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/*============================================================================
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This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
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Package, Release 2b.
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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://www.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 has
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been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
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RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
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AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
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COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
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EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
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INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
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OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) the source code for the derivative work includes prominent notice that
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the work is derivative, and (2) the source code includes prominent notice with
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these four paragraphs for those parts of this code that are retained.
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=============================================================================*/
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/* FIXME: Flush-To-Zero only effects results. Denormal inputs should also
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be flushed to zero. */
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#include "softfloat.h" |
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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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#include "softfloat-macros.h" |
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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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#include "softfloat-specialize.h" |
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void set_float_rounding_mode(int val STATUS_PARAM) |
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{ |
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STATUS(float_rounding_mode) = val; |
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} |
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void set_float_exception_flags(int val STATUS_PARAM) |
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{ |
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STATUS(float_exception_flags) = val; |
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} |
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#ifdef FLOATX80
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void set_floatx80_rounding_precision(int val STATUS_PARAM) |
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{ |
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STATUS(floatx80_rounding_precision) = val; |
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} |
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#endif
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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 1, the input is negated before being converted to an
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| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input
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| is simply rounded to an integer, with the inexact exception raised if the
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| input cannot be represented exactly as an integer. However, if the fixed-
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| point input is too large, 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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static int32 roundAndPackInt32( flag zSign, bits64 absZ STATUS_PARAM)
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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 = STATUS(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_raise( float_flag_invalid STATUS_VAR); |
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return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; |
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} |
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if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
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return z;
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} |
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/*----------------------------------------------------------------------------
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| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
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| `absZ1', with binary point between bits 63 and 64 (between the input words),
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| and returns the properly rounded 64-bit integer corresponding to the input.
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| If `zSign' is 1, the input is negated before being converted to an integer.
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| Ordinarily, the fixed-point input is simply rounded to an integer, with
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| the inexact exception raised if the input cannot be represented exactly as
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| an integer. However, if the fixed-point input is too large, the invalid
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| exception is raised and the largest positive or negative integer is
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| returned.
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*----------------------------------------------------------------------------*/
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static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 STATUS_PARAM)
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{ |
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int8 roundingMode; |
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flag roundNearestEven, increment; |
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int64 z; |
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roundingMode = STATUS(float_rounding_mode); |
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roundNearestEven = ( roundingMode == float_round_nearest_even ); |
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increment = ( (sbits64) absZ1 < 0 );
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if ( ! roundNearestEven ) {
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if ( roundingMode == float_round_to_zero ) {
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increment = 0;
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} |
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else {
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if ( zSign ) {
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increment = ( roundingMode == float_round_down ) && absZ1; |
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} |
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else {
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increment = ( roundingMode == float_round_up ) && absZ1; |
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} |
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} |
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} |
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if ( increment ) {
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++absZ0; |
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if ( absZ0 == 0 ) goto overflow; |
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absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven ); |
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} |
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z = absZ0; |
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if ( zSign ) z = - z;
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if ( z && ( ( z < 0 ) ^ zSign ) ) { |
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overflow:
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float_raise( float_flag_invalid STATUS_VAR); |
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return
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zSign ? (sbits64) LIT64( 0x8000000000000000 )
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: LIT64( 0x7FFFFFFFFFFFFFFF );
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} |
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if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact;
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return z;
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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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INLINE bits32 extractFloat32Frac( float32 a ) |
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{ |
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return float32_val(a) & 0x007FFFFF; |
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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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INLINE int16 extractFloat32Exp( float32 a ) |
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{ |
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return ( float32_val(a)>>23 ) & 0xFF; |
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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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INLINE flag extractFloat32Sign( float32 a ) |
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{ |
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return float32_val(a)>>31; |
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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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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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| 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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INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig ) |
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{ |
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return make_float32(
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( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig); |
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} |
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/*----------------------------------------------------------------------------
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| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
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| and significand `zSig', and returns the proper single-precision floating-
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| point value corresponding to the abstract input. Ordinarily, the abstract
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| value is simply rounded and packed into the single-precision format, with
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| the inexact exception raised if the abstract input cannot be represented
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| exactly. However, if the abstract value is too large, the overflow and
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| inexact exceptions are raised and an infinity or maximal finite value is
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| returned. If the abstract value is too small, the input value is rounded to
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| a subnormal number, and the underflow and inexact exceptions are raised if
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| the abstract input cannot be represented exactly as a subnormal single-
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| precision floating-point number.
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| The input significand `zSig' has its binary point between bits 30
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| and 29, which is 7 bits to the left of the usual location. This shifted
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| significand must be normalized or smaller. If `zSig' is not normalized,
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| `zExp' must be 0; in that case, the result returned is a subnormal number,
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| and it must not require rounding. In the usual case that `zSig' is
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| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
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| The handling of underflow and overflow follows the IEC/IEEE Standard for
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| Binary Floating-Point Arithmetic.
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*----------------------------------------------------------------------------*/
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static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
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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 = STATUS(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 STATUS_VAR); |
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return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 )); |
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} |
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if ( zExp < 0 ) { |
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if ( STATUS(flush_to_zero) ) return packFloat32( zSign, 0, 0 ); |
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isTiny = |
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( STATUS(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 STATUS_VAR);
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} |
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} |
310 |
if ( roundBits ) STATUS(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; |
314 |
return packFloat32( zSign, zExp, zSig );
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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.
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| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
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| floating-point exponent.
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*----------------------------------------------------------------------------*/
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326 |
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static float32
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normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM) |
329 |
{ |
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int8 shiftCount; |
331 |
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shiftCount = countLeadingZeros32( zSig ) - 1;
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return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
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335 |
} |
336 |
|
337 |
/*----------------------------------------------------------------------------
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338 |
| Returns the fraction bits of the double-precision floating-point value `a'.
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339 |
*----------------------------------------------------------------------------*/
|
340 |
|
341 |
INLINE bits64 extractFloat64Frac( float64 a ) |
342 |
{ |
343 |
|
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return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF ); |
345 |
|
346 |
} |
347 |
|
348 |
/*----------------------------------------------------------------------------
|
349 |
| Returns the exponent bits of the double-precision floating-point value `a'.
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*----------------------------------------------------------------------------*/
|
351 |
|
352 |
INLINE int16 extractFloat64Exp( float64 a ) |
353 |
{ |
354 |
|
355 |
return ( float64_val(a)>>52 ) & 0x7FF; |
356 |
|
357 |
} |
358 |
|
359 |
/*----------------------------------------------------------------------------
|
360 |
| Returns the sign bit of the double-precision floating-point value `a'.
|
361 |
*----------------------------------------------------------------------------*/
|
362 |
|
363 |
INLINE flag extractFloat64Sign( float64 a ) |
364 |
{ |
365 |
|
366 |
return float64_val(a)>>63; |
367 |
|
368 |
} |
369 |
|
370 |
/*----------------------------------------------------------------------------
|
371 |
| Normalizes the subnormal double-precision floating-point value represented
|
372 |
| by the denormalized significand `aSig'. The normalized exponent and
|
373 |
| significand are stored at the locations pointed to by `zExpPtr' and
|
374 |
| `zSigPtr', respectively.
|
375 |
*----------------------------------------------------------------------------*/
|
376 |
|
377 |
static void |
378 |
normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr ) |
379 |
{ |
380 |
int8 shiftCount; |
381 |
|
382 |
shiftCount = countLeadingZeros64( aSig ) - 11;
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383 |
*zSigPtr = aSig<<shiftCount; |
384 |
*zExpPtr = 1 - shiftCount;
|
385 |
|
386 |
} |
387 |
|
388 |
/*----------------------------------------------------------------------------
|
389 |
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
|
390 |
| double-precision floating-point value, returning the result. After being
|
391 |
| shifted into the proper positions, the three fields are simply added
|
392 |
| together to form the result. This means that any integer portion of `zSig'
|
393 |
| will be added into the exponent. Since a properly normalized significand
|
394 |
| will have an integer portion equal to 1, the `zExp' input should be 1 less
|
395 |
| than the desired result exponent whenever `zSig' is a complete, normalized
|
396 |
| significand.
|
397 |
*----------------------------------------------------------------------------*/
|
398 |
|
399 |
INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig ) |
400 |
{ |
401 |
|
402 |
return make_float64(
|
403 |
( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig); |
404 |
|
405 |
} |
406 |
|
407 |
/*----------------------------------------------------------------------------
|
408 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
409 |
| and significand `zSig', and returns the proper double-precision floating-
|
410 |
| point value corresponding to the abstract input. Ordinarily, the abstract
|
411 |
| value is simply rounded and packed into the double-precision format, with
|
412 |
| the inexact exception raised if the abstract input cannot be represented
|
413 |
| exactly. However, if the abstract value is too large, the overflow and
|
414 |
| inexact exceptions are raised and an infinity or maximal finite value is
|
415 |
| returned. If the abstract value is too small, the input value is rounded
|
416 |
| to a subnormal number, and the underflow and inexact exceptions are raised
|
417 |
| if the abstract input cannot be represented exactly as a subnormal double-
|
418 |
| precision floating-point number.
|
419 |
| The input significand `zSig' has its binary point between bits 62
|
420 |
| and 61, which is 10 bits to the left of the usual location. This shifted
|
421 |
| significand must be normalized or smaller. If `zSig' is not normalized,
|
422 |
| `zExp' must be 0; in that case, the result returned is a subnormal number,
|
423 |
| and it must not require rounding. In the usual case that `zSig' is
|
424 |
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
|
425 |
| The handling of underflow and overflow follows the IEC/IEEE Standard for
|
426 |
| Binary Floating-Point Arithmetic.
|
427 |
*----------------------------------------------------------------------------*/
|
428 |
|
429 |
static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
|
430 |
{ |
431 |
int8 roundingMode; |
432 |
flag roundNearestEven; |
433 |
int16 roundIncrement, roundBits; |
434 |
flag isTiny; |
435 |
|
436 |
roundingMode = STATUS(float_rounding_mode); |
437 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
438 |
roundIncrement = 0x200;
|
439 |
if ( ! roundNearestEven ) {
|
440 |
if ( roundingMode == float_round_to_zero ) {
|
441 |
roundIncrement = 0;
|
442 |
} |
443 |
else {
|
444 |
roundIncrement = 0x3FF;
|
445 |
if ( zSign ) {
|
446 |
if ( roundingMode == float_round_up ) roundIncrement = 0; |
447 |
} |
448 |
else {
|
449 |
if ( roundingMode == float_round_down ) roundIncrement = 0; |
450 |
} |
451 |
} |
452 |
} |
453 |
roundBits = zSig & 0x3FF;
|
454 |
if ( 0x7FD <= (bits16) zExp ) { |
455 |
if ( ( 0x7FD < zExp ) |
456 |
|| ( ( zExp == 0x7FD )
|
457 |
&& ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
|
458 |
) { |
459 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
460 |
return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 )); |
461 |
} |
462 |
if ( zExp < 0 ) { |
463 |
if ( STATUS(flush_to_zero) ) return packFloat64( zSign, 0, 0 ); |
464 |
isTiny = |
465 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
466 |
|| ( zExp < -1 )
|
467 |
|| ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
|
468 |
shift64RightJamming( zSig, - zExp, &zSig ); |
469 |
zExp = 0;
|
470 |
roundBits = zSig & 0x3FF;
|
471 |
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
|
472 |
} |
473 |
} |
474 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
475 |
zSig = ( zSig + roundIncrement )>>10;
|
476 |
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); |
477 |
if ( zSig == 0 ) zExp = 0; |
478 |
return packFloat64( zSign, zExp, zSig );
|
479 |
|
480 |
} |
481 |
|
482 |
/*----------------------------------------------------------------------------
|
483 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
484 |
| and significand `zSig', and returns the proper double-precision floating-
|
485 |
| point value corresponding to the abstract input. This routine is just like
|
486 |
| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
|
487 |
| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
|
488 |
| floating-point exponent.
|
489 |
*----------------------------------------------------------------------------*/
|
490 |
|
491 |
static float64
|
492 |
normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM) |
493 |
{ |
494 |
int8 shiftCount; |
495 |
|
496 |
shiftCount = countLeadingZeros64( zSig ) - 1;
|
497 |
return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
|
498 |
|
499 |
} |
500 |
|
501 |
#ifdef FLOATX80
|
502 |
|
503 |
/*----------------------------------------------------------------------------
|
504 |
| Returns the fraction bits of the extended double-precision floating-point
|
505 |
| value `a'.
|
506 |
*----------------------------------------------------------------------------*/
|
507 |
|
508 |
INLINE bits64 extractFloatx80Frac( floatx80 a ) |
509 |
{ |
510 |
|
511 |
return a.low;
|
512 |
|
513 |
} |
514 |
|
515 |
/*----------------------------------------------------------------------------
|
516 |
| Returns the exponent bits of the extended double-precision floating-point
|
517 |
| value `a'.
|
518 |
*----------------------------------------------------------------------------*/
|
519 |
|
520 |
INLINE int32 extractFloatx80Exp( floatx80 a ) |
521 |
{ |
522 |
|
523 |
return a.high & 0x7FFF; |
524 |
|
525 |
} |
526 |
|
527 |
/*----------------------------------------------------------------------------
|
528 |
| Returns the sign bit of the extended double-precision floating-point value
|
529 |
| `a'.
|
530 |
*----------------------------------------------------------------------------*/
|
531 |
|
532 |
INLINE flag extractFloatx80Sign( floatx80 a ) |
533 |
{ |
534 |
|
535 |
return a.high>>15; |
536 |
|
537 |
} |
538 |
|
539 |
/*----------------------------------------------------------------------------
|
540 |
| Normalizes the subnormal extended double-precision floating-point value
|
541 |
| represented by the denormalized significand `aSig'. The normalized exponent
|
542 |
| and significand are stored at the locations pointed to by `zExpPtr' and
|
543 |
| `zSigPtr', respectively.
|
544 |
*----------------------------------------------------------------------------*/
|
545 |
|
546 |
static void |
547 |
normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr ) |
548 |
{ |
549 |
int8 shiftCount; |
550 |
|
551 |
shiftCount = countLeadingZeros64( aSig ); |
552 |
*zSigPtr = aSig<<shiftCount; |
553 |
*zExpPtr = 1 - shiftCount;
|
554 |
|
555 |
} |
556 |
|
557 |
/*----------------------------------------------------------------------------
|
558 |
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
|
559 |
| extended double-precision floating-point value, returning the result.
|
560 |
*----------------------------------------------------------------------------*/
|
561 |
|
562 |
INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig ) |
563 |
{ |
564 |
floatx80 z; |
565 |
|
566 |
z.low = zSig; |
567 |
z.high = ( ( (bits16) zSign )<<15 ) + zExp;
|
568 |
return z;
|
569 |
|
570 |
} |
571 |
|
572 |
/*----------------------------------------------------------------------------
|
573 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
574 |
| and extended significand formed by the concatenation of `zSig0' and `zSig1',
|
575 |
| and returns the proper extended double-precision floating-point value
|
576 |
| corresponding to the abstract input. Ordinarily, the abstract value is
|
577 |
| rounded and packed into the extended double-precision format, with the
|
578 |
| inexact exception raised if the abstract input cannot be represented
|
579 |
| exactly. However, if the abstract value is too large, the overflow and
|
580 |
| inexact exceptions are raised and an infinity or maximal finite value is
|
581 |
| returned. If the abstract value is too small, the input value is rounded to
|
582 |
| a subnormal number, and the underflow and inexact exceptions are raised if
|
583 |
| the abstract input cannot be represented exactly as a subnormal extended
|
584 |
| double-precision floating-point number.
|
585 |
| If `roundingPrecision' is 32 or 64, the result is rounded to the same
|
586 |
| number of bits as single or double precision, respectively. Otherwise, the
|
587 |
| result is rounded to the full precision of the extended double-precision
|
588 |
| format.
|
589 |
| The input significand must be normalized or smaller. If the input
|
590 |
| significand is not normalized, `zExp' must be 0; in that case, the result
|
591 |
| returned is a subnormal number, and it must not require rounding. The
|
592 |
| handling of underflow and overflow follows the IEC/IEEE Standard for Binary
|
593 |
| Floating-Point Arithmetic.
