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xianfeng |
/*
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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 <asm/div64.h>
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#include "fpa11.h"
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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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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"
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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 (5) 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"
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/*
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-------------------------------------------------------------------------------
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Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
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and 7, and returns the properly rounded 32-bit integer corresponding to the
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input. If `zSign' is nonzero, the input is negated before being converted
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to an integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point
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input is simply rounded to an integer, with the inexact exception raised if
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the input cannot be represented exactly as an integer. If the fixed-point
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input is too large, however, the invalid exception is raised and the largest
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positive or negative integer is returned.
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-------------------------------------------------------------------------------
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*/
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static int32 roundAndPackInt32( struct roundingData *roundData, flag zSign, bits64 absZ )
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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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int32 z;
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roundingMode = roundData->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 = absZ & 0x7F;
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absZ = ( absZ + roundIncrement )>>7;
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absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
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z = absZ;
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if ( zSign ) z = - z;
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if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
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roundData->exception |= float_flag_invalid;
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return zSign ? 0x80000000 : 0x7FFFFFFF;
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}
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if ( roundBits ) roundData->exception |= float_flag_inexact;
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return z;
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}
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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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#if 0 /* in softfloat.h */
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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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#endif
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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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#if 0
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float32 f;
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__asm__("@ packFloat32 \n\
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mov %0, %1, asl #31 \n\
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orr %0, %2, asl #23 \n\
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orr %0, %3"
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: /* no outputs */
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: "g" (f), "g" (zSign), "g" (zExp), "g" (zSig)
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: "cc");
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return f;
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#else
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return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
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#endif
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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( struct roundingData *roundData, 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 = roundData->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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roundData->exception |= 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 ) roundData->exception |= float_flag_underflow;
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}
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}
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if ( roundBits ) roundData->exception |= 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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276 |
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point exponent.
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-------------------------------------------------------------------------------
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*/
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279 |
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static float32
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normalizeRoundAndPackFloat32( struct roundingData *roundData, flag zSign, int16 zExp, bits32 zSig )
|
281 |
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{
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282 |
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int8 shiftCount;
|
283 |
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shiftCount = countLeadingZeros32( zSig ) - 1;
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285 |
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return roundAndPackFloat32( roundData, zSign, zExp - shiftCount, zSig<<shiftCount );
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287 |
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}
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288 |
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289 |
|
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/*
|
290 |
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-------------------------------------------------------------------------------
|
291 |
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Returns the fraction bits of the double-precision floating-point value `a'.
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292 |
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-------------------------------------------------------------------------------
|
293 |
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*/
|
294 |
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INLINE bits64 extractFloat64Frac( float64 a )
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295 |
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{
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296 |
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|
297 |
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return a & LIT64( 0x000FFFFFFFFFFFFF );
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298 |
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299 |
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}
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300 |
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|
301 |
|
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/*
|
302 |
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-------------------------------------------------------------------------------
|
303 |
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Returns the exponent bits of the double-precision floating-point value `a'.
|
304 |
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-------------------------------------------------------------------------------
|
305 |
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*/
|
306 |
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INLINE int16 extractFloat64Exp( float64 a )
|
307 |
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{
|
308 |
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|
309 |
|
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return ( a>>52 ) & 0x7FF;
|
310 |
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|
311 |
|
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}
|
312 |
|
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|
313 |
|
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/*
|
314 |
|
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-------------------------------------------------------------------------------
|
315 |
|
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Returns the sign bit of the double-precision floating-point value `a'.
|
316 |
|
|
-------------------------------------------------------------------------------
|
317 |
|
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*/
|
318 |
|
|
#if 0 /* in softfloat.h */
|
319 |
|
|
INLINE flag extractFloat64Sign( float64 a )
|
320 |
|
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{
|
321 |
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|
|
322 |
|
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return a>>63;
|
323 |
|
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|
324 |
|
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}
|
325 |
|
|
#endif
|
326 |
|
|
|
327 |
|
|
/*
|
328 |
|
|
-------------------------------------------------------------------------------
|
329 |
|
|
Normalizes the subnormal double-precision floating-point value represented
|
330 |
|
|
by the denormalized significand `aSig'. The normalized exponent and
|
331 |
|
|
significand are stored at the locations pointed to by `zExpPtr' and
|
332 |
|
|
`zSigPtr', respectively.
|
333 |
|
|
-------------------------------------------------------------------------------
|
334 |
|
|
*/
|
335 |
|
|
static void
|
336 |
|
|
normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr )
|
337 |
|
|
{
|
338 |
|
|
int8 shiftCount;
|
339 |
|
|
|
340 |
|
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shiftCount = countLeadingZeros64( aSig ) - 11;
|
341 |
|
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*zSigPtr = aSig<<shiftCount;
|
342 |
|
|
*zExpPtr = 1 - shiftCount;
|
343 |
|
|
|
344 |
|
|
}
|
345 |
|
|
|
346 |
|
|
/*
|
347 |
|
|
-------------------------------------------------------------------------------
|
348 |
|
|
Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
|
349 |
|
|
double-precision floating-point value, returning the result. After being
|
350 |
|
|
shifted into the proper positions, the three fields are simply added
|
351 |
|
|
together to form the result. This means that any integer portion of `zSig'
|
352 |
|
|
will be added into the exponent. Since a properly normalized significand
|
353 |
|
|
will have an integer portion equal to 1, the `zExp' input should be 1 less
|
354 |
|
|
than the desired result exponent whenever `zSig' is a complete, normalized
|
355 |
|
|
significand.
|
356 |
|
|
-------------------------------------------------------------------------------
|
357 |
|
|
*/
|
358 |
|
|
INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
|
359 |
|
|
{
|
360 |
|
|
|
361 |
|
|
return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig;
|
362 |
|
|
|
363 |
|
|
}
|
364 |
|
|
|
365 |
|
|
/*
|
366 |
|
|
-------------------------------------------------------------------------------
|
367 |
|
|
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
368 |
|
|
and significand `zSig', and returns the proper double-precision floating-
|
369 |
|
|
point value corresponding to the abstract input. Ordinarily, the abstract
|
370 |
|
|
value is simply rounded and packed into the double-precision format, with
|
371 |
|
|
the inexact exception raised if the abstract input cannot be represented
|
372 |
|
|
exactly. If the abstract value is too large, however, the overflow and
|
373 |
|
|
inexact exceptions are raised and an infinity or maximal finite value is
|
374 |
|
|
returned. If the abstract value is too small, the input value is rounded to
|
375 |
|
|
a subnormal number, and the underflow and inexact exceptions are raised if
|
376 |
|
|
the abstract input cannot be represented exactly as a subnormal double-
|
377 |
|
|
precision floating-point number.
|
378 |
|
|
The input significand `zSig' has its binary point between bits 62
|
379 |
|
|
and 61, which is 10 bits to the left of the usual location. This shifted
|
380 |
|
|
significand must be normalized or smaller. If `zSig' is not normalized,
|
381 |
|
|
`zExp' must be 0; in that case, the result returned is a subnormal number,
|
382 |
|
|
and it must not require rounding. In the usual case that `zSig' is
|
383 |
|
|
normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
|
384 |
|
|
The handling of underflow and overflow follows the IEC/IEEE Standard for
|
385 |
|
|
Binary Floating-point Arithmetic.
|
386 |
|
|
-------------------------------------------------------------------------------
|
387 |
|
|
*/
|
388 |
|
|
static float64 roundAndPackFloat64( struct roundingData *roundData, flag zSign, int16 zExp, bits64 zSig )
|
389 |
|
|
{
|
390 |
|
|
int8 roundingMode;
|
391 |
|
|
flag roundNearestEven;
|
392 |
|
|
int16 roundIncrement, roundBits;
|
393 |
|
|
flag isTiny;
|
394 |
|
|
|
395 |
|
|
roundingMode = roundData->mode;
|
396 |
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
397 |
|
|
roundIncrement = 0x200;
|
398 |
|
|
if ( ! roundNearestEven ) {
|
399 |
|
|
if ( roundingMode == float_round_to_zero ) {
|
400 |
|
|
roundIncrement = 0;
|
401 |
|
|
}
|
402 |
|
|
else {
|
403 |
|
|
roundIncrement = 0x3FF;
|
404 |
|
|
if ( zSign ) {
|
405 |
|
|
if ( roundingMode == float_round_up ) roundIncrement = 0;
|
406 |
|
|
}
|
407 |
|
|
else {
|
408 |
|
|
if ( roundingMode == float_round_down ) roundIncrement = 0;
|
409 |
|
|
}
|
410 |
|
|
}
|
411 |
|
|
}
|
412 |
|
|
roundBits = zSig & 0x3FF;
|
413 |
|
|
if ( 0x7FD <= (bits16) zExp ) {
|
414 |
|
|
if ( ( 0x7FD < zExp )
|
415 |
|
|
|| ( ( zExp == 0x7FD )
|
416 |
|
|
&& ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
|
417 |
|
|
) {
|
418 |
|
|
//register int lr = __builtin_return_address(0);
|
419 |
|
|
//printk("roundAndPackFloat64 called from 0x%08x\n",lr);
|
420 |
|
|
roundData->exception |= float_flag_overflow | float_flag_inexact;
|
421 |
|
|
return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 );
|
422 |
|
|
}
|
423 |
|
|
if ( zExp < 0 ) {
|
424 |
|
|
isTiny =
|
425 |
|
|
( float_detect_tininess == float_tininess_before_rounding )
|
426 |
|
|
|| ( zExp < -1 )
|
427 |
|
|
|| ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
|
428 |
|
|
shift64RightJamming( zSig, - zExp, &zSig );
|
429 |
|
|
zExp = 0;
|
430 |
|
|
roundBits = zSig & 0x3FF;
|
431 |
|
|
if ( isTiny && roundBits ) roundData->exception |= float_flag_underflow;
|
432 |
|
|
}
|
433 |
|
|
}
|
434 |
|
|
if ( roundBits ) roundData->exception |= float_flag_inexact;
|
435 |
|
|
zSig = ( zSig + roundIncrement )>>10;
|
436 |
|
|
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
|
437 |
|
|
if ( zSig == 0 ) zExp = 0;
|
438 |
|
|
return packFloat64( zSign, zExp, zSig );
|
439 |
|
|
|
440 |
|
|
}
|
441 |
|
|
|
442 |
|
|
/*
|
443 |
|
|
-------------------------------------------------------------------------------
|
444 |
|
|
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
445 |
|
|
and significand `zSig', and returns the proper double-precision floating-
|
446 |
|
|
point value corresponding to the abstract input. This routine is just like
|
447 |
|
|
`roundAndPackFloat64' except that `zSig' does not have to be normalized in
|
448 |
|
|
any way. In all cases, `zExp' must be 1 less than the ``true'' floating-
|
449 |
|
|
point exponent.
|
450 |
|
|
-------------------------------------------------------------------------------
|
451 |
|
|
*/
|
452 |
|
|
static float64
|
453 |
|
|
normalizeRoundAndPackFloat64( struct roundingData *roundData, flag zSign, int16 zExp, bits64 zSig )
|
454 |
|
|
{
|
455 |
|
|
int8 shiftCount;
|
456 |
|
|
|
457 |
|
|
shiftCount = countLeadingZeros64( zSig ) - 1;
|
458 |
|
|
return roundAndPackFloat64( roundData, zSign, zExp - shiftCount, zSig<<shiftCount );
|
459 |
|
|
|
460 |
|
|
}
|
461 |
|
|
|
462 |
|
|
#ifdef FLOATX80
|
463 |
|
|
|
464 |
|
|
/*
|
465 |
|
|
-------------------------------------------------------------------------------
|
466 |
|
|
Returns the fraction bits of the extended double-precision floating-point
|
467 |
|
|
value `a'.
|
468 |
|
|
-------------------------------------------------------------------------------
|
469 |
|
|
*/
|
470 |
|
|
INLINE bits64 extractFloatx80Frac( floatx80 a )
|
471 |
|
|
{
|
472 |
|
|
|
473 |
|
|
return a.low;
|
474 |
|
|
|
475 |
|
|
}
|
476 |
|
|
|
477 |
|
|
/*
|
478 |
|
|
-------------------------------------------------------------------------------
|
479 |
|
|
Returns the exponent bits of the extended double-precision floating-point
|
480 |
|
|
value `a'.
|
481 |
|
|
-------------------------------------------------------------------------------
|
482 |
|
|
*/
|
483 |
|
|
INLINE int32 extractFloatx80Exp( floatx80 a )
|
484 |
|
|
{
|
485 |
|
|
|
486 |
|
|
return a.high & 0x7FFF;
|
487 |
|
|
|
488 |
|
|
}
|
489 |
|
|
|
490 |
|
|
/*
|
491 |
|
|
-------------------------------------------------------------------------------
|
492 |
|
|
Returns the sign bit of the extended double-precision floating-point value
|
493 |
|
|
`a'.
|
494 |
|
|
-------------------------------------------------------------------------------
|
495 |
|
|
*/
|
496 |
|
|
INLINE flag extractFloatx80Sign( floatx80 a )
|
497 |
|
|
{
|
498 |
|
|
|
499 |
|
|
return a.high>>15;
|
500 |
|
|
|
501 |
|
|
}
|
502 |
|
|
|
503 |
|
|
/*
|
504 |
|
|
-------------------------------------------------------------------------------
|
505 |
|
|
Normalizes the subnormal extended double-precision floating-point value
|
506 |
|
|
represented by the denormalized significand `aSig'. The normalized exponent
|
507 |
|
|
and significand are stored at the locations pointed to by `zExpPtr' and
|
508 |
|
|
`zSigPtr', respectively.
|
509 |
|
|
-------------------------------------------------------------------------------
|
510 |
|
|
*/
|
511 |
|
|
static void
|
512 |
|
|
normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
|
513 |
|
|
{
|
514 |
|
|
int8 shiftCount;
|
515 |
|
|
|
516 |
|
|
shiftCount = countLeadingZeros64( aSig );
|
517 |
|
|
*zSigPtr = aSig<<shiftCount;
|
518 |
|
|
*zExpPtr = 1 - shiftCount;
|
519 |
|
|
|
520 |
|
|
}
|
521 |
|
|
|
522 |
|
|
/*
|
523 |
|
|
-------------------------------------------------------------------------------
|
524 |
|
|
Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
|
525 |
|
|
extended double-precision floating-point value, returning the result.
|
526 |
|
|
-------------------------------------------------------------------------------
|
527 |
|
|
*/
|
528 |
|
|
INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
|
529 |
|
|
{
|
530 |
|
|
floatx80 z;
|
531 |
|
|
|
532 |
|
|
z.low = zSig;
|
533 |
|
|
z.high = ( ( (bits16) zSign )<<15 ) + zExp;
|
534 |
|
|
z.__padding = 0;
|
535 |
|
|
return z;
|
536 |
|
|
|
537 |
|
|
}
|
538 |
|
|
|
539 |
|
|
/*
|
540 |
|
|
-------------------------------------------------------------------------------
|
541 |
|
|
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
542 |
|
|
and extended significand formed by the concatenation of `zSig0' and `zSig1',
|
543 |
|
|
and returns the proper extended double-precision floating-point value
|
544 |
|
|
corresponding to the abstract input. Ordinarily, the abstract value is
|
545 |
|
|
rounded and packed into the extended double-precision format, with the
|
546 |
|
|
inexact exception raised if the abstract input cannot be represented
|
547 |
|
|
exactly. If the abstract value is too large, however, the overflow and
|
548 |
|
|
inexact exceptions are raised and an infinity or maximal finite value is
|
549 |
|
|
returned. If the abstract value is too small, the input value is rounded to
|
550 |
|
|
a subnormal number, and the underflow and inexact exceptions are raised if
|
551 |
|
|
the abstract input cannot be represented exactly as a subnormal extended
|
552 |
|
|
double-precision floating-point number.
|
553 |
|
|
If `roundingPrecision' is 32 or 64, the result is rounded to the same
|
554 |
|
|
number of bits as single or double precision, respectively. Otherwise, the
|
555 |
|
|
result is rounded to the full precision of the extended double-precision
|
556 |
|
|
format.
|
557 |
|
|
The input significand must be normalized or smaller. If the input
|
558 |
|
|
significand is not normalized, `zExp' must be 0; in that case, the result
|
559 |
|
|
returned is a subnormal number, and it must not require rounding. The
|
560 |
|
|
handling of underflow and overflow follows the IEC/IEEE Standard for Binary
|
561 |
|
|
Floating-point Arithmetic.
