1da177e4c3
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
3444 lines
115 KiB
C
3444 lines
115 KiB
C
/*
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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 "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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Floating-point rounding mode, extended double-precision rounding precision,
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and exception flags.
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-------------------------------------------------------------------------------
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*/
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int8 float_rounding_mode = float_round_nearest_even;
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int8 floatx80_rounding_precision = 80;
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int8 float_exception_flags;
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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( 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 = float_rounding_mode;
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roundNearestEven = ( roundingMode == float_round_nearest_even );
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roundIncrement = 0x40;
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if ( ! roundNearestEven ) {
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if ( roundingMode == float_round_to_zero ) {
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roundIncrement = 0;
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}
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else {
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roundIncrement = 0x7F;
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if ( zSign ) {
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if ( roundingMode == float_round_up ) roundIncrement = 0;
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}
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else {
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if ( roundingMode == float_round_down ) roundIncrement = 0;
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}
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}
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}
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roundBits = 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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float_exception_flags |= float_flag_invalid;
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return zSign ? 0x80000000 : 0x7FFFFFFF;
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}
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if ( roundBits ) float_exception_flags |= 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
|
|
exactly. If the abstract value is too large, however, the overflow and
|
|
inexact exceptions are raised and an infinity or maximal finite value is
|
|
returned. If the abstract value is too small, the input value is rounded to
|
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a subnormal number, and the underflow and inexact exceptions are raised if
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the abstract input cannot be represented exactly as a subnormal single-
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|
precision floating-point number.
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The input significand `zSig' has its binary point between bits 30
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and 29, which is 7 bits to the left of the usual location. This shifted
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significand must be normalized or smaller. If `zSig' is not normalized,
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`zExp' must be 0; in that case, the result returned is a subnormal number,
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and it must not require rounding. In the usual case that `zSig' is
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normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
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The handling of underflow and overflow follows the IEC/IEEE Standard for
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Binary Floating-point Arithmetic.
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-------------------------------------------------------------------------------
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*/
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static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
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{
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int8 roundingMode;
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flag roundNearestEven;
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int8 roundIncrement, roundBits;
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flag isTiny;
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roundingMode = float_rounding_mode;
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roundNearestEven = ( roundingMode == float_round_nearest_even );
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roundIncrement = 0x40;
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if ( ! roundNearestEven ) {
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if ( roundingMode == float_round_to_zero ) {
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roundIncrement = 0;
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}
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else {
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roundIncrement = 0x7F;
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if ( zSign ) {
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if ( roundingMode == float_round_up ) roundIncrement = 0;
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}
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else {
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if ( roundingMode == float_round_down ) roundIncrement = 0;
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}
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}
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}
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roundBits = zSig & 0x7F;
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if ( 0xFD <= (bits16) zExp ) {
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if ( ( 0xFD < zExp )
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|| ( ( zExp == 0xFD )
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&& ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
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) {
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float_raise( float_flag_overflow | float_flag_inexact );
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return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
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}
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if ( zExp < 0 ) {
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isTiny =
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( float_detect_tininess == float_tininess_before_rounding )
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|| ( zExp < -1 )
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|| ( zSig + roundIncrement < 0x80000000 );
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shift32RightJamming( zSig, - zExp, &zSig );
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zExp = 0;
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roundBits = zSig & 0x7F;
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if ( isTiny && roundBits ) float_raise( float_flag_underflow );
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}
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}
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if ( roundBits ) float_exception_flags |= float_flag_inexact;
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zSig = ( zSig + roundIncrement )>>7;
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zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
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if ( zSig == 0 ) zExp = 0;
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return packFloat32( zSign, zExp, zSig );
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}
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/*
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-------------------------------------------------------------------------------
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Takes an abstract floating-point value having sign `zSign', exponent `zExp',
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and significand `zSig', and returns the proper single-precision floating-
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|
point value corresponding to the abstract input. This routine is just like
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|
`roundAndPackFloat32' except that `zSig' does not have to be normalized in
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|
any way. In all cases, `zExp' must be 1 less than the ``true'' floating-
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point exponent.
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-------------------------------------------------------------------------------
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*/
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static float32
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normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
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{
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int8 shiftCount;
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shiftCount = countLeadingZeros32( zSig ) - 1;
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return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount );
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}
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/*
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-------------------------------------------------------------------------------
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Returns the fraction bits of the double-precision floating-point value `a'.
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-------------------------------------------------------------------------------
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*/
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INLINE bits64 extractFloat64Frac( float64 a )
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{
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return a & LIT64( 0x000FFFFFFFFFFFFF );
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}
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|
|
/*
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-------------------------------------------------------------------------------
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Returns the exponent bits of the double-precision floating-point value `a'.
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-------------------------------------------------------------------------------
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*/
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INLINE int16 extractFloat64Exp( float64 a )
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{
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return ( a>>52 ) & 0x7FF;
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}
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/*
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-------------------------------------------------------------------------------
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Returns the sign bit of the double-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 extractFloat64Sign( float64 a )
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{
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return a>>63;
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}
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#endif
|
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/*
|
|
-------------------------------------------------------------------------------
|
|
Normalizes the subnormal double-precision floating-point value represented
|
|
by the denormalized significand `aSig'. The normalized exponent and
|
|
significand are stored at the locations pointed to by `zExpPtr' and
|
|
`zSigPtr', respectively.
|
|
-------------------------------------------------------------------------------
|
|
*/
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static void
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normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr )
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{
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int8 shiftCount;
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shiftCount = countLeadingZeros64( aSig ) - 11;
|
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*zSigPtr = aSig<<shiftCount;
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*zExpPtr = 1 - shiftCount;
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|
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}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
|
|
double-precision floating-point value, returning the result. After being
|
|
shifted into the proper positions, the three fields are simply added
|
|
together to form the result. This means that any integer portion of `zSig'
|
|
will be added into the exponent. Since a properly normalized significand
|
|
will have an integer portion equal to 1, the `zExp' input should be 1 less
|
|
than the desired result exponent whenever `zSig' is a complete, normalized
|
|
significand.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
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INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
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{
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return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
and significand `zSig', and returns the proper double-precision floating-
|
|
point value corresponding to the abstract input. Ordinarily, the abstract
|
|
value is simply rounded and packed into the double-precision format, with
|
|
the inexact exception raised if the abstract input cannot be represented
|
|
exactly. If the abstract value is too large, however, the overflow and
|
|
inexact exceptions are raised and an infinity or maximal finite value is
|
|
returned. If the abstract value is too small, the input value is rounded to
|
|
a subnormal number, and the underflow and inexact exceptions are raised if
|
|
the abstract input cannot be represented exactly as a subnormal double-
|
|
precision floating-point number.