|
594 |
*----------------------------------------------------------------------------*/
|
595 |
|
596 |
static floatx80
|
597 |
roundAndPackFloatx80( |
598 |
int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 |
599 |
STATUS_PARAM) |
600 |
{ |
601 |
int8 roundingMode; |
602 |
flag roundNearestEven, increment, isTiny; |
603 |
int64 roundIncrement, roundMask, roundBits; |
604 |
|
605 |
roundingMode = STATUS(float_rounding_mode); |
606 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
607 |
if ( roundingPrecision == 80 ) goto precision80; |
608 |
if ( roundingPrecision == 64 ) { |
609 |
roundIncrement = LIT64( 0x0000000000000400 );
|
610 |
roundMask = LIT64( 0x00000000000007FF );
|
611 |
} |
612 |
else if ( roundingPrecision == 32 ) { |
613 |
roundIncrement = LIT64( 0x0000008000000000 );
|
614 |
roundMask = LIT64( 0x000000FFFFFFFFFF );
|
615 |
} |
616 |
else {
|
617 |
goto precision80;
|
618 |
} |
619 |
zSig0 |= ( zSig1 != 0 );
|
620 |
if ( ! roundNearestEven ) {
|
621 |
if ( roundingMode == float_round_to_zero ) {
|
622 |
roundIncrement = 0;
|
623 |
} |
624 |
else {
|
625 |
roundIncrement = roundMask; |
626 |
if ( zSign ) {
|
627 |
if ( roundingMode == float_round_up ) roundIncrement = 0; |
628 |
} |
629 |
else {
|
630 |
if ( roundingMode == float_round_down ) roundIncrement = 0; |
631 |
} |
632 |
} |
633 |
} |
634 |
roundBits = zSig0 & roundMask; |
635 |
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { |
636 |
if ( ( 0x7FFE < zExp ) |
637 |
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
|
638 |
) { |
639 |
goto overflow;
|
640 |
} |
641 |
if ( zExp <= 0 ) { |
642 |
if ( STATUS(flush_to_zero) ) return packFloatx80( zSign, 0, 0 ); |
643 |
isTiny = |
644 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
645 |
|| ( zExp < 0 )
|
646 |
|| ( zSig0 <= zSig0 + roundIncrement ); |
647 |
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
|
648 |
zExp = 0;
|
649 |
roundBits = zSig0 & roundMask; |
650 |
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
|
651 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
652 |
zSig0 += roundIncrement; |
653 |
if ( (sbits64) zSig0 < 0 ) zExp = 1; |
654 |
roundIncrement = roundMask + 1;
|
655 |
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { |
656 |
roundMask |= roundIncrement; |
657 |
} |
658 |
zSig0 &= ~ roundMask; |
659 |
return packFloatx80( zSign, zExp, zSig0 );
|
660 |
} |
661 |
} |
662 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
663 |
zSig0 += roundIncrement; |
664 |
if ( zSig0 < roundIncrement ) {
|
665 |
++zExp; |
666 |
zSig0 = LIT64( 0x8000000000000000 );
|
667 |
} |
668 |
roundIncrement = roundMask + 1;
|
669 |
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { |
670 |
roundMask |= roundIncrement; |
671 |
} |
672 |
zSig0 &= ~ roundMask; |
673 |
if ( zSig0 == 0 ) zExp = 0; |
674 |
return packFloatx80( zSign, zExp, zSig0 );
|
675 |
precision80:
|
676 |
increment = ( (sbits64) zSig1 < 0 );
|
677 |
if ( ! roundNearestEven ) {
|
678 |
if ( roundingMode == float_round_to_zero ) {
|
679 |
increment = 0;
|
680 |
} |
681 |
else {
|
682 |
if ( zSign ) {
|
683 |
increment = ( roundingMode == float_round_down ) && zSig1; |
684 |
} |
685 |
else {
|
686 |
increment = ( roundingMode == float_round_up ) && zSig1; |
687 |
} |
688 |
} |
689 |
} |
690 |
if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { |
691 |
if ( ( 0x7FFE < zExp ) |
692 |
|| ( ( zExp == 0x7FFE )
|
693 |
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
|
694 |
&& increment |
695 |
) |
696 |
) { |
697 |
roundMask = 0;
|
698 |
overflow:
|
699 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
700 |
if ( ( roundingMode == float_round_to_zero )
|
701 |
|| ( zSign && ( roundingMode == float_round_up ) ) |
702 |
|| ( ! zSign && ( roundingMode == float_round_down ) ) |
703 |
) { |
704 |
return packFloatx80( zSign, 0x7FFE, ~ roundMask ); |
705 |
} |
706 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
707 |
} |
708 |
if ( zExp <= 0 ) { |
709 |
isTiny = |
710 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
711 |
|| ( zExp < 0 )
|
712 |
|| ! increment |
713 |
|| ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
|
714 |
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
|
715 |
zExp = 0;
|
716 |
if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR);
|
717 |
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
718 |
if ( roundNearestEven ) {
|
719 |
increment = ( (sbits64) zSig1 < 0 );
|
720 |
} |
721 |
else {
|
722 |
if ( zSign ) {
|
723 |
increment = ( roundingMode == float_round_down ) && zSig1; |
724 |
} |
725 |
else {
|
726 |
increment = ( roundingMode == float_round_up ) && zSig1; |
727 |
} |
728 |
} |
729 |
if ( increment ) {
|
730 |
++zSig0; |
731 |
zSig0 &= |
732 |
~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
733 |
if ( (sbits64) zSig0 < 0 ) zExp = 1; |
734 |
} |
735 |
return packFloatx80( zSign, zExp, zSig0 );
|
736 |
} |
737 |
} |
738 |
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
739 |
if ( increment ) {
|
740 |
++zSig0; |
741 |
if ( zSig0 == 0 ) { |
742 |
++zExp; |
743 |
zSig0 = LIT64( 0x8000000000000000 );
|
744 |
} |
745 |
else {
|
746 |
zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
747 |
} |
748 |
} |
749 |
else {
|
750 |
if ( zSig0 == 0 ) zExp = 0; |
751 |
} |
752 |
return packFloatx80( zSign, zExp, zSig0 );
|
753 |
|
754 |
} |
755 |
|
756 |
/*----------------------------------------------------------------------------
|
757 |
| Takes an abstract floating-point value having sign `zSign', exponent
|
758 |
| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
|
759 |
| and returns the proper extended double-precision floating-point value
|
760 |
| corresponding to the abstract input. This routine is just like
|
761 |
| `roundAndPackFloatx80' except that the input significand does not have to be
|
762 |
| normalized.
|
763 |
*----------------------------------------------------------------------------*/
|
764 |
|
765 |
static floatx80
|
766 |
normalizeRoundAndPackFloatx80( |
767 |
int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 |
768 |
STATUS_PARAM) |
769 |
{ |
770 |
int8 shiftCount; |
771 |
|
772 |
if ( zSig0 == 0 ) { |
773 |
zSig0 = zSig1; |
774 |
zSig1 = 0;
|
775 |
zExp -= 64;
|
776 |
} |
777 |
shiftCount = countLeadingZeros64( zSig0 ); |
778 |
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
779 |
zExp -= shiftCount; |
780 |
return
|
781 |
roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); |
782 |
|
783 |
} |
784 |
|
785 |
#endif
|
786 |
|
787 |
#ifdef FLOAT128
|
788 |
|
789 |
/*----------------------------------------------------------------------------
|
790 |
| Returns the least-significant 64 fraction bits of the quadruple-precision
|
791 |
| floating-point value `a'.
|
792 |
*----------------------------------------------------------------------------*/
|
793 |
|
794 |
INLINE bits64 extractFloat128Frac1( float128 a ) |
795 |
{ |
796 |
|
797 |
return a.low;
|
798 |
|
799 |
} |
800 |
|
801 |
/*----------------------------------------------------------------------------
|
802 |
| Returns the most-significant 48 fraction bits of the quadruple-precision
|
803 |
| floating-point value `a'.
|
804 |
*----------------------------------------------------------------------------*/
|
805 |
|
806 |
INLINE bits64 extractFloat128Frac0( float128 a ) |
807 |
{ |
808 |
|
809 |
return a.high & LIT64( 0x0000FFFFFFFFFFFF ); |
810 |
|
811 |
} |
812 |
|
813 |
/*----------------------------------------------------------------------------
|
814 |
| Returns the exponent bits of the quadruple-precision floating-point value
|
815 |
| `a'.
|
816 |
*----------------------------------------------------------------------------*/
|
817 |
|
818 |
INLINE int32 extractFloat128Exp( float128 a ) |
819 |
{ |
820 |
|
821 |
return ( a.high>>48 ) & 0x7FFF; |
822 |
|
823 |
} |
824 |
|
825 |
/*----------------------------------------------------------------------------
|
826 |
| Returns the sign bit of the quadruple-precision floating-point value `a'.
|
827 |
*----------------------------------------------------------------------------*/
|
828 |
|
829 |
INLINE flag extractFloat128Sign( float128 a ) |
830 |
{ |
831 |
|
832 |
return a.high>>63; |
833 |
|
834 |
} |
835 |
|
836 |
/*----------------------------------------------------------------------------
|
837 |
| Normalizes the subnormal quadruple-precision floating-point value
|
838 |
| represented by the denormalized significand formed by the concatenation of
|
839 |
| `aSig0' and `aSig1'. The normalized exponent is stored at the location
|
840 |
| pointed to by `zExpPtr'. The most significant 49 bits of the normalized
|
841 |
| significand are stored at the location pointed to by `zSig0Ptr', and the
|
842 |
| least significant 64 bits of the normalized significand are stored at the
|
843 |
| location pointed to by `zSig1Ptr'.
|
844 |
*----------------------------------------------------------------------------*/
|
845 |
|
846 |
static void |
847 |
normalizeFloat128Subnormal( |
848 |
bits64 aSig0, |
849 |
bits64 aSig1, |
850 |
int32 *zExpPtr, |
851 |
bits64 *zSig0Ptr, |
852 |
bits64 *zSig1Ptr |
853 |
) |
854 |
{ |
855 |
int8 shiftCount; |
856 |
|
857 |
if ( aSig0 == 0 ) { |
858 |
shiftCount = countLeadingZeros64( aSig1 ) - 15;
|
859 |
if ( shiftCount < 0 ) { |
860 |
*zSig0Ptr = aSig1>>( - shiftCount ); |
861 |
*zSig1Ptr = aSig1<<( shiftCount & 63 );
|
862 |
} |
863 |
else {
|
864 |
*zSig0Ptr = aSig1<<shiftCount; |
865 |
*zSig1Ptr = 0;
|
866 |
} |
867 |
*zExpPtr = - shiftCount - 63;
|
868 |
} |
869 |
else {
|
870 |
shiftCount = countLeadingZeros64( aSig0 ) - 15;
|
871 |
shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); |
872 |
*zExpPtr = 1 - shiftCount;
|
873 |
} |
874 |
|
875 |
} |
876 |
|
877 |
/*----------------------------------------------------------------------------
|
878 |
| Packs the sign `zSign', the exponent `zExp', and the significand formed
|
879 |
| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
|
880 |
| floating-point value, returning the result. After being shifted into the
|
881 |
| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
|
882 |
| added together to form the most significant 32 bits of the result. This
|
883 |
| means that any integer portion of `zSig0' will be added into the exponent.
|
884 |
| Since a properly normalized significand will have an integer portion equal
|
885 |
| to 1, the `zExp' input should be 1 less than the desired result exponent
|
886 |
| whenever `zSig0' and `zSig1' concatenated form a complete, normalized
|
887 |
| significand.
|
888 |
*----------------------------------------------------------------------------*/
|
889 |
|
890 |
INLINE float128 |
891 |
packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 ) |
892 |
{ |
893 |
float128 z; |
894 |
|
895 |
z.low = zSig1; |
896 |
z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0; |
897 |
return z;
|
898 |
|
899 |
} |
900 |
|
901 |
/*----------------------------------------------------------------------------
|
902 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
903 |
| and extended significand formed by the concatenation of `zSig0', `zSig1',
|
904 |
| and `zSig2', and returns the proper quadruple-precision floating-point value
|
905 |
| corresponding to the abstract input. Ordinarily, the abstract value is
|
906 |
| simply rounded and packed into the quadruple-precision format, with the
|
907 |
| inexact exception raised if the abstract input cannot be represented
|
908 |
| exactly. However, if the abstract value is too large, the overflow and
|
909 |
| inexact exceptions are raised and an infinity or maximal finite value is
|
910 |
| returned. If the abstract value is too small, the input value is rounded to
|
911 |
| a subnormal number, and the underflow and inexact exceptions are raised if
|
912 |
| the abstract input cannot be represented exactly as a subnormal quadruple-
|
913 |
| precision floating-point number.
|
914 |
| The input significand must be normalized or smaller. If the input
|
915 |
| significand is not normalized, `zExp' must be 0; in that case, the result
|
916 |
| returned is a subnormal number, and it must not require rounding. In the
|
917 |
| usual case that the input significand is normalized, `zExp' must be 1 less
|
918 |
| than the ``true'' floating-point exponent. The handling of underflow and
|
919 |
| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
920 |
*----------------------------------------------------------------------------*/
|
921 |
|
922 |
static float128
|
923 |
roundAndPackFloat128( |
924 |
flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 STATUS_PARAM) |
925 |
{ |
926 |
int8 roundingMode; |
927 |
flag roundNearestEven, increment, isTiny; |
928 |
|
929 |
roundingMode = STATUS(float_rounding_mode); |
930 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
931 |
increment = ( (sbits64) zSig2 < 0 );
|
932 |
if ( ! roundNearestEven ) {
|
933 |
if ( roundingMode == float_round_to_zero ) {
|
934 |
increment = 0;
|
935 |
} |
936 |
else {
|
937 |
if ( zSign ) {
|
938 |
increment = ( roundingMode == float_round_down ) && zSig2; |
939 |
} |
940 |
else {
|
941 |
increment = ( roundingMode == float_round_up ) && zSig2; |
942 |
} |
943 |
} |
944 |
} |
945 |
if ( 0x7FFD <= (bits32) zExp ) { |
946 |
if ( ( 0x7FFD < zExp ) |
947 |
|| ( ( zExp == 0x7FFD )
|
948 |
&& eq128( |
949 |
LIT64( 0x0001FFFFFFFFFFFF ),
|
950 |
LIT64( 0xFFFFFFFFFFFFFFFF ),
|
951 |
zSig0, |
952 |
zSig1 |
953 |
) |
954 |
&& increment |
955 |
) |
956 |
) { |
957 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
958 |
if ( ( roundingMode == float_round_to_zero )
|
959 |
|| ( zSign && ( roundingMode == float_round_up ) ) |
960 |
|| ( ! zSign && ( roundingMode == float_round_down ) ) |
961 |
) { |
962 |
return
|
963 |
packFloat128( |
964 |
zSign, |
965 |
0x7FFE,
|
966 |
LIT64( 0x0000FFFFFFFFFFFF ),
|
967 |
LIT64( 0xFFFFFFFFFFFFFFFF )
|
968 |
); |
969 |
} |
970 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
971 |
} |
972 |
if ( zExp < 0 ) { |
973 |
if ( STATUS(flush_to_zero) ) return packFloat128( zSign, 0, 0, 0 ); |
974 |
isTiny = |
975 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
976 |
|| ( zExp < -1 )
|
977 |
|| ! increment |
978 |
|| lt128( |
979 |
zSig0, |
980 |
zSig1, |
981 |
LIT64( 0x0001FFFFFFFFFFFF ),
|
982 |
LIT64( 0xFFFFFFFFFFFFFFFF )
|
983 |
); |
984 |
shift128ExtraRightJamming( |
985 |
zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); |
986 |
zExp = 0;
|
987 |
if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR);
|
988 |
if ( roundNearestEven ) {
|
989 |
increment = ( (sbits64) zSig2 < 0 );
|
990 |
} |
991 |
else {
|
992 |
if ( zSign ) {
|
993 |
increment = ( roundingMode == float_round_down ) && zSig2; |
994 |
} |
995 |
else {
|
996 |
increment = ( roundingMode == float_round_up ) && zSig2; |
997 |
} |
998 |
} |
999 |
} |
1000 |
} |
1001 |
if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1002 |
if ( increment ) {
|
1003 |
add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); |
1004 |
zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
|
1005 |
} |
1006 |
else {
|
1007 |
if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; |
1008 |
} |
1009 |
return packFloat128( zSign, zExp, zSig0, zSig1 );
|
1010 |
|
1011 |
} |
1012 |
|
1013 |
/*----------------------------------------------------------------------------
|
1014 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
1015 |
| and significand formed by the concatenation of `zSig0' and `zSig1', and
|
1016 |
| returns the proper quadruple-precision floating-point value corresponding
|
1017 |
| to the abstract input. This routine is just like `roundAndPackFloat128'
|
1018 |
| except that the input significand has fewer bits and does not have to be
|
1019 |
| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
|
1020 |
| point exponent.
|
1021 |
*----------------------------------------------------------------------------*/
|
1022 |
|
1023 |
static float128
|
1024 |
normalizeRoundAndPackFloat128( |
1025 |
flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 STATUS_PARAM) |
1026 |
{ |
1027 |
int8 shiftCount; |
1028 |
bits64 zSig2; |
1029 |
|
1030 |
if ( zSig0 == 0 ) { |
1031 |
zSig0 = zSig1; |
1032 |
zSig1 = 0;
|
1033 |
zExp -= 64;
|
1034 |
} |
1035 |
shiftCount = countLeadingZeros64( zSig0 ) - 15;
|
1036 |
if ( 0 <= shiftCount ) { |
1037 |
zSig2 = 0;
|
1038 |
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
1039 |
} |
1040 |
else {
|
1041 |
shift128ExtraRightJamming( |
1042 |
zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
|
1043 |
} |
1044 |
zExp -= shiftCount; |
1045 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR);
|
1046 |
|
1047 |
} |
1048 |
|
1049 |
#endif
|
1050 |
|
1051 |
/*----------------------------------------------------------------------------
|
1052 |
| Returns the result of converting the 32-bit two's complement integer `a'
|
1053 |
| to the single-precision floating-point format. The conversion is performed
|
1054 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1055 |
*----------------------------------------------------------------------------*/
|
1056 |
|
1057 |
float32 int32_to_float32( int32 a STATUS_PARAM ) |
1058 |
{ |
1059 |
flag zSign; |
1060 |
|
1061 |
if ( a == 0 ) return float32_zero; |
1062 |
if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); |
1063 |
zSign = ( a < 0 );
|
1064 |
return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); |
1065 |
|
1066 |
} |
1067 |
|
1068 |
/*----------------------------------------------------------------------------
|
1069 |
| Returns the result of converting the 32-bit two's complement integer `a'
|
1070 |
| to the double-precision floating-point format. The conversion is performed
|
1071 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1072 |
*----------------------------------------------------------------------------*/
|
1073 |
|
1074 |
float64 int32_to_float64( int32 a STATUS_PARAM ) |
1075 |
{ |
1076 |
flag zSign; |
1077 |
uint32 absA; |
1078 |
int8 shiftCount; |
1079 |
bits64 zSig; |
1080 |
|
1081 |
if ( a == 0 ) return float64_zero; |
1082 |
zSign = ( a < 0 );
|
1083 |
absA = zSign ? - a : a; |
1084 |
shiftCount = countLeadingZeros32( absA ) + 21;
|
1085 |
zSig = absA; |
1086 |
return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); |
1087 |
|
1088 |
} |
1089 |
|
1090 |
#ifdef FLOATX80
|
1091 |
|
1092 |
/*----------------------------------------------------------------------------
|
1093 |
| Returns the result of converting the 32-bit two's complement integer `a'
|
1094 |
| to the extended double-precision floating-point format. The conversion
|
1095 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1096 |
| Arithmetic.
