1031 lines
34 KiB
C
1031 lines
34 KiB
C
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/*
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===============================================================================
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This C source file is part of the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2.
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Written by John R. Hauser. This work was made possible in part by the
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International Computer Science Institute, located at Suite 600, 1947 Center
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Street, Berkeley, California 94704. Funding was partially provided by the
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National Science Foundation under grant MIP-9311980. The original version
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of this code was written as part of a project to build a fixed-point vector
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processor in collaboration with the University of California at Berkeley,
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overseen by Profs. Nelson Morgan and John Wawrzynek. More information
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is available through the web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
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arithmetic/softfloat.html'.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
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has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
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TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
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PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
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AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) they include prominent notice that the work is derivative, and (2) they
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include prominent notice akin to these three paragraphs for those parts of
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this code that are retained.
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===============================================================================
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*/
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#include "milieu.h"
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#include "softfloat.h"
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/*
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-------------------------------------------------------------------------------
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Floating-point rounding mode and exception flags.
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-------------------------------------------------------------------------------
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*/
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int8 float_rounding_mode = float_round_nearest_even;
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int8 float_exception_flags = 0;
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/*
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-------------------------------------------------------------------------------
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Primitive arithmetic functions, including multi-word arithmetic, and
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division and square root approximations. (Can be specialized to target if
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desired.)
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-------------------------------------------------------------------------------
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*/
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#include "softfloat-macros.h"
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/*
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-------------------------------------------------------------------------------
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Functions and definitions to determine: (1) whether tininess for underflow
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is detected before or after rounding by default, (2) what (if anything)
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happens when exceptions are raised, (3) how signaling NaNs are distinguished
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from quiet NaNs, (4) the default generated quiet NaNs, and (4) how NaNs
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are propagated from function inputs to output. These details are target-
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specific.
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-------------------------------------------------------------------------------
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*/
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#include "softfloat-specialize.h"
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/*
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-------------------------------------------------------------------------------
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Returns the fraction bits of the single-precision floating-point value `a'.
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-------------------------------------------------------------------------------
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*/
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INLINE bits32 extractFloat32Frac( float32 a )
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{
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return a & 0x007FFFFF;
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}
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/*
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-------------------------------------------------------------------------------
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Returns the exponent bits of the single-precision floating-point value `a'.
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-------------------------------------------------------------------------------
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*/
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INLINE int16 extractFloat32Exp( float32 a )
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{
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return ( a>>23 ) & 0xFF;
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}
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/*
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-------------------------------------------------------------------------------
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Returns the sign bit of the single-precision floating-point value `a'.
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-------------------------------------------------------------------------------
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*/
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INLINE flag extractFloat32Sign( float32 a )
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{
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return a>>31;
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}
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/*
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-------------------------------------------------------------------------------
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Normalizes the subnormal single-precision floating-point value represented
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by the denormalized significand `aSig'. The normalized exponent and
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significand are stored at the locations pointed to by `zExpPtr' and
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`zSigPtr', respectively.
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-------------------------------------------------------------------------------
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*/
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static void
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normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
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{
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int8 shiftCount;
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shiftCount = countLeadingZeros32( aSig ) - 8;
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*zSigPtr = aSig<<shiftCount;
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*zExpPtr = 1 - shiftCount;
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}
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/*
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-------------------------------------------------------------------------------
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Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
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single-precision floating-point value, returning the result. After being
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shifted into the proper positions, the three fields are simply added
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together to form the result. This means that any integer portion of `zSig'
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will be added into the exponent. Since a properly normalized significand
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will have an integer portion equal to 1, the `zExp' input should be 1 less
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than the desired result exponent whenever `zSig' is a complete, normalized
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significand.