|
|
The input significand `zSig' has its binary point between bits 62
|
|
and 61, which is 10 bits to the left of the usual location. This shifted
|
|
significand must be normalized or smaller. If `zSig' is not normalized,
|
|
`zExp' must be 0; in that case, the result returned is a subnormal number,
|
|
and it must not require rounding. In the usual case that `zSig' is
|
|
normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
|
|
The handling of underflow and overflow follows the IEC/IEEE Standard for
|
|
Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig )
|
|
{
|
|
int8 roundingMode;
|
|
flag roundNearestEven;
|
|
int16 roundIncrement, roundBits;
|
|
flag isTiny;
|
|
|
|
roundingMode = float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
roundIncrement = 0x200;
|
|
if ( ! roundNearestEven ) {
|
|
if ( roundingMode == float_round_to_zero ) {
|
|
roundIncrement = 0;
|
|
}
|
|
else {
|
|
roundIncrement = 0x3FF;
|
|
if ( zSign ) {
|
|
if ( roundingMode == float_round_up ) roundIncrement = 0;
|
|
}
|
|
else {
|
|
if ( roundingMode == float_round_down ) roundIncrement = 0;
|
|
}
|
|
}
|
|
}
|
|
roundBits = zSig & 0x3FF;
|
|
if ( 0x7FD <= (bits16) zExp ) {
|
|
if ( ( 0x7FD < zExp )
|
|
|| ( ( zExp == 0x7FD )
|
|
&& ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
|
|
) {
|
|
//register int lr = __builtin_return_address(0);
|
|
//printk("roundAndPackFloat64 called from 0x%08x\n",lr);
|
|
float_raise( float_flag_overflow | float_flag_inexact );
|
|
return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 );
|
|
}
|
|
if ( zExp < 0 ) {
|
|
isTiny =
|
|
( float_detect_tininess == float_tininess_before_rounding )
|
|
|| ( zExp < -1 )
|
|
|| ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
|
|
shift64RightJamming( zSig, - zExp, &zSig );
|
|
zExp = 0;
|
|
roundBits = zSig & 0x3FF;
|
|
if ( isTiny && roundBits ) float_raise( float_flag_underflow );
|
|
}
|
|
}
|
|
if ( roundBits ) float_exception_flags |= float_flag_inexact;
|
|
zSig = ( zSig + roundIncrement )>>10;
|
|
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
|
|
if ( zSig == 0 ) zExp = 0;
|
|
return packFloat64( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
and significand `zSig', and returns the proper double-precision floating-
|
|
point value corresponding to the abstract input. This routine is just like
|
|
`roundAndPackFloat64' except that `zSig' does not have to be normalized in
|
|
any way. In all cases, `zExp' must be 1 less than the ``true'' floating-
|
|
point exponent.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static float64
|
|
normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig )
|
|
{
|
|
int8 shiftCount;
|
|
|
|
shiftCount = countLeadingZeros64( zSig ) - 1;
|
|
return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount );
|
|
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the fraction bits of the extended double-precision floating-point
|
|
value `a'.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
INLINE bits64 extractFloatx80Frac( floatx80 a )
|
|
{
|
|
|
|
return a.low;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the exponent bits of the extended double-precision floating-point
|
|
value `a'.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
INLINE int32 extractFloatx80Exp( floatx80 a )
|
|
{
|
|
|
|
return a.high & 0x7FFF;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the sign bit of the extended double-precision floating-point value
|
|
`a'.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
INLINE flag extractFloatx80Sign( floatx80 a )
|
|
{
|
|
|
|
return a.high>>15;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Normalizes the subnormal extended double-precision floating-point value
|
|
represented by the denormalized significand `aSig'. The normalized exponent
|
|
and significand are stored at the locations pointed to by `zExpPtr' and
|
|
`zSigPtr', respectively.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static void
|
|
normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
|
|
{
|
|
int8 shiftCount;
|
|
|
|
shiftCount = countLeadingZeros64( aSig );
|
|
*zSigPtr = aSig<<shiftCount;
|
|
*zExpPtr = 1 - shiftCount;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
|
|
extended double-precision floating-point value, returning the result.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
|
|
{
|
|
floatx80 z;
|
|
|
|
z.low = zSig;
|
|
z.high = ( ( (bits16) zSign )<<15 ) + zExp;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
and extended significand formed by the concatenation of `zSig0' and `zSig1',
|
|
and returns the proper extended double-precision floating-point value
|
|
corresponding to the abstract input. Ordinarily, the abstract value is
|
|
rounded and packed into the extended double-precision format, with the
|
|
inexact exception raised if the abstract input cannot be represented
|
|
exactly. If the abstract value is too large, however, the overflow and
|
|
inexact exceptions are raised and an infinity or maximal finite value is
|
|
returned. If the abstract value is too small, the input value is rounded to
|
|
a subnormal number, and the underflow and inexact exceptions are raised if
|
|
the abstract input cannot be represented exactly as a subnormal extended
|
|
double-precision floating-point number.
|
|
If `roundingPrecision' is 32 or 64, the result is rounded to the same
|
|
number of bits as single or double precision, respectively. Otherwise, the
|
|
result is rounded to the full precision of the extended double-precision
|
|
format.
|
|
The input significand must be normalized or smaller. If the input
|
|
significand is not normalized, `zExp' must be 0; in that case, the result
|
|
returned is a subnormal number, and it must not require rounding. The
|
|
handling of underflow and overflow follows the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static floatx80
|
|
roundAndPackFloatx80(
|
|
int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
|
|
)
|
|
{
|
|
int8 roundingMode;
|
|
flag roundNearestEven, increment, isTiny;
|
|
int64 roundIncrement, roundMask, roundBits;
|
|
|
|
roundingMode = float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
if ( roundingPrecision == 80 ) goto precision80;
|
|
if ( roundingPrecision == 64 ) {
|
|
roundIncrement = LIT64( 0x0000000000000400 );
|
|
roundMask = LIT64( 0x00000000000007FF );
|
|
}
|
|
else if ( roundingPrecision == 32 ) {
|
|
roundIncrement = LIT64( 0x0000008000000000 );
|
|
roundMask = LIT64( 0x000000FFFFFFFFFF );
|
|
}
|
|
else {
|
|
goto precision80;
|
|
}
|
|
zSig0 |= ( zSig1 != 0 );
|
|
if ( ! roundNearestEven ) {
|
|
if ( roundingMode == float_round_to_zero ) {
|
|
roundIncrement = 0;
|
|
}
|
|
else {
|
|
roundIncrement = roundMask;
|
|
if ( zSign ) {
|
|
if ( roundingMode == float_round_up ) roundIncrement = 0;
|
|
}
|
|
else {
|
|
if ( roundingMode == float_round_down ) roundIncrement = 0;
|
|
}
|
|
}
|
|
}
|
|
roundBits = zSig0 & roundMask;
|
|
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
|
|
if ( ( 0x7FFE < zExp )
|
|
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
|
|
) {
|
|
goto overflow;
|
|
}
|
|
if ( zExp <= 0 ) {
|
|
isTiny =
|
|
( float_detect_tininess == float_tininess_before_rounding )
|
|
|| ( zExp < 0 )
|
|
|| ( zSig0 <= zSig0 + roundIncrement );
|
|
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
|
|
zExp = 0;
|
|
roundBits = zSig0 & roundMask;
|
|
if ( isTiny && roundBits ) float_raise( float_flag_underflow );
|
|
if ( roundBits ) float_exception_flags |= float_flag_inexact;
|
|
zSig0 += roundIncrement;
|
|
if ( (sbits64) zSig0 < 0 ) zExp = 1;
|
|
roundIncrement = roundMask + 1;
|
|
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
|
|
roundMask |= roundIncrement;
|
|
}
|
|
zSig0 &= ~ roundMask;
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
}
|
|
}
|
|
if ( roundBits ) float_exception_flags |= float_flag_inexact;
|
|
zSig0 += roundIncrement;
|
|
if ( zSig0 < roundIncrement ) {
|
|
++zExp;
|
|
zSig0 = LIT64( 0x8000000000000000 );
|
|
}
|
|
roundIncrement = roundMask + 1;
|
|
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
|
|
roundMask |= roundIncrement;
|
|
}
|
|
zSig0 &= ~ roundMask;
|
|
if ( zSig0 == 0 ) zExp = 0;
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
precision80:
|
|
increment = ( (sbits64) zSig1 < 0 );
|
|
if ( ! roundNearestEven ) {
|
|
if ( roundingMode == float_round_to_zero ) {
|
|
increment = 0;
|
|
}
|
|
else {
|
|
if ( zSign ) {
|
|
increment = ( roundingMode == float_round_down ) && zSig1;
|
|
}
|
|
else {
|
|
increment = ( roundingMode == float_round_up ) && zSig1;
|
|
}
|
|
}
|
|
}
|
|
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
|
|
if ( ( 0x7FFE < zExp )
|
|
|| ( ( zExp == 0x7FFE )
|
|
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