|
1097 |
*----------------------------------------------------------------------------*/
|
1098 |
|
1099 |
floatx80 int32_to_floatx80( int32 a STATUS_PARAM ) |
1100 |
{ |
1101 |
flag zSign; |
1102 |
uint32 absA; |
1103 |
int8 shiftCount; |
1104 |
bits64 zSig; |
1105 |
|
1106 |
if ( a == 0 ) return packFloatx80( 0, 0, 0 ); |
1107 |
zSign = ( a < 0 );
|
1108 |
absA = zSign ? - a : a; |
1109 |
shiftCount = countLeadingZeros32( absA ) + 32;
|
1110 |
zSig = absA; |
1111 |
return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); |
1112 |
|
1113 |
} |
1114 |
|
1115 |
#endif
|
1116 |
|
1117 |
#ifdef FLOAT128
|
1118 |
|
1119 |
/*----------------------------------------------------------------------------
|
1120 |
| Returns the result of converting the 32-bit two's complement integer `a' to
|
1121 |
| the quadruple-precision floating-point format. The conversion is performed
|
1122 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1123 |
*----------------------------------------------------------------------------*/
|
1124 |
|
1125 |
float128 int32_to_float128( int32 a STATUS_PARAM ) |
1126 |
{ |
1127 |
flag zSign; |
1128 |
uint32 absA; |
1129 |
int8 shiftCount; |
1130 |
bits64 zSig0; |
1131 |
|
1132 |
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); |
1133 |
zSign = ( a < 0 );
|
1134 |
absA = zSign ? - a : a; |
1135 |
shiftCount = countLeadingZeros32( absA ) + 17;
|
1136 |
zSig0 = absA; |
1137 |
return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); |
1138 |
|
1139 |
} |
1140 |
|
1141 |
#endif
|
1142 |
|
1143 |
/*----------------------------------------------------------------------------
|
1144 |
| Returns the result of converting the 64-bit two's complement integer `a'
|
1145 |
| to the single-precision floating-point format. The conversion is performed
|
1146 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1147 |
*----------------------------------------------------------------------------*/
|
1148 |
|
1149 |
float32 int64_to_float32( int64 a STATUS_PARAM ) |
1150 |
{ |
1151 |
flag zSign; |
1152 |
uint64 absA; |
1153 |
int8 shiftCount; |
1154 |
|
1155 |
if ( a == 0 ) return float32_zero; |
1156 |
zSign = ( a < 0 );
|
1157 |
absA = zSign ? - a : a; |
1158 |
shiftCount = countLeadingZeros64( absA ) - 40;
|
1159 |
if ( 0 <= shiftCount ) { |
1160 |
return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); |
1161 |
} |
1162 |
else {
|
1163 |
shiftCount += 7;
|
1164 |
if ( shiftCount < 0 ) { |
1165 |
shift64RightJamming( absA, - shiftCount, &absA ); |
1166 |
} |
1167 |
else {
|
1168 |
absA <<= shiftCount; |
1169 |
} |
1170 |
return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); |
1171 |
} |
1172 |
|
1173 |
} |
1174 |
|
1175 |
float32 uint64_to_float32( uint64 a STATUS_PARAM ) |
1176 |
{ |
1177 |
int8 shiftCount; |
1178 |
|
1179 |
if ( a == 0 ) return float32_zero; |
1180 |
shiftCount = countLeadingZeros64( a ) - 40;
|
1181 |
if ( 0 <= shiftCount ) { |
1182 |
return packFloat32( 1 > 0, 0x95 - shiftCount, a<<shiftCount ); |
1183 |
} |
1184 |
else {
|
1185 |
shiftCount += 7;
|
1186 |
if ( shiftCount < 0 ) { |
1187 |
shift64RightJamming( a, - shiftCount, &a ); |
1188 |
} |
1189 |
else {
|
1190 |
a <<= shiftCount; |
1191 |
} |
1192 |
return roundAndPackFloat32( 1 > 0, 0x9C - shiftCount, a STATUS_VAR ); |
1193 |
} |
1194 |
} |
1195 |
|
1196 |
/*----------------------------------------------------------------------------
|
1197 |
| Returns the result of converting the 64-bit two's complement integer `a'
|
1198 |
| to the double-precision floating-point format. The conversion is performed
|
1199 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1200 |
*----------------------------------------------------------------------------*/
|
1201 |
|
1202 |
float64 int64_to_float64( int64 a STATUS_PARAM ) |
1203 |
{ |
1204 |
flag zSign; |
1205 |
|
1206 |
if ( a == 0 ) return float64_zero; |
1207 |
if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) { |
1208 |
return packFloat64( 1, 0x43E, 0 ); |
1209 |
} |
1210 |
zSign = ( a < 0 );
|
1211 |
return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); |
1212 |
|
1213 |
} |
1214 |
|
1215 |
float64 uint64_to_float64( uint64 a STATUS_PARAM ) |
1216 |
{ |
1217 |
if ( a == 0 ) return float64_zero; |
1218 |
return normalizeRoundAndPackFloat64( 0, 0x43C, a STATUS_VAR ); |
1219 |
|
1220 |
} |
1221 |
|
1222 |
#ifdef FLOATX80
|
1223 |
|
1224 |
/*----------------------------------------------------------------------------
|
1225 |
| Returns the result of converting the 64-bit two's complement integer `a'
|
1226 |
| to the extended double-precision floating-point format. The conversion
|
1227 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1228 |
| Arithmetic.
|
1229 |
*----------------------------------------------------------------------------*/
|
1230 |
|
1231 |
floatx80 int64_to_floatx80( int64 a STATUS_PARAM ) |
1232 |
{ |
1233 |
flag zSign; |
1234 |
uint64 absA; |
1235 |
int8 shiftCount; |
1236 |
|
1237 |
if ( a == 0 ) return packFloatx80( 0, 0, 0 ); |
1238 |
zSign = ( a < 0 );
|
1239 |
absA = zSign ? - a : a; |
1240 |
shiftCount = countLeadingZeros64( absA ); |
1241 |
return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); |
1242 |
|
1243 |
} |
1244 |
|
1245 |
#endif
|
1246 |
|
1247 |
#ifdef FLOAT128
|
1248 |
|
1249 |
/*----------------------------------------------------------------------------
|
1250 |
| Returns the result of converting the 64-bit two's complement integer `a' to
|
1251 |
| the quadruple-precision floating-point format. The conversion is performed
|
1252 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1253 |
*----------------------------------------------------------------------------*/
|
1254 |
|
1255 |
float128 int64_to_float128( int64 a STATUS_PARAM ) |
1256 |
{ |
1257 |
flag zSign; |
1258 |
uint64 absA; |
1259 |
int8 shiftCount; |
1260 |
int32 zExp; |
1261 |
bits64 zSig0, zSig1; |
1262 |
|
1263 |
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); |
1264 |
zSign = ( a < 0 );
|
1265 |
absA = zSign ? - a : a; |
1266 |
shiftCount = countLeadingZeros64( absA ) + 49;
|
1267 |
zExp = 0x406E - shiftCount;
|
1268 |
if ( 64 <= shiftCount ) { |
1269 |
zSig1 = 0;
|
1270 |
zSig0 = absA; |
1271 |
shiftCount -= 64;
|
1272 |
} |
1273 |
else {
|
1274 |
zSig1 = absA; |
1275 |
zSig0 = 0;
|
1276 |
} |
1277 |
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
1278 |
return packFloat128( zSign, zExp, zSig0, zSig1 );
|
1279 |
|
1280 |
} |
1281 |
|
1282 |
#endif
|
1283 |
|
1284 |
/*----------------------------------------------------------------------------
|
1285 |
| Returns the result of converting the single-precision floating-point value
|
1286 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
1287 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1288 |
| Arithmetic---which means in particular that the conversion is rounded
|
1289 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
1290 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
1291 |
| largest integer with the same sign as `a' is returned.
|
1292 |
*----------------------------------------------------------------------------*/
|
1293 |
|
1294 |
int32 float32_to_int32( float32 a STATUS_PARAM ) |
1295 |
{ |
1296 |
flag aSign; |
1297 |
int16 aExp, shiftCount; |
1298 |
bits32 aSig; |
1299 |
bits64 aSig64; |
1300 |
|
1301 |
aSig = extractFloat32Frac( a ); |
1302 |
aExp = extractFloat32Exp( a ); |
1303 |
aSign = extractFloat32Sign( a ); |
1304 |
if ( ( aExp == 0xFF ) && aSig ) aSign = 0; |
1305 |
if ( aExp ) aSig |= 0x00800000; |
1306 |
shiftCount = 0xAF - aExp;
|
1307 |
aSig64 = aSig; |
1308 |
aSig64 <<= 32;
|
1309 |
if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); |
1310 |
return roundAndPackInt32( aSign, aSig64 STATUS_VAR );
|
1311 |
|
1312 |
} |
1313 |
|
1314 |
/*----------------------------------------------------------------------------
|
1315 |
| Returns the result of converting the single-precision floating-point value
|
1316 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
1317 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1318 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
1319 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
1320 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
1321 |
| returned.
|
1322 |
*----------------------------------------------------------------------------*/
|
1323 |
|
1324 |
int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) |
1325 |
{ |
1326 |
flag aSign; |
1327 |
int16 aExp, shiftCount; |
1328 |
bits32 aSig; |
1329 |
int32 z; |
1330 |
|
1331 |
aSig = extractFloat32Frac( a ); |
1332 |
aExp = extractFloat32Exp( a ); |
1333 |
aSign = extractFloat32Sign( a ); |
1334 |
shiftCount = aExp - 0x9E;
|
1335 |
if ( 0 <= shiftCount ) { |
1336 |
if ( float32_val(a) != 0xCF000000 ) { |
1337 |
float_raise( float_flag_invalid STATUS_VAR); |
1338 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; |
1339 |
} |
1340 |
return (sbits32) 0x80000000; |
1341 |
} |
1342 |
else if ( aExp <= 0x7E ) { |
1343 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1344 |
return 0; |
1345 |
} |
1346 |
aSig = ( aSig | 0x00800000 )<<8; |
1347 |
z = aSig>>( - shiftCount ); |
1348 |
if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) { |
1349 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1350 |
} |
1351 |
if ( aSign ) z = - z;
|
1352 |
return z;
|
1353 |
|
1354 |
} |
1355 |
|
1356 |
/*----------------------------------------------------------------------------
|
1357 |
| Returns the result of converting the single-precision floating-point value
|
1358 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
1359 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1360 |
| Arithmetic---which means in particular that the conversion is rounded
|
1361 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
1362 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
1363 |
| largest integer with the same sign as `a' is returned.
|
1364 |
*----------------------------------------------------------------------------*/
|
1365 |
|
1366 |
int64 float32_to_int64( float32 a STATUS_PARAM ) |
1367 |
{ |
1368 |
flag aSign; |
1369 |
int16 aExp, shiftCount; |
1370 |
bits32 aSig; |
1371 |
bits64 aSig64, aSigExtra; |
1372 |
|
1373 |
aSig = extractFloat32Frac( a ); |
1374 |
aExp = extractFloat32Exp( a ); |
1375 |
aSign = extractFloat32Sign( a ); |
1376 |
shiftCount = 0xBE - aExp;
|
1377 |
if ( shiftCount < 0 ) { |
1378 |
float_raise( float_flag_invalid STATUS_VAR); |
1379 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
1380 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
1381 |
} |
1382 |
return (sbits64) LIT64( 0x8000000000000000 ); |
1383 |
} |
1384 |
if ( aExp ) aSig |= 0x00800000; |
1385 |
aSig64 = aSig; |
1386 |
aSig64 <<= 40;
|
1387 |
shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra );
|
1388 |
return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR );
|
1389 |
|
1390 |
} |
1391 |
|
1392 |
/*----------------------------------------------------------------------------
|
1393 |
| Returns the result of converting the single-precision floating-point value
|
1394 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
1395 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1396 |
| Arithmetic, except that the conversion is always rounded toward zero. If
|
1397 |
| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
1398 |
| conversion overflows, the largest integer with the same sign as `a' is
|
1399 |
| returned.
|
1400 |
*----------------------------------------------------------------------------*/
|
1401 |
|
1402 |
int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) |
1403 |
{ |
1404 |
flag aSign; |
1405 |
int16 aExp, shiftCount; |
1406 |
bits32 aSig; |
1407 |
bits64 aSig64; |
1408 |
int64 z; |
1409 |
|
1410 |
aSig = extractFloat32Frac( a ); |
1411 |
aExp = extractFloat32Exp( a ); |
1412 |
aSign = extractFloat32Sign( a ); |
1413 |
shiftCount = aExp - 0xBE;
|
1414 |
if ( 0 <= shiftCount ) { |
1415 |
if ( float32_val(a) != 0xDF000000 ) { |
1416 |
float_raise( float_flag_invalid STATUS_VAR); |
1417 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
1418 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
1419 |
} |
1420 |
} |
1421 |
return (sbits64) LIT64( 0x8000000000000000 ); |
1422 |
} |
1423 |
else if ( aExp <= 0x7E ) { |
1424 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1425 |
return 0; |
1426 |
} |
1427 |
aSig64 = aSig | 0x00800000;
|
1428 |
aSig64 <<= 40;
|
1429 |
z = aSig64>>( - shiftCount ); |
1430 |
if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) { |
1431 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1432 |
} |
1433 |
if ( aSign ) z = - z;
|
1434 |
return z;
|
1435 |
|
1436 |
} |
1437 |
|
1438 |
/*----------------------------------------------------------------------------
|
1439 |
| Returns the result of converting the single-precision floating-point value
|
1440 |
| `a' to the double-precision floating-point format. The conversion is
|
1441 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1442 |
| Arithmetic.
|
1443 |
*----------------------------------------------------------------------------*/
|
1444 |
|
1445 |
float64 float32_to_float64( float32 a STATUS_PARAM ) |
1446 |
{ |
1447 |
flag aSign; |
1448 |
int16 aExp; |
1449 |
bits32 aSig; |
1450 |
|
1451 |
aSig = extractFloat32Frac( a ); |
1452 |
aExp = extractFloat32Exp( a ); |
1453 |
aSign = extractFloat32Sign( a ); |
1454 |
if ( aExp == 0xFF ) { |
1455 |
if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR )); |
1456 |
return packFloat64( aSign, 0x7FF, 0 ); |
1457 |
} |
1458 |
if ( aExp == 0 ) { |
1459 |
if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); |
1460 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1461 |
--aExp; |
1462 |
} |
1463 |
return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 ); |
1464 |
|
1465 |
} |
1466 |
|
1467 |
#ifdef FLOATX80
|
1468 |
|
1469 |
/*----------------------------------------------------------------------------
|
1470 |
| Returns the result of converting the single-precision floating-point value
|
1471 |
| `a' to the extended double-precision floating-point format. The conversion
|
1472 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1473 |
| Arithmetic.
|
1474 |
*----------------------------------------------------------------------------*/
|
1475 |
|
1476 |
floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) |
1477 |
{ |
1478 |
flag aSign; |
1479 |
int16 aExp; |
1480 |
bits32 aSig; |
1481 |
|
1482 |
aSig = extractFloat32Frac( a ); |
1483 |
aExp = extractFloat32Exp( a ); |
1484 |
aSign = extractFloat32Sign( a ); |
1485 |
if ( aExp == 0xFF ) { |
1486 |
if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) ); |
1487 |
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
1488 |
} |
1489 |
if ( aExp == 0 ) { |
1490 |
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); |
1491 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1492 |
} |
1493 |
aSig |= 0x00800000;
|
1494 |
return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 ); |
1495 |
|
1496 |
} |
1497 |
|
1498 |
#endif
|
1499 |
|
1500 |
#ifdef FLOAT128
|
1501 |
|
1502 |
/*----------------------------------------------------------------------------
|
1503 |
| Returns the result of converting the single-precision floating-point value
|
1504 |
| `a' to the double-precision floating-point format. The conversion is
|
1505 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1506 |
| Arithmetic.
|
1507 |
*----------------------------------------------------------------------------*/
|
1508 |
|
1509 |
float128 float32_to_float128( float32 a STATUS_PARAM ) |
1510 |
{ |
1511 |
flag aSign; |
1512 |
int16 aExp; |
1513 |
bits32 aSig; |
1514 |
|
1515 |
aSig = extractFloat32Frac( a ); |
1516 |
aExp = extractFloat32Exp( a ); |
1517 |
aSign = extractFloat32Sign( a ); |
1518 |
if ( aExp == 0xFF ) { |
1519 |
if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) ); |
1520 |
return packFloat128( aSign, 0x7FFF, 0, 0 ); |
1521 |
} |
1522 |
if ( aExp == 0 ) { |
1523 |
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); |
1524 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1525 |
--aExp; |
1526 |
} |
1527 |
return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 ); |
1528 |
|
1529 |
} |
1530 |
|
1531 |
#endif
|
1532 |
|
1533 |
/*----------------------------------------------------------------------------
|
1534 |
| Rounds the single-precision floating-point value `a' to an integer, and
|
1535 |
| returns the result as a single-precision floating-point value. The
|
1536 |
| operation is performed according to the IEC/IEEE Standard for Binary
|
1537 |
| Floating-Point Arithmetic.
|
1538 |
*----------------------------------------------------------------------------*/
|
1539 |
|
1540 |
float32 float32_round_to_int( float32 a STATUS_PARAM) |
1541 |
{ |
1542 |
flag aSign; |
1543 |
int16 aExp; |
1544 |
bits32 lastBitMask, roundBitsMask; |
1545 |
int8 roundingMode; |
1546 |
bits32 z; |
1547 |
|
1548 |
aExp = extractFloat32Exp( a ); |
1549 |
if ( 0x96 <= aExp ) { |
1550 |
if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { |
1551 |
return propagateFloat32NaN( a, a STATUS_VAR );
|
1552 |
} |
1553 |
return a;
|
1554 |
} |
1555 |
if ( aExp <= 0x7E ) { |
1556 |
if ( (bits32) ( float32_val(a)<<1 ) == 0 ) return a; |
1557 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1558 |
aSign = extractFloat32Sign( a ); |
1559 |
switch ( STATUS(float_rounding_mode) ) {
|
1560 |
case float_round_nearest_even:
|
1561 |
if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { |
1562 |
return packFloat32( aSign, 0x7F, 0 ); |
1563 |
} |
1564 |
break;
|
1565 |
case float_round_down:
|
1566 |
return make_float32(aSign ? 0xBF800000 : 0); |
1567 |
case float_round_up:
|
1568 |
return make_float32(aSign ? 0x80000000 : 0x3F800000); |
1569 |
} |
1570 |
return packFloat32( aSign, 0, 0 ); |
1571 |
} |
1572 |
lastBitMask = 1;
|
1573 |
lastBitMask <<= 0x96 - aExp;
|
1574 |
roundBitsMask = lastBitMask - 1;
|
1575 |
z = float32_val(a); |
1576 |
roundingMode = STATUS(float_rounding_mode); |
1577 |
if ( roundingMode == float_round_nearest_even ) {
|
1578 |
z += lastBitMask>>1;
|
1579 |
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; |
1580 |
} |
1581 |
else if ( roundingMode != float_round_to_zero ) { |
1582 |
if ( extractFloat32Sign( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) {
|
1583 |
z += roundBitsMask; |
1584 |
} |
1585 |
} |
1586 |
z &= ~ roundBitsMask; |
1587 |
if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1588 |
return make_float32(z);
|
1589 |
|
1590 |
} |
1591 |
|
1592 |
/*----------------------------------------------------------------------------
|
1593 |
| Returns the result of adding the absolute values of the single-precision
|
1594 |
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
1595 |
| before being returned. `zSign' is ignored if the result is a NaN.
|
1596 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
1597 |
| Floating-Point Arithmetic.