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-------------------------------------------------------------------------------
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*/
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INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
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{
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return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
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}
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/*
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-------------------------------------------------------------------------------
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Takes an abstract floating-point value having sign `zSign', exponent `zExp',
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and significand `zSig', and returns the proper single-precision floating-
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point value corresponding to the abstract input. Ordinarily, the abstract
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value is simply rounded and packed into the single-precision format, with
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the inexact exception raised if the abstract input cannot be represented
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exactly. If the abstract value is too large, however, the overflow and
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inexact exceptions are raised and an infinity or maximal finite value is
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returned. If the abstract value is too small, the input value is rounded to
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a subnormal number, and the underflow and inexact exceptions are raised if
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the abstract input cannot be represented exactly as a subnormal single-
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precision floating-point number.
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The input significand `zSig' has its binary point between bits 30
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and 29, which is 7 bits to the left of the usual location. This shifted
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significand must be normalized or smaller. If `zSig' is not normalized,
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`zExp' must be 0; in that case, the result returned is a subnormal number,
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and it must not require rounding. In the usual case that `zSig' is
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normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
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The handling of underflow and overflow follows the IEC/IEEE Standard for
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Binary Floating-point Arithmetic.
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-------------------------------------------------------------------------------
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*/
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static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
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{
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int8 roundingMode;
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flag roundNearestEven;
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int8 roundIncrement, roundBits;
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flag isTiny;
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roundingMode = float_rounding_mode;
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roundNearestEven = roundingMode == float_round_nearest_even;
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roundIncrement = 0x40;
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if ( ! roundNearestEven ) {
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if ( roundingMode == float_round_to_zero ) {
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roundIncrement = 0;
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}
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else {
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roundIncrement = 0x7F;
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if ( zSign ) {
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if ( roundingMode == float_round_up ) roundIncrement = 0;
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}
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else {
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if ( roundingMode == float_round_down ) roundIncrement = 0;
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}
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}
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}
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roundBits = zSig & 0x7F;
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if ( 0xFD <= (bits16) zExp ) {
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if ( ( 0xFD < zExp )
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|| ( ( zExp == 0xFD )
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&& ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
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) {
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float_raise( float_flag_overflow | float_flag_inexact );
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return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
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}
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if ( zExp < 0 ) {
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isTiny =
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( float_detect_tininess == float_tininess_before_rounding )
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|| ( zExp < -1 )
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|| ( zSig + roundIncrement < 0x80000000 );
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shift32RightJamming( zSig, - zExp, &zSig );
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zExp = 0;
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roundBits = zSig & 0x7F;
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if ( isTiny && roundBits ) float_raise( float_flag_underflow );
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}
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}
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if ( roundBits ) float_exception_flags |= float_flag_inexact;
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zSig = ( zSig + roundIncrement )>>7;
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zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
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if ( zSig == 0 ) zExp = 0;
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return packFloat32( zSign, zExp, zSig );
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}
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/*
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-------------------------------------------------------------------------------
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Takes an abstract floating-point value having sign `zSign', exponent `zExp',
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and significand `zSig', and returns the proper single-precision floating-
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point value corresponding to the abstract input. This routine is just like
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`roundAndPackFloat32' except that `zSig' does not have to be normalized in
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any way. In all cases, `zExp' must be 1 less than the ``true'' floating-
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point exponent.
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-------------------------------------------------------------------------------
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*/
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static float32
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normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
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{
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int8 shiftCount;
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shiftCount = countLeadingZeros32( zSig ) - 1;
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return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount );
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}
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/*
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-------------------------------------------------------------------------------
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Returns the result of converting the 32-bit two's complement integer `a' to
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the single-precision floating-point format. The conversion is performed
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according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
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-------------------------------------------------------------------------------
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*/
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float32 int32_to_float32( int32 a )
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{
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flag zSign;
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if ( a == 0 ) return 0;
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if ( a == 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
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zSign = ( a < 0 );
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return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a );
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}
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/*
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-------------------------------------------------------------------------------
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Returns the result of converting the single-precision floating-point value
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`a' to the 32-bit two's complement integer format. The conversion is
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performed according to the IEC/IEEE Standard for Binary Floating-point
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Arithmetic---which means in particular that the conversion is rounded
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according to the current rounding mode. If `a' is a NaN, the largest
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positive integer is returned. Otherwise, if the conversion overflows, the
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largest integer with the same sign as `a' is returned.
