diff options
Diffstat (limited to 'arch/arm26/nwfpe/softfloat.c')
| -rw-r--r-- | arch/arm26/nwfpe/softfloat.c | 3439 |
1 files changed, 0 insertions, 3439 deletions
diff --git a/arch/arm26/nwfpe/softfloat.c b/arch/arm26/nwfpe/softfloat.c deleted file mode 100644 index 26c1b916e527..000000000000 --- a/arch/arm26/nwfpe/softfloat.c +++ /dev/null @@ -1,3439 +0,0 @@ -/* -=============================================================================== - -This C source file is part of the SoftFloat IEC/IEEE Floating-point -Arithmetic Package, Release 2. - -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://HTTP.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 ANY -AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. - -Derivative works are acceptable, even for commercial purposes, so long as -(1) they include prominent notice that the work is derivative, and (2) they -include prominent notice akin to these three paragraphs for those parts of -this code that are retained. - -=============================================================================== -*/ - -#include "fpa11.h" -#include "milieu.h" -#include "softfloat.h" - -/* -------------------------------------------------------------------------------- -Floating-point rounding mode, extended double-precision rounding precision, -and exception flags. -------------------------------------------------------------------------------- -*/ -int8 float_rounding_mode = float_round_nearest_even; -int8 floatx80_rounding_precision = 80; -int8 float_exception_flags; - -/* -------------------------------------------------------------------------------- -Primitive arithmetic functions, including multi-word arithmetic, and -division and square root approximations. (Can be specialized to target if -desired.) -------------------------------------------------------------------------------- -*/ -#include "softfloat-macros" - -/* -------------------------------------------------------------------------------- -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 nonzero, 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. If the fixed-point -input is too large, however, 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_exception_flags |= float_flag_invalid; - return zSign ? 0x80000000 : 0x7FFFFFFF; - } - if ( roundBits ) 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 ) -{ -#if 0 - float32 f; - __asm__("@ packFloat32; \n\ - mov %0, %1, asl #31; \n\ - orr %0, %2, asl #23; \n\ - orr %0, %3" - : /* no outputs */ - : "g" (f), "g" (zSign), "g" (zExp), "g" (zSig) - : "cc"); - return f; -#else - return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig; -#endif -} - -/* -------------------------------------------------------------------------------- -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. If the abstract value is too large, however, 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 in -any way. In all cases, `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. If the abstract value is too large, however, 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 ) ) - ) { - //register int lr = __builtin_return_address(0); - //printk("roundAndPackFloat64 called from 0x%08x\n",lr); - 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 in -any way. In all cases, `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 - -/* -------------------------------------------------------------------------------- -Returns the fraction bits of the extended double-precision floating-point -value `a'. -------------------------------------------------------------------------------- -*/ -INLINE bits64 extractFloatx80Frac( floatx80 a ) -{ - - return a.low; - -} - -/* -------------------------------------------------------------------------------- -Returns the exponent bits of the extended double-precision floating-point -value `a'. -------------------------------------------------------------------------------- -*/ -INLINE int32 extractFloatx80Exp( floatx80 a ) -{ - - return a.high & 0x7FFF; - -} - -/* -------------------------------------------------------------------------------- -Returns the sign bit of the extended double-precision floating-point value -`a'. -------------------------------------------------------------------------------- -*/ -INLINE flag extractFloatx80Sign( floatx80 a ) -{ - - return a.high>>15; - -} - -/* -------------------------------------------------------------------------------- -Normalizes the subnormal extended double-precision floating-point value -represented by the denormalized significand `aSig'. The normalized exponent -and significand are stored at the locations pointed to by `zExpPtr' and -`zSigPtr', respectively. -------------------------------------------------------------------------------- -*/ -static void - normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr ) -{ - int8 shiftCount; - - shiftCount = countLeadingZeros64( aSig ); - *zSigPtr = aSig<<shiftCount; - *zExpPtr = 1 - shiftCount; - -} - -/* -------------------------------------------------------------------------------- -Packs the sign `zSign', exponent `zExp', and significand `zSig' into an -extended double-precision floating-point value, returning the result. -------------------------------------------------------------------------------- -*/ -INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig ) -{ - floatx80 z; - - z.low = zSig; - z.high = ( ( (bits16) zSign )<<15 ) + zExp; - return z; - -} - -/* -------------------------------------------------------------------------------- -Takes an abstract floating-point value having sign `zSign', exponent `zExp', -and extended significand formed by the concatenation of `zSig0' and `zSig1', -and returns the proper extended double-precision floating-point value -corresponding to the abstract input. Ordinarily, the abstract value is -rounded and packed into the extended double-precision format, with the -inexact exception raised if the abstract input cannot be represented -exactly. If the abstract value is too large, however, the overflow and -inexact exceptions are raised and an infinity or maximal finite value is -returned. If the abstract value is too small, the input value is rounded to -a subnormal number, and the underflow and inexact exceptions are raised if -the abstract input cannot be represented exactly as a subnormal extended -double-precision floating-point number. - If `roundingPrecision' is 32 or 64, the result is rounded to the same -number of bits as single or double precision, respectively. Otherwise, the -result is rounded to the full precision of the extended double-precision -format. - The input significand must be normalized or smaller. If the input -significand is not normalized, `zExp' must be 0; in that case, the result -returned is a subnormal number, and it must not require rounding. The -handling of underflow and overflow follows the IEC/IEEE Standard for Binary -Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -static floatx80 - roundAndPackFloatx80( - int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 - ) -{ - 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 &= ~ ( ( zSig1 + zSig1 == 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 &= ~ ( ( zSig1 + zSig1 == 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 - -/* -------------------------------------------------------------------------------- -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 == 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 aSign; - uint32 absA; - int8 shiftCount; - bits64 zSig; - - if ( a == 0 ) return 0; - aSign = ( a < 0 ); - absA = aSign ? - a : a; - shiftCount = countLeadingZeros32( absA ) + 21; - zSig = absA; - return packFloat64( aSign, 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 - -/* -------------------------------------------------------------------------------- -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 zSig; - - aSig = extractFloat32Frac( a ); - aExp = extractFloat32Exp( a ); - aSign = extractFloat32Sign( a ); - if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; - if ( aExp ) aSig |= 0x00800000; - shiftCount = 0xAF - aExp; - zSig = aSig; - zSig <<= 32; - if ( 0 < shiftCount ) shift64RightJamming( zSig, shiftCount, &zSig ); - return roundAndPackInt32( aSign, zSig ); - -} - -/* -------------------------------------------------------------------------------- -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 ) return 0x80000000; - float_raise( float_flag_invalid ); - if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; - return 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; - } - return aSign ? - z : 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 - -/* -------------------------------------------------------------------------------- -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 true, 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 true, 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, bSign, 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 = 0xFFFFFFFF; - } - else { - 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 ); - 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 ); - shiftCount = 0x433 - aExp; - if ( shiftCount < 21 ) { - if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; - goto invalid; - } - else if ( 52 < shiftCount ) { - if ( aExp || aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - aSig |= LIT64( 0x0010000000000000 ); - savedASig = aSig; - aSig >>= shiftCount; - z = aSig; - if ( aSign ) z = - z; - if ( ( z < 0 ) ^ aSign ) { - invalid: - float_exception_flags |= float_flag_invalid; - return aSign ? 