|
1598 |
*----------------------------------------------------------------------------*/
|
1599 |
|
1600 |
static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
|
1601 |
{ |
1602 |
int16 aExp, bExp, zExp; |
1603 |
bits32 aSig, bSig, zSig; |
1604 |
int16 expDiff; |
1605 |
|
1606 |
aSig = extractFloat32Frac( a ); |
1607 |
aExp = extractFloat32Exp( a ); |
1608 |
bSig = extractFloat32Frac( b ); |
1609 |
bExp = extractFloat32Exp( b ); |
1610 |
expDiff = aExp - bExp; |
1611 |
aSig <<= 6;
|
1612 |
bSig <<= 6;
|
1613 |
if ( 0 < expDiff ) { |
1614 |
if ( aExp == 0xFF ) { |
1615 |
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1616 |
return a;
|
1617 |
} |
1618 |
if ( bExp == 0 ) { |
1619 |
--expDiff; |
1620 |
} |
1621 |
else {
|
1622 |
bSig |= 0x20000000;
|
1623 |
} |
1624 |
shift32RightJamming( bSig, expDiff, &bSig ); |
1625 |
zExp = aExp; |
1626 |
} |
1627 |
else if ( expDiff < 0 ) { |
1628 |
if ( bExp == 0xFF ) { |
1629 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1630 |
return packFloat32( zSign, 0xFF, 0 ); |
1631 |
} |
1632 |
if ( aExp == 0 ) { |
1633 |
++expDiff; |
1634 |
} |
1635 |
else {
|
1636 |
aSig |= 0x20000000;
|
1637 |
} |
1638 |
shift32RightJamming( aSig, - expDiff, &aSig ); |
1639 |
zExp = bExp; |
1640 |
} |
1641 |
else {
|
1642 |
if ( aExp == 0xFF ) { |
1643 |
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1644 |
return a;
|
1645 |
} |
1646 |
if ( aExp == 0 ) { |
1647 |
if ( STATUS(flush_to_zero) ) return packFloat32( zSign, 0, 0 ); |
1648 |
return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); |
1649 |
} |
1650 |
zSig = 0x40000000 + aSig + bSig;
|
1651 |
zExp = aExp; |
1652 |
goto roundAndPack;
|
1653 |
} |
1654 |
aSig |= 0x20000000;
|
1655 |
zSig = ( aSig + bSig )<<1;
|
1656 |
--zExp; |
1657 |
if ( (sbits32) zSig < 0 ) { |
1658 |
zSig = aSig + bSig; |
1659 |
++zExp; |
1660 |
} |
1661 |
roundAndPack:
|
1662 |
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
1663 |
|
1664 |
} |
1665 |
|
1666 |
/*----------------------------------------------------------------------------
|
1667 |
| Returns the result of subtracting the absolute values of the single-
|
1668 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
1669 |
| difference is negated before being returned. `zSign' is ignored if the
|
1670 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
1671 |
| Standard for Binary Floating-Point Arithmetic.
|
1672 |
*----------------------------------------------------------------------------*/
|
1673 |
|
1674 |
static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
|
1675 |
{ |
1676 |
int16 aExp, bExp, zExp; |
1677 |
bits32 aSig, bSig, zSig; |
1678 |
int16 expDiff; |
1679 |
|
1680 |
aSig = extractFloat32Frac( a ); |
1681 |
aExp = extractFloat32Exp( a ); |
1682 |
bSig = extractFloat32Frac( b ); |
1683 |
bExp = extractFloat32Exp( b ); |
1684 |
expDiff = aExp - bExp; |
1685 |
aSig <<= 7;
|
1686 |
bSig <<= 7;
|
1687 |
if ( 0 < expDiff ) goto aExpBigger; |
1688 |
if ( expDiff < 0 ) goto bExpBigger; |
1689 |
if ( aExp == 0xFF ) { |
1690 |
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1691 |
float_raise( float_flag_invalid STATUS_VAR); |
1692 |
return float32_default_nan;
|
1693 |
} |
1694 |
if ( aExp == 0 ) { |
1695 |
aExp = 1;
|
1696 |
bExp = 1;
|
1697 |
} |
1698 |
if ( bSig < aSig ) goto aBigger; |
1699 |
if ( aSig < bSig ) goto bBigger; |
1700 |
return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
1701 |
bExpBigger:
|
1702 |
if ( bExp == 0xFF ) { |
1703 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1704 |
return packFloat32( zSign ^ 1, 0xFF, 0 ); |
1705 |
} |
1706 |
if ( aExp == 0 ) { |
1707 |
++expDiff; |
1708 |
} |
1709 |
else {
|
1710 |
aSig |= 0x40000000;
|
1711 |
} |
1712 |
shift32RightJamming( aSig, - expDiff, &aSig ); |
1713 |
bSig |= 0x40000000;
|
1714 |
bBigger:
|
1715 |
zSig = bSig - aSig; |
1716 |
zExp = bExp; |
1717 |
zSign ^= 1;
|
1718 |
goto normalizeRoundAndPack;
|
1719 |
aExpBigger:
|
1720 |
if ( aExp == 0xFF ) { |
1721 |
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1722 |
return a;
|
1723 |
} |
1724 |
if ( bExp == 0 ) { |
1725 |
--expDiff; |
1726 |
} |
1727 |
else {
|
1728 |
bSig |= 0x40000000;
|
1729 |
} |
1730 |
shift32RightJamming( bSig, expDiff, &bSig ); |
1731 |
aSig |= 0x40000000;
|
1732 |
aBigger:
|
1733 |
zSig = aSig - bSig; |
1734 |
zExp = aExp; |
1735 |
normalizeRoundAndPack:
|
1736 |
--zExp; |
1737 |
return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
1738 |
|
1739 |
} |
1740 |
|
1741 |
/*----------------------------------------------------------------------------
|
1742 |
| Returns the result of adding the single-precision floating-point values `a'
|
1743 |
| and `b'. The operation is performed according to the IEC/IEEE Standard for
|
1744 |
| Binary Floating-Point Arithmetic.
|
1745 |
*----------------------------------------------------------------------------*/
|
1746 |
|
1747 |
float32 float32_add( float32 a, float32 b STATUS_PARAM ) |
1748 |
{ |
1749 |
flag aSign, bSign; |
1750 |
|
1751 |
aSign = extractFloat32Sign( a ); |
1752 |
bSign = extractFloat32Sign( b ); |
1753 |
if ( aSign == bSign ) {
|
1754 |
return addFloat32Sigs( a, b, aSign STATUS_VAR);
|
1755 |
} |
1756 |
else {
|
1757 |
return subFloat32Sigs( a, b, aSign STATUS_VAR );
|
1758 |
} |
1759 |
|
1760 |
} |
1761 |
|
1762 |
/*----------------------------------------------------------------------------
|
1763 |
| Returns the result of subtracting the single-precision floating-point values
|
1764 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
1765 |
| for Binary Floating-Point Arithmetic.
|
1766 |
*----------------------------------------------------------------------------*/
|
1767 |
|
1768 |
float32 float32_sub( float32 a, float32 b STATUS_PARAM ) |
1769 |
{ |
1770 |
flag aSign, bSign; |
1771 |
|
1772 |
aSign = extractFloat32Sign( a ); |
1773 |
bSign = extractFloat32Sign( b ); |
1774 |
if ( aSign == bSign ) {
|
1775 |
return subFloat32Sigs( a, b, aSign STATUS_VAR );
|
1776 |
} |
1777 |
else {
|
1778 |
return addFloat32Sigs( a, b, aSign STATUS_VAR );
|
1779 |
} |
1780 |
|
1781 |
} |
1782 |
|
1783 |
/*----------------------------------------------------------------------------
|
1784 |
| Returns the result of multiplying the single-precision floating-point values
|
1785 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
1786 |
| for Binary Floating-Point Arithmetic.
|
1787 |
*----------------------------------------------------------------------------*/
|
1788 |
|
1789 |
float32 float32_mul( float32 a, float32 b STATUS_PARAM ) |
1790 |
{ |
1791 |
flag aSign, bSign, zSign; |
1792 |
int16 aExp, bExp, zExp; |
1793 |
bits32 aSig, bSig; |
1794 |
bits64 zSig64; |
1795 |
bits32 zSig; |
1796 |
|
1797 |
aSig = extractFloat32Frac( a ); |
1798 |
aExp = extractFloat32Exp( a ); |
1799 |
aSign = extractFloat32Sign( a ); |
1800 |
bSig = extractFloat32Frac( b ); |
1801 |
bExp = extractFloat32Exp( b ); |
1802 |
bSign = extractFloat32Sign( b ); |
1803 |
zSign = aSign ^ bSign; |
1804 |
if ( aExp == 0xFF ) { |
1805 |
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { |
1806 |
return propagateFloat32NaN( a, b STATUS_VAR );
|
1807 |
} |
1808 |
if ( ( bExp | bSig ) == 0 ) { |
1809 |
float_raise( float_flag_invalid STATUS_VAR); |
1810 |
return float32_default_nan;
|
1811 |
} |
1812 |
return packFloat32( zSign, 0xFF, 0 ); |
1813 |
} |
1814 |
if ( bExp == 0xFF ) { |
1815 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1816 |
if ( ( aExp | aSig ) == 0 ) { |
1817 |
float_raise( float_flag_invalid STATUS_VAR); |
1818 |
return float32_default_nan;
|
1819 |
} |
1820 |
return packFloat32( zSign, 0xFF, 0 ); |
1821 |
} |
1822 |
if ( aExp == 0 ) { |
1823 |
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); |
1824 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1825 |
} |
1826 |
if ( bExp == 0 ) { |
1827 |
if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); |
1828 |
normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
1829 |
} |
1830 |
zExp = aExp + bExp - 0x7F;
|
1831 |
aSig = ( aSig | 0x00800000 )<<7; |
1832 |
bSig = ( bSig | 0x00800000 )<<8; |
1833 |
shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
|
1834 |
zSig = zSig64; |
1835 |
if ( 0 <= (sbits32) ( zSig<<1 ) ) { |
1836 |
zSig <<= 1;
|
1837 |
--zExp; |
1838 |
} |
1839 |
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
1840 |
|
1841 |
} |
1842 |
|
1843 |
/*----------------------------------------------------------------------------
|
1844 |
| Returns the result of dividing the single-precision floating-point value `a'
|
1845 |
| by the corresponding value `b'. The operation is performed according to the
|
1846 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1847 |
*----------------------------------------------------------------------------*/
|
1848 |
|
1849 |
float32 float32_div( float32 a, float32 b STATUS_PARAM ) |
1850 |
{ |
1851 |
flag aSign, bSign, zSign; |
1852 |
int16 aExp, bExp, zExp; |
1853 |
bits32 aSig, bSig, zSig; |
1854 |
|
1855 |
aSig = extractFloat32Frac( a ); |
1856 |
aExp = extractFloat32Exp( a ); |
1857 |
aSign = extractFloat32Sign( a ); |
1858 |
bSig = extractFloat32Frac( b ); |
1859 |
bExp = extractFloat32Exp( b ); |
1860 |
bSign = extractFloat32Sign( b ); |
1861 |
zSign = aSign ^ bSign; |
1862 |
if ( aExp == 0xFF ) { |
1863 |
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1864 |
if ( bExp == 0xFF ) { |
1865 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1866 |
float_raise( float_flag_invalid STATUS_VAR); |
1867 |
return float32_default_nan;
|
1868 |
} |
1869 |
return packFloat32( zSign, 0xFF, 0 ); |
1870 |
} |
1871 |
if ( bExp == 0xFF ) { |
1872 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1873 |
return packFloat32( zSign, 0, 0 ); |
1874 |
} |
1875 |
if ( bExp == 0 ) { |
1876 |
if ( bSig == 0 ) { |
1877 |
if ( ( aExp | aSig ) == 0 ) { |
1878 |
float_raise( float_flag_invalid STATUS_VAR); |
1879 |
return float32_default_nan;
|
1880 |
} |
1881 |
float_raise( float_flag_divbyzero STATUS_VAR); |
1882 |
return packFloat32( zSign, 0xFF, 0 ); |
1883 |
} |
1884 |
normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
1885 |
} |
1886 |
if ( aExp == 0 ) { |
1887 |
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); |
1888 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1889 |
} |
1890 |
zExp = aExp - bExp + 0x7D;
|
1891 |
aSig = ( aSig | 0x00800000 )<<7; |
1892 |
bSig = ( bSig | 0x00800000 )<<8; |
1893 |
if ( bSig <= ( aSig + aSig ) ) {
|
1894 |
aSig >>= 1;
|
1895 |
++zExp; |
1896 |
} |
1897 |
zSig = ( ( (bits64) aSig )<<32 ) / bSig;
|
1898 |
if ( ( zSig & 0x3F ) == 0 ) { |
1899 |
zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 );
|
1900 |
} |
1901 |
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
1902 |
|
1903 |
} |
1904 |
|
1905 |
/*----------------------------------------------------------------------------
|
1906 |
| Returns the remainder of the single-precision floating-point value `a'
|
1907 |
| with respect to the corresponding value `b'. The operation is performed
|
1908 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1909 |
*----------------------------------------------------------------------------*/
|
1910 |
|
1911 |
float32 float32_rem( float32 a, float32 b STATUS_PARAM ) |
1912 |
{ |
1913 |
flag aSign, bSign, zSign; |
1914 |
int16 aExp, bExp, expDiff; |
1915 |
bits32 aSig, bSig; |
1916 |
bits32 q; |
1917 |
bits64 aSig64, bSig64, q64; |
1918 |
bits32 alternateASig; |
1919 |
sbits32 sigMean; |
1920 |
|
1921 |
aSig = extractFloat32Frac( a ); |
1922 |
aExp = extractFloat32Exp( a ); |
1923 |
aSign = extractFloat32Sign( a ); |
1924 |
bSig = extractFloat32Frac( b ); |
1925 |
bExp = extractFloat32Exp( b ); |
1926 |
bSign = extractFloat32Sign( b ); |
1927 |
if ( aExp == 0xFF ) { |
1928 |
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { |
1929 |
return propagateFloat32NaN( a, b STATUS_VAR );
|
1930 |
} |
1931 |
float_raise( float_flag_invalid STATUS_VAR); |
1932 |
return float32_default_nan;
|
1933 |
} |
1934 |
if ( bExp == 0xFF ) { |
1935 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1936 |
return a;
|
1937 |
} |
1938 |
if ( bExp == 0 ) { |
1939 |
if ( bSig == 0 ) { |
1940 |
float_raise( float_flag_invalid STATUS_VAR); |
1941 |
return float32_default_nan;
|
1942 |
} |
1943 |
normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
1944 |
} |
1945 |
if ( aExp == 0 ) { |
1946 |
if ( aSig == 0 ) return a; |
1947 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1948 |
} |
1949 |
expDiff = aExp - bExp; |
1950 |
aSig |= 0x00800000;
|
1951 |
bSig |= 0x00800000;
|
1952 |
if ( expDiff < 32 ) { |
1953 |
aSig <<= 8;
|
1954 |
bSig <<= 8;
|
1955 |
if ( expDiff < 0 ) { |
1956 |
if ( expDiff < -1 ) return a; |
1957 |
aSig >>= 1;
|
1958 |
} |
1959 |
q = ( bSig <= aSig ); |
1960 |
if ( q ) aSig -= bSig;
|
1961 |
if ( 0 < expDiff ) { |
1962 |
q = ( ( (bits64) aSig )<<32 ) / bSig;
|
1963 |
q >>= 32 - expDiff;
|
1964 |
bSig >>= 2;
|
1965 |
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; |
1966 |
} |
1967 |
else {
|
1968 |
aSig >>= 2;
|
1969 |
bSig >>= 2;
|
1970 |
} |
1971 |
} |
1972 |
else {
|
1973 |
if ( bSig <= aSig ) aSig -= bSig;
|
1974 |
aSig64 = ( (bits64) aSig )<<40;
|
1975 |
bSig64 = ( (bits64) bSig )<<40;
|
1976 |
expDiff -= 64;
|
1977 |
while ( 0 < expDiff ) { |
1978 |
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
1979 |
q64 = ( 2 < q64 ) ? q64 - 2 : 0; |
1980 |
aSig64 = - ( ( bSig * q64 )<<38 );
|
1981 |
expDiff -= 62;
|
1982 |
} |
1983 |
expDiff += 64;
|
1984 |
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
1985 |
q64 = ( 2 < q64 ) ? q64 - 2 : 0; |
1986 |
q = q64>>( 64 - expDiff );
|
1987 |
bSig <<= 6;
|
1988 |
aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; |
1989 |
} |
1990 |
do {
|
1991 |
alternateASig = aSig; |
1992 |
++q; |
1993 |
aSig -= bSig; |
1994 |
} while ( 0 <= (sbits32) aSig ); |
1995 |
sigMean = aSig + alternateASig; |
1996 |
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { |
1997 |
aSig = alternateASig; |
1998 |
} |
1999 |
zSign = ( (sbits32) aSig < 0 );
|
2000 |
if ( zSign ) aSig = - aSig;
|
2001 |
return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR );
|
2002 |
|
2003 |
} |
2004 |
|
2005 |
/*----------------------------------------------------------------------------
|
2006 |
| Returns the square root of the single-precision floating-point value `a'.
|
2007 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
2008 |
| Floating-Point Arithmetic.
|
2009 |
*----------------------------------------------------------------------------*/
|
2010 |
|
2011 |
float32 float32_sqrt( float32 a STATUS_PARAM ) |
2012 |
{ |
2013 |
flag aSign; |
2014 |
int16 aExp, zExp; |
2015 |
bits32 aSig, zSig; |
2016 |
bits64 rem, term; |
2017 |
|
2018 |
aSig = extractFloat32Frac( a ); |
2019 |
aExp = extractFloat32Exp( a ); |
2020 |
aSign = extractFloat32Sign( a ); |
2021 |
if ( aExp == 0xFF ) { |
2022 |
if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
2023 |
if ( ! aSign ) return a; |
2024 |
float_raise( float_flag_invalid STATUS_VAR); |
2025 |
return float32_default_nan;
|
2026 |
} |
2027 |
if ( aSign ) {
|
2028 |
if ( ( aExp | aSig ) == 0 ) return a; |
2029 |
float_raise( float_flag_invalid STATUS_VAR); |
2030 |
return float32_default_nan;
|
2031 |
} |
2032 |
if ( aExp == 0 ) { |
2033 |
if ( aSig == 0 ) return float32_zero; |
2034 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2035 |
} |
2036 |
zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; |
2037 |
aSig = ( aSig | 0x00800000 )<<8; |
2038 |
zSig = estimateSqrt32( aExp, aSig ) + 2;
|
2039 |
if ( ( zSig & 0x7F ) <= 5 ) { |
2040 |
if ( zSig < 2 ) { |
2041 |
zSig = 0x7FFFFFFF;
|
2042 |
goto roundAndPack;
|
2043 |
} |
2044 |
aSig >>= aExp & 1;
|
2045 |
term = ( (bits64) zSig ) * zSig; |
2046 |
rem = ( ( (bits64) aSig )<<32 ) - term;
|
2047 |
while ( (sbits64) rem < 0 ) { |
2048 |
--zSig; |
2049 |
rem += ( ( (bits64) zSig )<<1 ) | 1; |
2050 |
} |
2051 |
zSig |= ( rem != 0 );
|
2052 |
} |
2053 |
shift32RightJamming( zSig, 1, &zSig );
|
2054 |
roundAndPack:
|
2055 |
return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); |
2056 |
|
2057 |
} |
2058 |
|
2059 |
/*----------------------------------------------------------------------------
|
2060 |
| Returns the binary log of the single-precision floating-point value `a'.