|
|
&& increment
|
|
)
|
|
) {
|
|
roundMask = 0;
|
|
overflow:
|
|
float_raise( float_flag_overflow | float_flag_inexact );
|
|
if ( ( roundingMode == float_round_to_zero )
|
|
|| ( zSign && ( roundingMode == float_round_up ) )
|
|
|| ( ! zSign && ( roundingMode == float_round_down ) )
|
|
) {
|
|
return packFloatx80( zSign, 0x7FFE, ~ roundMask );
|
|
}
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( zExp <= 0 ) {
|
|
isTiny =
|
|
( float_detect_tininess == float_tininess_before_rounding )
|
|
|| ( zExp < 0 )
|
|
|| ! increment
|
|
|| ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
|
|
zExp = 0;
|
|
if ( isTiny && zSig1 ) float_raise( float_flag_underflow );
|
|
if ( zSig1 ) float_exception_flags |= float_flag_inexact;
|
|
if ( roundNearestEven ) {
|
|
increment = ( (sbits64) zSig1 < 0 );
|
|
}
|
|
else {
|
|
if ( zSign ) {
|
|
increment = ( roundingMode == float_round_down ) && zSig1;
|
|
}
|
|
else {
|
|
increment = ( roundingMode == float_round_up ) && zSig1;
|
|
}
|
|
}
|
|
if ( increment ) {
|
|
++zSig0;
|
|
zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
|
|
if ( (sbits64) zSig0 < 0 ) zExp = 1;
|
|
}
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
}
|
|
}
|
|
if ( zSig1 ) float_exception_flags |= float_flag_inexact;
|
|
if ( increment ) {
|
|
++zSig0;
|
|
if ( zSig0 == 0 ) {
|
|
++zExp;
|
|
zSig0 = LIT64( 0x8000000000000000 );
|
|
}
|
|
else {
|
|
zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
|
|
}
|
|
}
|
|
else {
|
|
if ( zSig0 == 0 ) zExp = 0;
|
|
}
|
|
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Takes an abstract floating-point value having sign `zSign', exponent
|
|
`zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
|
|
and returns the proper extended double-precision floating-point value
|
|
corresponding to the abstract input. This routine is just like
|
|
`roundAndPackFloatx80' except that the input significand does not have to be
|
|
normalized.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static floatx80
|
|
normalizeRoundAndPackFloatx80(
|
|
int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
|
|
)
|
|
{
|
|
int8 shiftCount;
|
|
|
|
if ( zSig0 == 0 ) {
|
|
zSig0 = zSig1;
|
|
zSig1 = 0;
|
|
zExp -= 64;
|
|
}
|
|
shiftCount = countLeadingZeros64( zSig0 );
|
|
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
|
|
zExp -= shiftCount;
|
|
return
|
|
roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the 32-bit two's complement integer `a' to
|
|
the single-precision floating-point format. The conversion is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 int32_to_float32( int32 a )
|
|
{
|
|
flag zSign;
|
|
|
|
if ( a == 0 ) return 0;
|
|
if ( a == 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
|
|
zSign = ( a < 0 );
|
|
return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the 32-bit two's complement integer `a' to
|
|
the double-precision floating-point format. The conversion is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 int32_to_float64( int32 a )
|
|
{
|
|
flag aSign;
|
|
uint32 absA;
|
|
int8 shiftCount;
|
|
bits64 zSig;
|
|
|
|
if ( a == 0 ) return 0;
|
|
aSign = ( a < 0 );
|
|
absA = aSign ? - a : a;
|
|
shiftCount = countLeadingZeros32( absA ) + 21;
|
|
zSig = absA;
|
|
return packFloat64( aSign, 0x432 - shiftCount, zSig<<shiftCount );
|
|
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the 32-bit two's complement integer `a'
|
|
to the extended double-precision floating-point format. The conversion
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 int32_to_floatx80( int32 a )
|
|
{
|
|
flag zSign;
|
|
uint32 absA;
|
|
int8 shiftCount;
|
|
bits64 zSig;
|
|
|
|
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
|
|
zSign = ( a < 0 );
|
|
absA = zSign ? - a : a;
|
|
shiftCount = countLeadingZeros32( absA ) + 32;
|
|
zSig = absA;
|
|
return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the single-precision floating-point value
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic---which means in particular that the conversion is rounded
|
|
according to the current rounding mode. If `a' is a NaN, the largest
|
|
positive integer is returned. Otherwise, if the conversion overflows, the
|
|
largest integer with the same sign as `a' is returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 float32_to_int32( float32 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, shiftCount;
|
|
bits32 aSig;
|
|
bits64 zSig;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
|
if ( aExp ) aSig |= 0x00800000;
|
|
shiftCount = 0xAF - aExp;
|
|
zSig = aSig;
|
|
zSig <<= 32;
|
|
if ( 0 < shiftCount ) shift64RightJamming( zSig, shiftCount, &zSig );
|
|
return roundAndPackInt32( aSign, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the single-precision floating-point value
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic, except that the conversion is always rounded toward zero. If
|
|
`a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
|
conversion overflows, the largest integer with the same sign as `a' is
|
|
returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 float32_to_int32_round_to_zero( float32 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, shiftCount;
|
|
bits32 aSig;
|
|
int32 z;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
shiftCount = aExp - 0x9E;
|
|
if ( 0 <= shiftCount ) {
|
|
if ( a == 0xCF000000 ) return 0x80000000;
|
|
float_raise( float_flag_invalid );
|
|
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
|
|
return 0x80000000;
|
|
}
|
|
else if ( aExp <= 0x7E ) {
|
|
if ( aExp | aSig ) float_exception_flags |= float_flag_inexact;
|
|
return 0;
|
|
}
|
|
aSig = ( aSig | 0x00800000 )<<8;
|
|
z = aSig>>( - shiftCount );
|
|
if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return aSign ? - z : z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the single-precision floating-point value
|
|
`a' to the double-precision floating-point format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float32_to_float64( float32 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp;
|
|
bits32 aSig;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) );
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat64( aSign, 0, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
--aExp;
|
|
}
|
|
return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );
|
|
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the single-precision floating-point value
|
|
`a' to the extended double-precision floating-point format. The conversion
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 float32_to_floatx80( float32 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp;
|
|
bits32 aSig;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) );
|
|
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
aSig |= 0x00800000;
|
|
return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Rounds the single-precision floating-point value `a' to an integer, and
|
|
returns the result as a single-precision floating-point value. The
|
|
operation is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_round_to_int( float32 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp;
|
|
bits32 lastBitMask, roundBitsMask;
|
|
int8 roundingMode;
|
|
float32 z;
|
|
|
|
aExp = extractFloat32Exp( a );
|
|
if ( 0x96 <= aExp ) {
|
|
if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
|
|
return propagateFloat32NaN( a, a );
|
|
}
|
|
return a;
|
|
}
|
|
if ( aExp <= 0x7E ) {
|
|
if ( (bits32) ( a<<1 ) == 0 ) return a;
|
|
float_exception_flags |= float_flag_inexact;
|
|
aSign = extractFloat32Sign( a );
|
|
switch ( float_rounding_mode ) {
|
|
case float_round_nearest_even:
|
|
if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
|
|
return packFloat32( aSign, 0x7F, 0 );
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
return aSign ? 0xBF800000 : 0;
|
|
case float_round_up:
|
|
return aSign ? 0x80000000 : 0x3F800000;
|
|
}
|
|
return packFloat32( aSign, 0, 0 );
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask <<= 0x96 - aExp;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z = a;
|
|
roundingMode = float_rounding_mode;
|
|
if ( roundingMode == float_round_nearest_even ) {
|
|
z += lastBitMask>>1;
|
|
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
|
|
}
|
|
else if ( roundingMode != float_round_to_zero ) {
|
|
if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
|
z += roundBitsMask;
|
|
}
|
|
}
|
|
z &= ~ roundBitsMask;
|
|
if ( z != a ) float_exception_flags |= float_flag_inexact;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of adding the absolute values of the single-precision
|
|
floating-point values `a' and `b'. If `zSign' is true, the sum is negated
|
|
before being returned. `zSign' is ignored if the result is a NaN. The