|
562 |
|
|
-------------------------------------------------------------------------------
|
563 |
|
|
*/
|
564 |
|
|
static floatx80
|
565 |
|
|
roundAndPackFloatx80(
|
566 |
|
|
struct roundingData *roundData, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
|
567 |
|
|
)
|
568 |
|
|
{
|
569 |
|
|
int8 roundingMode, roundingPrecision;
|
570 |
|
|
flag roundNearestEven, increment, isTiny;
|
571 |
|
|
int64 roundIncrement, roundMask, roundBits;
|
572 |
|
|
|
573 |
|
|
roundingMode = roundData->mode;
|
574 |
|
|
roundingPrecision = roundData->precision;
|
575 |
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
576 |
|
|
if ( roundingPrecision == 80 ) goto precision80;
|
577 |
|
|
if ( roundingPrecision == 64 ) {
|
578 |
|
|
roundIncrement = LIT64( 0x0000000000000400 );
|
579 |
|
|
roundMask = LIT64( 0x00000000000007FF );
|
580 |
|
|
}
|
581 |
|
|
else if ( roundingPrecision == 32 ) {
|
582 |
|
|
roundIncrement = LIT64( 0x0000008000000000 );
|
583 |
|
|
roundMask = LIT64( 0x000000FFFFFFFFFF );
|
584 |
|
|
}
|
585 |
|
|
else {
|
586 |
|
|
goto precision80;
|
587 |
|
|
}
|
588 |
|
|
zSig0 |= ( zSig1 != 0 );
|
589 |
|
|
if ( ! roundNearestEven ) {
|
590 |
|
|
if ( roundingMode == float_round_to_zero ) {
|
591 |
|
|
roundIncrement = 0;
|
592 |
|
|
}
|
593 |
|
|
else {
|
594 |
|
|
roundIncrement = roundMask;
|
595 |
|
|
if ( zSign ) {
|
596 |
|
|
if ( roundingMode == float_round_up ) roundIncrement = 0;
|
597 |
|
|
}
|
598 |
|
|
else {
|
599 |
|
|
if ( roundingMode == float_round_down ) roundIncrement = 0;
|
600 |
|
|
}
|
601 |
|
|
}
|
602 |
|
|
}
|
603 |
|
|
roundBits = zSig0 & roundMask;
|
604 |
|
|
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
|
605 |
|
|
if ( ( 0x7FFE < zExp )
|
606 |
|
|
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
|
607 |
|
|
) {
|
608 |
|
|
goto overflow;
|
609 |
|
|
}
|
610 |
|
|
if ( zExp <= 0 ) {
|
611 |
|
|
isTiny =
|
612 |
|
|
( float_detect_tininess == float_tininess_before_rounding )
|
613 |
|
|
|| ( zExp < 0 )
|
614 |
|
|
|| ( zSig0 <= zSig0 + roundIncrement );
|
615 |
|
|
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
|
616 |
|
|
zExp = 0;
|
617 |
|
|
roundBits = zSig0 & roundMask;
|
618 |
|
|
if ( isTiny && roundBits ) roundData->exception |= float_flag_underflow;
|
619 |
|
|
if ( roundBits ) roundData->exception |= float_flag_inexact;
|
620 |
|
|
zSig0 += roundIncrement;
|
621 |
|
|
if ( (sbits64) zSig0 < 0 ) zExp = 1;
|
622 |
|
|
roundIncrement = roundMask + 1;
|
623 |
|
|
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
|
624 |
|
|
roundMask |= roundIncrement;
|
625 |
|
|
}
|
626 |
|
|
zSig0 &= ~ roundMask;
|
627 |
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
628 |
|
|
}
|
629 |
|
|
}
|
630 |
|
|
if ( roundBits ) roundData->exception |= float_flag_inexact;
|
631 |
|
|
zSig0 += roundIncrement;
|
632 |
|
|
if ( zSig0 < roundIncrement ) {
|
633 |
|
|
++zExp;
|
634 |
|
|
zSig0 = LIT64( 0x8000000000000000 );
|
635 |
|
|
}
|
636 |
|
|
roundIncrement = roundMask + 1;
|
637 |
|
|
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
|
638 |
|
|
roundMask |= roundIncrement;
|
639 |
|
|
}
|
640 |
|
|
zSig0 &= ~ roundMask;
|
641 |
|
|
if ( zSig0 == 0 ) zExp = 0;
|
642 |
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
643 |
|
|
precision80:
|
644 |
|
|
increment = ( (sbits64) zSig1 < 0 );
|
645 |
|
|
if ( ! roundNearestEven ) {
|
646 |
|
|
if ( roundingMode == float_round_to_zero ) {
|
647 |
|
|
increment = 0;
|
648 |
|
|
}
|
649 |
|
|
else {
|
650 |
|
|
if ( zSign ) {
|
651 |
|
|
increment = ( roundingMode == float_round_down ) && zSig1;
|
652 |
|
|
}
|
653 |
|
|
else {
|
654 |
|
|
increment = ( roundingMode == float_round_up ) && zSig1;
|
655 |
|
|
}
|
656 |
|
|
}
|
657 |
|
|
}
|
658 |
|
|
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
|
659 |
|
|
if ( ( 0x7FFE < zExp )
|
660 |
|
|
|| ( ( zExp == 0x7FFE )
|
661 |
|
|
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
|
662 |
|
|
&& increment
|
663 |
|
|
)
|
664 |
|
|
) {
|
665 |
|
|
roundMask = 0;
|
666 |
|
|
overflow:
|
667 |
|
|
roundData->exception |= float_flag_overflow | float_flag_inexact;
|
668 |
|
|
if ( ( roundingMode == float_round_to_zero )
|
669 |
|
|
|| ( zSign && ( roundingMode == float_round_up ) )
|
670 |
|
|
|| ( ! zSign && ( roundingMode == float_round_down ) )
|
671 |
|
|
) {
|
672 |
|
|
return packFloatx80( zSign, 0x7FFE, ~ roundMask );
|
673 |
|
|
}
|
674 |
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
675 |
|
|
}
|
676 |
|
|
if ( zExp <= 0 ) {
|
677 |
|
|
isTiny =
|
678 |
|
|
( float_detect_tininess == float_tininess_before_rounding )
|
679 |
|
|
|| ( zExp < 0 )
|
680 |
|
|
|| ! increment
|
681 |
|
|
|| ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
|
682 |
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
|
683 |
|
|
zExp = 0;
|
684 |
|
|
if ( isTiny && zSig1 ) roundData->exception |= float_flag_underflow;
|
685 |
|
|
if ( zSig1 ) roundData->exception |= float_flag_inexact;
|
686 |
|
|
if ( roundNearestEven ) {
|
687 |
|
|
increment = ( (sbits64) zSig1 < 0 );
|
688 |
|
|
}
|
689 |
|
|
else {
|
690 |
|
|
if ( zSign ) {
|
691 |
|
|
increment = ( roundingMode == float_round_down ) && zSig1;
|
692 |
|
|
}
|
693 |
|
|
else {
|
694 |
|
|
increment = ( roundingMode == float_round_up ) && zSig1;
|
695 |
|
|
}
|
696 |
|
|
}
|
697 |
|
|
if ( increment ) {
|
698 |
|
|
++zSig0;
|
699 |
|
|
zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
|
700 |
|
|
if ( (sbits64) zSig0 < 0 ) zExp = 1;
|
701 |
|
|
}
|
702 |
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
703 |
|
|
}
|
704 |
|
|
}
|
705 |
|
|
if ( zSig1 ) roundData->exception |= float_flag_inexact;
|
706 |
|
|
if ( increment ) {
|
707 |
|
|
++zSig0;
|
708 |
|
|
if ( zSig0 == 0 ) {
|
709 |
|
|
++zExp;
|
710 |
|
|
zSig0 = LIT64( 0x8000000000000000 );
|
711 |
|
|
}
|
712 |
|
|
else {
|
713 |
|
|
zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
|
714 |
|
|
}
|
715 |
|
|
}
|
716 |
|
|
else {
|
717 |
|
|
if ( zSig0 == 0 ) zExp = 0;
|
718 |
|
|
}
|
719 |
|
|
|
720 |
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
721 |
|
|
}
|
722 |
|
|
|
723 |
|
|
/*
|
724 |
|
|
-------------------------------------------------------------------------------
|
725 |
|
|
Takes an abstract floating-point value having sign `zSign', exponent
|
726 |
|
|
`zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
|
727 |
|
|
and returns the proper extended double-precision floating-point value
|
728 |
|
|
corresponding to the abstract input. This routine is just like
|
729 |
|
|
`roundAndPackFloatx80' except that the input significand does not have to be
|
730 |
|
|
normalized.
|
731 |
|
|
-------------------------------------------------------------------------------
|
732 |
|
|
*/
|
733 |
|
|
static floatx80
|
734 |
|
|
normalizeRoundAndPackFloatx80(
|
735 |
|
|
struct roundingData *roundData, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
|
736 |
|
|
)
|
737 |
|
|
{
|
738 |
|
|
int8 shiftCount;
|
739 |
|
|
|
740 |
|
|
if ( zSig0 == 0 ) {
|
741 |
|
|
zSig0 = zSig1;
|
742 |
|
|
zSig1 = 0;
|
743 |
|
|
zExp -= 64;
|
744 |
|
|
}
|
745 |
|
|
shiftCount = countLeadingZeros64( zSig0 );
|
746 |
|
|
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
|
747 |
|
|
zExp -= shiftCount;
|
748 |
|
|
return
|
749 |
|
|
roundAndPackFloatx80( roundData, zSign, zExp, zSig0, zSig1 );
|
750 |
|
|
|
751 |
|
|
}
|
752 |
|
|
|
753 |
|
|
#endif
|
754 |
|
|
|
755 |
|
|
/*
|
756 |
|
|
-------------------------------------------------------------------------------
|
757 |
|
|
Returns the result of converting the 32-bit two's complement integer `a' to
|
758 |
|
|
the single-precision floating-point format. The conversion is performed
|
759 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
760 |
|
|
-------------------------------------------------------------------------------
|
761 |
|
|
*/
|
762 |
|
|
float32 int32_to_float32(struct roundingData *roundData, int32 a)
|
763 |
|
|
{
|
764 |
|
|
flag zSign;
|
765 |
|
|
|
766 |
|
|
if ( a == 0 ) return 0;
|
767 |
|
|
if ( a == 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
|
768 |
|
|
zSign = ( a < 0 );
|
769 |
|
|
return normalizeRoundAndPackFloat32( roundData, zSign, 0x9C, zSign ? - a : a );
|
770 |
|
|
|
771 |
|
|
}
|
772 |
|
|
|
773 |
|
|
/*
|
774 |
|
|
-------------------------------------------------------------------------------
|
775 |
|
|
Returns the result of converting the 32-bit two's complement integer `a' to
|
776 |
|
|
the double-precision floating-point format. The conversion is performed
|
777 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
778 |
|
|
-------------------------------------------------------------------------------
|
779 |
|
|
*/
|
780 |
|
|
float64 int32_to_float64( int32 a )
|
781 |
|
|
{
|
782 |
|
|
flag aSign;
|
783 |
|
|
uint32 absA;
|
784 |
|
|
int8 shiftCount;
|
785 |
|
|
bits64 zSig;
|
786 |
|
|
|
787 |
|
|
if ( a == 0 ) return 0;
|
788 |
|
|
aSign = ( a < 0 );
|
789 |
|
|
absA = aSign ? - a : a;
|
790 |
|
|
shiftCount = countLeadingZeros32( absA ) + 21;
|
791 |
|
|
zSig = absA;
|
792 |
|
|
return packFloat64( aSign, 0x432 - shiftCount, zSig<<shiftCount );
|
793 |
|
|
|
794 |
|
|
}
|
795 |
|
|
|
796 |
|
|
#ifdef FLOATX80
|
797 |
|
|
|
798 |
|
|
/*
|
799 |
|
|
-------------------------------------------------------------------------------
|
800 |
|
|
Returns the result of converting the 32-bit two's complement integer `a'
|
801 |
|
|
to the extended double-precision floating-point format. The conversion
|
802 |
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
803 |
|
|
Arithmetic.
|
804 |
|
|
-------------------------------------------------------------------------------
|
805 |
|
|
*/
|
806 |
|
|
floatx80 int32_to_floatx80( int32 a )
|
807 |
|
|
{
|
808 |
|
|
flag zSign;
|
809 |
|
|
uint32 absA;
|
810 |
|
|
int8 shiftCount;
|
811 |
|
|
bits64 zSig;
|
812 |
|
|
|
813 |
|
|
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
|
814 |
|
|
zSign = ( a < 0 );
|
815 |
|
|
absA = zSign ? - a : a;
|
816 |
|
|
shiftCount = countLeadingZeros32( absA ) + 32;
|
817 |
|
|
zSig = absA;
|
818 |
|
|
return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
|
819 |
|
|
|
820 |
|
|
}
|
821 |
|
|
|
822 |
|
|
#endif
|
823 |
|
|
|
824 |
|
|
/*
|
825 |
|
|
-------------------------------------------------------------------------------
|
826 |
|
|
Returns the result of converting the single-precision floating-point value
|
827 |
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
828 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
829 |
|
|
Arithmetic---which means in particular that the conversion is rounded
|
830 |
|
|
according to the current rounding mode. If `a' is a NaN, the largest
|
831 |
|
|
positive integer is returned. Otherwise, if the conversion overflows, the
|
832 |
|
|
largest integer with the same sign as `a' is returned.
|
833 |
|
|
-------------------------------------------------------------------------------
|
834 |
|
|
*/
|
835 |
|
|
int32 float32_to_int32( struct roundingData *roundData, float32 a )
|
836 |
|
|
{
|
837 |
|
|
flag aSign;
|
838 |
|
|
int16 aExp, shiftCount;
|
839 |
|
|
bits32 aSig;
|
840 |
|
|
bits64 zSig;
|
841 |
|
|
|
842 |
|
|
aSig = extractFloat32Frac( a );
|
843 |
|
|
aExp = extractFloat32Exp( a );
|
844 |
|
|
aSign = extractFloat32Sign( a );
|
845 |
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
846 |
|
|
if ( aExp ) aSig |= 0x00800000;
|
847 |
|
|
shiftCount = 0xAF - aExp;
|
848 |
|
|
zSig = aSig;
|
849 |
|
|
zSig <<= 32;
|
850 |
|
|
if ( 0 < shiftCount ) shift64RightJamming( zSig, shiftCount, &zSig );
|
851 |
|
|
return roundAndPackInt32( roundData, aSign, zSig );
|
852 |
|
|
|
853 |
|
|
}
|
854 |
|
|
|
855 |
|
|
/*
|
856 |
|
|
-------------------------------------------------------------------------------
|
857 |
|
|
Returns the result of converting the single-precision floating-point value
|
858 |
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
859 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
860 |
|
|
Arithmetic, except that the conversion is always rounded toward zero. If
|
861 |
|
|
`a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
862 |
|
|
conversion overflows, the largest integer with the same sign as `a' is
|
863 |
|
|
returned.
|
864 |
|
|
-------------------------------------------------------------------------------
|
865 |
|
|
*/
|
866 |
|
|
int32 float32_to_int32_round_to_zero( float32 a )
|
867 |
|
|
{
|
868 |
|
|
flag aSign;
|
869 |
|
|
int16 aExp, shiftCount;
|
870 |
|
|
bits32 aSig;
|
871 |
|
|
int32 z;
|
872 |
|
|
|
873 |
|
|
aSig = extractFloat32Frac( a );
|
874 |
|
|
aExp = extractFloat32Exp( a );
|
875 |
|
|
aSign = extractFloat32Sign( a );
|
876 |
|
|
shiftCount = aExp - 0x9E;
|
877 |
|
|
if ( 0 <= shiftCount ) {
|
878 |
|
|
if ( a == 0xCF000000 ) return 0x80000000;
|
879 |
|
|
float_raise( float_flag_invalid );
|
880 |
|
|
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
|
881 |
|
|
return 0x80000000;
|
882 |
|
|
}
|
883 |
|
|
else if ( aExp <= 0x7E ) {
|
884 |
|
|
if ( aExp | aSig ) float_raise( float_flag_inexact );
|
885 |
|
|
return 0;
|
886 |
|
|
}
|
887 |
|
|
aSig = ( aSig | 0x00800000 )<<8;
|
888 |
|
|
z = aSig>>( - shiftCount );
|
889 |
|
|
if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
|
890 |
|
|
float_raise( float_flag_inexact );
|
891 |
|
|
}
|
892 |
|
|
return aSign ? - z : z;
|
893 |
|
|
|
894 |
|
|
}
|
895 |
|
|
|
896 |
|
|
/*
|
897 |
|
|
-------------------------------------------------------------------------------
|
898 |
|
|
Returns the result of converting the single-precision floating-point value
|
899 |
|
|
`a' to the double-precision floating-point format. The conversion is
|
900 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
901 |
|
|
Arithmetic.
|
902 |
|
|
-------------------------------------------------------------------------------
|
903 |
|
|
*/
|
904 |
|
|
float64 float32_to_float64( float32 a )
|
905 |
|
|
{
|
906 |
|
|
flag aSign;
|
907 |
|
|
int16 aExp;
|
908 |
|
|
bits32 aSig;
|
909 |
|
|
|
910 |
|
|
aSig = extractFloat32Frac( a );
|
911 |
|
|
aExp = extractFloat32Exp( a );
|
912 |
|
|
aSign = extractFloat32Sign( a );
|
913 |
|
|
if ( aExp == 0xFF ) {
|
914 |
|
|
if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) );
|
915 |
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
916 |
|
|
}
|
917 |
|
|
if ( aExp == 0 ) {
|
918 |
|
|
if ( aSig == 0 ) return packFloat64( aSign, 0, 0 );
|
919 |
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
920 |
|
|
--aExp;
|
921 |
|
|
}
|
922 |
|
|
return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );
|
923 |
|
|
|
924 |
|
|
}
|
925 |
|
|
|
926 |
|
|
#ifdef FLOATX80
|
927 |
|
|
|
928 |
|
|
/*
|
929 |
|
|
-------------------------------------------------------------------------------
|
930 |
|
|
Returns the result of converting the single-precision floating-point value
|
931 |
|
|
`a' to the extended double-precision floating-point format. The conversion
|
932 |
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
933 |
|
|
Arithmetic.
|
934 |
|
|
-------------------------------------------------------------------------------
|
935 |
|
|
*/
|
936 |
|
|
floatx80 float32_to_floatx80( float32 a )
|
937 |
|
|
{
|
938 |
|
|
flag aSign;
|
939 |
|
|
int16 aExp;
|
940 |
|
|
bits32 aSig;
|
941 |
|
|
|
942 |
|
|
aSig = extractFloat32Frac( a );
|
943 |
|
|
aExp = extractFloat32Exp( a );
|
944 |
|
|
aSign = extractFloat32Sign( a );
|
945 |
|
|
if ( aExp == 0xFF ) {
|
946 |
|
|
if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) );
|
947 |
|
|
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
948 |
|
|
}
|
949 |
|
|
if ( aExp == 0 ) {
|
950 |
|
|
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
|
951 |
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
952 |
|
|
}
|
953 |
|
|
aSig |= 0x00800000;
|
954 |
|
|
return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );
|
955 |
|
|
|
956 |
|
|
}
|
957 |
|
|
|
958 |
|
|
#endif
|
959 |
|
|
|
960 |
|
|
/*
|
961 |
|
|
-------------------------------------------------------------------------------
|
962 |
|
|
Rounds the single-precision floating-point value `a' to an integer, and
|
963 |
|
|
returns the result as a single-precision floating-point value. The
|
964 |
|
|
operation is performed according to the IEC/IEEE Standard for Binary
|
965 |
|
|
Floating-point Arithmetic.
|
966 |
|
|
-------------------------------------------------------------------------------
|
967 |
|
|
*/
|
968 |
|
|
float32 float32_round_to_int( struct roundingData *roundData, float32 a )
|
969 |
|
|
{
|
970 |
|
|
flag aSign;
|
971 |
|
|
int16 aExp;
|
972 |
|
|
bits32 lastBitMask, roundBitsMask;
|
973 |
|
|
int8 roundingMode;
|
974 |
|
|
float32 z;
|
975 |
|
|
|
976 |
|
|
aExp = extractFloat32Exp( a );
|
977 |
|
|
if ( 0x96 <= aExp ) {
|
978 |
|
|
if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
|
979 |
|
|
return propagateFloat32NaN( a, a );
|
980 |
|
|
}
|
981 |
|
|
return a;
|
982 |
|
|
}
|
983 |
|
|
roundingMode = roundData->mode;
|
984 |
|
|
if ( aExp <= 0x7E ) {
|
985 |
|
|
if ( (bits32) ( a<<1 ) == 0 ) return a;
|
986 |
|
|
roundData->exception |= float_flag_inexact;
|
987 |
|
|
aSign = extractFloat32Sign( a );
|
988 |
|
|
switch ( roundingMode ) {
|
989 |
|
|
case float_round_nearest_even:
|
990 |
|
|
if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
|
991 |
|
|
return packFloat32( aSign, 0x7F, 0 );
|
992 |
|
|
}
|
993 |
|
|
break;
|
994 |
|
|
case float_round_down:
|
995 |
|
|
return aSign ? 0xBF800000 : 0;
|
996 |
|
|
case float_round_up:
|
997 |
|
|
return aSign ? 0x80000000 : 0x3F800000;
|
998 |
|
|
}
|
999 |
|
|
return packFloat32( aSign, 0, 0 );
|
1000 |
|
|
}
|
1001 |
|
|
lastBitMask = 1;
|
1002 |
|
|
lastBitMask <<= 0x96 - aExp;
|
1003 |
|
|
roundBitsMask = lastBitMask - 1;
|
1004 |
|
|
z = a;
|
1005 |
|
|
if ( roundingMode == float_round_nearest_even ) {
|
1006 |
|
|
z += lastBitMask>>1;
|
1007 |
|
|
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
|
1008 |
|
|
}
|
1009 |
|
|
else if ( roundingMode != float_round_to_zero ) {
|
1010 |
|
|
if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
1011 |
|
|
z += roundBitsMask;
|
1012 |
|
|
}
|
1013 |
|
|
}
|
1014 |
|
|
z &= ~ roundBitsMask;
|
1015 |
|
|
if ( z != a ) roundData->exception |= float_flag_inexact;
|
1016 |
|
|
return z;
|
1017 |
|
|
|
1018 |
|
|
}
|
1019 |
|
|
|
1020 |
|
|
/*
|
1021 |
|
|
-------------------------------------------------------------------------------
|
1022 |
|
|
Returns the result of adding the absolute values of the single-precision
|
1023 |
|
|
floating-point values `a' and `b'. If `zSign' is true, the sum is negated
|
1024 |
|
|
before being returned. `zSign' is ignored if the result is a NaN. The
|
1025 |
|
|
addition is performed according to the IEC/IEEE Standard for Binary
|
1026 |
|
|
Floating-point Arithmetic.