|
2061 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
2062 |
| Floating-Point Arithmetic.
|
2063 |
*----------------------------------------------------------------------------*/
|
2064 |
float32 float32_log2( float32 a STATUS_PARAM ) |
2065 |
{ |
2066 |
flag aSign, zSign; |
2067 |
int16 aExp; |
2068 |
bits32 aSig, zSig, i; |
2069 |
|
2070 |
aSig = extractFloat32Frac( a ); |
2071 |
aExp = extractFloat32Exp( a ); |
2072 |
aSign = extractFloat32Sign( a ); |
2073 |
|
2074 |
if ( aExp == 0 ) { |
2075 |
if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 ); |
2076 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2077 |
} |
2078 |
if ( aSign ) {
|
2079 |
float_raise( float_flag_invalid STATUS_VAR); |
2080 |
return float32_default_nan;
|
2081 |
} |
2082 |
if ( aExp == 0xFF ) { |
2083 |
if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
2084 |
return a;
|
2085 |
} |
2086 |
|
2087 |
aExp -= 0x7F;
|
2088 |
aSig |= 0x00800000;
|
2089 |
zSign = aExp < 0;
|
2090 |
zSig = aExp << 23;
|
2091 |
|
2092 |
for (i = 1 << 22; i > 0; i >>= 1) { |
2093 |
aSig = ( (bits64)aSig * aSig ) >> 23;
|
2094 |
if ( aSig & 0x01000000 ) { |
2095 |
aSig >>= 1;
|
2096 |
zSig |= i; |
2097 |
} |
2098 |
} |
2099 |
|
2100 |
if ( zSign )
|
2101 |
zSig = -zSig; |
2102 |
|
2103 |
return normalizeRoundAndPackFloat32( zSign, 0x85, zSig STATUS_VAR ); |
2104 |
} |
2105 |
|
2106 |
/*----------------------------------------------------------------------------
|
2107 |
| Returns 1 if the single-precision floating-point value `a' is equal to
|
2108 |
| the corresponding value `b', and 0 otherwise. The comparison is performed
|
2109 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2110 |
*----------------------------------------------------------------------------*/
|
2111 |
|
2112 |
int float32_eq( float32 a, float32 b STATUS_PARAM )
|
2113 |
{ |
2114 |
|
2115 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2116 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2117 |
) { |
2118 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2119 |
float_raise( float_flag_invalid STATUS_VAR); |
2120 |
} |
2121 |
return 0; |
2122 |
} |
2123 |
return ( float32_val(a) == float32_val(b) ) ||
|
2124 |
( (bits32) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 ); |
2125 |
|
2126 |
} |
2127 |
|
2128 |
/*----------------------------------------------------------------------------
|
2129 |
| Returns 1 if the single-precision floating-point value `a' is less than
|
2130 |
| or equal to the corresponding value `b', and 0 otherwise. The comparison
|
2131 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2132 |
| Arithmetic.
|
2133 |
*----------------------------------------------------------------------------*/
|
2134 |
|
2135 |
int float32_le( float32 a, float32 b STATUS_PARAM )
|
2136 |
{ |
2137 |
flag aSign, bSign; |
2138 |
bits32 av, bv; |
2139 |
|
2140 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2141 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2142 |
) { |
2143 |
float_raise( float_flag_invalid STATUS_VAR); |
2144 |
return 0; |
2145 |
} |
2146 |
aSign = extractFloat32Sign( a ); |
2147 |
bSign = extractFloat32Sign( b ); |
2148 |
av = float32_val(a); |
2149 |
bv = float32_val(b); |
2150 |
if ( aSign != bSign ) return aSign || ( (bits32) ( ( av | bv )<<1 ) == 0 ); |
2151 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
2152 |
|
2153 |
} |
2154 |
|
2155 |
/*----------------------------------------------------------------------------
|
2156 |
| Returns 1 if the single-precision floating-point value `a' is less than
|
2157 |
| the corresponding value `b', and 0 otherwise. The comparison is performed
|
2158 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2159 |
*----------------------------------------------------------------------------*/
|
2160 |
|
2161 |
int float32_lt( float32 a, float32 b STATUS_PARAM )
|
2162 |
{ |
2163 |
flag aSign, bSign; |
2164 |
bits32 av, bv; |
2165 |
|
2166 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2167 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2168 |
) { |
2169 |
float_raise( float_flag_invalid STATUS_VAR); |
2170 |
return 0; |
2171 |
} |
2172 |
aSign = extractFloat32Sign( a ); |
2173 |
bSign = extractFloat32Sign( b ); |
2174 |
av = float32_val(a); |
2175 |
bv = float32_val(b); |
2176 |
if ( aSign != bSign ) return aSign && ( (bits32) ( ( av | bv )<<1 ) != 0 ); |
2177 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
2178 |
|
2179 |
} |
2180 |
|
2181 |
/*----------------------------------------------------------------------------
|
2182 |
| Returns 1 if the single-precision floating-point value `a' is equal to
|
2183 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
2184 |
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
2185 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2186 |
*----------------------------------------------------------------------------*/
|
2187 |
|
2188 |
int float32_eq_signaling( float32 a, float32 b STATUS_PARAM )
|
2189 |
{ |
2190 |
bits32 av, bv; |
2191 |
|
2192 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2193 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2194 |
) { |
2195 |
float_raise( float_flag_invalid STATUS_VAR); |
2196 |
return 0; |
2197 |
} |
2198 |
av = float32_val(a); |
2199 |
bv = float32_val(b); |
2200 |
return ( av == bv ) || ( (bits32) ( ( av | bv )<<1 ) == 0 ); |
2201 |
|
2202 |
} |
2203 |
|
2204 |
/*----------------------------------------------------------------------------
|
2205 |
| Returns 1 if the single-precision floating-point value `a' is less than or
|
2206 |
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
2207 |
| cause an exception. Otherwise, the comparison is performed according to the
|
2208 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2209 |
*----------------------------------------------------------------------------*/
|
2210 |
|
2211 |
int float32_le_quiet( float32 a, float32 b STATUS_PARAM )
|
2212 |
{ |
2213 |
flag aSign, bSign; |
2214 |
bits32 av, bv; |
2215 |
|
2216 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2217 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2218 |
) { |
2219 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2220 |
float_raise( float_flag_invalid STATUS_VAR); |
2221 |
} |
2222 |
return 0; |
2223 |
} |
2224 |
aSign = extractFloat32Sign( a ); |
2225 |
bSign = extractFloat32Sign( b ); |
2226 |
av = float32_val(a); |
2227 |
bv = float32_val(b); |
2228 |
if ( aSign != bSign ) return aSign || ( (bits32) ( ( av | bv )<<1 ) == 0 ); |
2229 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
2230 |
|
2231 |
} |
2232 |
|
2233 |
/*----------------------------------------------------------------------------
|
2234 |
| Returns 1 if the single-precision floating-point value `a' is less than
|
2235 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
2236 |
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
2237 |
| Standard for Binary Floating-Point Arithmetic.
|
2238 |
*----------------------------------------------------------------------------*/
|
2239 |
|
2240 |
int float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
|
2241 |
{ |
2242 |
flag aSign, bSign; |
2243 |
bits32 av, bv; |
2244 |
|
2245 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2246 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2247 |
) { |
2248 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2249 |
float_raise( float_flag_invalid STATUS_VAR); |
2250 |
} |
2251 |
return 0; |
2252 |
} |
2253 |
aSign = extractFloat32Sign( a ); |
2254 |
bSign = extractFloat32Sign( b ); |
2255 |
av = float32_val(a); |
2256 |
bv = float32_val(b); |
2257 |
if ( aSign != bSign ) return aSign && ( (bits32) ( ( av | bv )<<1 ) != 0 ); |
2258 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
2259 |
|
2260 |
} |
2261 |
|
2262 |
/*----------------------------------------------------------------------------
|
2263 |
| Returns the result of converting the double-precision floating-point value
|
2264 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
2265 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2266 |
| Arithmetic---which means in particular that the conversion is rounded
|
2267 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
2268 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
2269 |
| largest integer with the same sign as `a' is returned.
|
2270 |
*----------------------------------------------------------------------------*/
|
2271 |
|
2272 |
int32 float64_to_int32( float64 a STATUS_PARAM ) |
2273 |
{ |
2274 |
flag aSign; |
2275 |
int16 aExp, shiftCount; |
2276 |
bits64 aSig; |
2277 |
|
2278 |
aSig = extractFloat64Frac( a ); |
2279 |
aExp = extractFloat64Exp( a ); |
2280 |
aSign = extractFloat64Sign( a ); |
2281 |
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; |
2282 |
if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
2283 |
shiftCount = 0x42C - aExp;
|
2284 |
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); |
2285 |
return roundAndPackInt32( aSign, aSig STATUS_VAR );
|
2286 |
|
2287 |
} |
2288 |
|
2289 |
/*----------------------------------------------------------------------------
|
2290 |
| Returns the result of converting the double-precision floating-point value
|
2291 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
2292 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2293 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
2294 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
2295 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
2296 |
| returned.
|
2297 |
*----------------------------------------------------------------------------*/
|
2298 |
|
2299 |
int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) |
2300 |
{ |
2301 |
flag aSign; |
2302 |
int16 aExp, shiftCount; |
2303 |
bits64 aSig, savedASig; |
2304 |
int32 z; |
2305 |
|
2306 |
aSig = extractFloat64Frac( a ); |
2307 |
aExp = extractFloat64Exp( a ); |
2308 |
aSign = extractFloat64Sign( a ); |
2309 |
if ( 0x41E < aExp ) { |
2310 |
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; |
2311 |
goto invalid;
|
2312 |
} |
2313 |
else if ( aExp < 0x3FF ) { |
2314 |
if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
2315 |
return 0; |
2316 |
} |
2317 |
aSig |= LIT64( 0x0010000000000000 );
|
2318 |
shiftCount = 0x433 - aExp;
|
2319 |
savedASig = aSig; |
2320 |
aSig >>= shiftCount; |
2321 |
z = aSig; |
2322 |
if ( aSign ) z = - z;
|
2323 |
if ( ( z < 0 ) ^ aSign ) { |
2324 |
invalid:
|
2325 |
float_raise( float_flag_invalid STATUS_VAR); |
2326 |
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; |
2327 |
} |
2328 |
if ( ( aSig<<shiftCount ) != savedASig ) {
|
2329 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2330 |
} |
2331 |
return z;
|
2332 |
|
2333 |
} |
2334 |
|
2335 |
/*----------------------------------------------------------------------------
|
2336 |
| Returns the result of converting the double-precision floating-point value
|
2337 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
2338 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2339 |
| Arithmetic---which means in particular that the conversion is rounded
|
2340 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
2341 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
2342 |
| largest integer with the same sign as `a' is returned.
|
2343 |
*----------------------------------------------------------------------------*/
|
2344 |
|
2345 |
int64 float64_to_int64( float64 a STATUS_PARAM ) |
2346 |
{ |
2347 |
flag aSign; |
2348 |
int16 aExp, shiftCount; |
2349 |
bits64 aSig, aSigExtra; |
2350 |
|
2351 |
aSig = extractFloat64Frac( a ); |
2352 |
aExp = extractFloat64Exp( a ); |
2353 |
aSign = extractFloat64Sign( a ); |
2354 |
if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
2355 |
shiftCount = 0x433 - aExp;
|
2356 |
if ( shiftCount <= 0 ) { |
2357 |
if ( 0x43E < aExp ) { |
2358 |
float_raise( float_flag_invalid STATUS_VAR); |
2359 |
if ( ! aSign
|
2360 |
|| ( ( aExp == 0x7FF )
|
2361 |
&& ( aSig != LIT64( 0x0010000000000000 ) ) )
|
2362 |
) { |
2363 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
2364 |
} |
2365 |
return (sbits64) LIT64( 0x8000000000000000 ); |
2366 |
} |
2367 |
aSigExtra = 0;
|
2368 |
aSig <<= - shiftCount; |
2369 |
} |
2370 |
else {
|
2371 |
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
|
2372 |
} |
2373 |
return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
|
2374 |
|
2375 |
} |
2376 |
|
2377 |
/*----------------------------------------------------------------------------
|
2378 |
| Returns the result of converting the double-precision floating-point value
|
2379 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
2380 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2381 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
2382 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
2383 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
2384 |
| returned.
|
2385 |
*----------------------------------------------------------------------------*/
|
2386 |
|
2387 |
int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) |
2388 |
{ |
2389 |
flag aSign; |
2390 |
int16 aExp, shiftCount; |
2391 |
bits64 aSig; |
2392 |
int64 z; |
2393 |
|
2394 |
aSig = extractFloat64Frac( a ); |
2395 |
aExp = extractFloat64Exp( a ); |
2396 |
aSign = extractFloat64Sign( a ); |
2397 |
if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
2398 |
shiftCount = aExp - 0x433;
|
2399 |
if ( 0 <= shiftCount ) { |
2400 |
if ( 0x43E <= aExp ) { |
2401 |
if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) { |
2402 |
float_raise( float_flag_invalid STATUS_VAR); |
2403 |
if ( ! aSign
|
2404 |
|| ( ( aExp == 0x7FF )
|
2405 |
&& ( aSig != LIT64( 0x0010000000000000 ) ) )
|
2406 |
) { |
2407 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
2408 |
} |
2409 |
} |
2410 |
return (sbits64) LIT64( 0x8000000000000000 ); |
2411 |
} |
2412 |
z = aSig<<shiftCount; |
2413 |
} |
2414 |
else {
|
2415 |
if ( aExp < 0x3FE ) { |
2416 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
2417 |
return 0; |
2418 |
} |
2419 |
z = aSig>>( - shiftCount ); |
2420 |
if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { |
2421 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2422 |
} |
2423 |
} |
2424 |
if ( aSign ) z = - z;
|
2425 |
return z;
|
2426 |
|
2427 |
} |
2428 |
|
2429 |
/*----------------------------------------------------------------------------
|
2430 |
| Returns the result of converting the double-precision floating-point value
|
2431 |
| `a' to the single-precision floating-point format. The conversion is
|
2432 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2433 |
| Arithmetic.
|
2434 |
*----------------------------------------------------------------------------*/
|
2435 |
|
2436 |
float32 float64_to_float32( float64 a STATUS_PARAM ) |
2437 |
{ |
2438 |
flag aSign; |
2439 |
int16 aExp; |
2440 |
bits64 aSig; |
2441 |
bits32 zSig; |
2442 |
|
2443 |
aSig = extractFloat64Frac( a ); |
2444 |
aExp = extractFloat64Exp( a ); |
2445 |
aSign = extractFloat64Sign( a ); |
2446 |
if ( aExp == 0x7FF ) { |
2447 |
if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) ); |
2448 |
return packFloat32( aSign, 0xFF, 0 ); |
2449 |
} |
2450 |
shift64RightJamming( aSig, 22, &aSig );
|
2451 |
zSig = aSig; |
2452 |
if ( aExp || zSig ) {
|
2453 |
zSig |= 0x40000000;
|
2454 |
aExp -= 0x381;
|
2455 |
} |
2456 |
return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
|
2457 |
|
2458 |
} |
2459 |
|
2460 |
#ifdef FLOATX80
|
2461 |
|
2462 |
/*----------------------------------------------------------------------------
|
2463 |
| Returns the result of converting the double-precision floating-point value
|
2464 |
| `a' to the extended double-precision floating-point format. The conversion
|
2465 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2466 |
| Arithmetic.
|
2467 |
*----------------------------------------------------------------------------*/
|
2468 |
|
2469 |
floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) |
2470 |
{ |
2471 |
flag aSign; |
2472 |
int16 aExp; |
2473 |
bits64 aSig; |
2474 |
|
2475 |
aSig = extractFloat64Frac( a ); |
2476 |
aExp = extractFloat64Exp( a ); |
2477 |
aSign = extractFloat64Sign( a ); |
2478 |
if ( aExp == 0x7FF ) { |
2479 |
if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) ); |
2480 |
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
2481 |
} |
2482 |
if ( aExp == 0 ) { |
2483 |
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); |
2484 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
2485 |
} |
2486 |
return
|
2487 |
packFloatx80( |
2488 |
aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); |
2489 |
|
2490 |
} |
2491 |
|
2492 |
#endif
|
2493 |
|
2494 |
#ifdef FLOAT128
|
2495 |
|
2496 |
/*----------------------------------------------------------------------------
|
2497 |
| Returns the result of converting the double-precision floating-point value
|
2498 |
| `a' to the quadruple-precision floating-point format. The conversion is
|
2499 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2500 |
| Arithmetic.
|
2501 |
*----------------------------------------------------------------------------*/
|
2502 |
|
2503 |
float128 float64_to_float128( float64 a STATUS_PARAM ) |
2504 |
{ |
2505 |
flag aSign; |
2506 |
int16 aExp; |
2507 |
bits64 aSig, zSig0, zSig1; |
2508 |
|
2509 |
aSig = extractFloat64Frac( a ); |
2510 |
aExp = extractFloat64Exp( a ); |
2511 |
aSign = extractFloat64Sign( a ); |
2512 |
if ( aExp == 0x7FF ) { |
2513 |
if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) ); |
2514 |
return packFloat128( aSign, 0x7FFF, 0, 0 ); |
2515 |
} |
2516 |
if ( aExp == 0 ) { |
2517 |
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); |
2518 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
2519 |
--aExp; |
2520 |
} |
2521 |
shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); |
2522 |
return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); |
2523 |
|
2524 |
} |
2525 |
|
2526 |
#endif
|
2527 |
|
2528 |
/*----------------------------------------------------------------------------
|
2529 |
| Rounds the double-precision floating-point value `a' to an integer, and
|
2530 |
| returns the result as a double-precision floating-point value. The
|
2531 |
| operation is performed according to the IEC/IEEE Standard for Binary
|
2532 |
| Floating-Point Arithmetic.
