign( b ); - if ( aExp == 0x7FFF ) { - if ( ( aSig0 | aSig1 ) - || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { - return propagateFloat128NaN( a, b ); - } - goto invalid; - } - if ( bExp == 0x7FFF ) { - if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - if ( ( bSig0 | bSig1 ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = float128_default_nan_low; - z.high = float128_default_nan_high; - return z; - } - normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); - } - if ( aExp == 0 ) { - if ( ( aSig0 | aSig1 ) == 0 ) return a; - normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); - } - expDiff = aExp - bExp; - if ( expDiff < -1 ) return a; - shortShift128Left( - aSig0 | LIT64( 0x0001000000000000 ), - aSig1, - 15 - ( expDiff < 0 ), - &aSig0, - &aSig1 - ); - shortShift128Left( - bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); - q = le128( bSig0, bSig1, aSig0, aSig1 ); - if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); - expDiff -= 64; - while ( 0 < expDiff ) { - q = estimateDiv128To64( aSig0, aSig1, bSig0 ); - q = ( 4 < q ) ? q - 4 : 0; - mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); - shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); - shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); - sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); - expDiff -= 61; - } - if ( -64 < expDiff ) { - q = estimateDiv128To64( aSig0, aSig1, bSig0 ); - q = ( 4 < q ) ? q - 4 : 0; - q >>= - expDiff; - shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); - expDiff += 52; - if ( expDiff < 0 ) { - shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); - } - else { - shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); - } - mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); - sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); - } - else { - shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); - shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); - } - do { - alternateASig0 = aSig0; - alternateASig1 = aSig1; - ++q; - sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); - } while ( 0 <= (sbits64) aSig0 ); - add128( - aSig0, aSig1, alternateASig0, alternateASig1, (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 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the square root of the quadruple-precision floating-point value `a'. -| The operation is performed according to the IEC/IEEE Standard for Binary -| Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -float128 float128_sqrt( float128 a ) -{ - flag aSign; - int32 aExp, zExp; - bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; - bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; - float128 z; - - aSig1 = extractFloat128Frac1( a ); - aSig0 = extractFloat128Frac0( a ); - aExp = extractFloat128Exp( a ); - aSign = extractFloat128Sign( a ); - if ( aExp == 0x7FFF ) { - if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a ); - if ( ! aSign ) return a; - goto invalid; - } - if ( aSign ) { - if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; - invalid: - float_raise( float_flag_invalid ); - z.low = float128_default_nan_low; - z.high = float128_default_nan_high; - return z; - } - if ( aExp == 0 ) { - if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); - normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); - } - zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; - aSig0 |= LIT64( 0x0001000000000000 ); - zSig0 = estimateSqrt32( aExp, aSig0>>17 ); - shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); - zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); - doubleZSig0 = zSig0<<1; - mul64To128( zSig0, zSig0, &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); - while ( (sbits64) rem0 < 0 ) { - --zSig0; - doubleZSig0 -= 2; - add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); - } - zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); - if ( ( zSig1 & 0x1FFF ) <= 5 ) { - if ( zSig1 == 0 ) zSig1 = 1; - mul64To128( doubleZSig0, zSig1, &term1, &term2 ); - sub128( rem1, 0, term1, term2, &rem1, &rem2 ); - mul64To128( zSig1, zSig1, &term2, &term3 ); - sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); - while ( (sbits64) rem1 < 0 ) { - --zSig1; - shortShift128Left( 0, zSig1, 1, &term2, &term3 ); - term3 |= 1; - term2 |= doubleZSig0; - add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); - } - zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); - } - shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); - return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the quadruple-precision floating-point value `a' is equal to -| the corresponding value `b', and 0 otherwise. The comparison is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float128_eq( float128 a, float128 b ) -{ - if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) - || ( ( extractFloat128Exp( b ) == 0x7FFF ) - && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) - ) { - if ( float128_is_signaling_nan( a ) - || float128_is_signaling_nan( b ) ) { - float_raise( float_flag_invalid ); - } - return 0; - } - return - ( a.low == b.low ) - && ( ( a.high == b.high ) - || ( ( a.low == 0 ) - && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) - ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the quadruple-precision floating-point value `a' is less than -| or equal to the corresponding value `b', and 0 otherwise. The comparison -| is performed according to the IEC/IEEE Standard for Binary Floating-Point -| Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float128_le( float128 a, float128 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) - || ( ( extractFloat128Exp( b ) == 0x7FFF ) - && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloat128Sign( a ); - bSign = extractFloat128Sign( b ); - if ( aSign != bSign ) { - return - aSign - || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - == 0 ); - } - return - aSign ? le128( b.high, b.low, a.high, a.low ) - : le128( a.high, a.low, b.high, b.low ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the quadruple-precision floating-point value `a' is less than -| the corresponding value `b', and 0 otherwise. The comparison is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float128_lt( float128 a, float128 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) - || ( ( extractFloat128Exp( b ) == 0x7FFF ) - && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - aSign = extractFloat128Sign( a ); - bSign = extractFloat128Sign( b ); - if ( aSign != bSign ) { - return - aSign - && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - != 0 ); - } - return - aSign ? lt128( b.high, b.low, a.high, a.low ) - : lt128( a.high, a.low, b.high, b.low ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the quadruple-precision floating-point value `a' is equal to -| the corresponding value `b', and 0 otherwise. The invalid exception is -| raised if either operand is a NaN. Otherwise, the comparison is performed -| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float128_eq_signaling( float128 a, float128 b ) -{ - if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) - || ( ( extractFloat128Exp( b ) == 0x7FFF ) - && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) - ) { - float_raise( float_flag_invalid ); - return 0; - } - return - ( a.low == b.low ) - && ( ( a.high == b.high ) - || ( ( a.low == 0 ) - && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) - ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the quadruple-precision floating-point value `a' is less than -| or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not -| cause an exception. Otherwise, the comparison is performed according to the -| IEC/IEEE Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float128_le_quiet( float128 a, float128 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) - || ( ( extractFloat128Exp( b ) == 0x7FFF ) - && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) - ) { - if ( float128_is_signaling_nan( a ) - || float128_is_signaling_nan( b ) ) { - float_raise( float_flag_invalid ); - } - return 0; - } - aSign = extractFloat128Sign( a ); - bSign = extractFloat128Sign( b ); - if ( aSign != bSign ) { - return - aSign - || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - == 0 ); - } - return - aSign ? le128( b.high, b.low, a.high, a.low ) - : le128( a.high, a.low, b.high, b.low ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the quadruple-precision floating-point value `a' is less than -| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an -| exception. Otherwise, the comparison is performed according to the IEC/IEEE -| Standard for Binary Floating-Point Arithmetic. -*----------------------------------------------------------------------------*/ - -flag float128_lt_quiet( float128 a, float128 b ) -{ - flag aSign, bSign; - - if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) - && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) - || ( ( extractFloat128Exp( b ) == 0x7FFF ) - && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) - ) { - if ( float128_is_signaling_nan( a ) - || float128_is_signaling_nan( b ) ) { - float_raise( float_flag_invalid ); - } - return 0; - } - aSign = extractFloat128Sign( a ); - bSign = extractFloat128Sign( b ); - if ( aSign != bSign ) { - return - aSign - && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) - != 0 ); - } - return - aSign ? lt128( b.high, b.low, a.high, a.low ) - : lt128( a.high, a.low, b.high, b.low ); - -} - -#endif |