|
1027 |
|
|
-------------------------------------------------------------------------------
|
1028 |
|
|
*/
|
1029 |
|
|
static float32 addFloat32Sigs( struct roundingData *roundData, float32 a, float32 b, flag zSign )
|
1030 |
|
|
{
|
1031 |
|
|
int16 aExp, bExp, zExp;
|
1032 |
|
|
bits32 aSig, bSig, zSig;
|
1033 |
|
|
int16 expDiff;
|
1034 |
|
|
|
1035 |
|
|
aSig = extractFloat32Frac( a );
|
1036 |
|
|
aExp = extractFloat32Exp( a );
|
1037 |
|
|
bSig = extractFloat32Frac( b );
|
1038 |
|
|
bExp = extractFloat32Exp( b );
|
1039 |
|
|
expDiff = aExp - bExp;
|
1040 |
|
|
aSig <<= 6;
|
1041 |
|
|
bSig <<= 6;
|
1042 |
|
|
if ( 0 < expDiff ) {
|
1043 |
|
|
if ( aExp == 0xFF ) {
|
1044 |
|
|
if ( aSig ) return propagateFloat32NaN( a, b );
|
1045 |
|
|
return a;
|
1046 |
|
|
}
|
1047 |
|
|
if ( bExp == 0 ) {
|
1048 |
|
|
--expDiff;
|
1049 |
|
|
}
|
1050 |
|
|
else {
|
1051 |
|
|
bSig |= 0x20000000;
|
1052 |
|
|
}
|
1053 |
|
|
shift32RightJamming( bSig, expDiff, &bSig );
|
1054 |
|
|
zExp = aExp;
|
1055 |
|
|
}
|
1056 |
|
|
else if ( expDiff < 0 ) {
|
1057 |
|
|
if ( bExp == 0xFF ) {
|
1058 |
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
1059 |
|
|
return packFloat32( zSign, 0xFF, 0 );
|
1060 |
|
|
}
|
1061 |
|
|
if ( aExp == 0 ) {
|
1062 |
|
|
++expDiff;
|
1063 |
|
|
}
|
1064 |
|
|
else {
|
1065 |
|
|
aSig |= 0x20000000;
|
1066 |
|
|
}
|
1067 |
|
|
shift32RightJamming( aSig, - expDiff, &aSig );
|
1068 |
|
|
zExp = bExp;
|
1069 |
|
|
}
|
1070 |
|
|
else {
|
1071 |
|
|
if ( aExp == 0xFF ) {
|
1072 |
|
|
if ( aSig | bSig ) return propagateFloat32NaN( a, b );
|
1073 |
|
|
return a;
|
1074 |
|
|
}
|
1075 |
|
|
if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
|
1076 |
|
|
zSig = 0x40000000 + aSig + bSig;
|
1077 |
|
|
zExp = aExp;
|
1078 |
|
|
goto roundAndPack;
|
1079 |
|
|
}
|
1080 |
|
|
aSig |= 0x20000000;
|
1081 |
|
|
zSig = ( aSig + bSig )<<1;
|
1082 |
|
|
--zExp;
|
1083 |
|
|
if ( (sbits32) zSig < 0 ) {
|
1084 |
|
|
zSig = aSig + bSig;
|
1085 |
|
|
++zExp;
|
1086 |
|
|
}
|
1087 |
|
|
roundAndPack:
|
1088 |
|
|
return roundAndPackFloat32( roundData, zSign, zExp, zSig );
|
1089 |
|
|
|
1090 |
|
|
}
|
1091 |
|
|
|
1092 |
|
|
/*
|
1093 |
|
|
-------------------------------------------------------------------------------
|
1094 |
|
|
Returns the result of subtracting the absolute values of the single-
|
1095 |
|
|
precision floating-point values `a' and `b'. If `zSign' is true, the
|
1096 |
|
|
difference is negated before being returned. `zSign' is ignored if the
|
1097 |
|
|
result is a NaN. The subtraction is performed according to the IEC/IEEE
|
1098 |
|
|
Standard for Binary Floating-point Arithmetic.
|
1099 |
|
|
-------------------------------------------------------------------------------
|
1100 |
|
|
*/
|
1101 |
|
|
static float32 subFloat32Sigs( struct roundingData *roundData, float32 a, float32 b, flag zSign )
|
1102 |
|
|
{
|
1103 |
|
|
int16 aExp, bExp, zExp;
|
1104 |
|
|
bits32 aSig, bSig, zSig;
|
1105 |
|
|
int16 expDiff;
|
1106 |
|
|
|
1107 |
|
|
aSig = extractFloat32Frac( a );
|
1108 |
|
|
aExp = extractFloat32Exp( a );
|
1109 |
|
|
bSig = extractFloat32Frac( b );
|
1110 |
|
|
bExp = extractFloat32Exp( b );
|
1111 |
|
|
expDiff = aExp - bExp;
|
1112 |
|
|
aSig <<= 7;
|
1113 |
|
|
bSig <<= 7;
|
1114 |
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
1115 |
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
1116 |
|
|
if ( aExp == 0xFF ) {
|
1117 |
|
|
if ( aSig | bSig ) return propagateFloat32NaN( a, b );
|
1118 |
|
|
roundData->exception |= float_flag_invalid;
|
1119 |
|
|
return float32_default_nan;
|
1120 |
|
|
}
|
1121 |
|
|
if ( aExp == 0 ) {
|
1122 |
|
|
aExp = 1;
|
1123 |
|
|
bExp = 1;
|
1124 |
|
|
}
|
1125 |
|
|
if ( bSig < aSig ) goto aBigger;
|
1126 |
|
|
if ( aSig < bSig ) goto bBigger;
|
1127 |
|
|
return packFloat32( roundData->mode == float_round_down, 0, 0 );
|
1128 |
|
|
bExpBigger:
|
1129 |
|
|
if ( bExp == 0xFF ) {
|
1130 |
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
1131 |
|
|
return packFloat32( zSign ^ 1, 0xFF, 0 );
|
1132 |
|
|
}
|
1133 |
|
|
if ( aExp == 0 ) {
|
1134 |
|
|
++expDiff;
|
1135 |
|
|
}
|
1136 |
|
|
else {
|
1137 |
|
|
aSig |= 0x40000000;
|
1138 |
|
|
}
|
1139 |
|
|
shift32RightJamming( aSig, - expDiff, &aSig );
|
1140 |
|
|
bSig |= 0x40000000;
|
1141 |
|
|
bBigger:
|
1142 |
|
|
zSig = bSig - aSig;
|
1143 |
|
|
zExp = bExp;
|
1144 |
|
|
zSign ^= 1;
|
1145 |
|
|
goto normalizeRoundAndPack;
|
1146 |
|
|
aExpBigger:
|
1147 |
|
|
if ( aExp == 0xFF ) {
|
1148 |
|
|
if ( aSig ) return propagateFloat32NaN( a, b );
|
1149 |
|
|
return a;
|
1150 |
|
|
}
|
1151 |
|
|
if ( bExp == 0 ) {
|
1152 |
|
|
--expDiff;
|
1153 |
|
|
}
|
1154 |
|
|
else {
|
1155 |
|
|
bSig |= 0x40000000;
|
1156 |
|
|
}
|
1157 |
|
|
shift32RightJamming( bSig, expDiff, &bSig );
|
1158 |
|
|
aSig |= 0x40000000;
|
1159 |
|
|
aBigger:
|
1160 |
|
|
zSig = aSig - bSig;
|
1161 |
|
|
zExp = aExp;
|
1162 |
|
|
normalizeRoundAndPack:
|
1163 |
|
|
--zExp;
|
1164 |
|
|
return normalizeRoundAndPackFloat32( roundData, zSign, zExp, zSig );
|
1165 |
|
|
|
1166 |
|
|
}
|
1167 |
|
|
|
1168 |
|
|
/*
|
1169 |
|
|
-------------------------------------------------------------------------------
|
1170 |
|
|
Returns the result of adding the single-precision floating-point values `a'
|
1171 |
|
|
and `b'. The operation is performed according to the IEC/IEEE Standard for
|
1172 |
|
|
Binary Floating-point Arithmetic.
|
1173 |
|
|
-------------------------------------------------------------------------------
|
1174 |
|
|
*/
|
1175 |
|
|
float32 float32_add( struct roundingData *roundData, float32 a, float32 b )
|
1176 |
|
|
{
|
1177 |
|
|
flag aSign, bSign;
|
1178 |
|
|
|
1179 |
|
|
aSign = extractFloat32Sign( a );
|
1180 |
|
|
bSign = extractFloat32Sign( b );
|
1181 |
|
|
if ( aSign == bSign ) {
|
1182 |
|
|
return addFloat32Sigs( roundData, a, b, aSign );
|
1183 |
|
|
}
|
1184 |
|
|
else {
|
1185 |
|
|
return subFloat32Sigs( roundData, a, b, aSign );
|
1186 |
|
|
}
|
1187 |
|
|
|
1188 |
|
|
}
|
1189 |
|
|
|
1190 |
|
|
/*
|
1191 |
|
|
-------------------------------------------------------------------------------
|
1192 |
|
|
Returns the result of subtracting the single-precision floating-point values
|
1193 |
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
1194 |
|
|
for Binary Floating-point Arithmetic.
|
1195 |
|
|
-------------------------------------------------------------------------------
|
1196 |
|
|
*/
|
1197 |
|
|
float32 float32_sub( struct roundingData *roundData, float32 a, float32 b )
|
1198 |
|
|
{
|
1199 |
|
|
flag aSign, bSign;
|
1200 |
|
|
|
1201 |
|
|
aSign = extractFloat32Sign( a );
|
1202 |
|
|
bSign = extractFloat32Sign( b );
|
1203 |
|
|
if ( aSign == bSign ) {
|
1204 |
|
|
return subFloat32Sigs( roundData, a, b, aSign );
|
1205 |
|
|
}
|
1206 |
|
|
else {
|
1207 |
|
|
return addFloat32Sigs( roundData, a, b, aSign );
|
1208 |
|
|
}
|
1209 |
|
|
|
1210 |
|
|
}
|
1211 |
|
|
|
1212 |
|
|
/*
|
1213 |
|
|
-------------------------------------------------------------------------------
|
1214 |
|
|
Returns the result of multiplying the single-precision floating-point values
|
1215 |
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
1216 |
|
|
for Binary Floating-point Arithmetic.
|
1217 |
|
|
-------------------------------------------------------------------------------
|
1218 |
|
|
*/
|
1219 |
|
|
float32 float32_mul( struct roundingData *roundData, float32 a, float32 b )
|
1220 |
|
|
{
|
1221 |
|
|
flag aSign, bSign, zSign;
|
1222 |
|
|
int16 aExp, bExp, zExp;
|
1223 |
|
|
bits32 aSig, bSig;
|
1224 |
|
|
bits64 zSig64;
|
1225 |
|
|
bits32 zSig;
|
1226 |
|
|
|
1227 |
|
|
aSig = extractFloat32Frac( a );
|
1228 |
|
|
aExp = extractFloat32Exp( a );
|
1229 |
|
|
aSign = extractFloat32Sign( a );
|
1230 |
|
|
bSig = extractFloat32Frac( b );
|
1231 |
|
|
bExp = extractFloat32Exp( b );
|
1232 |
|
|
bSign = extractFloat32Sign( b );
|
1233 |
|
|
zSign = aSign ^ bSign;
|
1234 |
|
|
if ( aExp == 0xFF ) {
|
1235 |
|
|
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
|
1236 |
|
|
return propagateFloat32NaN( a, b );
|
1237 |
|
|
}
|
1238 |
|
|
if ( ( bExp | bSig ) == 0 ) {
|
1239 |
|
|
roundData->exception |= float_flag_invalid;
|
1240 |
|
|
return float32_default_nan;
|
1241 |
|
|
}
|
1242 |
|
|
return packFloat32( zSign, 0xFF, 0 );
|
1243 |
|
|
}
|
1244 |
|
|
if ( bExp == 0xFF ) {
|
1245 |
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
1246 |
|
|
if ( ( aExp | aSig ) == 0 ) {
|
1247 |
|
|
roundData->exception |= float_flag_invalid;
|
1248 |
|
|
return float32_default_nan;
|
1249 |
|
|
}
|
1250 |
|
|
return packFloat32( zSign, 0xFF, 0 );
|
1251 |
|
|
}
|
1252 |
|
|
if ( aExp == 0 ) {
|
1253 |
|
|
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
|
1254 |
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
1255 |
|
|
}
|
1256 |
|
|
if ( bExp == 0 ) {
|
1257 |
|
|
if ( bSig == 0 ) return packFloat32( zSign, 0, 0 );
|
1258 |
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
1259 |
|
|
}
|
1260 |
|
|
zExp = aExp + bExp - 0x7F;
|
1261 |
|
|
aSig = ( aSig | 0x00800000 )<<7;
|
1262 |
|
|
bSig = ( bSig | 0x00800000 )<<8;
|
1263 |
|
|
shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
|
1264 |
|
|
zSig = zSig64;
|
1265 |
|
|
if ( 0 <= (sbits32) ( zSig<<1 ) ) {
|
1266 |
|
|
zSig <<= 1;
|
1267 |
|
|
--zExp;
|
1268 |
|
|
}
|
1269 |
|
|
return roundAndPackFloat32( roundData, zSign, zExp, zSig );
|
1270 |
|
|
|
1271 |
|
|
}
|
1272 |
|
|
|
1273 |
|
|
/*
|
1274 |
|
|
-------------------------------------------------------------------------------
|
1275 |
|
|
Returns the result of dividing the single-precision floating-point value `a'
|
1276 |
|
|
by the corresponding value `b'. The operation is performed according to the
|
1277 |
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
1278 |
|
|
-------------------------------------------------------------------------------
|
1279 |
|
|
*/
|
1280 |
|
|
float32 float32_div( struct roundingData *roundData, float32 a, float32 b )
|
1281 |
|
|
{
|
1282 |
|
|
flag aSign, bSign, zSign;
|
1283 |
|
|
int16 aExp, bExp, zExp;
|
1284 |
|
|
bits32 aSig, bSig, zSig;
|
1285 |
|
|
|
1286 |
|
|
aSig = extractFloat32Frac( a );
|
1287 |
|
|
aExp = extractFloat32Exp( a );
|
1288 |
|
|
aSign = extractFloat32Sign( a );
|
1289 |
|
|
bSig = extractFloat32Frac( b );
|
1290 |
|
|
bExp = extractFloat32Exp( b );
|
1291 |
|
|
bSign = extractFloat32Sign( b );
|
1292 |
|
|
zSign = aSign ^ bSign;
|
1293 |
|
|
if ( aExp == 0xFF ) {
|
1294 |
|
|
if ( aSig ) return propagateFloat32NaN( a, b );
|
1295 |
|
|
if ( bExp == 0xFF ) {
|
1296 |
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
1297 |
|
|
roundData->exception |= float_flag_invalid;
|
1298 |
|
|
return float32_default_nan;
|
1299 |
|
|
}
|
1300 |
|
|
return packFloat32( zSign, 0xFF, 0 );
|
1301 |
|
|
}
|
1302 |
|
|
if ( bExp == 0xFF ) {
|
1303 |
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
1304 |
|
|
return packFloat32( zSign, 0, 0 );
|
1305 |
|
|
}
|
1306 |
|
|
if ( bExp == 0 ) {
|
1307 |
|
|
if ( bSig == 0 ) {
|
1308 |
|
|
if ( ( aExp | aSig ) == 0 ) {
|
1309 |
|
|
roundData->exception |= float_flag_invalid;
|
1310 |
|
|
return float32_default_nan;
|
1311 |
|
|
}
|
1312 |
|
|
roundData->exception |= float_flag_divbyzero;
|
1313 |
|
|
return packFloat32( zSign, 0xFF, 0 );
|
1314 |
|
|
}
|
1315 |
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
1316 |
|
|
}
|
1317 |
|
|
if ( aExp == 0 ) {
|
1318 |
|
|
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
|
1319 |
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
1320 |
|
|
}
|
1321 |
|
|
zExp = aExp - bExp + 0x7D;
|
1322 |
|
|
aSig = ( aSig | 0x00800000 )<<7;
|
1323 |
|
|
bSig = ( bSig | 0x00800000 )<<8;
|
1324 |
|
|
if ( bSig <= ( aSig + aSig ) ) {
|
1325 |
|
|
aSig >>= 1;
|
1326 |
|
|
++zExp;
|
1327 |
|
|
}
|
1328 |
|
|
{
|
1329 |
|
|
bits64 tmp = ( (bits64) aSig )<<32;
|
1330 |
|
|
do_div( tmp, bSig );
|
1331 |
|
|
zSig = tmp;
|
1332 |
|
|
}
|
1333 |
|
|
if ( ( zSig & 0x3F ) == 0 ) {
|
1334 |
|
|
zSig |= ( ( (bits64) bSig ) * zSig != ( (bits64) aSig )<<32 );
|
1335 |
|
|
}
|
1336 |
|
|
return roundAndPackFloat32( roundData, zSign, zExp, zSig );
|
1337 |
|
|
|
1338 |
|
|
}
|
1339 |
|
|
|
1340 |
|
|
/*
|
1341 |
|
|
-------------------------------------------------------------------------------
|
1342 |
|
|
Returns the remainder of the single-precision floating-point value `a'
|
1343 |
|
|
with respect to the corresponding value `b'. The operation is performed
|
1344 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
1345 |
|
|
-------------------------------------------------------------------------------
|
1346 |
|
|
*/
|
1347 |
|
|
float32 float32_rem( struct roundingData *roundData, float32 a, float32 b )
|
1348 |
|
|
{
|
1349 |
|
|
flag aSign, bSign, zSign;
|
1350 |
|
|
int16 aExp, bExp, expDiff;
|
1351 |
|
|
bits32 aSig, bSig;
|
1352 |
|
|
bits32 q;
|
1353 |
|
|
bits64 aSig64, bSig64, q64;
|
1354 |
|
|
bits32 alternateASig;
|
1355 |
|
|
sbits32 sigMean;
|
1356 |
|
|
|
1357 |
|
|
aSig = extractFloat32Frac( a );
|
1358 |
|
|
aExp = extractFloat32Exp( a );
|
1359 |
|
|
aSign = extractFloat32Sign( a );
|
1360 |
|
|
bSig = extractFloat32Frac( b );
|
1361 |
|
|
bExp = extractFloat32Exp( b );
|
1362 |
|
|
bSign = extractFloat32Sign( b );
|
1363 |
|
|
if ( aExp == 0xFF ) {
|
1364 |
|
|
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
|
1365 |
|
|
return propagateFloat32NaN( a, b );
|
1366 |
|
|
}
|
1367 |
|
|
roundData->exception |= float_flag_invalid;
|
1368 |
|
|
return float32_default_nan;
|
1369 |
|
|
}
|
1370 |
|
|
if ( bExp == 0xFF ) {
|
1371 |
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
1372 |
|
|
return a;
|
1373 |
|
|
}
|
1374 |
|
|
if ( bExp == 0 ) {
|
1375 |
|
|
if ( bSig == 0 ) {
|
1376 |
|
|
roundData->exception |= float_flag_invalid;
|
1377 |
|
|
return float32_default_nan;
|
1378 |
|
|
}
|
1379 |
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
1380 |
|
|
}
|
1381 |
|
|
if ( aExp == 0 ) {
|
1382 |
|
|
if ( aSig == 0 ) return a;
|
1383 |
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
1384 |
|
|
}
|
1385 |
|
|
expDiff = aExp - bExp;
|
1386 |
|
|
aSig |= 0x00800000;
|
1387 |
|
|
bSig |= 0x00800000;
|
1388 |
|
|
if ( expDiff < 32 ) {
|
1389 |
|
|
aSig <<= 8;
|
1390 |
|
|
bSig <<= 8;
|
1391 |
|
|
if ( expDiff < 0 ) {
|
1392 |
|
|
if ( expDiff < -1 ) return a;
|
1393 |
|
|
aSig >>= 1;
|
1394 |
|
|
}
|
1395 |
|
|
q = ( bSig <= aSig );
|
1396 |
|
|
if ( q ) aSig -= bSig;
|
1397 |
|
|
if ( 0 < expDiff ) {
|
1398 |
|
|
bits64 tmp = ( (bits64) aSig )<<32;
|
1399 |
|
|
do_div( tmp, bSig );
|
1400 |
|
|
q = tmp;
|
1401 |
|
|
q >>= 32 - expDiff;
|
1402 |
|
|
bSig >>= 2;
|
1403 |
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
1404 |
|
|
}
|
1405 |
|
|
else {
|
1406 |
|
|
aSig >>= 2;
|
1407 |
|
|
bSig >>= 2;
|
1408 |
|
|
}
|
1409 |
|
|
}
|
1410 |
|
|
else {
|
1411 |
|
|
if ( bSig <= aSig ) aSig -= bSig;
|
1412 |
|
|
aSig64 = ( (bits64) aSig )<<40;
|
1413 |
|
|
bSig64 = ( (bits64) bSig )<<40;
|
1414 |
|
|
expDiff -= 64;
|
1415 |
|
|
while ( 0 < expDiff ) {
|
1416 |
|
|
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
1417 |
|
|
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
|
1418 |
|
|
aSig64 = - ( ( bSig * q64 )<<38 );
|
1419 |
|
|
expDiff -= 62;
|
1420 |
|
|
}
|
1421 |
|
|
expDiff += 64;
|
1422 |
|
|
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
1423 |
|
|
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
|
1424 |
|
|
q = q64>>( 64 - expDiff );
|
1425 |
|
|
bSig <<= 6;
|
1426 |
|
|
aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
|
1427 |
|
|
}
|
1428 |
|
|
do {
|
1429 |
|
|
alternateASig = aSig;
|
1430 |
|
|
++q;
|
1431 |
|
|
aSig -= bSig;
|
1432 |
|
|
} while ( 0 <= (sbits32) aSig );
|
1433 |
|
|
sigMean = aSig + alternateASig;
|
1434 |
|
|
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
|
1435 |
|
|
aSig = alternateASig;
|
1436 |
|
|
}
|
1437 |
|
|
zSign = ( (sbits32) aSig < 0 );
|
1438 |
|
|
if ( zSign ) aSig = - aSig;
|
1439 |
|
|
return normalizeRoundAndPackFloat32( roundData, aSign ^ zSign, bExp, aSig );
|
1440 |
|
|
|
1441 |
|
|
}
|
1442 |
|
|
|
1443 |
|
|
/*
|
1444 |
|
|
-------------------------------------------------------------------------------
|
1445 |
|
|
Returns the square root of the single-precision floating-point value `a'.