|
2533 |
*----------------------------------------------------------------------------*/
|
2534 |
|
2535 |
float64 float64_round_to_int( float64 a STATUS_PARAM ) |
2536 |
{ |
2537 |
flag aSign; |
2538 |
int16 aExp; |
2539 |
bits64 lastBitMask, roundBitsMask; |
2540 |
int8 roundingMode; |
2541 |
bits64 z; |
2542 |
|
2543 |
aExp = extractFloat64Exp( a ); |
2544 |
if ( 0x433 <= aExp ) { |
2545 |
if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { |
2546 |
return propagateFloat64NaN( a, a STATUS_VAR );
|
2547 |
} |
2548 |
return a;
|
2549 |
} |
2550 |
if ( aExp < 0x3FF ) { |
2551 |
if ( (bits64) ( float64_val(a)<<1 ) == 0 ) return a; |
2552 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2553 |
aSign = extractFloat64Sign( a ); |
2554 |
switch ( STATUS(float_rounding_mode) ) {
|
2555 |
case float_round_nearest_even:
|
2556 |
if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { |
2557 |
return packFloat64( aSign, 0x3FF, 0 ); |
2558 |
} |
2559 |
break;
|
2560 |
case float_round_down:
|
2561 |
return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0); |
2562 |
case float_round_up:
|
2563 |
return make_float64(
|
2564 |
aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 )); |
2565 |
} |
2566 |
return packFloat64( aSign, 0, 0 ); |
2567 |
} |
2568 |
lastBitMask = 1;
|
2569 |
lastBitMask <<= 0x433 - aExp;
|
2570 |
roundBitsMask = lastBitMask - 1;
|
2571 |
z = float64_val(a); |
2572 |
roundingMode = STATUS(float_rounding_mode); |
2573 |
if ( roundingMode == float_round_nearest_even ) {
|
2574 |
z += lastBitMask>>1;
|
2575 |
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; |
2576 |
} |
2577 |
else if ( roundingMode != float_round_to_zero ) { |
2578 |
if ( extractFloat64Sign( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) {
|
2579 |
z += roundBitsMask; |
2580 |
} |
2581 |
} |
2582 |
z &= ~ roundBitsMask; |
2583 |
if ( z != float64_val(a) )
|
2584 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2585 |
return make_float64(z);
|
2586 |
|
2587 |
} |
2588 |
|
2589 |
float64 float64_trunc_to_int( float64 a STATUS_PARAM) |
2590 |
{ |
2591 |
int oldmode;
|
2592 |
float64 res; |
2593 |
oldmode = STATUS(float_rounding_mode); |
2594 |
STATUS(float_rounding_mode) = float_round_to_zero; |
2595 |
res = float64_round_to_int(a STATUS_VAR); |
2596 |
STATUS(float_rounding_mode) = oldmode; |
2597 |
return res;
|
2598 |
} |
2599 |
|
2600 |
/*----------------------------------------------------------------------------
|
2601 |
| Returns the result of adding the absolute values of the double-precision
|
2602 |
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
2603 |
| before being returned. `zSign' is ignored if the result is a NaN.
|
2604 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
2605 |
| Floating-Point Arithmetic.
|
2606 |
*----------------------------------------------------------------------------*/
|
2607 |
|
2608 |
static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
|
2609 |
{ |
2610 |
int16 aExp, bExp, zExp; |
2611 |
bits64 aSig, bSig, zSig; |
2612 |
int16 expDiff; |
2613 |
|
2614 |
aSig = extractFloat64Frac( a ); |
2615 |
aExp = extractFloat64Exp( a ); |
2616 |
bSig = extractFloat64Frac( b ); |
2617 |
bExp = extractFloat64Exp( b ); |
2618 |
expDiff = aExp - bExp; |
2619 |
aSig <<= 9;
|
2620 |
bSig <<= 9;
|
2621 |
if ( 0 < expDiff ) { |
2622 |
if ( aExp == 0x7FF ) { |
2623 |
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2624 |
return a;
|
2625 |
} |
2626 |
if ( bExp == 0 ) { |
2627 |
--expDiff; |
2628 |
} |
2629 |
else {
|
2630 |
bSig |= LIT64( 0x2000000000000000 );
|
2631 |
} |
2632 |
shift64RightJamming( bSig, expDiff, &bSig ); |
2633 |
zExp = aExp; |
2634 |
} |
2635 |
else if ( expDiff < 0 ) { |
2636 |
if ( bExp == 0x7FF ) { |
2637 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2638 |
return packFloat64( zSign, 0x7FF, 0 ); |
2639 |
} |
2640 |
if ( aExp == 0 ) { |
2641 |
++expDiff; |
2642 |
} |
2643 |
else {
|
2644 |
aSig |= LIT64( 0x2000000000000000 );
|
2645 |
} |
2646 |
shift64RightJamming( aSig, - expDiff, &aSig ); |
2647 |
zExp = bExp; |
2648 |
} |
2649 |
else {
|
2650 |
if ( aExp == 0x7FF ) { |
2651 |
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2652 |
return a;
|
2653 |
} |
2654 |
if ( aExp == 0 ) { |
2655 |
if ( STATUS(flush_to_zero) ) return packFloat64( zSign, 0, 0 ); |
2656 |
return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); |
2657 |
} |
2658 |
zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
|
2659 |
zExp = aExp; |
2660 |
goto roundAndPack;
|
2661 |
} |
2662 |
aSig |= LIT64( 0x2000000000000000 );
|
2663 |
zSig = ( aSig + bSig )<<1;
|
2664 |
--zExp; |
2665 |
if ( (sbits64) zSig < 0 ) { |
2666 |
zSig = aSig + bSig; |
2667 |
++zExp; |
2668 |
} |
2669 |
roundAndPack:
|
2670 |
return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
|
2671 |
|
2672 |
} |
2673 |
|
2674 |
/*----------------------------------------------------------------------------
|
2675 |
| Returns the result of subtracting the absolute values of the double-
|
2676 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
2677 |
| difference is negated before being returned. `zSign' is ignored if the
|
2678 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
2679 |
| Standard for Binary Floating-Point Arithmetic.
|
2680 |
*----------------------------------------------------------------------------*/
|
2681 |
|
2682 |
static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
|
2683 |
{ |
2684 |
int16 aExp, bExp, zExp; |
2685 |
bits64 aSig, bSig, zSig; |
2686 |
int16 expDiff; |
2687 |
|
2688 |
aSig = extractFloat64Frac( a ); |
2689 |
aExp = extractFloat64Exp( a ); |
2690 |
bSig = extractFloat64Frac( b ); |
2691 |
bExp = extractFloat64Exp( b ); |
2692 |
expDiff = aExp - bExp; |
2693 |
aSig <<= 10;
|
2694 |
bSig <<= 10;
|
2695 |
if ( 0 < expDiff ) goto aExpBigger; |
2696 |
if ( expDiff < 0 ) goto bExpBigger; |
2697 |
if ( aExp == 0x7FF ) { |
2698 |
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2699 |
float_raise( float_flag_invalid STATUS_VAR); |
2700 |
return float64_default_nan;
|
2701 |
} |
2702 |
if ( aExp == 0 ) { |
2703 |
aExp = 1;
|
2704 |
bExp = 1;
|
2705 |
} |
2706 |
if ( bSig < aSig ) goto aBigger; |
2707 |
if ( aSig < bSig ) goto bBigger; |
2708 |
return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
2709 |
bExpBigger:
|
2710 |
if ( bExp == 0x7FF ) { |
2711 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2712 |
return packFloat64( zSign ^ 1, 0x7FF, 0 ); |
2713 |
} |
2714 |
if ( aExp == 0 ) { |
2715 |
++expDiff; |
2716 |
} |
2717 |
else {
|
2718 |
aSig |= LIT64( 0x4000000000000000 );
|
2719 |
} |
2720 |
shift64RightJamming( aSig, - expDiff, &aSig ); |
2721 |
bSig |= LIT64( 0x4000000000000000 );
|
2722 |
bBigger:
|
2723 |
zSig = bSig - aSig; |
2724 |
zExp = bExp; |
2725 |
zSign ^= 1;
|
2726 |
goto normalizeRoundAndPack;
|
2727 |
aExpBigger:
|
2728 |
if ( aExp == 0x7FF ) { |
2729 |
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2730 |
return a;
|
2731 |
} |
2732 |
if ( bExp == 0 ) { |
2733 |
--expDiff; |
2734 |
} |
2735 |
else {
|
2736 |
bSig |= LIT64( 0x4000000000000000 );
|
2737 |
} |
2738 |
shift64RightJamming( bSig, expDiff, &bSig ); |
2739 |
aSig |= LIT64( 0x4000000000000000 );
|
2740 |
aBigger:
|
2741 |
zSig = aSig - bSig; |
2742 |
zExp = aExp; |
2743 |
normalizeRoundAndPack:
|
2744 |
--zExp; |
2745 |
return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
|
2746 |
|
2747 |
} |
2748 |
|
2749 |
/*----------------------------------------------------------------------------
|
2750 |
| Returns the result of adding the double-precision floating-point values `a'
|
2751 |
| and `b'. The operation is performed according to the IEC/IEEE Standard for
|
2752 |
| Binary Floating-Point Arithmetic.
|
2753 |
*----------------------------------------------------------------------------*/
|
2754 |
|
2755 |
float64 float64_add( float64 a, float64 b STATUS_PARAM ) |
2756 |
{ |
2757 |
flag aSign, bSign; |
2758 |
|
2759 |
aSign = extractFloat64Sign( a ); |
2760 |
bSign = extractFloat64Sign( b ); |
2761 |
if ( aSign == bSign ) {
|
2762 |
return addFloat64Sigs( a, b, aSign STATUS_VAR );
|
2763 |
} |
2764 |
else {
|
2765 |
return subFloat64Sigs( a, b, aSign STATUS_VAR );
|
2766 |
} |
2767 |
|
2768 |
} |
2769 |
|
2770 |
/*----------------------------------------------------------------------------
|
2771 |
| Returns the result of subtracting the double-precision floating-point values
|
2772 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
2773 |
| for Binary Floating-Point Arithmetic.
|
2774 |
*----------------------------------------------------------------------------*/
|
2775 |
|
2776 |
float64 float64_sub( float64 a, float64 b STATUS_PARAM ) |
2777 |
{ |
2778 |
flag aSign, bSign; |
2779 |
|
2780 |
aSign = extractFloat64Sign( a ); |
2781 |
bSign = extractFloat64Sign( b ); |
2782 |
if ( aSign == bSign ) {
|
2783 |
return subFloat64Sigs( a, b, aSign STATUS_VAR );
|
2784 |
} |
2785 |
else {
|
2786 |
return addFloat64Sigs( a, b, aSign STATUS_VAR );
|
2787 |
} |
2788 |
|
2789 |
} |
2790 |
|
2791 |
/*----------------------------------------------------------------------------
|
2792 |
| Returns the result of multiplying the double-precision floating-point values
|
2793 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
2794 |
| for Binary Floating-Point Arithmetic.
|
2795 |
*----------------------------------------------------------------------------*/
|
2796 |
|
2797 |
float64 float64_mul( float64 a, float64 b STATUS_PARAM ) |
2798 |
{ |
2799 |
flag aSign, bSign, zSign; |
2800 |
int16 aExp, bExp, zExp; |
2801 |
bits64 aSig, bSig, zSig0, zSig1; |
2802 |
|
2803 |
aSig = extractFloat64Frac( a ); |
2804 |
aExp = extractFloat64Exp( a ); |
2805 |
aSign = extractFloat64Sign( a ); |
2806 |
bSig = extractFloat64Frac( b ); |
2807 |
bExp = extractFloat64Exp( b ); |
2808 |
bSign = extractFloat64Sign( b ); |
2809 |
zSign = aSign ^ bSign; |
2810 |
if ( aExp == 0x7FF ) { |
2811 |
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { |
2812 |
return propagateFloat64NaN( a, b STATUS_VAR );
|
2813 |
} |
2814 |
if ( ( bExp | bSig ) == 0 ) { |
2815 |
float_raise( float_flag_invalid STATUS_VAR); |
2816 |
return float64_default_nan;
|
2817 |
} |
2818 |
return packFloat64( zSign, 0x7FF, 0 ); |
2819 |
} |
2820 |
if ( bExp == 0x7FF ) { |
2821 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2822 |
if ( ( aExp | aSig ) == 0 ) { |
2823 |
float_raise( float_flag_invalid STATUS_VAR); |
2824 |
return float64_default_nan;
|
2825 |
} |
2826 |
return packFloat64( zSign, 0x7FF, 0 ); |
2827 |
} |
2828 |
if ( aExp == 0 ) { |
2829 |
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); |
2830 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
2831 |
} |
2832 |
if ( bExp == 0 ) { |
2833 |
if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); |
2834 |
normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
2835 |
} |
2836 |
zExp = aExp + bExp - 0x3FF;
|
2837 |
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; |
2838 |
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
2839 |
mul64To128( aSig, bSig, &zSig0, &zSig1 ); |
2840 |
zSig0 |= ( zSig1 != 0 );
|
2841 |
if ( 0 <= (sbits64) ( zSig0<<1 ) ) { |
2842 |
zSig0 <<= 1;
|
2843 |
--zExp; |
2844 |
} |
2845 |
return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR );
|
2846 |
|
2847 |
} |
2848 |
|
2849 |
/*----------------------------------------------------------------------------
|
2850 |
| Returns the result of dividing the double-precision floating-point value `a'
|
2851 |
| by the corresponding value `b'. The operation is performed according to
|
2852 |
| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2853 |
*----------------------------------------------------------------------------*/
|
2854 |
|
2855 |
float64 float64_div( float64 a, float64 b STATUS_PARAM ) |
2856 |
{ |
2857 |
flag aSign, bSign, zSign; |
2858 |
int16 aExp, bExp, zExp; |
2859 |
bits64 aSig, bSig, zSig; |
2860 |
bits64 rem0, rem1; |
2861 |
bits64 term0, term1; |
2862 |
|
2863 |
aSig = extractFloat64Frac( a ); |
2864 |
aExp = extractFloat64Exp( a ); |
2865 |
aSign = extractFloat64Sign( a ); |
2866 |
bSig = extractFloat64Frac( b ); |
2867 |
bExp = extractFloat64Exp( b ); |
2868 |
bSign = extractFloat64Sign( b ); |
2869 |
zSign = aSign ^ bSign; |
2870 |
if ( aExp == 0x7FF ) { |
2871 |
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2872 |
if ( bExp == 0x7FF ) { |
2873 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2874 |
float_raise( float_flag_invalid STATUS_VAR); |
2875 |
return float64_default_nan;
|
2876 |
} |
2877 |
return packFloat64( zSign, 0x7FF, 0 ); |
2878 |
} |
2879 |
if ( bExp == 0x7FF ) { |
2880 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2881 |
return packFloat64( zSign, 0, 0 ); |
2882 |
} |
2883 |
if ( bExp == 0 ) { |
2884 |
if ( bSig == 0 ) { |
2885 |
if ( ( aExp | aSig ) == 0 ) { |
2886 |
float_raise( float_flag_invalid STATUS_VAR); |
2887 |
return float64_default_nan;
|
2888 |
} |
2889 |
float_raise( float_flag_divbyzero STATUS_VAR); |
2890 |
return packFloat64( zSign, 0x7FF, 0 ); |
2891 |
} |
2892 |
normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
2893 |
} |
2894 |
if ( aExp == 0 ) { |
2895 |
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); |
2896 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
2897 |
} |
2898 |
zExp = aExp - bExp + 0x3FD;
|
2899 |
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; |
2900 |
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
2901 |
if ( bSig <= ( aSig + aSig ) ) {
|
2902 |
aSig >>= 1;
|
2903 |
++zExp; |
2904 |
} |
2905 |
zSig = estimateDiv128To64( aSig, 0, bSig );
|
2906 |
if ( ( zSig & 0x1FF ) <= 2 ) { |
2907 |
mul64To128( bSig, zSig, &term0, &term1 ); |
2908 |
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
2909 |
while ( (sbits64) rem0 < 0 ) { |
2910 |
--zSig; |
2911 |
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
2912 |
} |
2913 |
zSig |= ( rem1 != 0 );
|
2914 |
} |
2915 |
return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
|
2916 |
|
2917 |
} |
2918 |
|
2919 |
/*----------------------------------------------------------------------------
|
2920 |
| Returns the remainder of the double-precision floating-point value `a'
|
2921 |
| with respect to the corresponding value `b'. The operation is performed
|
2922 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2923 |
*----------------------------------------------------------------------------*/
|
2924 |
|
2925 |
float64 float64_rem( float64 a, float64 b STATUS_PARAM ) |
2926 |
{ |
2927 |
flag aSign, bSign, zSign; |
2928 |
int16 aExp, bExp, expDiff; |
2929 |
bits64 aSig, bSig; |
2930 |
bits64 q, alternateASig; |
2931 |
sbits64 sigMean; |
2932 |
|
2933 |
aSig = extractFloat64Frac( a ); |
2934 |
aExp = extractFloat64Exp( a ); |
2935 |
aSign = extractFloat64Sign( a ); |
2936 |
bSig = extractFloat64Frac( b ); |
2937 |
bExp = extractFloat64Exp( b ); |
2938 |
bSign = extractFloat64Sign( b ); |
2939 |
if ( aExp == 0x7FF ) { |
2940 |
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { |
2941 |
return propagateFloat64NaN( a, b STATUS_VAR );
|
2942 |
} |
2943 |
float_raise( float_flag_invalid STATUS_VAR); |
2944 |
return float64_default_nan;
|
2945 |
} |
2946 |
if ( bExp == 0x7FF ) { |
2947 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
2948 |
return a;
|
2949 |
} |
2950 |
if ( bExp == 0 ) { |
2951 |
if ( bSig == 0 ) { |
2952 |
float_raise( float_flag_invalid STATUS_VAR); |
2953 |
return float64_default_nan;
|
2954 |
} |
2955 |
normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
2956 |
} |
2957 |
if ( aExp == 0 ) { |
2958 |
if ( aSig == 0 ) return a; |
2959 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
2960 |
} |
2961 |
expDiff = aExp - bExp; |
2962 |
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; |
2963 |
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
2964 |
if ( expDiff < 0 ) { |
2965 |
if ( expDiff < -1 ) return a; |
2966 |
aSig >>= 1;
|
2967 |
} |
2968 |
q = ( bSig <= aSig ); |
2969 |
if ( q ) aSig -= bSig;
|
2970 |
expDiff -= 64;
|
2971 |
while ( 0 < expDiff ) { |
2972 |
q = estimateDiv128To64( aSig, 0, bSig );
|
2973 |
q = ( 2 < q ) ? q - 2 : 0; |
2974 |
aSig = - ( ( bSig>>2 ) * q );
|
2975 |
expDiff -= 62;
|
2976 |
} |
2977 |
expDiff += 64;
|
2978 |
if ( 0 < expDiff ) { |
2979 |
q = estimateDiv128To64( aSig, 0, bSig );
|
2980 |
q = ( 2 < q ) ? q - 2 : 0; |
2981 |
q >>= 64 - expDiff;
|
2982 |
bSig >>= 2;
|
2983 |
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; |
2984 |
} |
2985 |
else {
|
2986 |
aSig >>= 2;
|
2987 |
bSig >>= 2;
|
2988 |
} |
2989 |
do {
|
2990 |
alternateASig = aSig; |
2991 |
++q; |
2992 |
aSig -= bSig; |
2993 |
} while ( 0 <= (sbits64) aSig ); |
2994 |
sigMean = aSig + alternateASig; |
2995 |
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { |
2996 |
aSig = alternateASig; |
2997 |
} |
2998 |
zSign = ( (sbits64) aSig < 0 );
|
2999 |
if ( zSign ) aSig = - aSig;
|
3000 |
return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR );
|
3001 |
|
3002 |
} |
3003 |
|
3004 |
/*----------------------------------------------------------------------------
|
3005 |
| Returns the square root of the double-precision floating-point value `a'.