|
|
addition is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static float32 addFloat32Sigs( float32 a, float32 b, flag zSign )
|
|
{
|
|
int16 aExp, bExp, zExp;
|
|
bits32 aSig, bSig, zSig;
|
|
int16 expDiff;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
bSig = extractFloat32Frac( b );
|
|
bExp = extractFloat32Exp( b );
|
|
expDiff = aExp - bExp;
|
|
aSig <<= 6;
|
|
bSig <<= 6;
|
|
if ( 0 < expDiff ) {
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig ) return propagateFloat32NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig |= 0x20000000;
|
|
}
|
|
shift32RightJamming( bSig, expDiff, &bSig );
|
|
zExp = aExp;
|
|
}
|
|
else if ( expDiff < 0 ) {
|
|
if ( bExp == 0xFF ) {
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
|
return packFloat32( zSign, 0xFF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig |= 0x20000000;
|
|
}
|
|
shift32RightJamming( aSig, - expDiff, &aSig );
|
|
zExp = bExp;
|
|
}
|
|
else {
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig | bSig ) return propagateFloat32NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
|
|
zSig = 0x40000000 + aSig + bSig;
|
|
zExp = aExp;
|
|
goto roundAndPack;
|
|
}
|
|
aSig |= 0x20000000;
|
|
zSig = ( aSig + bSig )<<1;
|
|
--zExp;
|
|
if ( (sbits32) zSig < 0 ) {
|
|
zSig = aSig + bSig;
|
|
++zExp;
|
|
}
|
|
roundAndPack:
|
|
return roundAndPackFloat32( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of subtracting the absolute values of the single-
|
|
precision floating-point values `a' and `b'. If `zSign' is true, the
|
|
difference is negated before being returned. `zSign' is ignored if the
|
|
result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static float32 subFloat32Sigs( float32 a, float32 b, flag zSign )
|
|
{
|
|
int16 aExp, bExp, zExp;
|
|
bits32 aSig, bSig, zSig;
|
|
int16 expDiff;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
bSig = extractFloat32Frac( b );
|
|
bExp = extractFloat32Exp( b );
|
|
expDiff = aExp - bExp;
|
|
aSig <<= 7;
|
|
bSig <<= 7;
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig | bSig ) return propagateFloat32NaN( a, b );
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
if ( bSig < aSig ) goto aBigger;
|
|
if ( aSig < bSig ) goto bBigger;
|
|
return packFloat32( float_rounding_mode == float_round_down, 0, 0 );
|
|
bExpBigger:
|
|
if ( bExp == 0xFF ) {
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
|
return packFloat32( zSign ^ 1, 0xFF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig |= 0x40000000;
|
|
}
|
|
shift32RightJamming( aSig, - expDiff, &aSig );
|
|
bSig |= 0x40000000;
|
|
bBigger:
|
|
zSig = bSig - aSig;
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig ) return propagateFloat32NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig |= 0x40000000;
|
|
}
|
|
shift32RightJamming( bSig, expDiff, &bSig );
|
|
aSig |= 0x40000000;
|
|
aBigger:
|
|
zSig = aSig - bSig;
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
--zExp;
|
|
return normalizeRoundAndPackFloat32( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of adding the single-precision floating-point values `a'
|
|
and `b'. The operation is performed according to the IEC/IEEE Standard for
|
|
Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_add( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloat32Sign( a );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloat32Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return subFloat32Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of subtracting the single-precision floating-point values
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
|
for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_sub( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloat32Sign( a );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloat32Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return addFloat32Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of multiplying the single-precision floating-point values
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
|
for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_mul( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int16 aExp, bExp, zExp;
|
|
bits32 aSig, bSig;
|
|
bits64 zSig64;
|
|
bits32 zSig;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
bSig = extractFloat32Frac( b );
|
|
bExp = extractFloat32Exp( b );
|
|
bSign = extractFloat32Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
|
|
return propagateFloat32NaN( a, b );
|
|
}
|
|
if ( ( bExp | bSig ) == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
return packFloat32( zSign, 0xFF, 0 );
|
|
}
|
|
if ( bExp == 0xFF ) {
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
return packFloat32( zSign, 0xFF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) return packFloat32( zSign, 0, 0 );
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
zExp = aExp + bExp - 0x7F;
|
|
aSig = ( aSig | 0x00800000 )<<7;
|
|
bSig = ( bSig | 0x00800000 )<<8;
|
|
shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
|
|
zSig = zSig64;
|
|
if ( 0 <= (sbits32) ( zSig<<1 ) ) {
|
|
zSig <<= 1;
|
|
--zExp;
|
|
}
|
|
return roundAndPackFloat32( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of dividing the single-precision floating-point value `a'
|
|
by the corresponding value `b'. The operation is performed according to the
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_div( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int16 aExp, bExp, zExp;
|
|
bits32 aSig, bSig, zSig;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
bSig = extractFloat32Frac( b );
|
|
bExp = extractFloat32Exp( b );
|
|
bSign = extractFloat32Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig ) return propagateFloat32NaN( a, b );
|
|
if ( bExp == 0xFF ) {
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
return packFloat32( zSign, 0xFF, 0 );
|
|
}
|
|
if ( bExp == 0xFF ) {
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
|
return packFloat32( zSign, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
float_raise( float_flag_divbyzero );
|
|
return packFloat32( zSign, 0xFF, 0 );
|
|
}
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = aExp - bExp + 0x7D;
|
|
aSig = ( aSig | 0x00800000 )<<7;
|
|
bSig = ( bSig | 0x00800000 )<<8;
|
|
if ( bSig <= ( aSig + aSig ) ) {
|
|
aSig >>= 1;
|
|
++zExp;
|
|
}
|
|
zSig = ( ( (bits64) aSig )<<32 ) / bSig;
|
|
if ( ( zSig & 0x3F ) == 0 ) {
|
|
zSig |= ( ( (bits64) bSig ) * zSig != ( (bits64) aSig )<<32 );
|
|
}
|
|
return roundAndPackFloat32( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the remainder of the single-precision floating-point value `a'
|
|
with respect to the corresponding value `b'. The operation is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_rem( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int16 aExp, bExp, expDiff;
|
|
bits32 aSig, bSig;
|
|
bits32 q;
|
|
bits64 aSig64, bSig64, q64;
|
|
bits32 alternateASig;
|
|
sbits32 sigMean;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
bSig = extractFloat32Frac( b );
|
|
bExp = extractFloat32Exp( b );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
|
|
return propagateFloat32NaN( a, b );
|
|
}
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
if ( bExp == 0xFF ) {
|
|
if ( bSig ) return propagateFloat32NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return a;
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
expDiff = aExp - bExp;
|
|
aSig |= 0x00800000;
|
|
bSig |= 0x00800000;
|
|
if ( expDiff < 32 ) {
|
|
aSig <<= 8;
|
|
bSig <<= 8;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
aSig >>= 1;
|
|
}
|
|
q = ( bSig <= aSig );
|
|
if ( q ) aSig -= bSig;
|
|
if ( 0 < expDiff ) {
|
|
q = ( ( (bits64) aSig )<<32 ) / bSig;
|
|
q >>= 32 - expDiff;
|
|
bSig >>= 2;
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
else {
|
|
aSig >>= 2;
|
|
bSig >>= 2;
|
|
}
|
|
}
|
|
else {
|
|
if ( bSig <= aSig ) aSig -= bSig;
|
|
aSig64 = ( (bits64) aSig )<<40;
|
|
bSig64 = ( (bits64) bSig )<<40;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
|
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
|
|
aSig64 = - ( ( bSig * q64 )<<38 );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
|
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
|
|
q = q64>>( 64 - expDiff );
|
|
bSig <<= 6;
|
|
aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
do {
|
|
alternateASig = aSig;
|
|
++q;
|
|
aSig -= bSig;
|
|
} while ( 0 <= (sbits32) aSig );
|
|
sigMean = aSig + alternateASig;
|
|
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
|
|
aSig = alternateASig;
|
|
}
|
|
zSign = ( (sbits32) aSig < 0 );
|
|
if ( zSign ) aSig = - aSig;
|
|
return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the square root of the single-precision floating-point value `a'.