|
1446 |
|
|
The operation is performed according to the IEC/IEEE Standard for Binary
|
1447 |
|
|
Floating-point Arithmetic.
|
1448 |
|
|
-------------------------------------------------------------------------------
|
1449 |
|
|
*/
|
1450 |
|
|
float32 float32_sqrt( struct roundingData *roundData, float32 a )
|
1451 |
|
|
{
|
1452 |
|
|
flag aSign;
|
1453 |
|
|
int16 aExp, zExp;
|
1454 |
|
|
bits32 aSig, zSig;
|
1455 |
|
|
bits64 rem, term;
|
1456 |
|
|
|
1457 |
|
|
aSig = extractFloat32Frac( a );
|
1458 |
|
|
aExp = extractFloat32Exp( a );
|
1459 |
|
|
aSign = extractFloat32Sign( a );
|
1460 |
|
|
if ( aExp == 0xFF ) {
|
1461 |
|
|
if ( aSig ) return propagateFloat32NaN( a, 0 );
|
1462 |
|
|
if ( ! aSign ) return a;
|
1463 |
|
|
roundData->exception |= float_flag_invalid;
|
1464 |
|
|
return float32_default_nan;
|
1465 |
|
|
}
|
1466 |
|
|
if ( aSign ) {
|
1467 |
|
|
if ( ( aExp | aSig ) == 0 ) return a;
|
1468 |
|
|
roundData->exception |= float_flag_invalid;
|
1469 |
|
|
return float32_default_nan;
|
1470 |
|
|
}
|
1471 |
|
|
if ( aExp == 0 ) {
|
1472 |
|
|
if ( aSig == 0 ) return 0;
|
1473 |
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
1474 |
|
|
}
|
1475 |
|
|
zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E;
|
1476 |
|
|
aSig = ( aSig | 0x00800000 )<<8;
|
1477 |
|
|
zSig = estimateSqrt32( aExp, aSig ) + 2;
|
1478 |
|
|
if ( ( zSig & 0x7F ) <= 5 ) {
|
1479 |
|
|
if ( zSig < 2 ) {
|
1480 |
|
|
zSig = 0xFFFFFFFF;
|
1481 |
|
|
}
|
1482 |
|
|
else {
|
1483 |
|
|
aSig >>= aExp & 1;
|
1484 |
|
|
term = ( (bits64) zSig ) * zSig;
|
1485 |
|
|
rem = ( ( (bits64) aSig )<<32 ) - term;
|
1486 |
|
|
while ( (sbits64) rem < 0 ) {
|
1487 |
|
|
--zSig;
|
1488 |
|
|
rem += ( ( (bits64) zSig )<<1 ) | 1;
|
1489 |
|
|
}
|
1490 |
|
|
zSig |= ( rem != 0 );
|
1491 |
|
|
}
|
1492 |
|
|
}
|
1493 |
|
|
shift32RightJamming( zSig, 1, &zSig );
|
1494 |
|
|
return roundAndPackFloat32( roundData, 0, zExp, zSig );
|
1495 |
|
|
|
1496 |
|
|
}
|
1497 |
|
|
|
1498 |
|
|
/*
|
1499 |
|
|
-------------------------------------------------------------------------------
|
1500 |
|
|
Returns 1 if the single-precision floating-point value `a' is equal to the
|
1501 |
|
|
corresponding value `b', and 0 otherwise. The comparison is performed
|
1502 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
1503 |
|
|
-------------------------------------------------------------------------------
|
1504 |
|
|
*/
|
1505 |
|
|
flag float32_eq( float32 a, float32 b )
|
1506 |
|
|
{
|
1507 |
|
|
|
1508 |
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
1509 |
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
1510 |
|
|
) {
|
1511 |
|
|
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
1512 |
|
|
float_raise( float_flag_invalid );
|
1513 |
|
|
}
|
1514 |
|
|
return 0;
|
1515 |
|
|
}
|
1516 |
|
|
return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
1517 |
|
|
|
1518 |
|
|
}
|
1519 |
|
|
|
1520 |
|
|
/*
|
1521 |
|
|
-------------------------------------------------------------------------------
|
1522 |
|
|
Returns 1 if the single-precision floating-point value `a' is less than or
|
1523 |
|
|
equal to the corresponding value `b', and 0 otherwise. The comparison is
|
1524 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
1525 |
|
|
Arithmetic.
|
1526 |
|
|
-------------------------------------------------------------------------------
|
1527 |
|
|
*/
|
1528 |
|
|
flag float32_le( float32 a, float32 b )
|
1529 |
|
|
{
|
1530 |
|
|
flag aSign, bSign;
|
1531 |
|
|
|
1532 |
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
1533 |
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
1534 |
|
|
) {
|
1535 |
|
|
float_raise( float_flag_invalid );
|
1536 |
|
|
return 0;
|
1537 |
|
|
}
|
1538 |
|
|
aSign = extractFloat32Sign( a );
|
1539 |
|
|
bSign = extractFloat32Sign( b );
|
1540 |
|
|
if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
1541 |
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
1542 |
|
|
|
1543 |
|
|
}
|
1544 |
|
|
|
1545 |
|
|
/*
|
1546 |
|
|
-------------------------------------------------------------------------------
|
1547 |
|
|
Returns 1 if the single-precision floating-point value `a' is less than
|
1548 |
|
|
the corresponding value `b', and 0 otherwise. The comparison is performed
|
1549 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
1550 |
|
|
-------------------------------------------------------------------------------
|
1551 |
|
|
*/
|
1552 |
|
|
flag float32_lt( float32 a, float32 b )
|
1553 |
|
|
{
|
1554 |
|
|
flag aSign, bSign;
|
1555 |
|
|
|
1556 |
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
1557 |
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
1558 |
|
|
) {
|
1559 |
|
|
float_raise( float_flag_invalid );
|
1560 |
|
|
return 0;
|
1561 |
|
|
}
|
1562 |
|
|
aSign = extractFloat32Sign( a );
|
1563 |
|
|
bSign = extractFloat32Sign( b );
|
1564 |
|
|
if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
|
1565 |
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
1566 |
|
|
|
1567 |
|
|
}
|
1568 |
|
|
|
1569 |
|
|
/*
|
1570 |
|
|
-------------------------------------------------------------------------------
|
1571 |
|
|
Returns 1 if the single-precision floating-point value `a' is equal to the
|
1572 |
|
|
corresponding value `b', and 0 otherwise. The invalid exception is raised
|
1573 |
|
|
if either operand is a NaN. Otherwise, the comparison is performed
|
1574 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
1575 |
|
|
-------------------------------------------------------------------------------
|
1576 |
|
|
*/
|
1577 |
|
|
flag float32_eq_signaling( float32 a, float32 b )
|
1578 |
|
|
{
|
1579 |
|
|
|
1580 |
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
1581 |
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
1582 |
|
|
) {
|
1583 |
|
|
float_raise( float_flag_invalid );
|
1584 |
|
|
return 0;
|
1585 |
|
|
}
|
1586 |
|
|
return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
1587 |
|
|
|
1588 |
|
|
}
|
1589 |
|
|
|
1590 |
|
|
/*
|
1591 |
|
|
-------------------------------------------------------------------------------
|
1592 |
|
|
Returns 1 if the single-precision floating-point value `a' is less than or
|
1593 |
|
|
equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
1594 |
|
|
cause an exception. Otherwise, the comparison is performed according to the
|
1595 |
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
1596 |
|
|
-------------------------------------------------------------------------------
|
1597 |
|
|
*/
|
1598 |
|
|
flag float32_le_quiet( float32 a, float32 b )
|
1599 |
|
|
{
|
1600 |
|
|
flag aSign, bSign;
|
1601 |
|
|
//int16 aExp, bExp;
|
1602 |
|
|
|
1603 |
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
1604 |
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
1605 |
|
|
) {
|
1606 |
|
|
/* Do nothing, even if NaN as we're quiet */
|
1607 |
|
|
return 0;
|
1608 |
|
|
}
|
1609 |
|
|
aSign = extractFloat32Sign( a );
|
1610 |
|
|
bSign = extractFloat32Sign( b );
|
1611 |
|
|
if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
1612 |
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
1613 |
|
|
|
1614 |
|
|
}
|
1615 |
|
|
|
1616 |
|
|
/*
|
1617 |
|
|
-------------------------------------------------------------------------------
|
1618 |
|
|
Returns 1 if the single-precision floating-point value `a' is less than
|
1619 |
|
|
the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
1620 |
|
|
exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
1621 |
|
|
Standard for Binary Floating-point Arithmetic.
|
1622 |
|
|
-------------------------------------------------------------------------------
|
1623 |
|
|
*/
|
1624 |
|
|
flag float32_lt_quiet( float32 a, float32 b )
|
1625 |
|
|
{
|
1626 |
|
|
flag aSign, bSign;
|
1627 |
|
|
|
1628 |
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
1629 |
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
1630 |
|
|
) {
|
1631 |
|
|
/* Do nothing, even if NaN as we're quiet */
|
1632 |
|
|
return 0;
|
1633 |
|
|
}
|
1634 |
|
|
aSign = extractFloat32Sign( a );
|
1635 |
|
|
bSign = extractFloat32Sign( b );
|
1636 |
|
|
if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
|
1637 |
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
1638 |
|
|
|
1639 |
|
|
}
|
1640 |
|
|
|
1641 |
|
|
/*
|
1642 |
|
|
-------------------------------------------------------------------------------
|
1643 |
|
|
Returns the result of converting the double-precision floating-point value
|
1644 |
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
1645 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
1646 |
|
|
Arithmetic---which means in particular that the conversion is rounded
|
1647 |
|
|
according to the current rounding mode. If `a' is a NaN, the largest
|
1648 |
|
|
positive integer is returned. Otherwise, if the conversion overflows, the
|
1649 |
|
|
largest integer with the same sign as `a' is returned.
|
1650 |
|
|
-------------------------------------------------------------------------------
|
1651 |
|
|
*/
|
1652 |
|
|
int32 float64_to_int32( struct roundingData *roundData, float64 a )
|
1653 |
|
|
{
|
1654 |
|
|
flag aSign;
|
1655 |
|
|
int16 aExp, shiftCount;
|
1656 |
|
|
bits64 aSig;
|
1657 |
|
|
|
1658 |
|
|
aSig = extractFloat64Frac( a );
|
1659 |
|
|
aExp = extractFloat64Exp( a );
|
1660 |
|
|
aSign = extractFloat64Sign( a );
|
1661 |
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
1662 |
|
|
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
|
1663 |
|
|
shiftCount = 0x42C - aExp;
|
1664 |
|
|
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
|
1665 |
|
|
return roundAndPackInt32( roundData, aSign, aSig );
|
1666 |
|
|
|
1667 |
|
|
}
|
1668 |
|
|
|
1669 |
|
|
/*
|
1670 |
|
|
-------------------------------------------------------------------------------
|
1671 |
|
|
Returns the result of converting the double-precision floating-point value
|
1672 |
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
1673 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
1674 |
|
|
Arithmetic, except that the conversion is always rounded toward zero. If
|
1675 |
|
|
`a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
1676 |
|
|
conversion overflows, the largest integer with the same sign as `a' is
|
1677 |
|
|
returned.
|
1678 |
|
|
-------------------------------------------------------------------------------
|
1679 |
|
|
*/
|
1680 |
|
|
int32 float64_to_int32_round_to_zero( float64 a )
|
1681 |
|
|
{
|
1682 |
|
|
flag aSign;
|
1683 |
|
|
int16 aExp, shiftCount;
|
1684 |
|
|
bits64 aSig, savedASig;
|
1685 |
|
|
int32 z;
|
1686 |
|
|
|
1687 |
|
|
aSig = extractFloat64Frac( a );
|
1688 |
|
|
aExp = extractFloat64Exp( a );
|
1689 |
|
|
aSign = extractFloat64Sign( a );
|
1690 |
|
|
shiftCount = 0x433 - aExp;
|
1691 |
|
|
if ( shiftCount < 21 ) {
|
1692 |
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
1693 |
|
|
goto invalid;
|
1694 |
|
|
}
|
1695 |
|
|
else if ( 52 < shiftCount ) {
|
1696 |
|
|
if ( aExp || aSig ) float_raise( float_flag_inexact );
|
1697 |
|
|
return 0;
|
1698 |
|
|
}
|
1699 |
|
|
aSig |= LIT64( 0x0010000000000000 );
|
1700 |
|
|
savedASig = aSig;
|
1701 |
|
|
aSig >>= shiftCount;
|
1702 |
|
|
z = aSig;
|
1703 |
|
|
if ( aSign ) z = - z;
|
1704 |
|
|
if ( ( z < 0 ) ^ aSign ) {
|
1705 |
|
|
invalid:
|
1706 |
|
|
float_raise( float_flag_invalid );
|
1707 |
|
|
return aSign ? 0x80000000 : 0x7FFFFFFF;
|
1708 |
|
|
}
|
1709 |
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
1710 |
|
|
float_raise( float_flag_inexact );
|
1711 |
|
|
}
|
1712 |
|
|
return z;
|
1713 |
|
|
|
1714 |
|
|
}
|
1715 |
|
|
|
1716 |
|
|
/*
|
1717 |
|
|
-------------------------------------------------------------------------------
|
1718 |
|
|
Returns the result of converting the double-precision floating-point value
|
1719 |
|
|
`a' to the 32-bit two's complement unsigned integer format. The conversion
|
1720 |
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
1721 |
|
|
Arithmetic---which means in particular that the conversion is rounded
|
1722 |
|
|
according to the current rounding mode. If `a' is a NaN, the largest
|
1723 |
|
|
positive integer is returned. Otherwise, if the conversion overflows, the
|
1724 |
|
|
largest positive integer is returned.
|
1725 |
|
|
-------------------------------------------------------------------------------
|
1726 |
|
|
*/
|
1727 |
|
|
int32 float64_to_uint32( struct roundingData *roundData, float64 a )
|
1728 |
|
|
{
|
1729 |
|
|
flag aSign;
|
1730 |
|
|
int16 aExp, shiftCount;
|
1731 |
|
|
bits64 aSig;
|
1732 |
|
|
|
1733 |
|
|
aSig = extractFloat64Frac( a );
|
1734 |
|
|
aExp = extractFloat64Exp( a );
|
1735 |
|
|
aSign = 0; //extractFloat64Sign( a );
|
1736 |
|
|
//if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
1737 |
|
|
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
|
1738 |
|
|
shiftCount = 0x42C - aExp;
|
1739 |
|
|
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
|
1740 |
|
|
return roundAndPackInt32( roundData, aSign, aSig );
|
1741 |
|
|
}
|
1742 |
|
|
|
1743 |
|
|
/*
|
1744 |
|
|
-------------------------------------------------------------------------------
|
1745 |
|
|
Returns the result of converting the double-precision floating-point value
|
1746 |
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
1747 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
1748 |
|
|
Arithmetic, except that the conversion is always rounded toward zero. If
|
1749 |
|
|
`a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
1750 |
|
|
conversion overflows, the largest positive integer is returned.
|
1751 |
|
|
-------------------------------------------------------------------------------
|
1752 |
|
|
*/
|
1753 |
|
|
int32 float64_to_uint32_round_to_zero( float64 a )
|
1754 |
|
|
{
|
1755 |
|
|
flag aSign;
|
1756 |
|
|
int16 aExp, shiftCount;
|
1757 |
|
|
bits64 aSig, savedASig;
|
1758 |
|
|
int32 z;
|
1759 |
|
|
|
1760 |
|
|
aSig = extractFloat64Frac( a );
|
1761 |
|
|
aExp = extractFloat64Exp( a );
|
1762 |
|
|
aSign = extractFloat64Sign( a );
|
1763 |
|
|
shiftCount = 0x433 - aExp;
|
1764 |
|
|
if ( shiftCount < 21 ) {
|
1765 |
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
1766 |
|
|
goto invalid;
|
1767 |
|
|
}
|
1768 |
|
|
else if ( 52 < shiftCount ) {
|
1769 |
|
|
if ( aExp || aSig ) float_raise( float_flag_inexact );
|
1770 |
|
|
return 0;
|
1771 |
|
|
}
|
1772 |
|
|
aSig |= LIT64( 0x0010000000000000 );
|
1773 |
|
|
savedASig = aSig;
|
1774 |
|
|
aSig >>= shiftCount;
|
1775 |
|
|
z = aSig;
|
1776 |
|
|
if ( aSign ) z = - z;
|
1777 |
|
|
if ( ( z < 0 ) ^ aSign ) {
|
1778 |
|
|
invalid:
|
1779 |
|
|
float_raise( float_flag_invalid );
|
1780 |
|
|
return aSign ? 0x80000000 : 0x7FFFFFFF;
|
1781 |
|
|
}
|
1782 |
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
1783 |
|
|
float_raise( float_flag_inexact );
|
1784 |
|
|
}
|
1785 |
|
|
return z;
|
1786 |
|
|
}
|
1787 |
|
|
|
1788 |
|
|
/*
|
1789 |
|
|
-------------------------------------------------------------------------------
|
1790 |
|
|
Returns the result of converting the double-precision floating-point value
|
1791 |
|
|
`a' to the single-precision floating-point format. The conversion is
|
1792 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
1793 |
|
|
Arithmetic.
|
1794 |
|
|
-------------------------------------------------------------------------------
|
1795 |
|
|
*/
|
1796 |
|
|
float32 float64_to_float32( struct roundingData *roundData, float64 a )
|
1797 |
|
|
{
|
1798 |
|
|
flag aSign;
|
1799 |
|
|
int16 aExp;
|
1800 |
|
|
bits64 aSig;
|
1801 |
|
|
bits32 zSig;
|
1802 |
|
|
|
1803 |
|
|
aSig = extractFloat64Frac( a );
|
1804 |
|
|
aExp = extractFloat64Exp( a );
|
1805 |
|
|
aSign = extractFloat64Sign( a );
|
1806 |
|
|
if ( aExp == 0x7FF ) {
|
1807 |
|
|
if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a ) );
|
1808 |
|
|
return packFloat32( aSign, 0xFF, 0 );
|
1809 |
|
|
}
|
1810 |
|
|
shift64RightJamming( aSig, 22, &aSig );
|
1811 |
|
|
zSig = aSig;
|
1812 |
|
|
if ( aExp || zSig ) {
|
1813 |
|
|
zSig |= 0x40000000;
|
1814 |
|
|
aExp -= 0x381;
|
1815 |
|
|
}
|
1816 |
|
|
return roundAndPackFloat32( roundData, aSign, aExp, zSig );
|
1817 |
|
|
|
1818 |
|
|
}
|
1819 |
|
|
|
1820 |
|
|
#ifdef FLOATX80
|
1821 |
|
|
|
1822 |
|
|
/*
|
1823 |
|
|
-------------------------------------------------------------------------------
|
1824 |
|
|
Returns the result of converting the double-precision floating-point value
|
1825 |
|
|
`a' to the extended double-precision floating-point format. The conversion
|
1826 |
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
1827 |
|
|
Arithmetic.
|
1828 |
|
|
-------------------------------------------------------------------------------
|
1829 |
|
|
*/
|
1830 |
|
|
floatx80 float64_to_floatx80( float64 a )
|
1831 |
|
|
{
|
1832 |
|
|
flag aSign;
|
1833 |
|
|
int16 aExp;
|
1834 |
|
|
bits64 aSig;
|
1835 |
|
|
|
1836 |
|
|
aSig = extractFloat64Frac( a );
|
1837 |
|
|
aExp = extractFloat64Exp( a );
|
1838 |
|
|
aSign = extractFloat64Sign( a );
|
1839 |
|
|
if ( aExp == 0x7FF ) {
|
1840 |
|
|
if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a ) );
|
1841 |
|
|
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
1842 |
|
|
}
|
1843 |
|
|
if ( aExp == 0 ) {
|
1844 |
|
|
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
|
1845 |
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
1846 |
|
|
}
|
1847 |
|
|
return
|
1848 |
|
|
packFloatx80(
|
1849 |
|
|
aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 );
|
1850 |
|
|
|
1851 |
|
|
}
|
1852 |
|
|
|
1853 |
|
|
#endif
|
1854 |
|
|
|
1855 |
|
|
/*
|
1856 |
|
|
-------------------------------------------------------------------------------
|
1857 |
|
|
Rounds the double-precision floating-point value `a' to an integer, and
|
1858 |
|
|
returns the result as a double-precision floating-point value. The
|
1859 |
|
|
operation is performed according to the IEC/IEEE Standard for Binary
|
1860 |
|
|
Floating-point Arithmetic.