|
3006 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
3007 |
| Floating-Point Arithmetic.
|
3008 |
*----------------------------------------------------------------------------*/
|
3009 |
|
3010 |
float64 float64_sqrt( float64 a STATUS_PARAM ) |
3011 |
{ |
3012 |
flag aSign; |
3013 |
int16 aExp, zExp; |
3014 |
bits64 aSig, zSig, doubleZSig; |
3015 |
bits64 rem0, rem1, term0, term1; |
3016 |
|
3017 |
aSig = extractFloat64Frac( a ); |
3018 |
aExp = extractFloat64Exp( a ); |
3019 |
aSign = extractFloat64Sign( a ); |
3020 |
if ( aExp == 0x7FF ) { |
3021 |
if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); |
3022 |
if ( ! aSign ) return a; |
3023 |
float_raise( float_flag_invalid STATUS_VAR); |
3024 |
return float64_default_nan;
|
3025 |
} |
3026 |
if ( aSign ) {
|
3027 |
if ( ( aExp | aSig ) == 0 ) return a; |
3028 |
float_raise( float_flag_invalid STATUS_VAR); |
3029 |
return float64_default_nan;
|
3030 |
} |
3031 |
if ( aExp == 0 ) { |
3032 |
if ( aSig == 0 ) return float64_zero; |
3033 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3034 |
} |
3035 |
zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; |
3036 |
aSig |= LIT64( 0x0010000000000000 );
|
3037 |
zSig = estimateSqrt32( aExp, aSig>>21 );
|
3038 |
aSig <<= 9 - ( aExp & 1 ); |
3039 |
zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); |
3040 |
if ( ( zSig & 0x1FF ) <= 5 ) { |
3041 |
doubleZSig = zSig<<1;
|
3042 |
mul64To128( zSig, zSig, &term0, &term1 ); |
3043 |
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
3044 |
while ( (sbits64) rem0 < 0 ) { |
3045 |
--zSig; |
3046 |
doubleZSig -= 2;
|
3047 |
add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); |
3048 |
} |
3049 |
zSig |= ( ( rem0 | rem1 ) != 0 );
|
3050 |
} |
3051 |
return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); |
3052 |
|
3053 |
} |
3054 |
|
3055 |
/*----------------------------------------------------------------------------
|
3056 |
| Returns the binary log of the double-precision floating-point value `a'.
|
3057 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
3058 |
| Floating-Point Arithmetic.
|
3059 |
*----------------------------------------------------------------------------*/
|
3060 |
float64 float64_log2( float64 a STATUS_PARAM ) |
3061 |
{ |
3062 |
flag aSign, zSign; |
3063 |
int16 aExp; |
3064 |
bits64 aSig, aSig0, aSig1, zSig, i; |
3065 |
|
3066 |
aSig = extractFloat64Frac( a ); |
3067 |
aExp = extractFloat64Exp( a ); |
3068 |
aSign = extractFloat64Sign( a ); |
3069 |
|
3070 |
if ( aExp == 0 ) { |
3071 |
if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 ); |
3072 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3073 |
} |
3074 |
if ( aSign ) {
|
3075 |
float_raise( float_flag_invalid STATUS_VAR); |
3076 |
return float64_default_nan;
|
3077 |
} |
3078 |
if ( aExp == 0x7FF ) { |
3079 |
if ( aSig ) return propagateFloat64NaN( a, float64_zero STATUS_VAR ); |
3080 |
return a;
|
3081 |
} |
3082 |
|
3083 |
aExp -= 0x3FF;
|
3084 |
aSig |= LIT64( 0x0010000000000000 );
|
3085 |
zSign = aExp < 0;
|
3086 |
zSig = (bits64)aExp << 52;
|
3087 |
for (i = 1LL << 51; i > 0; i >>= 1) { |
3088 |
mul64To128( aSig, aSig, &aSig0, &aSig1 ); |
3089 |
aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 ); |
3090 |
if ( aSig & LIT64( 0x0020000000000000 ) ) { |
3091 |
aSig >>= 1;
|
3092 |
zSig |= i; |
3093 |
} |
3094 |
} |
3095 |
|
3096 |
if ( zSign )
|
3097 |
zSig = -zSig; |
3098 |
return normalizeRoundAndPackFloat64( zSign, 0x408, zSig STATUS_VAR ); |
3099 |
} |
3100 |
|
3101 |
/*----------------------------------------------------------------------------
|
3102 |
| Returns 1 if the double-precision floating-point value `a' is equal to the
|
3103 |
| corresponding value `b', and 0 otherwise. The comparison is performed
|
3104 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3105 |
*----------------------------------------------------------------------------*/
|
3106 |
|
3107 |
int float64_eq( float64 a, float64 b STATUS_PARAM )
|
3108 |
{ |
3109 |
bits64 av, bv; |
3110 |
|
3111 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3112 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
3113 |
) { |
3114 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
3115 |
float_raise( float_flag_invalid STATUS_VAR); |
3116 |
} |
3117 |
return 0; |
3118 |
} |
3119 |
av = float64_val(a); |
3120 |
bv = float64_val(b); |
3121 |
return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 ); |
3122 |
|
3123 |
} |
3124 |
|
3125 |
/*----------------------------------------------------------------------------
|
3126 |
| Returns 1 if the double-precision floating-point value `a' is less than or
|
3127 |
| equal to the corresponding value `b', and 0 otherwise. The comparison is
|
3128 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
3129 |
| Arithmetic.
|
3130 |
*----------------------------------------------------------------------------*/
|
3131 |
|
3132 |
int float64_le( float64 a, float64 b STATUS_PARAM )
|
3133 |
{ |
3134 |
flag aSign, bSign; |
3135 |
bits64 av, bv; |
3136 |
|
3137 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3138 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
3139 |
) { |
3140 |
float_raise( float_flag_invalid STATUS_VAR); |
3141 |
return 0; |
3142 |
} |
3143 |
aSign = extractFloat64Sign( a ); |
3144 |
bSign = extractFloat64Sign( b ); |
3145 |
av = float64_val(a); |
3146 |
bv = float64_val(b); |
3147 |
if ( aSign != bSign ) return aSign || ( (bits64) ( ( av | bv )<<1 ) == 0 ); |
3148 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
3149 |
|
3150 |
} |
3151 |
|
3152 |
/*----------------------------------------------------------------------------
|
3153 |
| Returns 1 if the double-precision floating-point value `a' is less than
|
3154 |
| the corresponding value `b', and 0 otherwise. The comparison is performed
|
3155 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3156 |
*----------------------------------------------------------------------------*/
|
3157 |
|
3158 |
int float64_lt( float64 a, float64 b STATUS_PARAM )
|
3159 |
{ |
3160 |
flag aSign, bSign; |
3161 |
bits64 av, bv; |
3162 |
|
3163 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3164 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
3165 |
) { |
3166 |
float_raise( float_flag_invalid STATUS_VAR); |
3167 |
return 0; |
3168 |
} |
3169 |
aSign = extractFloat64Sign( a ); |
3170 |
bSign = extractFloat64Sign( b ); |
3171 |
av = float64_val(a); |
3172 |
bv = float64_val(b); |
3173 |
if ( aSign != bSign ) return aSign && ( (bits64) ( ( av | bv )<<1 ) != 0 ); |
3174 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
3175 |
|
3176 |
} |
3177 |
|
3178 |
/*----------------------------------------------------------------------------
|
3179 |
| Returns 1 if the double-precision floating-point value `a' is equal to the
|
3180 |
| corresponding value `b', and 0 otherwise. The invalid exception is raised
|
3181 |
| if either operand is a NaN. Otherwise, the comparison is performed
|
3182 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3183 |
*----------------------------------------------------------------------------*/
|
3184 |
|
3185 |
int float64_eq_signaling( float64 a, float64 b STATUS_PARAM )
|
3186 |
{ |
3187 |
bits64 av, bv; |
3188 |
|
3189 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3190 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
3191 |
) { |
3192 |
float_raise( float_flag_invalid STATUS_VAR); |
3193 |
return 0; |
3194 |
} |
3195 |
av = float64_val(a); |
3196 |
bv = float64_val(b); |
3197 |
return ( av == bv ) || ( (bits64) ( ( av | bv )<<1 ) == 0 ); |
3198 |
|
3199 |
} |
3200 |
|
3201 |
/*----------------------------------------------------------------------------
|
3202 |
| Returns 1 if the double-precision floating-point value `a' is less than or
|
3203 |
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
3204 |
| cause an exception. Otherwise, the comparison is performed according to the
|
3205 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3206 |
*----------------------------------------------------------------------------*/
|
3207 |
|
3208 |
int float64_le_quiet( float64 a, float64 b STATUS_PARAM )
|
3209 |
{ |
3210 |
flag aSign, bSign; |
3211 |
bits64 av, bv; |
3212 |
|
3213 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3214 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
3215 |
) { |
3216 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
3217 |
float_raise( float_flag_invalid STATUS_VAR); |
3218 |
} |
3219 |
return 0; |
3220 |
} |
3221 |
aSign = extractFloat64Sign( a ); |
3222 |
bSign = extractFloat64Sign( b ); |
3223 |
av = float64_val(a); |
3224 |
bv = float64_val(b); |
3225 |
if ( aSign != bSign ) return aSign || ( (bits64) ( ( av | bv )<<1 ) == 0 ); |
3226 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
3227 |
|
3228 |
} |
3229 |
|
3230 |
/*----------------------------------------------------------------------------
|
3231 |
| Returns 1 if the double-precision floating-point value `a' is less than
|
3232 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
3233 |
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
3234 |
| Standard for Binary Floating-Point Arithmetic.
|
3235 |
*----------------------------------------------------------------------------*/
|
3236 |
|
3237 |
int float64_lt_quiet( float64 a, float64 b STATUS_PARAM )
|
3238 |
{ |
3239 |
flag aSign, bSign; |
3240 |
bits64 av, bv; |
3241 |
|
3242 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
3243 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
3244 |
) { |
3245 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
3246 |
float_raise( float_flag_invalid STATUS_VAR); |
3247 |
} |
3248 |
return 0; |
3249 |
} |
3250 |
aSign = extractFloat64Sign( a ); |
3251 |
bSign = extractFloat64Sign( b ); |
3252 |
av = float64_val(a); |
3253 |
bv = float64_val(b); |
3254 |
if ( aSign != bSign ) return aSign && ( (bits64) ( ( av | bv )<<1 ) != 0 ); |
3255 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
3256 |
|
3257 |
} |
3258 |
|
3259 |
#ifdef FLOATX80
|
3260 |
|
3261 |
/*----------------------------------------------------------------------------
|
3262 |
| Returns the result of converting the extended double-precision floating-
|
3263 |
| point value `a' to the 32-bit two's complement integer format. The
|
3264 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3265 |
| Floating-Point Arithmetic---which means in particular that the conversion
|
3266 |
| is rounded according to the current rounding mode. If `a' is a NaN, the
|
3267 |
| largest positive integer is returned. Otherwise, if the conversion
|
3268 |
| overflows, the largest integer with the same sign as `a' is returned.
|
3269 |
*----------------------------------------------------------------------------*/
|
3270 |
|
3271 |
int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) |
3272 |
{ |
3273 |
flag aSign; |
3274 |
int32 aExp, shiftCount; |
3275 |
bits64 aSig; |
3276 |
|
3277 |
aSig = extractFloatx80Frac( a ); |
3278 |
aExp = extractFloatx80Exp( a ); |
3279 |
aSign = extractFloatx80Sign( a ); |
3280 |
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; |
3281 |
shiftCount = 0x4037 - aExp;
|
3282 |
if ( shiftCount <= 0 ) shiftCount = 1; |
3283 |
shift64RightJamming( aSig, shiftCount, &aSig ); |
3284 |
return roundAndPackInt32( aSign, aSig STATUS_VAR );
|
3285 |
|
3286 |
} |
3287 |
|
3288 |
/*----------------------------------------------------------------------------
|
3289 |
| Returns the result of converting the extended double-precision floating-
|
3290 |
| point value `a' to the 32-bit two's complement integer format. The
|
3291 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3292 |
| Floating-Point Arithmetic, except that the conversion is always rounded
|
3293 |
| toward zero. If `a' is a NaN, the largest positive integer is returned.
|
3294 |
| Otherwise, if the conversion overflows, the largest integer with the same
|
3295 |
| sign as `a' is returned.
|
3296 |
*----------------------------------------------------------------------------*/
|
3297 |
|
3298 |
int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) |
3299 |
{ |
3300 |
flag aSign; |
3301 |
int32 aExp, shiftCount; |
3302 |
bits64 aSig, savedASig; |
3303 |
int32 z; |
3304 |
|
3305 |
aSig = extractFloatx80Frac( a ); |
3306 |
aExp = extractFloatx80Exp( a ); |
3307 |
aSign = extractFloatx80Sign( a ); |
3308 |
if ( 0x401E < aExp ) { |
3309 |
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; |
3310 |
goto invalid;
|
3311 |
} |
3312 |
else if ( aExp < 0x3FFF ) { |
3313 |
if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
3314 |
return 0; |
3315 |
} |
3316 |
shiftCount = 0x403E - aExp;
|
3317 |
savedASig = aSig; |
3318 |
aSig >>= shiftCount; |
3319 |
z = aSig; |
3320 |
if ( aSign ) z = - z;
|
3321 |
if ( ( z < 0 ) ^ aSign ) { |
3322 |
invalid:
|
3323 |
float_raise( float_flag_invalid STATUS_VAR); |
3324 |
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; |
3325 |
} |
3326 |
if ( ( aSig<<shiftCount ) != savedASig ) {
|
3327 |
STATUS(float_exception_flags) |= float_flag_inexact; |
3328 |
} |
3329 |
return z;
|
3330 |
|
3331 |
} |
3332 |
|
3333 |
/*----------------------------------------------------------------------------
|
3334 |
| Returns the result of converting the extended double-precision floating-
|
3335 |
| point value `a' to the 64-bit two's complement integer format. The
|
3336 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3337 |
| Floating-Point Arithmetic---which means in particular that the conversion
|
3338 |
| is rounded according to the current rounding mode. If `a' is a NaN,
|
3339 |
| the largest positive integer is returned. Otherwise, if the conversion
|
3340 |
| overflows, the largest integer with the same sign as `a' is returned.
|
3341 |
*----------------------------------------------------------------------------*/
|
3342 |
|
3343 |
int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) |
3344 |
{ |
3345 |
flag aSign; |
3346 |
int32 aExp, shiftCount; |
3347 |
bits64 aSig, aSigExtra; |
3348 |
|
3349 |
aSig = extractFloatx80Frac( a ); |
3350 |
aExp = extractFloatx80Exp( a ); |
3351 |
aSign = extractFloatx80Sign( a ); |
3352 |
shiftCount = 0x403E - aExp;
|
3353 |
if ( shiftCount <= 0 ) { |
3354 |
if ( shiftCount ) {
|
3355 |
float_raise( float_flag_invalid STATUS_VAR); |
3356 |
if ( ! aSign
|
3357 |
|| ( ( aExp == 0x7FFF )
|
3358 |
&& ( aSig != LIT64( 0x8000000000000000 ) ) )
|
3359 |
) { |
3360 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
3361 |
} |
3362 |
return (sbits64) LIT64( 0x8000000000000000 ); |
3363 |
} |
3364 |
aSigExtra = 0;
|
3365 |
} |
3366 |
else {
|
3367 |
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
|
3368 |
} |
3369 |
return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
|
3370 |
|
3371 |
} |
3372 |
|
3373 |
/*----------------------------------------------------------------------------
|
3374 |
| Returns the result of converting the extended double-precision floating-
|
3375 |
| point value `a' to the 64-bit two's complement integer format. The
|
3376 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3377 |
| Floating-Point Arithmetic, except that the conversion is always rounded
|
3378 |
| toward zero. If `a' is a NaN, the largest positive integer is returned.
|
3379 |
| Otherwise, if the conversion overflows, the largest integer with the same
|
3380 |
| sign as `a' is returned.
|
3381 |
*----------------------------------------------------------------------------*/
|
3382 |
|
3383 |
int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) |
3384 |
{ |
3385 |
flag aSign; |
3386 |
int32 aExp, shiftCount; |
3387 |
bits64 aSig; |
3388 |
int64 z; |
3389 |
|
3390 |
aSig = extractFloatx80Frac( a ); |
3391 |
aExp = extractFloatx80Exp( a ); |
3392 |
aSign = extractFloatx80Sign( a ); |
3393 |
shiftCount = aExp - 0x403E;
|
3394 |
if ( 0 <= shiftCount ) { |
3395 |
aSig &= LIT64( 0x7FFFFFFFFFFFFFFF );
|
3396 |
if ( ( a.high != 0xC03E ) || aSig ) { |
3397 |
float_raise( float_flag_invalid STATUS_VAR); |
3398 |
if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { |
3399 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
3400 |
} |
3401 |
} |
3402 |
return (sbits64) LIT64( 0x8000000000000000 ); |
3403 |
} |
3404 |
else if ( aExp < 0x3FFF ) { |
3405 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
3406 |
return 0; |
3407 |
} |
3408 |
z = aSig>>( - shiftCount ); |
3409 |
if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { |
3410 |
STATUS(float_exception_flags) |= float_flag_inexact; |
3411 |
} |
3412 |
if ( aSign ) z = - z;
|
3413 |
return z;
|
3414 |
|
3415 |
} |
3416 |
|
3417 |
/*----------------------------------------------------------------------------
|
3418 |
| Returns the result of converting the extended double-precision floating-
|
3419 |
| point value `a' to the single-precision floating-point format. The
|
3420 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3421 |
| Floating-Point Arithmetic.