|
|
The operation is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float32_sqrt( float32 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, zExp;
|
|
bits32 aSig, zSig;
|
|
bits64 rem, term;
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig ) return propagateFloat32NaN( a, 0 );
|
|
if ( ! aSign ) return a;
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig ) == 0 ) return a;
|
|
float_raise( float_flag_invalid );
|
|
return float32_default_nan;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return 0;
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E;
|
|
aSig = ( aSig | 0x00800000 )<<8;
|
|
zSig = estimateSqrt32( aExp, aSig ) + 2;
|
|
if ( ( zSig & 0x7F ) <= 5 ) {
|
|
if ( zSig < 2 ) {
|
|
zSig = 0xFFFFFFFF;
|
|
}
|
|
else {
|
|
aSig >>= aExp & 1;
|
|
term = ( (bits64) zSig ) * zSig;
|
|
rem = ( ( (bits64) aSig )<<32 ) - term;
|
|
while ( (sbits64) rem < 0 ) {
|
|
--zSig;
|
|
rem += ( ( (bits64) zSig )<<1 ) | 1;
|
|
}
|
|
zSig |= ( rem != 0 );
|
|
}
|
|
}
|
|
shift32RightJamming( zSig, 1, &zSig );
|
|
return roundAndPackFloat32( 0, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the single-precision floating-point value `a' is equal to the
|
|
corresponding value `b', and 0 otherwise. The comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float32_eq( float32 a, float32 b )
|
|
{
|
|
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
|
) {
|
|
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the single-precision floating-point value `a' is less than or
|
|
equal to the corresponding value `b', and 0 otherwise. The comparison is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float32_le( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloat32Sign( a );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the single-precision floating-point value `a' is less than
|
|
the corresponding value `b', and 0 otherwise. The comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float32_lt( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloat32Sign( a );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the single-precision floating-point value `a' is equal to the
|
|
corresponding value `b', and 0 otherwise. The invalid exception is raised
|
|
if either operand is a NaN. Otherwise, the comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float32_eq_signaling( float32 a, float32 b )
|
|
{
|
|
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the single-precision floating-point value `a' is less than or
|
|
equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
|
cause an exception. Otherwise, the comparison is performed according to the
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float32_le_quiet( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign;
|
|
//int16 aExp, bExp;
|
|
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
|
) {
|
|
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloat32Sign( a );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the single-precision floating-point value `a' is less than
|
|
the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
|
exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
|
Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float32_lt_quiet( float32 a, float32 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
|
|
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
|
) {
|
|
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloat32Sign( a );
|
|
bSign = extractFloat32Sign( b );
|
|
if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the double-precision floating-point value
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic---which means in particular that the conversion is rounded
|
|
according to the current rounding mode. If `a' is a NaN, the largest
|
|
positive integer is returned. Otherwise, if the conversion overflows, the
|
|
largest integer with the same sign as `a' is returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 float64_to_int32( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, shiftCount;
|
|
bits64 aSig;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
|
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
|
|
shiftCount = 0x42C - aExp;
|
|
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
|
|
return roundAndPackInt32( aSign, aSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the double-precision floating-point value
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic, except that the conversion is always rounded toward zero. If
|
|
`a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
|
conversion overflows, the largest integer with the same sign as `a' is
|
|
returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 float64_to_int32_round_to_zero( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, shiftCount;
|
|
bits64 aSig, savedASig;
|
|
int32 z;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
shiftCount = 0x433 - aExp;
|
|
if ( shiftCount < 21 ) {
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
|
goto invalid;
|
|
}
|
|
else if ( 52 < shiftCount ) {
|
|
if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
|
|
return 0;
|
|
}
|
|
aSig |= LIT64( 0x0010000000000000 );
|
|
savedASig = aSig;
|
|
aSig >>= shiftCount;
|
|
z = aSig;
|
|
if ( aSign ) z = - z;
|
|
if ( ( z < 0 ) ^ aSign ) {
|
|
invalid:
|
|
float_exception_flags |= float_flag_invalid;
|
|
return aSign ? 0x80000000 : 0x7FFFFFFF;
|
|
}
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the double-precision floating-point value
|
|
`a' to the 32-bit two's complement unsigned integer format. The conversion
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic---which means in particular that the conversion is rounded
|
|
according to the current rounding mode. If `a' is a NaN, the largest
|
|
positive integer is returned. Otherwise, if the conversion overflows, the
|
|
largest positive integer is returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 float64_to_uint32( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, shiftCount;
|
|
bits64 aSig;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = 0; //extractFloat64Sign( a );
|
|
//if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
|
if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
|
|
shiftCount = 0x42C - aExp;
|
|
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
|
|
return roundAndPackInt32( aSign, aSig );
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the double-precision floating-point value
|
|
`a' to the 32-bit two's complement integer format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic, except that the conversion is always rounded toward zero. If
|
|
`a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
|
conversion overflows, the largest positive integer is returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 float64_to_uint32_round_to_zero( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, shiftCount;
|
|
bits64 aSig, savedASig;
|
|
int32 z;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
shiftCount = 0x433 - aExp;
|
|
if ( shiftCount < 21 ) {
|
|
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
|
|
goto invalid;
|
|
}
|
|
else if ( 52 < shiftCount ) {
|
|
if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
|
|
return 0;
|
|
}
|
|
aSig |= LIT64( 0x0010000000000000 );
|
|
savedASig = aSig;
|
|
aSig >>= shiftCount;
|
|
z = aSig;
|
|
if ( aSign ) z = - z;
|
|
if ( ( z < 0 ) ^ aSign ) {
|
|
invalid:
|
|
float_exception_flags |= float_flag_invalid;
|
|
return aSign ? 0x80000000 : 0x7FFFFFFF;
|
|
}
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the double-precision floating-point value
|
|
`a' to the single-precision floating-point format. The conversion is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 float64_to_float32( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp;
|
|
bits64 aSig;
|
|
bits32 zSig;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a ) );
|
|
return packFloat32( aSign, 0xFF, 0 );
|
|
}
|
|
shift64RightJamming( aSig, 22, &aSig );
|
|
zSig = aSig;
|
|
if ( aExp || zSig ) {
|
|
zSig |= 0x40000000;
|
|
aExp -= 0x381;
|
|
}
|
|
return roundAndPackFloat32( aSign, aExp, zSig );
|
|
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the double-precision floating-point value
|
|
`a' to the extended double-precision floating-point format. The conversion
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 float64_to_floatx80( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp;
|
|
bits64 aSig;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a ) );
|
|
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
return
|
|
packFloatx80(
|
|
aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 );
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Rounds the double-precision floating-point value `a' to an integer, and
|
|
returns the result as a double-precision floating-point value. The
|
|
operation is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_round_to_int( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp;
|
|
bits64 lastBitMask, roundBitsMask;
|
|
int8 roundingMode;
|
|
float64 z;
|
|
|
|
aExp = extractFloat64Exp( a );
|
|
if ( 0x433 <= aExp ) {
|
|
if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) {
|
|
return propagateFloat64NaN( a, a );
|
|
}
|
|
return a;
|
|
}
|
|
if ( aExp <= 0x3FE ) {
|
|
if ( (bits64) ( a<<1 ) == 0 ) return a;
|
|
float_exception_flags |= float_flag_inexact;
|
|
aSign = extractFloat64Sign( a );
|
|
switch ( float_rounding_mode ) {
|
|
case float_round_nearest_even:
|
|
if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) {
|
|
return packFloat64( aSign, 0x3FF, 0 );