|
1861 |
|
|
-------------------------------------------------------------------------------
|
1862 |
|
|
*/
|
1863 |
|
|
float64 float64_round_to_int( struct roundingData *roundData, float64 a )
|
1864 |
|
|
{
|
1865 |
|
|
flag aSign;
|
1866 |
|
|
int16 aExp;
|
1867 |
|
|
bits64 lastBitMask, roundBitsMask;
|
1868 |
|
|
int8 roundingMode;
|
1869 |
|
|
float64 z;
|
1870 |
|
|
|
1871 |
|
|
aExp = extractFloat64Exp( a );
|
1872 |
|
|
if ( 0x433 <= aExp ) {
|
1873 |
|
|
if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) {
|
1874 |
|
|
return propagateFloat64NaN( a, a );
|
1875 |
|
|
}
|
1876 |
|
|
return a;
|
1877 |
|
|
}
|
1878 |
|
|
if ( aExp <= 0x3FE ) {
|
1879 |
|
|
if ( (bits64) ( a<<1 ) == 0 ) return a;
|
1880 |
|
|
roundData->exception |= float_flag_inexact;
|
1881 |
|
|
aSign = extractFloat64Sign( a );
|
1882 |
|
|
switch ( roundData->mode ) {
|
1883 |
|
|
case float_round_nearest_even:
|
1884 |
|
|
if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) {
|
1885 |
|
|
return packFloat64( aSign, 0x3FF, 0 );
|
1886 |
|
|
}
|
1887 |
|
|
break;
|
1888 |
|
|
case float_round_down:
|
1889 |
|
|
return aSign ? LIT64( 0xBFF0000000000000 ) : 0;
|
1890 |
|
|
case float_round_up:
|
1891 |
|
|
return
|
1892 |
|
|
aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 );
|
1893 |
|
|
}
|
1894 |
|
|
return packFloat64( aSign, 0, 0 );
|
1895 |
|
|
}
|
1896 |
|
|
lastBitMask = 1;
|
1897 |
|
|
lastBitMask <<= 0x433 - aExp;
|
1898 |
|
|
roundBitsMask = lastBitMask - 1;
|
1899 |
|
|
z = a;
|
1900 |
|
|
roundingMode = roundData->mode;
|
1901 |
|
|
if ( roundingMode == float_round_nearest_even ) {
|
1902 |
|
|
z += lastBitMask>>1;
|
1903 |
|
|
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
|
1904 |
|
|
}
|
1905 |
|
|
else if ( roundingMode != float_round_to_zero ) {
|
1906 |
|
|
if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
1907 |
|
|
z += roundBitsMask;
|
1908 |
|
|
}
|
1909 |
|
|
}
|
1910 |
|
|
z &= ~ roundBitsMask;
|
1911 |
|
|
if ( z != a ) roundData->exception |= float_flag_inexact;
|
1912 |
|
|
return z;
|
1913 |
|
|
|
1914 |
|
|
}
|
1915 |
|
|
|
1916 |
|
|
/*
|
1917 |
|
|
-------------------------------------------------------------------------------
|
1918 |
|
|
Returns the result of adding the absolute values of the double-precision
|
1919 |
|
|
floating-point values `a' and `b'. If `zSign' is true, the sum is negated
|
1920 |
|
|
before being returned. `zSign' is ignored if the result is a NaN. The
|
1921 |
|
|
addition is performed according to the IEC/IEEE Standard for Binary
|
1922 |
|
|
Floating-point Arithmetic.
|
1923 |
|
|
-------------------------------------------------------------------------------
|
1924 |
|
|
*/
|
1925 |
|
|
static float64 addFloat64Sigs( struct roundingData *roundData, float64 a, float64 b, flag zSign )
|
1926 |
|
|
{
|
1927 |
|
|
int16 aExp, bExp, zExp;
|
1928 |
|
|
bits64 aSig, bSig, zSig;
|
1929 |
|
|
int16 expDiff;
|
1930 |
|
|
|
1931 |
|
|
aSig = extractFloat64Frac( a );
|
1932 |
|
|
aExp = extractFloat64Exp( a );
|
1933 |
|
|
bSig = extractFloat64Frac( b );
|
1934 |
|
|
bExp = extractFloat64Exp( b );
|
1935 |
|
|
expDiff = aExp - bExp;
|
1936 |
|
|
aSig <<= 9;
|
1937 |
|
|
bSig <<= 9;
|
1938 |
|
|
if ( 0 < expDiff ) {
|
1939 |
|
|
if ( aExp == 0x7FF ) {
|
1940 |
|
|
if ( aSig ) return propagateFloat64NaN( a, b );
|
1941 |
|
|
return a;
|
1942 |
|
|
}
|
1943 |
|
|
if ( bExp == 0 ) {
|
1944 |
|
|
--expDiff;
|
1945 |
|
|
}
|
1946 |
|
|
else {
|
1947 |
|
|
bSig |= LIT64( 0x2000000000000000 );
|
1948 |
|
|
}
|
1949 |
|
|
shift64RightJamming( bSig, expDiff, &bSig );
|
1950 |
|
|
zExp = aExp;
|
1951 |
|
|
}
|
1952 |
|
|
else if ( expDiff < 0 ) {
|
1953 |
|
|
if ( bExp == 0x7FF ) {
|
1954 |
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
1955 |
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
1956 |
|
|
}
|
1957 |
|
|
if ( aExp == 0 ) {
|
1958 |
|
|
++expDiff;
|
1959 |
|
|
}
|
1960 |
|
|
else {
|
1961 |
|
|
aSig |= LIT64( 0x2000000000000000 );
|
1962 |
|
|
}
|
1963 |
|
|
shift64RightJamming( aSig, - expDiff, &aSig );
|
1964 |
|
|
zExp = bExp;
|
1965 |
|
|
}
|
1966 |
|
|
else {
|
1967 |
|
|
if ( aExp == 0x7FF ) {
|
1968 |
|
|
if ( aSig | bSig ) return propagateFloat64NaN( a, b );
|
1969 |
|
|
return a;
|
1970 |
|
|
}
|
1971 |
|
|
if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
|
1972 |
|
|
zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
|
1973 |
|
|
zExp = aExp;
|
1974 |
|
|
goto roundAndPack;
|
1975 |
|
|
}
|
1976 |
|
|
aSig |= LIT64( 0x2000000000000000 );
|
1977 |
|
|
zSig = ( aSig + bSig )<<1;
|
1978 |
|
|
--zExp;
|
1979 |
|
|
if ( (sbits64) zSig < 0 ) {
|
1980 |
|
|
zSig = aSig + bSig;
|
1981 |
|
|
++zExp;
|
1982 |
|
|
}
|
1983 |
|
|
roundAndPack:
|
1984 |
|
|
return roundAndPackFloat64( roundData, zSign, zExp, zSig );
|
1985 |
|
|
|
1986 |
|
|
}
|
1987 |
|
|
|
1988 |
|
|
/*
|
1989 |
|
|
-------------------------------------------------------------------------------
|
1990 |
|
|
Returns the result of subtracting the absolute values of the double-
|
1991 |
|
|
precision floating-point values `a' and `b'. If `zSign' is true, the
|
1992 |
|
|
difference is negated before being returned. `zSign' is ignored if the
|
1993 |
|
|
result is a NaN. The subtraction is performed according to the IEC/IEEE
|
1994 |
|
|
Standard for Binary Floating-point Arithmetic.
|
1995 |
|
|
-------------------------------------------------------------------------------
|
1996 |
|
|
*/
|
1997 |
|
|
static float64 subFloat64Sigs( struct roundingData *roundData, float64 a, float64 b, flag zSign )
|
1998 |
|
|
{
|
1999 |
|
|
int16 aExp, bExp, zExp;
|
2000 |
|
|
bits64 aSig, bSig, zSig;
|
2001 |
|
|
int16 expDiff;
|
2002 |
|
|
|
2003 |
|
|
aSig = extractFloat64Frac( a );
|
2004 |
|
|
aExp = extractFloat64Exp( a );
|
2005 |
|
|
bSig = extractFloat64Frac( b );
|
2006 |
|
|
bExp = extractFloat64Exp( b );
|
2007 |
|
|
expDiff = aExp - bExp;
|
2008 |
|
|
aSig <<= 10;
|
2009 |
|
|
bSig <<= 10;
|
2010 |
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
2011 |
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
2012 |
|
|
if ( aExp == 0x7FF ) {
|
2013 |
|
|
if ( aSig | bSig ) return propagateFloat64NaN( a, b );
|
2014 |
|
|
roundData->exception |= float_flag_invalid;
|
2015 |
|
|
return float64_default_nan;
|
2016 |
|
|
}
|
2017 |
|
|
if ( aExp == 0 ) {
|
2018 |
|
|
aExp = 1;
|
2019 |
|
|
bExp = 1;
|
2020 |
|
|
}
|
2021 |
|
|
if ( bSig < aSig ) goto aBigger;
|
2022 |
|
|
if ( aSig < bSig ) goto bBigger;
|
2023 |
|
|
return packFloat64( roundData->mode == float_round_down, 0, 0 );
|
2024 |
|
|
bExpBigger:
|
2025 |
|
|
if ( bExp == 0x7FF ) {
|
2026 |
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
2027 |
|
|
return packFloat64( zSign ^ 1, 0x7FF, 0 );
|
2028 |
|
|
}
|
2029 |
|
|
if ( aExp == 0 ) {
|
2030 |
|
|
++expDiff;
|
2031 |
|
|
}
|
2032 |
|
|
else {
|
2033 |
|
|
aSig |= LIT64( 0x4000000000000000 );
|
2034 |
|
|
}
|
2035 |
|
|
shift64RightJamming( aSig, - expDiff, &aSig );
|
2036 |
|
|
bSig |= LIT64( 0x4000000000000000 );
|
2037 |
|
|
bBigger:
|
2038 |
|
|
zSig = bSig - aSig;
|
2039 |
|
|
zExp = bExp;
|
2040 |
|
|
zSign ^= 1;
|
2041 |
|
|
goto normalizeRoundAndPack;
|
2042 |
|
|
aExpBigger:
|
2043 |
|
|
if ( aExp == 0x7FF ) {
|
2044 |
|
|
if ( aSig ) return propagateFloat64NaN( a, b );
|
2045 |
|
|
return a;
|
2046 |
|
|
}
|
2047 |
|
|
if ( bExp == 0 ) {
|
2048 |
|
|
--expDiff;
|
2049 |
|
|
}
|
2050 |
|
|
else {
|
2051 |
|
|
bSig |= LIT64( 0x4000000000000000 );
|
2052 |
|
|
}
|
2053 |
|
|
shift64RightJamming( bSig, expDiff, &bSig );
|
2054 |
|
|
aSig |= LIT64( 0x4000000000000000 );
|
2055 |
|
|
aBigger:
|
2056 |
|
|
zSig = aSig - bSig;
|
2057 |
|
|
zExp = aExp;
|
2058 |
|
|
normalizeRoundAndPack:
|
2059 |
|
|
--zExp;
|
2060 |
|
|
return normalizeRoundAndPackFloat64( roundData, zSign, zExp, zSig );
|
2061 |
|
|
|
2062 |
|
|
}
|
2063 |
|
|
|
2064 |
|
|
/*
|
2065 |
|
|
-------------------------------------------------------------------------------
|
2066 |
|
|
Returns the result of adding the double-precision floating-point values `a'
|
2067 |
|
|
and `b'. The operation is performed according to the IEC/IEEE Standard for
|
2068 |
|
|
Binary Floating-point Arithmetic.
|
2069 |
|
|
-------------------------------------------------------------------------------
|
2070 |
|
|
*/
|
2071 |
|
|
float64 float64_add( struct roundingData *roundData, float64 a, float64 b )
|
2072 |
|
|
{
|
2073 |
|
|
flag aSign, bSign;
|
2074 |
|
|
|
2075 |
|
|
aSign = extractFloat64Sign( a );
|
2076 |
|
|
bSign = extractFloat64Sign( b );
|
2077 |
|
|
if ( aSign == bSign ) {
|
2078 |
|
|
return addFloat64Sigs( roundData, a, b, aSign );
|
2079 |
|
|
}
|
2080 |
|
|
else {
|
2081 |
|
|
return subFloat64Sigs( roundData, a, b, aSign );
|
2082 |
|
|
}
|
2083 |
|
|
|
2084 |
|
|
}
|
2085 |
|
|
|
2086 |
|
|
/*
|
2087 |
|
|
-------------------------------------------------------------------------------
|
2088 |
|
|
Returns the result of subtracting the double-precision floating-point values
|
2089 |
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
2090 |
|
|
for Binary Floating-point Arithmetic.
|
2091 |
|
|
-------------------------------------------------------------------------------
|
2092 |
|
|
*/
|
2093 |
|
|
float64 float64_sub( struct roundingData *roundData, float64 a, float64 b )
|
2094 |
|
|
{
|
2095 |
|
|
flag aSign, bSign;
|
2096 |
|
|
|
2097 |
|
|
aSign = extractFloat64Sign( a );
|
2098 |
|
|
bSign = extractFloat64Sign( b );
|
2099 |
|
|
if ( aSign == bSign ) {
|
2100 |
|
|
return subFloat64Sigs( roundData, a, b, aSign );
|
2101 |
|
|
}
|
2102 |
|
|
else {
|
2103 |
|
|
return addFloat64Sigs( roundData, a, b, aSign );
|
2104 |
|
|
}
|
2105 |
|
|
|
2106 |
|
|
}
|
2107 |
|
|
|
2108 |
|
|
/*
|
2109 |
|
|
-------------------------------------------------------------------------------
|
2110 |
|
|
Returns the result of multiplying the double-precision floating-point values
|
2111 |
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
2112 |
|
|
for Binary Floating-point Arithmetic.
|
2113 |
|
|
-------------------------------------------------------------------------------
|
2114 |
|
|
*/
|
2115 |
|
|
float64 float64_mul( struct roundingData *roundData, float64 a, float64 b )
|
2116 |
|
|
{
|
2117 |
|
|
flag aSign, bSign, zSign;
|
2118 |
|
|
int16 aExp, bExp, zExp;
|
2119 |
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
2120 |
|
|
|
2121 |
|
|
aSig = extractFloat64Frac( a );
|
2122 |
|
|
aExp = extractFloat64Exp( a );
|
2123 |
|
|
aSign = extractFloat64Sign( a );
|
2124 |
|
|
bSig = extractFloat64Frac( b );
|
2125 |
|
|
bExp = extractFloat64Exp( b );
|
2126 |
|
|
bSign = extractFloat64Sign( b );
|
2127 |
|
|
zSign = aSign ^ bSign;
|
2128 |
|
|
if ( aExp == 0x7FF ) {
|
2129 |
|
|
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
|
2130 |
|
|
return propagateFloat64NaN( a, b );
|
2131 |
|
|
}
|
2132 |
|
|
if ( ( bExp | bSig ) == 0 ) {
|
2133 |
|
|
roundData->exception |= float_flag_invalid;
|
2134 |
|
|
return float64_default_nan;
|
2135 |
|
|
}
|
2136 |
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
2137 |
|
|
}
|
2138 |
|
|
if ( bExp == 0x7FF ) {
|
2139 |
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
2140 |
|
|
if ( ( aExp | aSig ) == 0 ) {
|
2141 |
|
|
roundData->exception |= float_flag_invalid;
|
2142 |
|
|
return float64_default_nan;
|
2143 |
|
|
}
|
2144 |
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
2145 |
|
|
}
|
2146 |
|
|
if ( aExp == 0 ) {
|
2147 |
|
|
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
|
2148 |
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
2149 |
|
|
}
|
2150 |
|
|
if ( bExp == 0 ) {
|
2151 |
|
|
if ( bSig == 0 ) return packFloat64( zSign, 0, 0 );
|
2152 |
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
2153 |
|
|
}
|
2154 |
|
|
zExp = aExp + bExp - 0x3FF;
|
2155 |
|
|
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
|
2156 |
|
|
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
|
2157 |
|
|
mul64To128( aSig, bSig, &zSig0, &zSig1 );
|
2158 |
|
|
zSig0 |= ( zSig1 != 0 );
|
2159 |
|
|
if ( 0 <= (sbits64) ( zSig0<<1 ) ) {
|
2160 |
|
|
zSig0 <<= 1;
|
2161 |
|
|
--zExp;
|
2162 |
|
|
}
|
2163 |
|
|
return roundAndPackFloat64( roundData, zSign, zExp, zSig0 );
|
2164 |
|
|
|
2165 |
|
|
}
|
2166 |
|
|
|
2167 |
|
|
/*
|
2168 |
|
|
-------------------------------------------------------------------------------
|
2169 |
|
|
Returns the result of dividing the double-precision floating-point value `a'
|
2170 |
|
|
by the corresponding value `b'. The operation is performed according to
|
2171 |
|
|
the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2172 |
|
|
-------------------------------------------------------------------------------
|
2173 |
|
|
*/
|
2174 |
|
|
float64 float64_div( struct roundingData *roundData, float64 a, float64 b )
|
2175 |
|
|
{
|
2176 |
|
|
flag aSign, bSign, zSign;
|
2177 |
|
|
int16 aExp, bExp, zExp;
|
2178 |
|
|
bits64 aSig, bSig, zSig;
|
2179 |
|
|
bits64 rem0, rem1;
|
2180 |
|
|
bits64 term0, term1;
|
2181 |
|
|
|
2182 |
|
|
aSig = extractFloat64Frac( a );
|
2183 |
|
|
aExp = extractFloat64Exp( a );
|
2184 |
|
|
aSign = extractFloat64Sign( a );
|
2185 |
|
|
bSig = extractFloat64Frac( b );
|
2186 |
|
|
bExp = extractFloat64Exp( b );
|
2187 |
|
|
bSign = extractFloat64Sign( b );
|
2188 |
|
|
zSign = aSign ^ bSign;
|
2189 |
|
|
if ( aExp == 0x7FF ) {
|
2190 |
|
|
if ( aSig ) return propagateFloat64NaN( a, b );
|
2191 |
|
|
if ( bExp == 0x7FF ) {
|
2192 |
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
2193 |
|
|
roundData->exception |= float_flag_invalid;
|
2194 |
|
|
return float64_default_nan;
|
2195 |
|
|
}
|
2196 |
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
2197 |
|
|
}
|
2198 |
|
|
if ( bExp == 0x7FF ) {
|
2199 |
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
2200 |
|
|
return packFloat64( zSign, 0, 0 );
|
2201 |
|
|
}
|
2202 |
|
|
if ( bExp == 0 ) {
|
2203 |
|
|
if ( bSig == 0 ) {
|
2204 |
|
|
if ( ( aExp | aSig ) == 0 ) {
|
2205 |
|
|
roundData->exception |= float_flag_invalid;
|
2206 |
|
|
return float64_default_nan;
|
2207 |
|
|
}
|
2208 |
|
|
roundData->exception |= float_flag_divbyzero;
|
2209 |
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
2210 |
|
|
}
|
2211 |
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
2212 |
|
|
}
|
2213 |
|
|
if ( aExp == 0 ) {
|
2214 |
|
|
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
|
2215 |
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
2216 |
|
|
}
|
2217 |
|
|
zExp = aExp - bExp + 0x3FD;
|
2218 |
|
|
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
|
2219 |
|
|
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
|
2220 |
|
|
if ( bSig <= ( aSig + aSig ) ) {
|
2221 |
|
|
aSig >>= 1;
|
2222 |
|
|
++zExp;
|
2223 |
|
|
}
|
2224 |
|
|
zSig = estimateDiv128To64( aSig, 0, bSig );
|
2225 |
|
|
if ( ( zSig & 0x1FF ) <= 2 ) {
|
2226 |
|
|
mul64To128( bSig, zSig, &term0, &term1 );
|
2227 |
|
|
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
2228 |
|
|
while ( (sbits64) rem0 < 0 ) {
|
2229 |
|
|
--zSig;
|
2230 |
|
|
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
2231 |
|
|
}
|
2232 |
|
|
zSig |= ( rem1 != 0 );
|
2233 |
|
|
}
|
2234 |
|
|
return roundAndPackFloat64( roundData, zSign, zExp, zSig );
|
2235 |
|
|
|
2236 |
|
|
}
|
2237 |
|
|
|
2238 |
|
|
/*
|
2239 |
|
|
-------------------------------------------------------------------------------
|
2240 |
|
|
Returns the remainder of the double-precision floating-point value `a'
|
2241 |
|
|
with respect to the corresponding value `b'. The operation is performed
|
2242 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2243 |
|
|
-------------------------------------------------------------------------------
|
2244 |
|
|
*/
|
2245 |
|
|
float64 float64_rem( struct roundingData *roundData, float64 a, float64 b )
|
2246 |
|
|
{
|
2247 |
|
|
flag aSign, bSign, zSign;
|
2248 |
|
|
int16 aExp, bExp, expDiff;
|
2249 |
|
|
bits64 aSig, bSig;
|
2250 |
|
|
bits64 q, alternateASig;
|
2251 |
|
|
sbits64 sigMean;
|
2252 |
|
|
|
2253 |
|
|
aSig = extractFloat64Frac( a );
|
2254 |
|
|
aExp = extractFloat64Exp( a );
|
2255 |
|
|
aSign = extractFloat64Sign( a );
|
2256 |
|
|
bSig = extractFloat64Frac( b );
|
2257 |
|
|
bExp = extractFloat64Exp( b );
|
2258 |
|
|
bSign = extractFloat64Sign( b );
|
2259 |
|
|
if ( aExp == 0x7FF ) {
|
2260 |
|
|
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
|
2261 |
|
|
return propagateFloat64NaN( a, b );
|
2262 |
|
|
}
|
2263 |
|
|
roundData->exception |= float_flag_invalid;
|
2264 |
|
|
return float64_default_nan;
|
2265 |
|
|
}
|
2266 |
|
|
if ( bExp == 0x7FF ) {
|
2267 |
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
2268 |
|
|
return a;
|
2269 |
|
|
}
|
2270 |
|
|
if ( bExp == 0 ) {
|
2271 |
|
|
if ( bSig == 0 ) {
|
2272 |
|
|
roundData->exception |= float_flag_invalid;
|
2273 |
|
|
return float64_default_nan;
|
2274 |
|
|
}
|
2275 |
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
2276 |
|
|
}
|
2277 |
|
|
if ( aExp == 0 ) {
|
2278 |
|
|
if ( aSig == 0 ) return a;
|
2279 |
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
2280 |
|
|
}
|
2281 |
|
|
expDiff = aExp - bExp;
|
2282 |
|
|
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11;
|
2283 |
|
|
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
|
2284 |
|
|
if ( expDiff < 0 ) {
|
2285 |
|
|
if ( expDiff < -1 ) return a;
|
2286 |
|
|
aSig >>= 1;
|
2287 |
|
|
}
|
2288 |
|
|
q = ( bSig <= aSig );
|
2289 |
|
|
if ( q ) aSig -= bSig;
|
2290 |
|
|
expDiff -= 64;
|
2291 |
|
|
while ( 0 < expDiff ) {
|
2292 |
|
|
q = estimateDiv128To64( aSig, 0, bSig );
|
2293 |
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
2294 |
|
|
aSig = - ( ( bSig>>2 ) * q );
|
2295 |
|
|
expDiff -= 62;
|
2296 |
|
|
}
|
2297 |
|
|
expDiff += 64;
|
2298 |
|
|
if ( 0 < expDiff ) {
|
2299 |
|
|
q = estimateDiv128To64( aSig, 0, bSig );
|
2300 |
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
2301 |
|
|
q >>= 64 - expDiff;
|
2302 |
|
|
bSig >>= 2;
|
2303 |
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
2304 |
|
|
}
|
2305 |
|
|
else {
|
2306 |
|
|
aSig >>= 2;
|
2307 |
|
|
bSig >>= 2;
|
2308 |
|
|
}
|
2309 |
|
|
do {
|
2310 |
|
|
alternateASig = aSig;
|
2311 |
|
|
++q;
|
2312 |
|
|
aSig -= bSig;
|
2313 |
|
|
} while ( 0 <= (sbits64) aSig );
|
2314 |
|
|
sigMean = aSig + alternateASig;
|
2315 |
|
|
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
|
2316 |
|
|
aSig = alternateASig;
|
2317 |
|
|
}
|
2318 |
|
|
zSign = ( (sbits64) aSig < 0 );
|
2319 |
|
|
if ( zSign ) aSig = - aSig;
|
2320 |
|
|
return normalizeRoundAndPackFloat64( roundData, aSign ^ zSign, bExp, aSig );
|
2321 |
|
|
|
2322 |
|
|
}
|
2323 |
|
|
|
2324 |
|
|
/*
|
2325 |
|
|
-------------------------------------------------------------------------------
|
2326 |
|
|
Returns the square root of the double-precision floating-point value `a'.