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-------------------------------------------------------------------------------
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*/
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int32 float32_to_int32( float32 a )
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{
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flag aSign;
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int16 aExp, shiftCount;
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bits32 aSig, zExtra;
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int32 z;
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int8 roundingMode;
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aSig = extractFloat32Frac( a );
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aExp = extractFloat32Exp( a );
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aSign = extractFloat32Sign( a );
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shiftCount = aExp - 0x96;
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if ( 0 <= shiftCount ) {
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if ( 0x9E <= aExp ) {
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if ( a == 0xCF000000 ) return 0x80000000;
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float_raise( float_flag_invalid );
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if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
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return 0x80000000;
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}
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z = ( aSig | 0x00800000 )<<shiftCount;
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if ( aSign ) z = - z;
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}
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else {
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if ( aExp < 0x7E ) {
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zExtra = aExp | aSig;
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z = 0;
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}
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else {
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aSig |= 0x00800000;
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zExtra = aSig<<( shiftCount & 31 );
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z = aSig>>( - shiftCount );
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}
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if ( zExtra ) float_exception_flags |= float_flag_inexact;
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roundingMode = float_rounding_mode;
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if ( roundingMode == float_round_nearest_even ) {
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if ( (sbits32) zExtra < 0 ) {
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++z;
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if ( (bits32) ( zExtra<<1 ) == 0 ) z &= ~1;
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}
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if ( aSign ) z = - z;
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}
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else {
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zExtra = ( zExtra != 0 );
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if ( aSign ) {
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z += ( roundingMode == float_round_down ) & zExtra;
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z = - z;
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}
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else {
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z += ( roundingMode == float_round_up ) & zExtra;
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}
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}
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}
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return z;
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}
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/*
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-------------------------------------------------------------------------------
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Returns the result of converting the single-precision floating-point value
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`a' to the 32-bit two's complement integer format. The conversion is
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performed according to the IEC/IEEE Standard for Binary Floating-point
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Arithmetic, except that the conversion is always rounded toward zero. If
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`a' is a NaN, the largest positive integer is returned. Otherwise, if the
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conversion overflows, the largest integer with the same sign as `a' is
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returned.
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-------------------------------------------------------------------------------
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*/
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int32 float32_to_int32_round_to_zero( float32 a )
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{
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flag aSign;
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int16 aExp, shiftCount;
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bits32 aSig;
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int32 z;
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aSig = extractFloat32Frac( a );
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aExp = extractFloat32Exp( a );
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aSign = extractFloat32Sign( a );
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shiftCount = aExp - 0x9E;
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if ( 0 <= shiftCount ) {
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if ( a == 0xCF000000 ) return 0x80000000;
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float_raise( float_flag_invalid );
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if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
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return 0x80000000;
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}
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else if ( aExp <= 0x7E ) {
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if ( aExp | aSig ) float_exception_flags |= float_flag_inexact;
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return 0;
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}
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aSig = ( aSig | 0x00800000 )<<8;
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z = aSig>>( - shiftCount );
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if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
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float_exception_flags |= float_flag_inexact;
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}
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return aSign ? - z : z;
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}
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/*
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-------------------------------------------------------------------------------
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Rounds the single-precision floating-point value `a' to an integer, and
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returns the result as a single-precision floating-point value. The
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operation is performed according to the IEC/IEEE Standard for Binary
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Floating-point Arithmetic.