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
return aSign ? LIT64( 0xBFF0000000000000 ) : 0;
|
|
case float_round_up:
|
|
return
|
|
aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 );
|
|
}
|
|
return packFloat64( aSign, 0, 0 );
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask <<= 0x433 - aExp;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z = a;
|
|
roundingMode = float_rounding_mode;
|
|
if ( roundingMode == float_round_nearest_even ) {
|
|
z += lastBitMask>>1;
|
|
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
|
|
}
|
|
else if ( roundingMode != float_round_to_zero ) {
|
|
if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
|
z += roundBitsMask;
|
|
}
|
|
}
|
|
z &= ~ roundBitsMask;
|
|
if ( z != a ) float_exception_flags |= float_flag_inexact;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of adding the absolute values of the double-precision
|
|
floating-point values `a' and `b'. If `zSign' is true, the sum is negated
|
|
before being returned. `zSign' is ignored if the result is a NaN. The
|
|
addition is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static float64 addFloat64Sigs( float64 a, float64 b, flag zSign )
|
|
{
|
|
int16 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig;
|
|
int16 expDiff;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
bSig = extractFloat64Frac( b );
|
|
bExp = extractFloat64Exp( b );
|
|
expDiff = aExp - bExp;
|
|
aSig <<= 9;
|
|
bSig <<= 9;
|
|
if ( 0 < expDiff ) {
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig ) return propagateFloat64NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig |= LIT64( 0x2000000000000000 );
|
|
}
|
|
shift64RightJamming( bSig, expDiff, &bSig );
|
|
zExp = aExp;
|
|
}
|
|
else if ( expDiff < 0 ) {
|
|
if ( bExp == 0x7FF ) {
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig |= LIT64( 0x2000000000000000 );
|
|
}
|
|
shift64RightJamming( aSig, - expDiff, &aSig );
|
|
zExp = bExp;
|
|
}
|
|
else {
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig | bSig ) return propagateFloat64NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
|
|
zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
|
|
zExp = aExp;
|
|
goto roundAndPack;
|
|
}
|
|
aSig |= LIT64( 0x2000000000000000 );
|
|
zSig = ( aSig + bSig )<<1;
|
|
--zExp;
|
|
if ( (sbits64) zSig < 0 ) {
|
|
zSig = aSig + bSig;
|
|
++zExp;
|
|
}
|
|
roundAndPack:
|
|
return roundAndPackFloat64( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of subtracting the absolute values of the double-
|
|
precision floating-point values `a' and `b'. If `zSign' is true, the
|
|
difference is negated before being returned. `zSign' is ignored if the
|
|
result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static float64 subFloat64Sigs( float64 a, float64 b, flag zSign )
|
|
{
|
|
int16 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig;
|
|
int16 expDiff;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
bSig = extractFloat64Frac( b );
|
|
bExp = extractFloat64Exp( b );
|
|
expDiff = aExp - bExp;
|
|
aSig <<= 10;
|
|
bSig <<= 10;
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig | bSig ) return propagateFloat64NaN( a, b );
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
if ( bSig < aSig ) goto aBigger;
|
|
if ( aSig < bSig ) goto bBigger;
|
|
return packFloat64( float_rounding_mode == float_round_down, 0, 0 );
|
|
bExpBigger:
|
|
if ( bExp == 0x7FF ) {
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
|
return packFloat64( zSign ^ 1, 0x7FF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig |= LIT64( 0x4000000000000000 );
|
|
}
|
|
shift64RightJamming( aSig, - expDiff, &aSig );
|
|
bSig |= LIT64( 0x4000000000000000 );
|
|
bBigger:
|
|
zSig = bSig - aSig;
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig ) return propagateFloat64NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig |= LIT64( 0x4000000000000000 );
|
|
}
|
|
shift64RightJamming( bSig, expDiff, &bSig );
|
|
aSig |= LIT64( 0x4000000000000000 );
|
|
aBigger:
|
|
zSig = aSig - bSig;
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
--zExp;
|
|
return normalizeRoundAndPackFloat64( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of adding the double-precision floating-point values `a'
|
|
and `b'. The operation is performed according to the IEC/IEEE Standard for
|
|
Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_add( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloat64Sign( a );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloat64Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return subFloat64Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of subtracting the double-precision floating-point values
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
|
for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_sub( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloat64Sign( a );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloat64Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return addFloat64Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of multiplying the double-precision floating-point values
|
|
`a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
|
for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_mul( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int16 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
bSig = extractFloat64Frac( b );
|
|
bExp = extractFloat64Exp( b );
|
|
bSign = extractFloat64Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
|
|
return propagateFloat64NaN( a, b );
|
|
}
|
|
if ( ( bExp | bSig ) == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
|
}
|
|
if ( bExp == 0x7FF ) {
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) return packFloat64( zSign, 0, 0 );
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
zExp = aExp + bExp - 0x3FF;
|
|
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
|
|
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
|
|
mul64To128( aSig, bSig, &zSig0, &zSig1 );
|
|
zSig0 |= ( zSig1 != 0 );
|
|
if ( 0 <= (sbits64) ( zSig0<<1 ) ) {
|
|
zSig0 <<= 1;
|
|
--zExp;
|
|
}
|
|
return roundAndPackFloat64( zSign, zExp, zSig0 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of dividing the double-precision floating-point value `a'
|
|
by the corresponding value `b'. The operation is performed according to
|
|
the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_div( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int16 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig;
|
|
bits64 rem0, rem1;
|
|
bits64 term0, term1;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
bSig = extractFloat64Frac( b );
|
|
bExp = extractFloat64Exp( b );
|
|
bSign = extractFloat64Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig ) return propagateFloat64NaN( a, b );
|
|
if ( bExp == 0x7FF ) {
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
|
}
|
|
if ( bExp == 0x7FF ) {
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
|
return packFloat64( zSign, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
float_raise( float_flag_divbyzero );
|
|
return packFloat64( zSign, 0x7FF, 0 );
|
|
}
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = aExp - bExp + 0x3FD;
|
|
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
|
|
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
|
|
if ( bSig <= ( aSig + aSig ) ) {
|
|
aSig >>= 1;
|
|
++zExp;
|
|
}
|
|
zSig = estimateDiv128To64( aSig, 0, bSig );
|
|
if ( ( zSig & 0x1FF ) <= 2 ) {
|
|
mul64To128( bSig, zSig, &term0, &term1 );
|
|
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig;
|
|
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
|
}
|
|
zSig |= ( rem1 != 0 );
|
|
}
|
|
return roundAndPackFloat64( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the remainder of the double-precision floating-point value `a'
|
|
with respect to the corresponding value `b'. The operation is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_rem( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int16 aExp, bExp, expDiff;
|
|
bits64 aSig, bSig;
|
|
bits64 q, alternateASig;
|
|
sbits64 sigMean;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
bSig = extractFloat64Frac( b );
|
|
bExp = extractFloat64Exp( b );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
|
|
return propagateFloat64NaN( a, b );
|
|
}
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
if ( bExp == 0x7FF ) {
|
|
if ( bSig ) return propagateFloat64NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return a;
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
expDiff = aExp - bExp;
|
|
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11;
|
|
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
aSig >>= 1;
|
|
}
|
|
q = ( bSig <= aSig );
|
|
if ( q ) aSig -= bSig;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig, 0, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
aSig = - ( ( bSig>>2 ) * q );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
if ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig, 0, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
q >>= 64 - expDiff;
|
|
bSig >>= 2;
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
else {
|
|
aSig >>= 2;
|
|
bSig >>= 2;
|
|
}
|
|
do {
|
|
alternateASig = aSig;
|
|
++q;
|
|
aSig -= bSig;
|
|
} while ( 0 <= (sbits64) aSig );
|
|
sigMean = aSig + alternateASig;
|
|
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
|
|
aSig = alternateASig;
|
|
}
|
|
zSign = ( (sbits64) aSig < 0 );
|
|
if ( zSign ) aSig = - aSig;
|
|
return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the square root of the double-precision floating-point value `a'.