|
2327 |
|
|
The operation is performed according to the IEC/IEEE Standard for Binary
|
2328 |
|
|
Floating-point Arithmetic.
|
2329 |
|
|
-------------------------------------------------------------------------------
|
2330 |
|
|
*/
|
2331 |
|
|
float64 float64_sqrt( struct roundingData *roundData, float64 a )
|
2332 |
|
|
{
|
2333 |
|
|
flag aSign;
|
2334 |
|
|
int16 aExp, zExp;
|
2335 |
|
|
bits64 aSig, zSig;
|
2336 |
|
|
bits64 rem0, rem1, term0, term1; //, shiftedRem;
|
2337 |
|
|
//float64 z;
|
2338 |
|
|
|
2339 |
|
|
aSig = extractFloat64Frac( a );
|
2340 |
|
|
aExp = extractFloat64Exp( a );
|
2341 |
|
|
aSign = extractFloat64Sign( a );
|
2342 |
|
|
if ( aExp == 0x7FF ) {
|
2343 |
|
|
if ( aSig ) return propagateFloat64NaN( a, a );
|
2344 |
|
|
if ( ! aSign ) return a;
|
2345 |
|
|
roundData->exception |= float_flag_invalid;
|
2346 |
|
|
return float64_default_nan;
|
2347 |
|
|
}
|
2348 |
|
|
if ( aSign ) {
|
2349 |
|
|
if ( ( aExp | aSig ) == 0 ) return a;
|
2350 |
|
|
roundData->exception |= float_flag_invalid;
|
2351 |
|
|
return float64_default_nan;
|
2352 |
|
|
}
|
2353 |
|
|
if ( aExp == 0 ) {
|
2354 |
|
|
if ( aSig == 0 ) return 0;
|
2355 |
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
2356 |
|
|
}
|
2357 |
|
|
zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
|
2358 |
|
|
aSig |= LIT64( 0x0010000000000000 );
|
2359 |
|
|
zSig = estimateSqrt32( aExp, aSig>>21 );
|
2360 |
|
|
zSig <<= 31;
|
2361 |
|
|
aSig <<= 9 - ( aExp & 1 );
|
2362 |
|
|
zSig = estimateDiv128To64( aSig, 0, zSig ) + zSig + 2;
|
2363 |
|
|
if ( ( zSig & 0x3FF ) <= 5 ) {
|
2364 |
|
|
if ( zSig < 2 ) {
|
2365 |
|
|
zSig = LIT64( 0xFFFFFFFFFFFFFFFF );
|
2366 |
|
|
}
|
2367 |
|
|
else {
|
2368 |
|
|
aSig <<= 2;
|
2369 |
|
|
mul64To128( zSig, zSig, &term0, &term1 );
|
2370 |
|
|
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
2371 |
|
|
while ( (sbits64) rem0 < 0 ) {
|
2372 |
|
|
--zSig;
|
2373 |
|
|
shortShift128Left( 0, zSig, 1, &term0, &term1 );
|
2374 |
|
|
term1 |= 1;
|
2375 |
|
|
add128( rem0, rem1, term0, term1, &rem0, &rem1 );
|
2376 |
|
|
}
|
2377 |
|
|
zSig |= ( ( rem0 | rem1 ) != 0 );
|
2378 |
|
|
}
|
2379 |
|
|
}
|
2380 |
|
|
shift64RightJamming( zSig, 1, &zSig );
|
2381 |
|
|
return roundAndPackFloat64( roundData, 0, zExp, zSig );
|
2382 |
|
|
|
2383 |
|
|
}
|
2384 |
|
|
|
2385 |
|
|
/*
|
2386 |
|
|
-------------------------------------------------------------------------------
|
2387 |
|
|
Returns 1 if the double-precision floating-point value `a' is equal to the
|
2388 |
|
|
corresponding value `b', and 0 otherwise. The comparison is performed
|
2389 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2390 |
|
|
-------------------------------------------------------------------------------
|
2391 |
|
|
*/
|
2392 |
|
|
flag float64_eq( float64 a, float64 b )
|
2393 |
|
|
{
|
2394 |
|
|
|
2395 |
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
2396 |
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
2397 |
|
|
) {
|
2398 |
|
|
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
2399 |
|
|
float_raise( float_flag_invalid );
|
2400 |
|
|
}
|
2401 |
|
|
return 0;
|
2402 |
|
|
}
|
2403 |
|
|
return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
2404 |
|
|
|
2405 |
|
|
}
|
2406 |
|
|
|
2407 |
|
|
/*
|
2408 |
|
|
-------------------------------------------------------------------------------
|
2409 |
|
|
Returns 1 if the double-precision floating-point value `a' is less than or
|
2410 |
|
|
equal to the corresponding value `b', and 0 otherwise. The comparison is
|
2411 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
2412 |
|
|
Arithmetic.
|
2413 |
|
|
-------------------------------------------------------------------------------
|
2414 |
|
|
*/
|
2415 |
|
|
flag float64_le( float64 a, float64 b )
|
2416 |
|
|
{
|
2417 |
|
|
flag aSign, bSign;
|
2418 |
|
|
|
2419 |
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
2420 |
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
2421 |
|
|
) {
|
2422 |
|
|
float_raise( float_flag_invalid );
|
2423 |
|
|
return 0;
|
2424 |
|
|
}
|
2425 |
|
|
aSign = extractFloat64Sign( a );
|
2426 |
|
|
bSign = extractFloat64Sign( b );
|
2427 |
|
|
if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
2428 |
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
2429 |
|
|
|
2430 |
|
|
}
|
2431 |
|
|
|
2432 |
|
|
/*
|
2433 |
|
|
-------------------------------------------------------------------------------
|
2434 |
|
|
Returns 1 if the double-precision floating-point value `a' is less than
|
2435 |
|
|
the corresponding value `b', and 0 otherwise. The comparison is performed
|
2436 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2437 |
|
|
-------------------------------------------------------------------------------
|
2438 |
|
|
*/
|
2439 |
|
|
flag float64_lt( float64 a, float64 b )
|
2440 |
|
|
{
|
2441 |
|
|
flag aSign, bSign;
|
2442 |
|
|
|
2443 |
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
2444 |
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
2445 |
|
|
) {
|
2446 |
|
|
float_raise( float_flag_invalid );
|
2447 |
|
|
return 0;
|
2448 |
|
|
}
|
2449 |
|
|
aSign = extractFloat64Sign( a );
|
2450 |
|
|
bSign = extractFloat64Sign( b );
|
2451 |
|
|
if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
|
2452 |
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
2453 |
|
|
|
2454 |
|
|
}
|
2455 |
|
|
|
2456 |
|
|
/*
|
2457 |
|
|
-------------------------------------------------------------------------------
|
2458 |
|
|
Returns 1 if the double-precision floating-point value `a' is equal to the
|
2459 |
|
|
corresponding value `b', and 0 otherwise. The invalid exception is raised
|
2460 |
|
|
if either operand is a NaN. Otherwise, the comparison is performed
|
2461 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2462 |
|
|
-------------------------------------------------------------------------------
|
2463 |
|
|
*/
|
2464 |
|
|
flag float64_eq_signaling( float64 a, float64 b )
|
2465 |
|
|
{
|
2466 |
|
|
|
2467 |
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
2468 |
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
2469 |
|
|
) {
|
2470 |
|
|
float_raise( float_flag_invalid );
|
2471 |
|
|
return 0;
|
2472 |
|
|
}
|
2473 |
|
|
return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
2474 |
|
|
|
2475 |
|
|
}
|
2476 |
|
|
|
2477 |
|
|
/*
|
2478 |
|
|
-------------------------------------------------------------------------------
|
2479 |
|
|
Returns 1 if the double-precision floating-point value `a' is less than or
|
2480 |
|
|
equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
2481 |
|
|
cause an exception. Otherwise, the comparison is performed according to the
|
2482 |
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2483 |
|
|
-------------------------------------------------------------------------------
|
2484 |
|
|
*/
|
2485 |
|
|
flag float64_le_quiet( float64 a, float64 b )
|
2486 |
|
|
{
|
2487 |
|
|
flag aSign, bSign;
|
2488 |
|
|
//int16 aExp, bExp;
|
2489 |
|
|
|
2490 |
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
2491 |
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
2492 |
|
|
) {
|
2493 |
|
|
/* Do nothing, even if NaN as we're quiet */
|
2494 |
|
|
return 0;
|
2495 |
|
|
}
|
2496 |
|
|
aSign = extractFloat64Sign( a );
|
2497 |
|
|
bSign = extractFloat64Sign( b );
|
2498 |
|
|
if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
2499 |
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
2500 |
|
|
|
2501 |
|
|
}
|
2502 |
|
|
|
2503 |
|
|
/*
|
2504 |
|
|
-------------------------------------------------------------------------------
|
2505 |
|
|
Returns 1 if the double-precision floating-point value `a' is less than
|
2506 |
|
|
the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
2507 |
|
|
exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
2508 |
|
|
Standard for Binary Floating-point Arithmetic.
|
2509 |
|
|
-------------------------------------------------------------------------------
|
2510 |
|
|
*/
|
2511 |
|
|
flag float64_lt_quiet( float64 a, float64 b )
|
2512 |
|
|
{
|
2513 |
|
|
flag aSign, bSign;
|
2514 |
|
|
|
2515 |
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
2516 |
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
2517 |
|
|
) {
|
2518 |
|
|
/* Do nothing, even if NaN as we're quiet */
|
2519 |
|
|
return 0;
|
2520 |
|
|
}
|
2521 |
|
|
aSign = extractFloat64Sign( a );
|
2522 |
|
|
bSign = extractFloat64Sign( b );
|
2523 |
|
|
if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
|
2524 |
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
2525 |
|
|
|
2526 |
|
|
}
|
2527 |
|
|
|
2528 |
|
|
#ifdef FLOATX80
|
2529 |
|
|
|
2530 |
|
|
/*
|
2531 |
|
|
-------------------------------------------------------------------------------
|
2532 |
|
|
Returns the result of converting the extended double-precision floating-
|
2533 |
|
|
point value `a' to the 32-bit two's complement integer format. The
|
2534 |
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
2535 |
|
|
Floating-point Arithmetic---which means in particular that the conversion
|
2536 |
|
|
is rounded according to the current rounding mode. If `a' is a NaN, the
|
2537 |
|
|
largest positive integer is returned. Otherwise, if the conversion
|
2538 |
|
|
overflows, the largest integer with the same sign as `a' is returned.
|
2539 |
|
|
-------------------------------------------------------------------------------
|
2540 |
|
|
*/
|
2541 |
|
|
int32 floatx80_to_int32( struct roundingData *roundData, floatx80 a )
|
2542 |
|
|
{
|
2543 |
|
|
flag aSign;
|
2544 |
|
|
int32 aExp, shiftCount;
|
2545 |
|
|
bits64 aSig;
|
2546 |
|
|
|
2547 |
|
|
aSig = extractFloatx80Frac( a );
|
2548 |
|
|
aExp = extractFloatx80Exp( a );
|
2549 |
|
|
aSign = extractFloatx80Sign( a );
|
2550 |
|
|
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
|
2551 |
|
|
shiftCount = 0x4037 - aExp;
|
2552 |
|
|
if ( shiftCount <= 0 ) shiftCount = 1;
|
2553 |
|
|
shift64RightJamming( aSig, shiftCount, &aSig );
|
2554 |
|
|
return roundAndPackInt32( roundData, aSign, aSig );
|
2555 |
|
|
|
2556 |
|
|
}
|
2557 |
|
|
|
2558 |
|
|
/*
|
2559 |
|
|
-------------------------------------------------------------------------------
|
2560 |
|
|
Returns the result of converting the extended double-precision floating-
|
2561 |
|
|
point value `a' to the 32-bit two's complement integer format. The
|
2562 |
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
2563 |
|
|
Floating-point Arithmetic, except that the conversion is always rounded
|
2564 |
|
|
toward zero. If `a' is a NaN, the largest positive integer is returned.
|
2565 |
|
|
Otherwise, if the conversion overflows, the largest integer with the same
|
2566 |
|
|
sign as `a' is returned.
|
2567 |
|
|
-------------------------------------------------------------------------------
|
2568 |
|
|
*/
|
2569 |
|
|
int32 floatx80_to_int32_round_to_zero( floatx80 a )
|
2570 |
|
|
{
|
2571 |
|
|
flag aSign;
|
2572 |
|
|
int32 aExp, shiftCount;
|
2573 |
|
|
bits64 aSig, savedASig;
|
2574 |
|
|
int32 z;
|
2575 |
|
|
|
2576 |
|
|
aSig = extractFloatx80Frac( a );
|
2577 |
|
|
aExp = extractFloatx80Exp( a );
|
2578 |
|
|
aSign = extractFloatx80Sign( a );
|
2579 |
|
|
shiftCount = 0x403E - aExp;
|
2580 |
|
|
if ( shiftCount < 32 ) {
|
2581 |
|
|
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
|
2582 |
|
|
goto invalid;
|
2583 |
|
|
}
|
2584 |
|
|
else if ( 63 < shiftCount ) {
|
2585 |
|
|
if ( aExp || aSig ) float_raise( float_flag_inexact );
|
2586 |
|
|
return 0;
|
2587 |
|
|
}
|
2588 |
|
|
savedASig = aSig;
|
2589 |
|
|
aSig >>= shiftCount;
|
2590 |
|
|
z = aSig;
|
2591 |
|
|
if ( aSign ) z = - z;
|
2592 |
|
|
if ( ( z < 0 ) ^ aSign ) {
|
2593 |
|
|
invalid:
|
2594 |
|
|
float_raise( float_flag_invalid );
|
2595 |
|
|
return aSign ? 0x80000000 : 0x7FFFFFFF;
|
2596 |
|
|
}
|
2597 |
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
2598 |
|
|
float_raise( float_flag_inexact );
|
2599 |
|
|
}
|
2600 |
|
|
return z;
|
2601 |
|
|
|
2602 |
|
|
}
|
2603 |
|
|
|
2604 |
|
|
/*
|
2605 |
|
|
-------------------------------------------------------------------------------
|
2606 |
|
|
Returns the result of converting the extended double-precision floating-
|
2607 |
|
|
point value `a' to the single-precision floating-point format. The
|
2608 |
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
2609 |
|
|
Floating-point Arithmetic.
|
2610 |
|
|
-------------------------------------------------------------------------------
|
2611 |
|
|
*/
|
2612 |
|
|
float32 floatx80_to_float32( struct roundingData *roundData, floatx80 a )
|
2613 |
|
|
{
|
2614 |
|
|
flag aSign;
|
2615 |
|
|
int32 aExp;
|
2616 |
|
|
bits64 aSig;
|
2617 |
|
|
|
2618 |
|
|
aSig = extractFloatx80Frac( a );
|
2619 |
|
|
aExp = extractFloatx80Exp( a );
|
2620 |
|
|
aSign = extractFloatx80Sign( a );
|
2621 |
|
|
if ( aExp == 0x7FFF ) {
|
2622 |
|
|
if ( (bits64) ( aSig<<1 ) ) {
|
2623 |
|
|
return commonNaNToFloat32( floatx80ToCommonNaN( a ) );
|
2624 |
|
|
}
|
2625 |
|
|
return packFloat32( aSign, 0xFF, 0 );
|
2626 |
|
|
}
|
2627 |
|
|
shift64RightJamming( aSig, 33, &aSig );
|
2628 |
|
|
if ( aExp || aSig ) aExp -= 0x3F81;
|
2629 |
|
|
return roundAndPackFloat32( roundData, aSign, aExp, aSig );
|
2630 |
|
|
|
2631 |
|
|
}
|
2632 |
|
|
|
2633 |
|
|
/*
|
2634 |
|
|
-------------------------------------------------------------------------------
|
2635 |
|
|
Returns the result of converting the extended double-precision floating-
|
2636 |
|
|
point value `a' to the double-precision floating-point format. The
|
2637 |
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
2638 |
|
|
Floating-point Arithmetic.