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-------------------------------------------------------------------------------
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*/
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float32 float32_round_to_int( float32 a )
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{
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flag aSign;
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int16 aExp;
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bits32 lastBitMask, roundBitsMask;
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int8 roundingMode;
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float32 z;
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aExp = extractFloat32Exp( a );
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if ( 0x96 <= aExp ) {
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if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
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return propagateFloat32NaN( a, a );
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}
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return a;
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}
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if ( aExp <= 0x7E ) {
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if ( (bits32) ( a<<1 ) == 0 ) return a;
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float_exception_flags |= float_flag_inexact;
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aSign = extractFloat32Sign( a );
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switch ( float_rounding_mode ) {
|
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case float_round_nearest_even:
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if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
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return packFloat32( aSign, 0x7F, 0 );
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}
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break;
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case float_round_down:
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return aSign ? 0xBF800000 : 0;
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case float_round_up:
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return aSign ? 0x80000000 : 0x3F800000;
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}
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return packFloat32( aSign, 0, 0 );
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}
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lastBitMask = 1;
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lastBitMask <<= 0x96 - aExp;
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roundBitsMask = lastBitMask - 1;
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z = a;
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roundingMode = float_rounding_mode;
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if ( roundingMode == float_round_nearest_even ) {
|
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z += lastBitMask>>1;
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if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
|
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}
|
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else if ( roundingMode != float_round_to_zero ) {
|
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if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
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z += roundBitsMask;
|
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}
|
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}
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z &= ~ roundBitsMask;
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if ( z != a ) float_exception_flags |= float_flag_inexact;
|
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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 );
|
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aExp = extractFloat32Exp( a );
|
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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, zSig0, zSig1;
|
|
|
|
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;
|
|
mul32To64( aSig, bSig, &zSig0, &zSig1 );
|
|
zSig0 |= ( zSig1 != 0 );
|
|
if ( 0 <= (sbits32) ( zSig0<<1 ) ) {
|
|
zSig0 <<= 1;
|
|
--zExp;
|
|
}
|
|
return roundAndPackFloat32( zSign, zExp, zSig0 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
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;
|
|
bits32 rem0, rem1;
|
|
bits32 term0, term1;
|
|
|
|
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 = estimateDiv64To32( aSig, 0, bSig );
|
|
if ( ( zSig & 0x3F ) <= 2 ) {
|
|
mul32To64( bSig, zSig, &term0, &term1 );
|
|
sub64( aSig, 0, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits32) rem0 < 0 ) {
|
|
--zSig;
|
|
add64( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
|
}
|
|
zSig |= ( rem1 != 0 );
|
|
}
|
|
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, 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 = ( aSig | 0x00800000 )<<8;
|
|
bSig = ( bSig | 0x00800000 )<<8;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
aSig >>= 1;
|
|
}
|
|
q = ( bSig <= aSig );
|
|
if ( q ) aSig -= bSig;
|
|
expDiff -= 32;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv64To32( aSig, 0, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
aSig = - ( ( bSig>>2 ) * q );
|
|
expDiff -= 30;
|
|
}
|
|
expDiff += 32;
|
|
if ( 0 < expDiff ) {
|
|
q = estimateDiv64To32( aSig, 0, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
q >>= 32 - expDiff;
|
|
bSig >>= 2;
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
else {
|
|
aSig >>= 2;
|
|
bSig >>= 2;
|
|
}
|
|
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;
|
|
bits32 rem0, rem1;
|
|
bits32 term0, term1;
|
|
|
|
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;
|
|
mul32To64( zSig, zSig, &term0, &term1 );
|
|
sub64( aSig, 0, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits32) rem0 < 0 ) {
|
|
--zSig;
|
|
shortShift64Left( 0, zSig, 1, &term0, &term1 );
|
|
term1 |= 1;
|
|
add64( rem0, rem1, term0, term1, &rem0, &rem1 );
|
|
}
|
|
zSig |= ( ( rem0 | rem1 ) != 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;
|
|
|
|
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 ) );
|
|
|
|
}
|
|
|