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 32-bit two's complement unsigned 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 positive integer is returned. -------------------------------------------------------------------------------- -*/ -int32 float64_to_uint32( float64 a ) -{ - flag aSign; - int16 aExp, shiftCount; - bits64 aSig; - - aSig = extractFloat64Frac( a ); - aExp = extractFloat64Exp( a ); - aSign = 0; //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 positive integer is returned. -------------------------------------------------------------------------------- -*/ -int32 float64_to_uint32_round_to_zero( float64 a ) -{ - flag aSign; - int16 aExp, shiftCount; - bits64 aSig, savedASig; - int32 z; - - aSig = extractFloat64Frac( a ); - aExp = extractFloat64Exp( a ); - aSign = extractFloat64Sign( a ); - shiftCount = 0x433 - aExp; - if ( shiftCount < 21 ) { - if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; - goto invalid; - } - else if ( 52 < shiftCount ) { - if ( aExp || aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - aSig |= LIT64( 0x0010000000000000 ); - savedASig = aSig; - aSig >>= shiftCount; - z = aSig; - if ( aSign ) z = - z; - if ( ( z < 0 ) ^ aSign ) { - invalid: - float_exception_flags |= float_flag_invalid; - return aSign ? 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 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 - -/* -------------------------------------------------------------------------------- -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 <= 0x3FE ) { - 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 true, 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 true, 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, bSign, 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; - bits64 rem0, rem1, term0, term1; //, shiftedRem; - //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 ); - zSig <<= 31; - aSig <<= 9 - ( aExp & 1 ); - zSig = estimateDiv128To64( aSig, 0, zSig ) + zSig + 2; - if ( ( zSig & 0x3FF ) <= 5 ) { - if ( zSig < 2 ) { - zSig = LIT64( 0xFFFFFFFFFFFFFFFF ); - } - else { - aSig <<= 2; - mul64To128( zSig, zSig, &term0, &term1 ); - sub128( aSig, 0, term0, term1, &rem0, &rem1 ); - while ( (sbits64) rem0 < 0 ) { - --zSig; - shortShift128Left( 0, zSig, 1, &term0, &term1 ); - term1 |= 1; - add128( rem0, rem1, term0, term1, &rem0, &rem1 ); - } - zSig |= ( ( rem0 | rem1 ) != 0 ); - } - } - shift64RightJamming( zSig, 1, &zSig ); - 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 ); - shiftCount = 0x403E - aExp; - if ( shiftCount < 32 ) { - if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; - goto invalid; - } - else if ( 63 < shiftCount ) { - if ( aExp || aSig ) float_exception_flags |= float_flag_inexact; - return 0; - } - savedASig = aSig; - aSig >>= shiftCount; - z = aSig; - if ( aSign ) z = - z; - if ( ( z < 0 ) ^ aSign ) { - invalid: - float_exception_flags |= float_flag_invalid; - return aSign ? 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 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 ); - -} - -/* -------------------------------------------------------------------------------- -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 <= 0x3FFE ) { - 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 true, 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 true, -the difference is negated before being returned. `zSign' is ignored if the -result is a NaN. The subtraction is performed according to the IEC/IEEE -Standard for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign ) -{ - int32 aExp, bExp, zExp; - bits64 aSig, bSig, zSig0, zSig1; - int32 expDiff; - floatx80 z; - - aSig = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - expDiff = aExp - bExp; - if ( 0 < expDiff ) goto aExpBigger; - if ( expDiff < 0 ) goto bExpBigger; - if ( aExp == 0x7FFF ) { - if ( (bits64) ( ( aSig | bSig )<<1 ) ) { - return propagateFloatx80NaN( a, b ); - } - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - if ( aExp == 0 ) { - aExp = 1; - bExp = 1; - } - zSig1 = 0; - if ( bSig < aSig ) goto aBigger; - if ( aSig < bSig ) goto bBigger; - return packFloatx80( float_rounding_mode == float_round_down, 0, 0 ); - bExpBigger: - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( aExp == 0 ) ++expDiff; - shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); - bBigger: - sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); - zExp = bExp; - zSign ^= 1; - goto normalizeRoundAndPack; - aExpBigger: - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return a; - } - if ( bExp == 0 ) --expDiff; - shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); - aBigger: - sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); - zExp = aExp; - normalizeRoundAndPack: - return - normalizeRoundAndPackFloatx80( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/* -------------------------------------------------------------------------------- -Returns the result of adding the extended double-precision floating-point -values `a' and `b'. The operation is performed according to the IEC/IEEE -Standard for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -floatx80 floatx80_add( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign == bSign ) { - return addFloatx80Sigs( a, b, aSign ); - } - else { - return subFloatx80Sigs( a, b, aSign ); - } - -} - -/* -------------------------------------------------------------------------------- -Returns the result of subtracting the extended double-precision floating- -point values `a' and `b'. The operation is performed according to the -IEC/IEEE Standard for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -floatx80 floatx80_sub( floatx80 a, floatx80 b ) -{ - flag aSign, bSign; - - aSign = extractFloatx80Sign( a ); - bSign = extractFloatx80Sign( b ); - if ( aSign == bSign ) { - return subFloatx80Sigs( a, b, aSign ); - } - else { - return addFloatx80Sigs( a, b, aSign ); - } - -} - -/* -------------------------------------------------------------------------------- -Returns the result of multiplying the extended double-precision floating- -point values `a' and `b'. The operation is performed according to the -IEC/IEEE Standard for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -floatx80 floatx80_mul( floatx80 a, floatx80 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, zExp; - bits64 aSig, bSig, zSig0, zSig1; - floatx80 z; - - aSig = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - bSign = extractFloatx80Sign( b ); - zSign = aSign ^ bSign; - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig<<1 ) - || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { - return propagateFloatx80NaN( a, b ); - } - if ( ( bExp | bSig ) == 0 ) goto invalid; - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - if ( ( aExp | aSig ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); - normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); - } - if ( bExp == 0 ) { - if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); - normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); - } - zExp = aExp + bExp - 0x3FFE; - mul64To128( aSig, bSig, &zSig0, &zSig1 ); - if ( 0 < (sbits64) zSig0 ) { - shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); - --zExp; - } - return - roundAndPackFloatx80( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/* -------------------------------------------------------------------------------- -Returns the result of dividing the extended double-precision floating-point -value `a' by the corresponding value `b'. The operation is performed -according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -floatx80 floatx80_div( floatx80 a, floatx80 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, zExp; - bits64 aSig, bSig, zSig0, zSig1; - bits64 rem0, rem1, rem2, term0, term1, term2; - floatx80 z; - - aSig = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - bSign = extractFloatx80Sign( b ); - zSign = aSign ^ bSign; - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - goto invalid; - } - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return packFloatx80( zSign, 0, 0 ); - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - if ( ( aExp | aSig ) == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - float_raise( float_flag_divbyzero ); - return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); - } - normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); - } - if ( aExp == 0 ) { - if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); - normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); - } - zExp = aExp - bExp + 0x3FFE; - rem1 = 0; - if ( bSig <= aSig ) { - shift128Right( aSig, 0, 1, &aSig, &rem1 ); - ++zExp; - } - zSig0 = estimateDiv128To64( aSig, rem1, bSig ); - mul64To128( bSig, zSig0, &term0, &term1 ); - sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); - while ( (sbits64) rem0 < 0 ) { - --zSig0; - add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); - } - zSig1 = estimateDiv128To64( rem1, 0, bSig ); - if ( (bits64) ( zSig1<<1 ) <= 8 ) { - mul64To128( bSig, zSig1, &term1, &term2 ); - sub128( rem1, 0, term1, term2, &rem1, &rem2 ); - while ( (sbits64) rem1 < 0 ) { - --zSig1; - add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); - } - zSig1 |= ( ( rem1 | rem2 ) != 0 ); - } - return - roundAndPackFloatx80( - floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 ); - -} - -/* -------------------------------------------------------------------------------- -Returns the remainder of the extended double-precision floating-point value -`a' with respect to the corresponding value `b'. The operation is performed -according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -floatx80 floatx80_rem( floatx80 a, floatx80 b ) -{ - flag aSign, bSign, zSign; - int32 aExp, bExp, expDiff; - bits64 aSig0, aSig1, bSig; - bits64 q, term0, term1, alternateASig0, alternateASig1; - floatx80 z; - - aSig0 = extractFloatx80Frac( a ); - aExp = extractFloatx80Exp( a ); - aSign = extractFloatx80Sign( a ); - bSig = extractFloatx80Frac( b ); - bExp = extractFloatx80Exp( b ); - bSign = extractFloatx80Sign( b ); - if ( aExp == 0x7FFF ) { - if ( (bits64) ( aSig0<<1 ) - || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { - return propagateFloatx80NaN( a, b ); - } - goto invalid; - } - if ( bExp == 0x7FFF ) { - if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); - return a; - } - if ( bExp == 0 ) { - if ( bSig == 0 ) { - invalid: - float_raise( float_flag_invalid ); - z.low = floatx80_default_nan_low; - z.high = floatx80_default_nan_high; - return z; - } - normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); - } - if ( aExp == 0 ) { - if ( (bits64) ( aSig0<<1 ) == 0 ) return a; - normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); - } - bSig |= LIT64( 0x8000000000000000 ); - zSign = aSign; - expDiff = aExp - bExp; - aSig1 = 0; - if ( expDiff < 0 ) { - if ( expDiff < -1 ) return a; - shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); - expDiff = 0; - } - q = ( bSig <= aSig0 ); - if ( q ) aSig0 -= bSig; - expDiff -= 64; - while ( 0 < expDiff ) { - q = estimateDiv128To64( aSig0, aSig1, bSig ); - q = ( 2 < q ) ? q - 2 : 0; - mul64To128( bSig, q, &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); - shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); - expDiff -= 62; - } - expDiff += 64; - if ( 0 < expDiff ) { - q = estimateDiv128To64( aSig0, aSig1, bSig ); - q = ( 2 < q ) ? q - 2 : 0; - q >>= 64 - expDiff; - mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); - shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); - while ( le128( term0, term1, aSig0, aSig1 ) ) { - ++q; - sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); - } - } - else { - term1 = 0; - term0 = bSig; - } - sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); - if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) - || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) - && ( q & 1 ) ) - ) { - aSig0 = alternateASig0; - aSig1 = alternateASig1; - zSign = ! zSign; - } - return - normalizeRoundAndPackFloatx80( - 80, zSign, bExp + expDiff, aSig0, aSig1 ); - -} - -/* -------------------------------------------------------------------------------- -Returns the square root of the extended double-precision floating-point -value `a'. The operation is performed according to the IEC/IEEE Standard -for Binary Floating-point Arithmetic. -------------------------------------------------------------------------------- -*/ -floatx80 floatx80_sqrt( floatx80 a ) -{ - flag aSign; - int32 aExp, zExp; - bits64 aSig0, aSig1, zSig0, zSig1; - bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; - bits64 shiftedRem0, shiftedRem1; - 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 ); - zSig0 <<= 31; - aSig1 = 0; - shift128Right( aSig0, 0, ( aExp & 1 ) + 2, &aSig0, &aSig1 ); - zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0 ) + zSig0 + 4; - if ( 0 <= (sbits64) zSig0 ) zSig0 = LIT64( 0xFFFFFFFFFFFFFFFF ); - shortShift128Left( aSig0, aSig1, 2, &aSig0, &aSig1 ); - mul64To128( zSig0, zSig0, &term0, &term1 ); - sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); - while ( (sbits64) rem0 < 0 ) { - --zSig0; - shortShift128Left( 0, zSig0, 1, &term0, &term1 ); - term1 |= 1; - add128( rem0, rem1, term0, term1, &rem0, &rem1 ); - } - shortShift128Left( rem0, rem1, 63, &shiftedRem0, &shiftedRem1 ); - zSig1 = estimateDiv128To64( shiftedRem0, shiftedRem1, zSig0 ); - if ( (bits64) ( zSig1<<1 ) <= 10 ) { - if ( zSig1 == 0 ) zSig1 = 1; - mul64To128( zSig0, zSig1, &term1, &term2 ); - shortShift128Left( term1, term2, 1, &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; - shortShift192Left( 0, zSig0, zSig1, 1, &term1, &term2, &term3 ); - term3 |= 1; - add192( - rem1, rem2, rem3, term1, term2, term3, &rem1, &rem2, &rem3 ); - } - zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); - } - 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 - |