|
2639 |
|
|
-------------------------------------------------------------------------------
|
2640 |
|
|
*/
|
2641 |
|
|
float64 floatx80_to_float64( struct roundingData *roundData, floatx80 a )
|
2642 |
|
|
{
|
2643 |
|
|
flag aSign;
|
2644 |
|
|
int32 aExp;
|
2645 |
|
|
bits64 aSig, zSig;
|
2646 |
|
|
|
2647 |
|
|
aSig = extractFloatx80Frac( a );
|
2648 |
|
|
aExp = extractFloatx80Exp( a );
|
2649 |
|
|
aSign = extractFloatx80Sign( a );
|
2650 |
|
|
if ( aExp == 0x7FFF ) {
|
2651 |
|
|
if ( (bits64) ( aSig<<1 ) ) {
|
2652 |
|
|
return commonNaNToFloat64( floatx80ToCommonNaN( a ) );
|
2653 |
|
|
}
|
2654 |
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
2655 |
|
|
}
|
2656 |
|
|
shift64RightJamming( aSig, 1, &zSig );
|
2657 |
|
|
if ( aExp || aSig ) aExp -= 0x3C01;
|
2658 |
|
|
return roundAndPackFloat64( roundData, aSign, aExp, zSig );
|
2659 |
|
|
|
2660 |
|
|
}
|
2661 |
|
|
|
2662 |
|
|
/*
|
2663 |
|
|
-------------------------------------------------------------------------------
|
2664 |
|
|
Rounds the extended double-precision floating-point value `a' to an integer,
|
2665 |
|
|
and returns the result as an extended quadruple-precision floating-point
|
2666 |
|
|
value. The operation is performed according to the IEC/IEEE Standard for
|
2667 |
|
|
Binary Floating-point Arithmetic.
|
2668 |
|
|
-------------------------------------------------------------------------------
|
2669 |
|
|
*/
|
2670 |
|
|
floatx80 floatx80_round_to_int( struct roundingData *roundData, floatx80 a )
|
2671 |
|
|
{
|
2672 |
|
|
flag aSign;
|
2673 |
|
|
int32 aExp;
|
2674 |
|
|
bits64 lastBitMask, roundBitsMask;
|
2675 |
|
|
int8 roundingMode;
|
2676 |
|
|
floatx80 z;
|
2677 |
|
|
|
2678 |
|
|
aExp = extractFloatx80Exp( a );
|
2679 |
|
|
if ( 0x403E <= aExp ) {
|
2680 |
|
|
if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) {
|
2681 |
|
|
return propagateFloatx80NaN( a, a );
|
2682 |
|
|
}
|
2683 |
|
|
return a;
|
2684 |
|
|
}
|
2685 |
|
|
if ( aExp <= 0x3FFE ) {
|
2686 |
|
|
if ( ( aExp == 0 )
|
2687 |
|
|
&& ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
|
2688 |
|
|
return a;
|
2689 |
|
|
}
|
2690 |
|
|
roundData->exception |= float_flag_inexact;
|
2691 |
|
|
aSign = extractFloatx80Sign( a );
|
2692 |
|
|
switch ( roundData->mode ) {
|
2693 |
|
|
case float_round_nearest_even:
|
2694 |
|
|
if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 )
|
2695 |
|
|
) {
|
2696 |
|
|
return
|
2697 |
|
|
packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) );
|
2698 |
|
|
}
|
2699 |
|
|
break;
|
2700 |
|
|
case float_round_down:
|
2701 |
|
|
return
|
2702 |
|
|
aSign ?
|
2703 |
|
|
packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) )
|
2704 |
|
|
: packFloatx80( 0, 0, 0 );
|
2705 |
|
|
case float_round_up:
|
2706 |
|
|
return
|
2707 |
|
|
aSign ? packFloatx80( 1, 0, 0 )
|
2708 |
|
|
: packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) );
|
2709 |
|
|
}
|
2710 |
|
|
return packFloatx80( aSign, 0, 0 );
|
2711 |
|
|
}
|
2712 |
|
|
lastBitMask = 1;
|
2713 |
|
|
lastBitMask <<= 0x403E - aExp;
|
2714 |
|
|
roundBitsMask = lastBitMask - 1;
|
2715 |
|
|
z = a;
|
2716 |
|
|
roundingMode = roundData->mode;
|
2717 |
|
|
if ( roundingMode == float_round_nearest_even ) {
|
2718 |
|
|
z.low += lastBitMask>>1;
|
2719 |
|
|
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
|
2720 |
|
|
}
|
2721 |
|
|
else if ( roundingMode != float_round_to_zero ) {
|
2722 |
|
|
if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
2723 |
|
|
z.low += roundBitsMask;
|
2724 |
|
|
}
|
2725 |
|
|
}
|
2726 |
|
|
z.low &= ~ roundBitsMask;
|
2727 |
|
|
if ( z.low == 0 ) {
|
2728 |
|
|
++z.high;
|
2729 |
|
|
z.low = LIT64( 0x8000000000000000 );
|
2730 |
|
|
}
|
2731 |
|
|
if ( z.low != a.low ) roundData->exception |= float_flag_inexact;
|
2732 |
|
|
return z;
|
2733 |
|
|
|
2734 |
|
|
}
|
2735 |
|
|
|
2736 |
|
|
/*
|
2737 |
|
|
-------------------------------------------------------------------------------
|
2738 |
|
|
Returns the result of adding the absolute values of the extended double-
|
2739 |
|
|
precision floating-point values `a' and `b'. If `zSign' is true, the sum is
|
2740 |
|
|
negated before being returned. `zSign' is ignored if the result is a NaN.
|
2741 |
|
|
The addition is performed according to the IEC/IEEE Standard for Binary
|
2742 |
|
|
Floating-point Arithmetic.
|
2743 |
|
|
-------------------------------------------------------------------------------
|
2744 |
|
|
*/
|
2745 |
|
|
static floatx80 addFloatx80Sigs( struct roundingData *roundData, floatx80 a, floatx80 b, flag zSign )
|
2746 |
|
|
{
|
2747 |
|
|
int32 aExp, bExp, zExp;
|
2748 |
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
2749 |
|
|
int32 expDiff;
|
2750 |
|
|
|
2751 |
|
|
aSig = extractFloatx80Frac( a );
|
2752 |
|
|
aExp = extractFloatx80Exp( a );
|
2753 |
|
|
bSig = extractFloatx80Frac( b );
|
2754 |
|
|
bExp = extractFloatx80Exp( b );
|
2755 |
|
|
expDiff = aExp - bExp;
|
2756 |
|
|
if ( 0 < expDiff ) {
|
2757 |
|
|
if ( aExp == 0x7FFF ) {
|
2758 |
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
2759 |
|
|
return a;
|
2760 |
|
|
}
|
2761 |
|
|
if ( bExp == 0 ) --expDiff;
|
2762 |
|
|
shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
2763 |
|
|
zExp = aExp;
|
2764 |
|
|
}
|
2765 |
|
|
else if ( expDiff < 0 ) {
|
2766 |
|
|
if ( bExp == 0x7FFF ) {
|
2767 |
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
2768 |
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
2769 |
|
|
}
|
2770 |
|
|
if ( aExp == 0 ) ++expDiff;
|
2771 |
|
|
shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
2772 |
|
|
zExp = bExp;
|
2773 |
|
|
}
|
2774 |
|
|
else {
|
2775 |
|
|
if ( aExp == 0x7FFF ) {
|
2776 |
|
|
if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
|
2777 |
|
|
return propagateFloatx80NaN( a, b );
|
2778 |
|
|
}
|
2779 |
|
|
return a;
|
2780 |
|
|
}
|
2781 |
|
|
zSig1 = 0;
|
2782 |
|
|
zSig0 = aSig + bSig;
|
2783 |
|
|
if ( aExp == 0 ) {
|
2784 |
|
|
normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
|
2785 |
|
|
goto roundAndPack;
|
2786 |
|
|
}
|
2787 |
|
|
zExp = aExp;
|
2788 |
|
|
goto shiftRight1;
|
2789 |
|
|
}
|
2790 |
|
|
|
2791 |
|
|
zSig0 = aSig + bSig;
|
2792 |
|
|
|
2793 |
|
|
if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
|
2794 |
|
|
shiftRight1:
|
2795 |
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
2796 |
|
|
zSig0 |= LIT64( 0x8000000000000000 );
|
2797 |
|
|
++zExp;
|
2798 |
|
|
roundAndPack:
|
2799 |
|
|
return
|
2800 |
|
|
roundAndPackFloatx80(
|
2801 |
|
|
roundData, zSign, zExp, zSig0, zSig1 );
|
2802 |
|
|
|
2803 |
|
|
}
|
2804 |
|
|
|
2805 |
|
|
/*
|
2806 |
|
|
-------------------------------------------------------------------------------
|
2807 |
|
|
Returns the result of subtracting the absolute values of the extended
|
2808 |
|
|
double-precision floating-point values `a' and `b'. If `zSign' is true,
|
2809 |
|
|
the difference is negated before being returned. `zSign' is ignored if the
|
2810 |
|
|
result is a NaN. The subtraction is performed according to the IEC/IEEE
|
2811 |
|
|
Standard for Binary Floating-point Arithmetic.
|
2812 |
|
|
-------------------------------------------------------------------------------
|
2813 |
|
|
*/
|
2814 |
|
|
static floatx80 subFloatx80Sigs( struct roundingData *roundData, floatx80 a, floatx80 b, flag zSign )
|
2815 |
|
|
{
|
2816 |
|
|
int32 aExp, bExp, zExp;
|
2817 |
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
2818 |
|
|
int32 expDiff;
|
2819 |
|
|
floatx80 z;
|
2820 |
|
|
|
2821 |
|
|
aSig = extractFloatx80Frac( a );
|
2822 |
|
|
aExp = extractFloatx80Exp( a );
|
2823 |
|
|
bSig = extractFloatx80Frac( b );
|
2824 |
|
|
bExp = extractFloatx80Exp( b );
|
2825 |
|
|
expDiff = aExp - bExp;
|
2826 |
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
2827 |
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
2828 |
|
|
if ( aExp == 0x7FFF ) {
|
2829 |
|
|
if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
|
2830 |
|
|
return propagateFloatx80NaN( a, b );
|
2831 |
|
|
}
|
2832 |
|
|
roundData->exception |= float_flag_invalid;
|
2833 |
|
|
z.low = floatx80_default_nan_low;
|
2834 |
|
|
z.high = floatx80_default_nan_high;
|
2835 |
|
|
z.__padding = 0;
|
2836 |
|
|
return z;
|
2837 |
|
|
}
|
2838 |
|
|
if ( aExp == 0 ) {
|
2839 |
|
|
aExp = 1;
|
2840 |
|
|
bExp = 1;
|
2841 |
|
|
}
|
2842 |
|
|
zSig1 = 0;
|
2843 |
|
|
if ( bSig < aSig ) goto aBigger;
|
2844 |
|
|
if ( aSig < bSig ) goto bBigger;
|
2845 |
|
|
return packFloatx80( roundData->mode == float_round_down, 0, 0 );
|
2846 |
|
|
bExpBigger:
|
2847 |
|
|
if ( bExp == 0x7FFF ) {
|
2848 |
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
2849 |
|
|
return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
2850 |
|
|
}
|
2851 |
|
|
if ( aExp == 0 ) ++expDiff;
|
2852 |
|
|
shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
2853 |
|
|
bBigger:
|
2854 |
|
|
sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
|
2855 |
|
|
zExp = bExp;
|
2856 |
|
|
zSign ^= 1;
|
2857 |
|
|
goto normalizeRoundAndPack;
|
2858 |
|
|
aExpBigger:
|
2859 |
|
|
if ( aExp == 0x7FFF ) {
|
2860 |
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
2861 |
|
|
return a;
|
2862 |
|
|
}
|
2863 |
|
|
if ( bExp == 0 ) --expDiff;
|
2864 |
|
|
shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
2865 |
|
|
aBigger:
|
2866 |
|
|
sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
|
2867 |
|
|
zExp = aExp;
|
2868 |
|
|
normalizeRoundAndPack:
|
2869 |
|
|
return
|
2870 |
|
|
normalizeRoundAndPackFloatx80(
|
2871 |
|
|
roundData, zSign, zExp, zSig0, zSig1 );
|
2872 |
|
|
|
2873 |
|
|
}
|
2874 |
|
|
|
2875 |
|
|
/*
|
2876 |
|
|
-------------------------------------------------------------------------------
|
2877 |
|
|
Returns the result of adding the extended double-precision floating-point
|
2878 |
|
|
values `a' and `b'. The operation is performed according to the IEC/IEEE
|
2879 |
|
|
Standard for Binary Floating-point Arithmetic.
|
2880 |
|
|
-------------------------------------------------------------------------------
|
2881 |
|
|
*/
|
2882 |
|
|
floatx80 floatx80_add( struct roundingData *roundData, floatx80 a, floatx80 b )
|
2883 |
|
|
{
|
2884 |
|
|
flag aSign, bSign;
|
2885 |
|
|
|
2886 |
|
|
aSign = extractFloatx80Sign( a );
|
2887 |
|
|
bSign = extractFloatx80Sign( b );
|
2888 |
|
|
if ( aSign == bSign ) {
|
2889 |
|
|
return addFloatx80Sigs( roundData, a, b, aSign );
|
2890 |
|
|
}
|
2891 |
|
|
else {
|
2892 |
|
|
return subFloatx80Sigs( roundData, a, b, aSign );
|
2893 |
|
|
}
|
2894 |
|
|
|
2895 |
|
|
}
|
2896 |
|
|
|
2897 |
|
|
/*
|
2898 |
|
|
-------------------------------------------------------------------------------
|
2899 |
|
|
Returns the result of subtracting the extended double-precision floating-
|
2900 |
|
|
point values `a' and `b'. The operation is performed according to the
|
2901 |
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2902 |
|
|
-------------------------------------------------------------------------------
|
2903 |
|
|
*/
|
2904 |
|
|
floatx80 floatx80_sub( struct roundingData *roundData, floatx80 a, floatx80 b )
|
2905 |
|
|
{
|
2906 |
|
|
flag aSign, bSign;
|
2907 |
|
|
|
2908 |
|
|
aSign = extractFloatx80Sign( a );
|
2909 |
|
|
bSign = extractFloatx80Sign( b );
|
2910 |
|
|
if ( aSign == bSign ) {
|
2911 |
|
|
return subFloatx80Sigs( roundData, a, b, aSign );
|
2912 |
|
|
}
|
2913 |
|
|
else {
|
2914 |
|
|
return addFloatx80Sigs( roundData, a, b, aSign );
|
2915 |
|
|
}
|
2916 |
|
|
|
2917 |
|
|
}
|
2918 |
|
|
|
2919 |
|
|
/*
|
2920 |
|
|
-------------------------------------------------------------------------------
|
2921 |
|
|
Returns the result of multiplying the extended double-precision floating-
|
2922 |
|
|
point values `a' and `b'. The operation is performed according to the
|
2923 |
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2924 |
|
|
-------------------------------------------------------------------------------
|
2925 |
|
|
*/
|
2926 |
|
|
floatx80 floatx80_mul( struct roundingData *roundData, floatx80 a, floatx80 b )
|
2927 |
|
|
{
|
2928 |
|
|
flag aSign, bSign, zSign;
|
2929 |
|
|
int32 aExp, bExp, zExp;
|
2930 |
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
2931 |
|
|
floatx80 z;
|
2932 |
|
|
|
2933 |
|
|
aSig = extractFloatx80Frac( a );
|
2934 |
|
|
aExp = extractFloatx80Exp( a );
|
2935 |
|
|
aSign = extractFloatx80Sign( a );
|
2936 |
|
|
bSig = extractFloatx80Frac( b );
|
2937 |
|
|
bExp = extractFloatx80Exp( b );
|
2938 |
|
|
bSign = extractFloatx80Sign( b );
|
2939 |
|
|
zSign = aSign ^ bSign;
|
2940 |
|
|
if ( aExp == 0x7FFF ) {
|
2941 |
|
|
if ( (bits64) ( aSig<<1 )
|
2942 |
|
|
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
|
2943 |
|
|
return propagateFloatx80NaN( a, b );
|
2944 |
|
|
}
|
2945 |
|
|
if ( ( bExp | bSig ) == 0 ) goto invalid;
|
2946 |
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
2947 |
|
|
}
|
2948 |
|
|
if ( bExp == 0x7FFF ) {
|
2949 |
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
2950 |
|
|
if ( ( aExp | aSig ) == 0 ) {
|
2951 |
|
|
invalid:
|
2952 |
|
|
roundData->exception |= float_flag_invalid;
|
2953 |
|
|
z.low = floatx80_default_nan_low;
|
2954 |
|
|
z.high = floatx80_default_nan_high;
|
2955 |
|
|
z.__padding = 0;
|
2956 |
|
|
return z;
|
2957 |
|
|
}
|
2958 |
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
2959 |
|
|
}
|
2960 |
|
|
if ( aExp == 0 ) {
|
2961 |
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
2962 |
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
2963 |
|
|
}
|
2964 |
|
|
if ( bExp == 0 ) {
|
2965 |
|
|
if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
2966 |
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
2967 |
|
|
}
|
2968 |
|
|
zExp = aExp + bExp - 0x3FFE;
|
2969 |
|
|
mul64To128( aSig, bSig, &zSig0, &zSig1 );
|
2970 |
|
|
if ( 0 < (sbits64) zSig0 ) {
|
2971 |
|
|
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
2972 |
|
|
--zExp;
|
2973 |
|
|
}
|
2974 |
|
|
return
|
2975 |
|
|
roundAndPackFloatx80(
|
2976 |
|
|
roundData, zSign, zExp, zSig0, zSig1 );
|
2977 |
|
|
|
2978 |
|
|
}
|
2979 |
|
|
|
2980 |
|
|
/*
|
2981 |
|
|
-------------------------------------------------------------------------------
|
2982 |
|
|
Returns the result of dividing the extended double-precision floating-point
|
2983 |
|
|
value `a' by the corresponding value `b'. The operation is performed
|
2984 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
2985 |
|
|
-------------------------------------------------------------------------------
|
2986 |
|
|
*/
|
2987 |
|
|
floatx80 floatx80_div( struct roundingData *roundData, floatx80 a, floatx80 b )
|
2988 |
|
|
{
|
2989 |
|
|
flag aSign, bSign, zSign;
|
2990 |
|
|
int32 aExp, bExp, zExp;
|
2991 |
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
2992 |
|
|
bits64 rem0, rem1, rem2, term0, term1, term2;
|
2993 |
|
|
floatx80 z;
|
2994 |
|
|
|
2995 |
|
|
aSig = extractFloatx80Frac( a );
|
2996 |
|
|
aExp = extractFloatx80Exp( a );
|
2997 |
|
|
aSign = extractFloatx80Sign( a );
|
2998 |
|
|
bSig = extractFloatx80Frac( b );
|
2999 |
|
|
bExp = extractFloatx80Exp( b );
|
3000 |
|
|
bSign = extractFloatx80Sign( b );
|
3001 |
|
|
zSign = aSign ^ bSign;
|
3002 |
|
|
if ( aExp == 0x7FFF ) {
|
3003 |
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
3004 |
|
|
if ( bExp == 0x7FFF ) {
|
3005 |
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
3006 |
|
|
goto invalid;
|
3007 |
|
|
}
|
3008 |
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
3009 |
|
|
}
|
3010 |
|
|
if ( bExp == 0x7FFF ) {
|
3011 |
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
3012 |
|
|
return packFloatx80( zSign, 0, 0 );
|
3013 |
|
|
}
|
3014 |
|
|
if ( bExp == 0 ) {
|
3015 |
|
|
if ( bSig == 0 ) {
|
3016 |
|
|
if ( ( aExp | aSig ) == 0 ) {
|
3017 |
|
|
invalid:
|
3018 |
|
|
roundData->exception |= float_flag_invalid;
|
3019 |
|
|
z.low = floatx80_default_nan_low;
|
3020 |
|
|
z.high = floatx80_default_nan_high;
|
3021 |
|
|
z.__padding = 0;
|
3022 |
|
|
return z;
|
3023 |
|
|
}
|
3024 |
|
|
roundData->exception |= float_flag_divbyzero;
|
3025 |
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
3026 |
|
|
}
|
3027 |
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
3028 |
|
|
}
|
3029 |
|
|
if ( aExp == 0 ) {
|
3030 |
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
3031 |
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
3032 |
|
|
}
|
3033 |
|
|
zExp = aExp - bExp + 0x3FFE;
|
3034 |
|
|
rem1 = 0;
|
3035 |
|
|
if ( bSig <= aSig ) {
|
3036 |
|
|
shift128Right( aSig, 0, 1, &aSig, &rem1 );
|
3037 |
|
|
++zExp;
|
3038 |
|
|
}
|
3039 |
|
|
zSig0 = estimateDiv128To64( aSig, rem1, bSig );