|
|
The operation is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 float64_sqrt( float64 a )
|
|
{
|
|
flag aSign;
|
|
int16 aExp, zExp;
|
|
bits64 aSig, zSig;
|
|
bits64 rem0, rem1, term0, term1; //, shiftedRem;
|
|
//float64 z;
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig ) return propagateFloat64NaN( a, a );
|
|
if ( ! aSign ) return a;
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig ) == 0 ) return a;
|
|
float_raise( float_flag_invalid );
|
|
return float64_default_nan;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return 0;
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
|
|
aSig |= LIT64( 0x0010000000000000 );
|
|
zSig = estimateSqrt32( aExp, aSig>>21 );
|
|
zSig <<= 31;
|
|
aSig <<= 9 - ( aExp & 1 );
|
|
zSig = estimateDiv128To64( aSig, 0, zSig ) + zSig + 2;
|
|
if ( ( zSig & 0x3FF ) <= 5 ) {
|
|
if ( zSig < 2 ) {
|
|
zSig = LIT64( 0xFFFFFFFFFFFFFFFF );
|
|
}
|
|
else {
|
|
aSig <<= 2;
|
|
mul64To128( zSig, zSig, &term0, &term1 );
|
|
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig;
|
|
shortShift128Left( 0, zSig, 1, &term0, &term1 );
|
|
term1 |= 1;
|
|
add128( rem0, rem1, term0, term1, &rem0, &rem1 );
|
|
}
|
|
zSig |= ( ( rem0 | rem1 ) != 0 );
|
|
}
|
|
}
|
|
shift64RightJamming( zSig, 1, &zSig );
|
|
return roundAndPackFloat64( 0, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the double-precision floating-point value `a' is equal to the
|
|
corresponding value `b', and 0 otherwise. The comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float64_eq( float64 a, float64 b )
|
|
{
|
|
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
|
) {
|
|
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the double-precision floating-point value `a' is less than or
|
|
equal to the corresponding value `b', and 0 otherwise. The comparison is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float64_le( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloat64Sign( a );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the double-precision floating-point value `a' is less than
|
|
the corresponding value `b', and 0 otherwise. The comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float64_lt( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloat64Sign( a );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the double-precision floating-point value `a' is equal to the
|
|
corresponding value `b', and 0 otherwise. The invalid exception is raised
|
|
if either operand is a NaN. Otherwise, the comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float64_eq_signaling( float64 a, float64 b )
|
|
{
|
|
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the double-precision floating-point value `a' is less than or
|
|
equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
|
cause an exception. Otherwise, the comparison is performed according to the
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float64_le_quiet( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign;
|
|
//int16 aExp, bExp;
|
|
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
|
) {
|
|
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloat64Sign( a );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
|
|
return ( a == b ) || ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the double-precision floating-point value `a' is less than
|
|
the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
|
exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
|
Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag float64_lt_quiet( float64 a, float64 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
|
|
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
|
) {
|
|
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloat64Sign( a );
|
|
bSign = extractFloat64Sign( b );
|
|
if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
|
|
return ( a != b ) && ( aSign ^ ( a < b ) );
|
|
|
|
}
|
|
|
|
#ifdef FLOATX80
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the extended double-precision floating-
|
|
point value `a' to the 32-bit two's complement integer format. The
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic---which means in particular that the conversion
|
|
is rounded according to the current rounding mode. If `a' is a NaN, the
|
|
largest positive integer is returned. Otherwise, if the conversion
|
|
overflows, the largest integer with the same sign as `a' is returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 floatx80_to_int32( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, shiftCount;
|
|
bits64 aSig;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
|
|
shiftCount = 0x4037 - aExp;
|
|
if ( shiftCount <= 0 ) shiftCount = 1;
|
|
shift64RightJamming( aSig, shiftCount, &aSig );
|
|
return roundAndPackInt32( aSign, aSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the extended double-precision floating-
|
|
point value `a' to the 32-bit two's complement integer format. The
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic, except that the conversion is always rounded
|
|
toward zero. If `a' is a NaN, the largest positive integer is returned.
|
|
Otherwise, if the conversion overflows, the largest integer with the same
|
|
sign as `a' is returned.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
int32 floatx80_to_int32_round_to_zero( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, shiftCount;
|
|
bits64 aSig, savedASig;
|
|
int32 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
shiftCount = 0x403E - aExp;
|
|
if ( shiftCount < 32 ) {
|
|
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
|
|
goto invalid;
|
|
}
|
|
else if ( 63 < shiftCount ) {
|
|
if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
|
|
return 0;
|
|
}
|
|
savedASig = aSig;
|
|
aSig >>= shiftCount;
|
|
z = aSig;
|
|
if ( aSign ) z = - z;
|
|
if ( ( z < 0 ) ^ aSign ) {
|
|
invalid:
|
|
float_exception_flags |= float_flag_invalid;
|
|
return aSign ? 0x80000000 : 0x7FFFFFFF;
|
|
}
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
|
float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the extended double-precision floating-
|
|
point value `a' to the single-precision floating-point format. The
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float32 floatx80_to_float32( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 aSig;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) {
|
|
return commonNaNToFloat32( floatx80ToCommonNaN( a ) );
|
|
}
|
|
return packFloat32( aSign, 0xFF, 0 );
|
|
}
|
|
shift64RightJamming( aSig, 33, &aSig );
|
|
if ( aExp || aSig ) aExp -= 0x3F81;
|
|
return roundAndPackFloat32( aSign, aExp, aSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of converting the extended double-precision floating-
|
|
point value `a' to the double-precision floating-point format. The
|
|
conversion is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
float64 floatx80_to_float64( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 aSig, zSig;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) {
|
|
return commonNaNToFloat64( floatx80ToCommonNaN( a ) );
|
|
}
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
|
}
|
|
shift64RightJamming( aSig, 1, &zSig );
|
|
if ( aExp || aSig ) aExp -= 0x3C01;
|
|
return roundAndPackFloat64( aSign, aExp, zSig );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Rounds the extended double-precision floating-point value `a' to an integer,
|
|
and returns the result as an extended quadruple-precision floating-point
|
|
value. The operation is performed according to the IEC/IEEE Standard for
|
|
Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_round_to_int( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp;
|
|
bits64 lastBitMask, roundBitsMask;
|
|
int8 roundingMode;
|
|
floatx80 z;
|
|
|
|
aExp = extractFloatx80Exp( a );
|
|
if ( 0x403E <= aExp ) {
|
|
if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) {
|
|
return propagateFloatx80NaN( a, a );
|
|
}
|
|
return a;
|
|
}
|
|
if ( aExp <= 0x3FFE ) {
|
|
if ( ( aExp == 0 )
|
|
&& ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
|
|
return a;
|
|
}
|
|
float_exception_flags |= float_flag_inexact;
|
|
aSign = extractFloatx80Sign( a );
|
|
switch ( float_rounding_mode ) {
|
|
case float_round_nearest_even:
|
|
if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 )
|
|
) {
|
|
return
|
|
packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
return
|
|
aSign ?
|
|
packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) )
|
|
: packFloatx80( 0, 0, 0 );
|
|
case float_round_up:
|
|
return
|
|
aSign ? packFloatx80( 1, 0, 0 )
|
|
: packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
return packFloatx80( aSign, 0, 0 );
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask <<= 0x403E - aExp;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z = a;
|
|
roundingMode = float_rounding_mode;
|
|
if ( roundingMode == float_round_nearest_even ) {
|
|
z.low += lastBitMask>>1;
|
|
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
|
|
}
|
|
else if ( roundingMode != float_round_to_zero ) {
|
|
if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
|
z.low += roundBitsMask;
|
|
}
|
|
}
|
|
z.low &= ~ roundBitsMask;
|
|
if ( z.low == 0 ) {
|
|
++z.high;
|
|
z.low = LIT64( 0x8000000000000000 );
|
|
}
|
|
if ( z.low != a.low ) float_exception_flags |= float_flag_inexact;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of adding the absolute values of the extended double-
|
|
precision floating-point values `a' and `b'. If `zSign' is true, the sum is
|
|
negated before being returned. `zSign' is ignored if the result is a NaN.