|
3040 |
|
|
mul64To128( bSig, zSig0, &term0, &term1 );
|
3041 |
|
|
sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
|
3042 |
|
|
while ( (sbits64) rem0 < 0 ) {
|
3043 |
|
|
--zSig0;
|
3044 |
|
|
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
3045 |
|
|
}
|
3046 |
|
|
zSig1 = estimateDiv128To64( rem1, 0, bSig );
|
3047 |
|
|
if ( (bits64) ( zSig1<<1 ) <= 8 ) {
|
3048 |
|
|
mul64To128( bSig, zSig1, &term1, &term2 );
|
3049 |
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
3050 |
|
|
while ( (sbits64) rem1 < 0 ) {
|
3051 |
|
|
--zSig1;
|
3052 |
|
|
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
|
3053 |
|
|
}
|
3054 |
|
|
zSig1 |= ( ( rem1 | rem2 ) != 0 );
|
3055 |
|
|
}
|
3056 |
|
|
return
|
3057 |
|
|
roundAndPackFloatx80(
|
3058 |
|
|
roundData, zSign, zExp, zSig0, zSig1 );
|
3059 |
|
|
|
3060 |
|
|
}
|
3061 |
|
|
|
3062 |
|
|
/*
|
3063 |
|
|
-------------------------------------------------------------------------------
|
3064 |
|
|
Returns the remainder of the extended double-precision floating-point value
|
3065 |
|
|
`a' with respect to the corresponding value `b'. The operation is performed
|
3066 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
3067 |
|
|
-------------------------------------------------------------------------------
|
3068 |
|
|
*/
|
3069 |
|
|
floatx80 floatx80_rem( struct roundingData *roundData, floatx80 a, floatx80 b )
|
3070 |
|
|
{
|
3071 |
|
|
flag aSign, bSign, zSign;
|
3072 |
|
|
int32 aExp, bExp, expDiff;
|
3073 |
|
|
bits64 aSig0, aSig1, bSig;
|
3074 |
|
|
bits64 q, term0, term1, alternateASig0, alternateASig1;
|
3075 |
|
|
floatx80 z;
|
3076 |
|
|
|
3077 |
|
|
aSig0 = extractFloatx80Frac( a );
|
3078 |
|
|
aExp = extractFloatx80Exp( a );
|
3079 |
|
|
aSign = extractFloatx80Sign( a );
|
3080 |
|
|
bSig = extractFloatx80Frac( b );
|
3081 |
|
|
bExp = extractFloatx80Exp( b );
|
3082 |
|
|
bSign = extractFloatx80Sign( b );
|
3083 |
|
|
if ( aExp == 0x7FFF ) {
|
3084 |
|
|
if ( (bits64) ( aSig0<<1 )
|
3085 |
|
|
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
|
3086 |
|
|
return propagateFloatx80NaN( a, b );
|
3087 |
|
|
}
|
3088 |
|
|
goto invalid;
|
3089 |
|
|
}
|
3090 |
|
|
if ( bExp == 0x7FFF ) {
|
3091 |
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
3092 |
|
|
return a;
|
3093 |
|
|
}
|
3094 |
|
|
if ( bExp == 0 ) {
|
3095 |
|
|
if ( bSig == 0 ) {
|
3096 |
|
|
invalid:
|
3097 |
|
|
roundData->exception |= float_flag_invalid;
|
3098 |
|
|
z.low = floatx80_default_nan_low;
|
3099 |
|
|
z.high = floatx80_default_nan_high;
|
3100 |
|
|
z.__padding = 0;
|
3101 |
|
|
return z;
|
3102 |
|
|
}
|
3103 |
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
3104 |
|
|
}
|
3105 |
|
|
if ( aExp == 0 ) {
|
3106 |
|
|
if ( (bits64) ( aSig0<<1 ) == 0 ) return a;
|
3107 |
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
3108 |
|
|
}
|
3109 |
|
|
bSig |= LIT64( 0x8000000000000000 );
|
3110 |
|
|
zSign = aSign;
|
3111 |
|
|
expDiff = aExp - bExp;
|
3112 |
|
|
aSig1 = 0;
|
3113 |
|
|
if ( expDiff < 0 ) {
|
3114 |
|
|
if ( expDiff < -1 ) return a;
|
3115 |
|
|
shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
|
3116 |
|
|
expDiff = 0;
|
3117 |
|
|
}
|
3118 |
|
|
q = ( bSig <= aSig0 );
|
3119 |
|
|
if ( q ) aSig0 -= bSig;
|
3120 |
|
|
expDiff -= 64;
|
3121 |
|
|
while ( 0 < expDiff ) {
|
3122 |
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
3123 |
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
3124 |
|
|
mul64To128( bSig, q, &term0, &term1 );
|
3125 |
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
3126 |
|
|
shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
|
3127 |
|
|
expDiff -= 62;
|
3128 |
|
|
}
|
3129 |
|
|
expDiff += 64;
|
3130 |
|
|
if ( 0 < expDiff ) {
|
3131 |
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
3132 |
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
3133 |
|
|
q >>= 64 - expDiff;
|
3134 |
|
|
mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
|
3135 |
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
3136 |
|
|
shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
|
3137 |
|
|
while ( le128( term0, term1, aSig0, aSig1 ) ) {
|
3138 |
|
|
++q;
|
3139 |
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
3140 |
|
|
}
|
3141 |
|
|
}
|
3142 |
|
|
else {
|
3143 |
|
|
term1 = 0;
|
3144 |
|
|
term0 = bSig;
|
3145 |
|
|
}
|
3146 |
|
|
sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
|
3147 |
|
|
if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
3148 |
|
|
|| ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
3149 |
|
|
&& ( q & 1 ) )
|
3150 |
|
|
) {
|
3151 |
|
|
aSig0 = alternateASig0;
|
3152 |
|
|
aSig1 = alternateASig1;
|
3153 |
|
|
zSign = ! zSign;
|
3154 |
|
|
}
|
3155 |
|
|
|
3156 |
|
|
return
|
3157 |
|
|
normalizeRoundAndPackFloatx80(
|
3158 |
|
|
roundData, zSign, bExp + expDiff, aSig0, aSig1 );
|
3159 |
|
|
|
3160 |
|
|
}
|
3161 |
|
|
|
3162 |
|
|
/*
|
3163 |
|
|
-------------------------------------------------------------------------------
|
3164 |
|
|
Returns the square root of the extended double-precision floating-point
|
3165 |
|
|
value `a'. The operation is performed according to the IEC/IEEE Standard
|
3166 |
|
|
for Binary Floating-point Arithmetic.
|
3167 |
|
|
-------------------------------------------------------------------------------
|
3168 |
|
|
*/
|
3169 |
|
|
floatx80 floatx80_sqrt( struct roundingData *roundData, floatx80 a )
|
3170 |
|
|
{
|
3171 |
|
|
flag aSign;
|
3172 |
|
|
int32 aExp, zExp;
|
3173 |
|
|
bits64 aSig0, aSig1, zSig0, zSig1;
|
3174 |
|
|
bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
|
3175 |
|
|
bits64 shiftedRem0, shiftedRem1;
|
3176 |
|
|
floatx80 z;
|
3177 |
|
|
|
3178 |
|
|
aSig0 = extractFloatx80Frac( a );
|
3179 |
|
|
aExp = extractFloatx80Exp( a );
|
3180 |
|
|
aSign = extractFloatx80Sign( a );
|
3181 |
|
|
if ( aExp == 0x7FFF ) {
|
3182 |
|
|
if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a );
|
3183 |
|
|
if ( ! aSign ) return a;
|
3184 |
|
|
goto invalid;
|
3185 |
|
|
}
|
3186 |
|
|
if ( aSign ) {
|
3187 |
|
|
if ( ( aExp | aSig0 ) == 0 ) return a;
|
3188 |
|
|
invalid:
|
3189 |
|
|
roundData->exception |= float_flag_invalid;
|
3190 |
|
|
z.low = floatx80_default_nan_low;
|
3191 |
|
|
z.high = floatx80_default_nan_high;
|
3192 |
|
|
z.__padding = 0;
|
3193 |
|
|
return z;
|
3194 |
|
|
}
|
3195 |
|
|
if ( aExp == 0 ) {
|
3196 |
|
|
if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
|
3197 |
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
3198 |
|
|
}
|
3199 |
|
|
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
|
3200 |
|
|
zSig0 = estimateSqrt32( aExp, aSig0>>32 );
|
3201 |
|
|
zSig0 <<= 31;
|
3202 |
|
|
aSig1 = 0;
|
3203 |
|
|
shift128Right( aSig0, 0, ( aExp & 1 ) + 2, &aSig0, &aSig1 );
|
3204 |
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0 ) + zSig0 + 4;
|
3205 |
|
|
if ( 0 <= (sbits64) zSig0 ) zSig0 = LIT64( 0xFFFFFFFFFFFFFFFF );
|
3206 |
|
|
shortShift128Left( aSig0, aSig1, 2, &aSig0, &aSig1 );
|
3207 |
|
|
mul64To128( zSig0, zSig0, &term0, &term1 );
|
3208 |
|
|
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
|
3209 |
|
|
while ( (sbits64) rem0 < 0 ) {
|
3210 |
|
|
--zSig0;
|
3211 |
|
|
shortShift128Left( 0, zSig0, 1, &term0, &term1 );
|
3212 |
|
|
term1 |= 1;
|
3213 |
|
|
add128( rem0, rem1, term0, term1, &rem0, &rem1 );
|
3214 |
|
|
}
|
3215 |
|
|
shortShift128Left( rem0, rem1, 63, &shiftedRem0, &shiftedRem1 );
|
3216 |
|
|
zSig1 = estimateDiv128To64( shiftedRem0, shiftedRem1, zSig0 );
|
3217 |
|
|
if ( (bits64) ( zSig1<<1 ) <= 10 ) {
|
3218 |
|
|
if ( zSig1 == 0 ) zSig1 = 1;
|
3219 |
|
|
mul64To128( zSig0, zSig1, &term1, &term2 );
|
3220 |
|
|
shortShift128Left( term1, term2, 1, &term1, &term2 );
|
3221 |
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
3222 |
|
|
mul64To128( zSig1, zSig1, &term2, &term3 );
|
3223 |
|
|
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
|
3224 |
|
|
while ( (sbits64) rem1 < 0 ) {
|
3225 |
|
|
--zSig1;
|
3226 |
|
|
shortShift192Left( 0, zSig0, zSig1, 1, &term1, &term2, &term3 );
|
3227 |
|
|
term3 |= 1;
|
3228 |
|
|
add192(
|
3229 |
|
|
rem1, rem2, rem3, term1, term2, term3, &rem1, &rem2, &rem3 );
|
3230 |
|
|
}
|
3231 |
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
3232 |
|
|
}
|
3233 |
|
|
return
|
3234 |
|
|
roundAndPackFloatx80(
|
3235 |
|
|
roundData, 0, zExp, zSig0, zSig1 );
|
3236 |
|
|
|
3237 |
|
|
}
|
3238 |
|
|
|
3239 |
|
|
/*
|
3240 |
|
|
-------------------------------------------------------------------------------
|
3241 |
|
|
Returns 1 if the extended double-precision floating-point value `a' is
|
3242 |
|
|
equal to the corresponding value `b', and 0 otherwise. The comparison is
|
3243 |
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
3244 |
|
|
Arithmetic.
|
3245 |
|
|
-------------------------------------------------------------------------------
|
3246 |
|
|
*/
|
3247 |
|
|
flag floatx80_eq( floatx80 a, floatx80 b )
|
3248 |
|
|
{
|
3249 |
|
|
|
3250 |
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
3251 |
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
3252 |
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
3253 |
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
3254 |
|
|
) {
|
3255 |
|
|
if ( floatx80_is_signaling_nan( a )
|
3256 |
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
3257 |
|
|
float_raise( float_flag_invalid );
|
3258 |
|
|
}
|
3259 |
|
|
return 0;
|
3260 |
|
|
}
|
3261 |
|
|
return
|
3262 |
|
|
( a.low == b.low )
|
3263 |
|
|
&& ( ( a.high == b.high )
|
3264 |
|
|
|| ( ( a.low == 0 )
|
3265 |
|
|
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
|
3266 |
|
|
);
|
3267 |
|
|
|
3268 |
|
|
}
|
3269 |
|
|
|
3270 |
|
|
/*
|
3271 |
|
|
-------------------------------------------------------------------------------
|
3272 |
|
|
Returns 1 if the extended double-precision floating-point value `a' is
|
3273 |
|
|
less than or equal to the corresponding value `b', and 0 otherwise. The
|
3274 |
|
|
comparison is performed according to the IEC/IEEE Standard for Binary
|
3275 |
|
|
Floating-point Arithmetic.
|
3276 |
|
|
-------------------------------------------------------------------------------
|
3277 |
|
|
*/
|
3278 |
|
|
flag floatx80_le( floatx80 a, floatx80 b )
|
3279 |
|
|
{
|
3280 |
|
|
flag aSign, bSign;
|
3281 |
|
|
|
3282 |
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
3283 |
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
3284 |
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
3285 |
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
3286 |
|
|
) {
|
3287 |
|
|
float_raise( float_flag_invalid );
|
3288 |
|
|
return 0;
|
3289 |
|
|
}
|
3290 |
|
|
aSign = extractFloatx80Sign( a );
|
3291 |
|
|
bSign = extractFloatx80Sign( b );
|
3292 |
|
|
if ( aSign != bSign ) {
|
3293 |
|
|
return
|
3294 |
|
|
aSign
|
3295 |
|
|
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
3296 |
|
|
== 0 );
|
3297 |
|
|
}
|
3298 |
|
|
return
|
3299 |
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
3300 |
|
|
: le128( a.high, a.low, b.high, b.low );
|
3301 |
|
|
|
3302 |
|
|
}
|
3303 |
|
|
|
3304 |
|
|
/*
|
3305 |
|
|
-------------------------------------------------------------------------------
|
3306 |
|
|
Returns 1 if the extended double-precision floating-point value `a' is
|
3307 |
|
|
less than the corresponding value `b', and 0 otherwise. The comparison
|
3308 |
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
3309 |
|
|
Arithmetic.
|
3310 |
|
|
-------------------------------------------------------------------------------
|
3311 |
|
|
*/
|
3312 |
|
|
flag floatx80_lt( floatx80 a, floatx80 b )
|
3313 |
|
|
{
|
3314 |
|
|
flag aSign, bSign;
|
3315 |
|
|
|
3316 |
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
3317 |
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
3318 |
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
3319 |
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
3320 |
|
|
) {
|
3321 |
|
|
float_raise( float_flag_invalid );
|
3322 |
|
|
return 0;
|
3323 |
|
|
}
|
3324 |
|
|
aSign = extractFloatx80Sign( a );
|
3325 |
|
|
bSign = extractFloatx80Sign( b );
|
3326 |
|
|
if ( aSign != bSign ) {
|
3327 |
|
|
return
|
3328 |
|
|
aSign
|
3329 |
|
|
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
3330 |
|
|
!= 0 );
|
3331 |
|
|
}
|
3332 |
|
|
return
|
3333 |
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
3334 |
|
|
: lt128( a.high, a.low, b.high, b.low );
|
3335 |
|
|
|
3336 |
|
|
}
|
3337 |
|
|
|
3338 |
|
|
/*
|
3339 |
|
|
-------------------------------------------------------------------------------
|
3340 |
|
|
Returns 1 if the extended double-precision floating-point value `a' is equal
|
3341 |
|
|
to the corresponding value `b', and 0 otherwise. The invalid exception is
|
3342 |
|
|
raised if either operand is a NaN. Otherwise, the comparison is performed
|
3343 |
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
3344 |
|
|
-------------------------------------------------------------------------------
|
3345 |
|
|
*/
|
3346 |
|
|
flag floatx80_eq_signaling( floatx80 a, floatx80 b )
|
3347 |
|
|
{
|
3348 |
|
|
|
3349 |
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
3350 |
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
3351 |
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
3352 |
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
3353 |
|
|
) {
|
3354 |
|
|
float_raise( float_flag_invalid );
|
3355 |
|
|
return 0;
|
3356 |
|
|
}
|
3357 |
|
|
return
|
3358 |
|
|
( a.low == b.low )
|
3359 |
|
|
&& ( ( a.high == b.high )
|
3360 |
|
|
|| ( ( a.low == 0 )
|
3361 |
|
|
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
|
3362 |
|
|
);
|
3363 |
|
|
|
3364 |
|
|
}
|
3365 |
|
|
|
3366 |
|
|
/*
|
3367 |
|
|
-------------------------------------------------------------------------------
|
3368 |
|
|
Returns 1 if the extended double-precision floating-point value `a' is less
|
3369 |
|
|
than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs
|
3370 |
|
|
do not cause an exception. Otherwise, the comparison is performed according
|
3371 |
|
|
to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
3372 |
|
|
-------------------------------------------------------------------------------
|
3373 |
|
|
*/
|
3374 |
|
|
flag floatx80_le_quiet( floatx80 a, floatx80 b )
|
3375 |
|
|
{
|
3376 |
|
|
flag aSign, bSign;
|
3377 |
|
|
|
3378 |
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
3379 |
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
3380 |
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
3381 |
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
3382 |
|
|
) {
|
3383 |
|
|
/* Do nothing, even if NaN as we're quiet */
|
3384 |
|
|
return 0;
|
3385 |
|
|
}
|
3386 |
|
|
aSign = extractFloatx80Sign( a );
|
3387 |
|
|
bSign = extractFloatx80Sign( b );
|
3388 |
|
|
if ( aSign != bSign ) {
|
3389 |
|
|
return
|
3390 |
|
|
aSign
|
3391 |
|
|
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
3392 |
|
|
== 0 );
|
3393 |
|
|
}
|
3394 |
|
|
return
|
3395 |
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
3396 |
|
|
: le128( a.high, a.low, b.high, b.low );
|
3397 |
|
|
|
3398 |
|
|
}
|
3399 |
|
|
|
3400 |
|
|
/*
|
3401 |
|
|
-------------------------------------------------------------------------------
|
3402 |
|
|
Returns 1 if the extended double-precision floating-point value `a' is less
|
3403 |
|
|
than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
|
3404 |
|
|
an exception. Otherwise, the comparison is performed according to the
|
3405 |
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
3406 |
|
|
-------------------------------------------------------------------------------
|
3407 |
|
|
*/
|
3408 |
|
|
flag floatx80_lt_quiet( floatx80 a, floatx80 b )
|
3409 |
|
|
{
|
3410 |
|
|
flag aSign, bSign;
|
3411 |
|
|
|
3412 |
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
3413 |
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
3414 |
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
3415 |
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
3416 |
|
|
) {
|
3417 |
|
|
/* Do nothing, even if NaN as we're quiet */
|
3418 |
|
|
return 0;
|
3419 |
|
|
}
|
3420 |
|
|
aSign = extractFloatx80Sign( a );
|
3421 |
|
|
bSign = extractFloatx80Sign( b );
|
3422 |
|
|
if ( aSign != bSign ) {
|
3423 |
|
|
return
|
3424 |
|
|
aSign
|
3425 |
|
|
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
3426 |
|
|
!= 0 );
|
3427 |
|
|
}
|
3428 |
|
|
return
|
3429 |
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
3430 |
|
|
: lt128( a.high, a.low, b.high, b.low );
|
3431 |
|
|
|
3432 |
|
|
}
|
3433 |
|
|
|
3434 |
|
|
#endif
|
3435 |
|
|
|