|
|
The addition is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign )
|
|
{
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
int32 expDiff;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) --expDiff;
|
|
shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
|
zExp = aExp;
|
|
}
|
|
else if ( expDiff < 0 ) {
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) ++expDiff;
|
|
shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
|
zExp = bExp;
|
|
}
|
|
else {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
return a;
|
|
}
|
|
zSig1 = 0;
|
|
zSig0 = aSig + bSig;
|
|
if ( aExp == 0 ) {
|
|
normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
|
|
goto roundAndPack;
|
|
}
|
|
zExp = aExp;
|
|
goto shiftRight1;
|
|
}
|
|
|
|
zSig0 = aSig + bSig;
|
|
|
|
if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
|
|
shiftRight1:
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
|
zSig0 |= LIT64( 0x8000000000000000 );
|
|
++zExp;
|
|
roundAndPack:
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of subtracting the absolute values of the extended
|
|
double-precision floating-point values `a' and `b'. If `zSign' is true,
|
|
the difference is negated before being returned. `zSign' is ignored if the
|
|
result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign )
|
|
{
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
int32 expDiff;
|
|
floatx80 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
zSig1 = 0;
|
|
if ( bSig < aSig ) goto aBigger;
|
|
if ( aSig < bSig ) goto bBigger;
|
|
return packFloatx80( float_rounding_mode == float_round_down, 0, 0 );
|
|
bExpBigger:
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) ++expDiff;
|
|
shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
|
bBigger:
|
|
sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) --expDiff;
|
|
shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
|
aBigger:
|
|
sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
return
|
|
normalizeRoundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of adding the extended double-precision floating-point
|
|
values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_add( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloatx80Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return subFloatx80Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of subtracting the extended double-precision floating-
|
|
point values `a' and `b'. The operation is performed according to the
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_sub( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloatx80Sigs( a, b, aSign );
|
|
}
|
|
else {
|
|
return addFloatx80Sigs( a, b, aSign );
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of multiplying the extended double-precision floating-
|
|
point values `a' and `b'. The operation is performed according to the
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_mul( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
floatx80 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 )
|
|
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
if ( ( bExp | bSig ) == 0 ) goto invalid;
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
zExp = aExp + bExp - 0x3FFE;
|
|
mul64To128( aSig, bSig, &zSig0, &zSig1 );
|
|
if ( 0 < (sbits64) zSig0 ) {
|
|
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
|
--zExp;
|
|
}
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the result of dividing the extended double-precision floating-point
|
|
value `a' by the corresponding value `b'. The operation is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_div( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, zExp;
|
|
bits64 aSig, bSig, zSig0, zSig1;
|
|
bits64 rem0, rem1, rem2, term0, term1, term2;
|
|
floatx80 z;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
goto invalid;
|
|
}
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return packFloatx80( zSign, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
float_raise( float_flag_divbyzero );
|
|
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
|
|
}
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = aExp - bExp + 0x3FFE;
|
|
rem1 = 0;
|
|
if ( bSig <= aSig ) {
|
|
shift128Right( aSig, 0, 1, &aSig, &rem1 );
|
|
++zExp;
|
|
}
|
|
zSig0 = estimateDiv128To64( aSig, rem1, bSig );
|
|
mul64To128( bSig, zSig0, &term0, &term1 );
|
|
sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig0;
|
|
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, bSig );
|
|
if ( (bits64) ( zSig1<<1 ) <= 8 ) {
|
|
mul64To128( bSig, zSig1, &term1, &term2 );
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
|
while ( (sbits64) rem1 < 0 ) {
|
|
--zSig1;
|
|
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 ) != 0 );
|
|
}
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the remainder of the extended double-precision floating-point value
|
|
`a' with respect to the corresponding value `b'. The operation is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_rem( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign, zSign;
|
|
int32 aExp, bExp, expDiff;
|
|
bits64 aSig0, aSig1, bSig;
|
|
bits64 q, term0, term1, alternateASig0, alternateASig1;
|
|
floatx80 z;
|
|
|
|
aSig0 = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig0<<1 )
|
|
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
|
|
return propagateFloatx80NaN( a, b );
|
|
}
|
|
goto invalid;
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( (bits64) ( aSig0<<1 ) == 0 ) return a;
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
|
}
|
|
bSig |= LIT64( 0x8000000000000000 );
|
|
zSign = aSign;
|
|
expDiff = aExp - bExp;
|
|
aSig1 = 0;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
|
|
expDiff = 0;
|
|
}
|
|
q = ( bSig <= aSig0 );
|
|
if ( q ) aSig0 -= bSig;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
mul64To128( bSig, q, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
if ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
q >>= 64 - expDiff;
|
|
mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
|
|
while ( le128( term0, term1, aSig0, aSig1 ) ) {
|
|
++q;
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
}
|
|
}
|
|
else {
|
|
term1 = 0;
|
|
term0 = bSig;
|
|
}
|
|
sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
|
|
if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
|
|| ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
|
&& ( q & 1 ) )
|
|
) {
|
|
aSig0 = alternateASig0;
|
|
aSig1 = alternateASig1;
|
|
zSign = ! zSign;
|
|
}
|
|
return
|
|
normalizeRoundAndPackFloatx80(
|
|
80, zSign, bExp + expDiff, aSig0, aSig1 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns the square root of the extended double-precision floating-point
|
|
value `a'. The operation is performed according to the IEC/IEEE Standard
|
|
for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
floatx80 floatx80_sqrt( floatx80 a )
|
|
{
|
|
flag aSign;
|
|
int32 aExp, zExp;
|
|
bits64 aSig0, aSig1, zSig0, zSig1;
|
|
bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
|
|
bits64 shiftedRem0, shiftedRem1;
|
|
floatx80 z;
|
|
|
|
aSig0 = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a );
|
|
if ( ! aSign ) return a;
|
|
goto invalid;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig0 ) == 0 ) return a;
|
|
invalid:
|
|
float_raise( float_flag_invalid );
|
|
z.low = floatx80_default_nan_low;
|
|
z.high = floatx80_default_nan_high;
|
|
return z;
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
|
}
|
|
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
|
|
zSig0 = estimateSqrt32( aExp, aSig0>>32 );
|
|
zSig0 <<= 31;
|
|
aSig1 = 0;
|
|
shift128Right( aSig0, 0, ( aExp & 1 ) + 2, &aSig0, &aSig1 );
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0 ) + zSig0 + 4;
|
|
if ( 0 <= (sbits64) zSig0 ) zSig0 = LIT64( 0xFFFFFFFFFFFFFFFF );
|
|
shortShift128Left( aSig0, aSig1, 2, &aSig0, &aSig1 );
|
|
mul64To128( zSig0, zSig0, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
|
|
while ( (sbits64) rem0 < 0 ) {
|
|
--zSig0;
|
|
shortShift128Left( 0, zSig0, 1, &term0, &term1 );
|
|
term1 |= 1;
|
|
add128( rem0, rem1, term0, term1, &rem0, &rem1 );
|
|
}
|
|
shortShift128Left( rem0, rem1, 63, &shiftedRem0, &shiftedRem1 );
|
|
zSig1 = estimateDiv128To64( shiftedRem0, shiftedRem1, zSig0 );
|
|
if ( (bits64) ( zSig1<<1 ) <= 10 ) {
|
|
if ( zSig1 == 0 ) zSig1 = 1;
|
|
mul64To128( zSig0, zSig1, &term1, &term2 );
|
|
shortShift128Left( term1, term2, 1, &term1, &term2 );
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
|
mul64To128( zSig1, zSig1, &term2, &term3 );
|
|
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
while ( (sbits64) rem1 < 0 ) {
|
|
--zSig1;
|
|
shortShift192Left( 0, zSig0, zSig1, 1, &term1, &term2, &term3 );
|
|
term3 |= 1;
|
|
add192(
|
|
rem1, rem2, rem3, term1, term2, term3, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
return
|
|
roundAndPackFloatx80(
|
|
floatx80_rounding_precision, 0, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the extended double-precision floating-point value `a' is
|
|
equal to the corresponding value `b', and 0 otherwise. The comparison is
|
|
performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag floatx80_eq( floatx80 a, floatx80 b )
|
|
{
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if ( floatx80_is_signaling_nan( a )
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
|
|
);
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the extended double-precision floating-point value `a' is
|
|
less than or equal to the corresponding value `b', and 0 otherwise. The
|
|
comparison is performed according to the IEC/IEEE Standard for Binary
|
|
Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag floatx80_le( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the extended double-precision floating-point value `a' is
|
|
less than the corresponding value `b', and 0 otherwise. The comparison
|
|
is performed according to the IEC/IEEE Standard for Binary Floating-point
|
|
Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag floatx80_lt( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the extended double-precision floating-point value `a' is equal
|
|
to the corresponding value `b', and 0 otherwise. The invalid exception is
|
|
raised if either operand is a NaN. Otherwise, the comparison is performed
|
|
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag floatx80_eq_signaling( floatx80 a, floatx80 b )
|
|
{
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
float_raise( float_flag_invalid );
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
|
|
);
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the extended double-precision floating-point value `a' is less
|
|
than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs
|
|
do not cause an exception. Otherwise, the comparison is performed according
|
|
to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag floatx80_le_quiet( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if ( floatx80_is_signaling_nan( a )
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*
|
|
-------------------------------------------------------------------------------
|
|
Returns 1 if the extended double-precision floating-point value `a' is less
|
|
than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
|
|
an exception. Otherwise, the comparison is performed according to the
|
|
IEC/IEEE Standard for Binary Floating-point Arithmetic.
|
|
-------------------------------------------------------------------------------
|
|
*/
|
|
flag floatx80_lt_quiet( floatx80 a, floatx80 b )
|
|
{
|
|
flag aSign, bSign;
|
|
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if ( floatx80_is_signaling_nan( a )
|
|
|| floatx80_is_signaling_nan( b ) ) {
|
|
float_raise( float_flag_invalid );
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
#endif
|
|
|