|
3422 |
*----------------------------------------------------------------------------*/
|
3423 |
|
3424 |
float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) |
3425 |
{ |
3426 |
flag aSign; |
3427 |
int32 aExp; |
3428 |
bits64 aSig; |
3429 |
|
3430 |
aSig = extractFloatx80Frac( a ); |
3431 |
aExp = extractFloatx80Exp( a ); |
3432 |
aSign = extractFloatx80Sign( a ); |
3433 |
if ( aExp == 0x7FFF ) { |
3434 |
if ( (bits64) ( aSig<<1 ) ) { |
3435 |
return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) );
|
3436 |
} |
3437 |
return packFloat32( aSign, 0xFF, 0 ); |
3438 |
} |
3439 |
shift64RightJamming( aSig, 33, &aSig );
|
3440 |
if ( aExp || aSig ) aExp -= 0x3F81; |
3441 |
return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
|
3442 |
|
3443 |
} |
3444 |
|
3445 |
/*----------------------------------------------------------------------------
|
3446 |
| Returns the result of converting the extended double-precision floating-
|
3447 |
| point value `a' to the double-precision floating-point format. The
|
3448 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3449 |
| Floating-Point Arithmetic.
|
3450 |
*----------------------------------------------------------------------------*/
|
3451 |
|
3452 |
float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) |
3453 |
{ |
3454 |
flag aSign; |
3455 |
int32 aExp; |
3456 |
bits64 aSig, zSig; |
3457 |
|
3458 |
aSig = extractFloatx80Frac( a ); |
3459 |
aExp = extractFloatx80Exp( a ); |
3460 |
aSign = extractFloatx80Sign( a ); |
3461 |
if ( aExp == 0x7FFF ) { |
3462 |
if ( (bits64) ( aSig<<1 ) ) { |
3463 |
return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) );
|
3464 |
} |
3465 |
return packFloat64( aSign, 0x7FF, 0 ); |
3466 |
} |
3467 |
shift64RightJamming( aSig, 1, &zSig );
|
3468 |
if ( aExp || aSig ) aExp -= 0x3C01; |
3469 |
return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR );
|
3470 |
|
3471 |
} |
3472 |
|
3473 |
#ifdef FLOAT128
|
3474 |
|
3475 |
/*----------------------------------------------------------------------------
|
3476 |
| Returns the result of converting the extended double-precision floating-
|
3477 |
| point value `a' to the quadruple-precision floating-point format. The
|
3478 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
3479 |
| Floating-Point Arithmetic.
|
3480 |
*----------------------------------------------------------------------------*/
|
3481 |
|
3482 |
float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) |
3483 |
{ |
3484 |
flag aSign; |
3485 |
int16 aExp; |
3486 |
bits64 aSig, zSig0, zSig1; |
3487 |
|
3488 |
aSig = extractFloatx80Frac( a ); |
3489 |
aExp = extractFloatx80Exp( a ); |
3490 |
aSign = extractFloatx80Sign( a ); |
3491 |
if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) { |
3492 |
return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) );
|
3493 |
} |
3494 |
shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); |
3495 |
return packFloat128( aSign, aExp, zSig0, zSig1 );
|
3496 |
|
3497 |
} |
3498 |
|
3499 |
#endif
|
3500 |
|
3501 |
/*----------------------------------------------------------------------------
|
3502 |
| Rounds the extended double-precision floating-point value `a' to an integer,
|
3503 |
| and returns the result as an extended quadruple-precision floating-point
|
3504 |
| value. The operation is performed according to the IEC/IEEE Standard for
|
3505 |
| Binary Floating-Point Arithmetic.
|
3506 |
*----------------------------------------------------------------------------*/
|
3507 |
|
3508 |
floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) |
3509 |
{ |
3510 |
flag aSign; |
3511 |
int32 aExp; |
3512 |
bits64 lastBitMask, roundBitsMask; |
3513 |
int8 roundingMode; |
3514 |
floatx80 z; |
3515 |
|
3516 |
aExp = extractFloatx80Exp( a ); |
3517 |
if ( 0x403E <= aExp ) { |
3518 |
if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) { |
3519 |
return propagateFloatx80NaN( a, a STATUS_VAR );
|
3520 |
} |
3521 |
return a;
|
3522 |
} |
3523 |
if ( aExp < 0x3FFF ) { |
3524 |
if ( ( aExp == 0 ) |
3525 |
&& ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { |
3526 |
return a;
|
3527 |
} |
3528 |
STATUS(float_exception_flags) |= float_flag_inexact; |
3529 |
aSign = extractFloatx80Sign( a ); |
3530 |
switch ( STATUS(float_rounding_mode) ) {
|
3531 |
case float_round_nearest_even:
|
3532 |
if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 ) |
3533 |
) { |
3534 |
return
|
3535 |
packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); |
3536 |
} |
3537 |
break;
|
3538 |
case float_round_down:
|
3539 |
return
|
3540 |
aSign ? |
3541 |
packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) |
3542 |
: packFloatx80( 0, 0, 0 ); |
3543 |
case float_round_up:
|
3544 |
return
|
3545 |
aSign ? packFloatx80( 1, 0, 0 ) |
3546 |
: packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); |
3547 |
} |
3548 |
return packFloatx80( aSign, 0, 0 ); |
3549 |
} |
3550 |
lastBitMask = 1;
|
3551 |
lastBitMask <<= 0x403E - aExp;
|
3552 |
roundBitsMask = lastBitMask - 1;
|
3553 |
z = a; |
3554 |
roundingMode = STATUS(float_rounding_mode); |
3555 |
if ( roundingMode == float_round_nearest_even ) {
|
3556 |
z.low += lastBitMask>>1;
|
3557 |
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; |
3558 |
} |
3559 |
else if ( roundingMode != float_round_to_zero ) { |
3560 |
if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
3561 |
z.low += roundBitsMask; |
3562 |
} |
3563 |
} |
3564 |
z.low &= ~ roundBitsMask; |
3565 |
if ( z.low == 0 ) { |
3566 |
++z.high; |
3567 |
z.low = LIT64( 0x8000000000000000 );
|
3568 |
} |
3569 |
if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact;
|
3570 |
return z;
|
3571 |
|
3572 |
} |
3573 |
|
3574 |
/*----------------------------------------------------------------------------
|
3575 |
| Returns the result of adding the absolute values of the extended double-
|
3576 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the sum is
|
3577 |
| negated before being returned. `zSign' is ignored if the result is a NaN.
|
3578 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
3579 |
| Floating-Point Arithmetic.
|
3580 |
*----------------------------------------------------------------------------*/
|
3581 |
|
3582 |
static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM)
|
3583 |
{ |
3584 |
int32 aExp, bExp, zExp; |
3585 |
bits64 aSig, bSig, zSig0, zSig1; |
3586 |
int32 expDiff; |
3587 |
|
3588 |
aSig = extractFloatx80Frac( a ); |
3589 |
aExp = extractFloatx80Exp( a ); |
3590 |
bSig = extractFloatx80Frac( b ); |
3591 |
bExp = extractFloatx80Exp( b ); |
3592 |
expDiff = aExp - bExp; |
3593 |
if ( 0 < expDiff ) { |
3594 |
if ( aExp == 0x7FFF ) { |
3595 |
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3596 |
return a;
|
3597 |
} |
3598 |
if ( bExp == 0 ) --expDiff; |
3599 |
shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
3600 |
zExp = aExp; |
3601 |
} |
3602 |
else if ( expDiff < 0 ) { |
3603 |
if ( bExp == 0x7FFF ) { |
3604 |
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3605 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3606 |
} |
3607 |
if ( aExp == 0 ) ++expDiff; |
3608 |
shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
3609 |
zExp = bExp; |
3610 |
} |
3611 |
else {
|
3612 |
if ( aExp == 0x7FFF ) { |
3613 |
if ( (bits64) ( ( aSig | bSig )<<1 ) ) { |
3614 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
3615 |
} |
3616 |
return a;
|
3617 |
} |
3618 |
zSig1 = 0;
|
3619 |
zSig0 = aSig + bSig; |
3620 |
if ( aExp == 0 ) { |
3621 |
normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); |
3622 |
goto roundAndPack;
|
3623 |
} |
3624 |
zExp = aExp; |
3625 |
goto shiftRight1;
|
3626 |
} |
3627 |
zSig0 = aSig + bSig; |
3628 |
if ( (sbits64) zSig0 < 0 ) goto roundAndPack; |
3629 |
shiftRight1:
|
3630 |
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
3631 |
zSig0 |= LIT64( 0x8000000000000000 );
|
3632 |
++zExp; |
3633 |
roundAndPack:
|
3634 |
return
|
3635 |
roundAndPackFloatx80( |
3636 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
3637 |
|
3638 |
} |
3639 |
|
3640 |
/*----------------------------------------------------------------------------
|
3641 |
| Returns the result of subtracting the absolute values of the extended
|
3642 |
| double-precision floating-point values `a' and `b'. If `zSign' is 1, the
|
3643 |
| difference is negated before being returned. `zSign' is ignored if the
|
3644 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
3645 |
| Standard for Binary Floating-Point Arithmetic.
|
3646 |
*----------------------------------------------------------------------------*/
|
3647 |
|
3648 |
static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM )
|
3649 |
{ |
3650 |
int32 aExp, bExp, zExp; |
3651 |
bits64 aSig, bSig, zSig0, zSig1; |
3652 |
int32 expDiff; |
3653 |
floatx80 z; |
3654 |
|
3655 |
aSig = extractFloatx80Frac( a ); |
3656 |
aExp = extractFloatx80Exp( a ); |
3657 |
bSig = extractFloatx80Frac( b ); |
3658 |
bExp = extractFloatx80Exp( b ); |
3659 |
expDiff = aExp - bExp; |
3660 |
if ( 0 < expDiff ) goto aExpBigger; |
3661 |
if ( expDiff < 0 ) goto bExpBigger; |
3662 |
if ( aExp == 0x7FFF ) { |
3663 |
if ( (bits64) ( ( aSig | bSig )<<1 ) ) { |
3664 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
3665 |
} |
3666 |
float_raise( float_flag_invalid STATUS_VAR); |
3667 |
z.low = floatx80_default_nan_low; |
3668 |
z.high = floatx80_default_nan_high; |
3669 |
return z;
|
3670 |
} |
3671 |
if ( aExp == 0 ) { |
3672 |
aExp = 1;
|
3673 |
bExp = 1;
|
3674 |
} |
3675 |
zSig1 = 0;
|
3676 |
if ( bSig < aSig ) goto aBigger; |
3677 |
if ( aSig < bSig ) goto bBigger; |
3678 |
return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
3679 |
bExpBigger:
|
3680 |
if ( bExp == 0x7FFF ) { |
3681 |
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3682 |
return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3683 |
} |
3684 |
if ( aExp == 0 ) ++expDiff; |
3685 |
shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
3686 |
bBigger:
|
3687 |
sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
|
3688 |
zExp = bExp; |
3689 |
zSign ^= 1;
|
3690 |
goto normalizeRoundAndPack;
|
3691 |
aExpBigger:
|
3692 |
if ( aExp == 0x7FFF ) { |
3693 |
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3694 |
return a;
|
3695 |
} |
3696 |
if ( bExp == 0 ) --expDiff; |
3697 |
shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
3698 |
aBigger:
|
3699 |
sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
|
3700 |
zExp = aExp; |
3701 |
normalizeRoundAndPack:
|
3702 |
return
|
3703 |
normalizeRoundAndPackFloatx80( |
3704 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
3705 |
|
3706 |
} |
3707 |
|
3708 |
/*----------------------------------------------------------------------------
|
3709 |
| Returns the result of adding the extended double-precision floating-point
|
3710 |
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
3711 |
| Standard for Binary Floating-Point Arithmetic.
|
3712 |
*----------------------------------------------------------------------------*/
|
3713 |
|
3714 |
floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) |
3715 |
{ |
3716 |
flag aSign, bSign; |
3717 |
|
3718 |
aSign = extractFloatx80Sign( a ); |
3719 |
bSign = extractFloatx80Sign( b ); |
3720 |
if ( aSign == bSign ) {
|
3721 |
return addFloatx80Sigs( a, b, aSign STATUS_VAR );
|
3722 |
} |
3723 |
else {
|
3724 |
return subFloatx80Sigs( a, b, aSign STATUS_VAR );
|
3725 |
} |
3726 |
|
3727 |
} |
3728 |
|
3729 |
/*----------------------------------------------------------------------------
|
3730 |
| Returns the result of subtracting the extended double-precision floating-
|
3731 |
| point values `a' and `b'. The operation is performed according to the
|
3732 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3733 |
*----------------------------------------------------------------------------*/
|
3734 |
|
3735 |
floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) |
3736 |
{ |
3737 |
flag aSign, bSign; |
3738 |
|
3739 |
aSign = extractFloatx80Sign( a ); |
3740 |
bSign = extractFloatx80Sign( b ); |
3741 |
if ( aSign == bSign ) {
|
3742 |
return subFloatx80Sigs( a, b, aSign STATUS_VAR );
|
3743 |
} |
3744 |
else {
|
3745 |
return addFloatx80Sigs( a, b, aSign STATUS_VAR );
|
3746 |
} |
3747 |
|
3748 |
} |
3749 |
|
3750 |
/*----------------------------------------------------------------------------
|
3751 |
| Returns the result of multiplying the extended double-precision floating-
|
3752 |
| point values `a' and `b'. The operation is performed according to the
|
3753 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3754 |
*----------------------------------------------------------------------------*/
|
3755 |
|
3756 |
floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) |
3757 |
{ |
3758 |
flag aSign, bSign, zSign; |
3759 |
int32 aExp, bExp, zExp; |
3760 |
bits64 aSig, bSig, zSig0, zSig1; |
3761 |
floatx80 z; |
3762 |
|
3763 |
aSig = extractFloatx80Frac( a ); |
3764 |
aExp = extractFloatx80Exp( a ); |
3765 |
aSign = extractFloatx80Sign( a ); |
3766 |
bSig = extractFloatx80Frac( b ); |
3767 |
bExp = extractFloatx80Exp( b ); |
3768 |
bSign = extractFloatx80Sign( b ); |
3769 |
zSign = aSign ^ bSign; |
3770 |
if ( aExp == 0x7FFF ) { |
3771 |
if ( (bits64) ( aSig<<1 ) |
3772 |
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { |
3773 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
3774 |
} |
3775 |
if ( ( bExp | bSig ) == 0 ) goto invalid; |
3776 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3777 |
} |
3778 |
if ( bExp == 0x7FFF ) { |
3779 |
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3780 |
if ( ( aExp | aSig ) == 0 ) { |
3781 |
invalid:
|
3782 |
float_raise( float_flag_invalid STATUS_VAR); |
3783 |
z.low = floatx80_default_nan_low; |
3784 |
z.high = floatx80_default_nan_high; |
3785 |
return z;
|
3786 |
} |
3787 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3788 |
} |
3789 |
if ( aExp == 0 ) { |
3790 |
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
3791 |
normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); |
3792 |
} |
3793 |
if ( bExp == 0 ) { |
3794 |
if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
3795 |
normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
3796 |
} |
3797 |
zExp = aExp + bExp - 0x3FFE;
|
3798 |
mul64To128( aSig, bSig, &zSig0, &zSig1 ); |
3799 |
if ( 0 < (sbits64) zSig0 ) { |
3800 |
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
3801 |
--zExp; |
3802 |
} |
3803 |
return
|
3804 |
roundAndPackFloatx80( |
3805 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
3806 |
|
3807 |
} |
3808 |
|
3809 |
/*----------------------------------------------------------------------------
|
3810 |
| Returns the result of dividing the extended double-precision floating-point
|
3811 |
| value `a' by the corresponding value `b'. The operation is performed
|
3812 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3813 |
*----------------------------------------------------------------------------*/
|
3814 |
|
3815 |
floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) |
3816 |
{ |
3817 |
flag aSign, bSign, zSign; |
3818 |
int32 aExp, bExp, zExp; |
3819 |
bits64 aSig, bSig, zSig0, zSig1; |
3820 |
bits64 rem0, rem1, rem2, term0, term1, term2; |
3821 |
floatx80 z; |
3822 |
|
3823 |
aSig = extractFloatx80Frac( a ); |
3824 |
aExp = extractFloatx80Exp( a ); |
3825 |
aSign = extractFloatx80Sign( a ); |
3826 |
bSig = extractFloatx80Frac( b ); |
3827 |
bExp = extractFloatx80Exp( b ); |
3828 |
bSign = extractFloatx80Sign( b ); |
3829 |
zSign = aSign ^ bSign; |
3830 |
if ( aExp == 0x7FFF ) { |
3831 |
if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3832 |
if ( bExp == 0x7FFF ) { |
3833 |
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3834 |
goto invalid;
|
3835 |
} |
3836 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3837 |
} |
3838 |
if ( bExp == 0x7FFF ) { |
3839 |
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3840 |
return packFloatx80( zSign, 0, 0 ); |
3841 |
} |
3842 |
if ( bExp == 0 ) { |
3843 |
if ( bSig == 0 ) { |
3844 |
if ( ( aExp | aSig ) == 0 ) { |
3845 |
invalid:
|
3846 |
float_raise( float_flag_invalid STATUS_VAR); |
3847 |
z.low = floatx80_default_nan_low; |
3848 |
z.high = floatx80_default_nan_high; |
3849 |
return z;
|
3850 |
} |
3851 |
float_raise( float_flag_divbyzero STATUS_VAR); |
3852 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3853 |
} |
3854 |
normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
3855 |
} |
3856 |
if ( aExp == 0 ) { |
3857 |
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
3858 |
normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); |
3859 |
} |
3860 |
zExp = aExp - bExp + 0x3FFE;
|
3861 |
rem1 = 0;
|
3862 |
if ( bSig <= aSig ) {
|
3863 |
shift128Right( aSig, 0, 1, &aSig, &rem1 ); |
3864 |
++zExp; |
3865 |
} |
3866 |
zSig0 = estimateDiv128To64( aSig, rem1, bSig ); |
3867 |
mul64To128( bSig, zSig0, &term0, &term1 ); |
3868 |
sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); |
3869 |
while ( (sbits64) rem0 < 0 ) { |
3870 |
--zSig0; |
3871 |
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
3872 |
} |
3873 |
zSig1 = estimateDiv128To64( rem1, 0, bSig );
|
3874 |
if ( (bits64) ( zSig1<<1 ) <= 8 ) { |
3875 |
mul64To128( bSig, zSig1, &term1, &term2 ); |
3876 |
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
3877 |
while ( (sbits64) rem1 < 0 ) { |
3878 |
--zSig1; |
3879 |
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
|
3880 |
} |
3881 |
zSig1 |= ( ( rem1 | rem2 ) != 0 );
|
3882 |
} |
3883 |
return
|
3884 |
roundAndPackFloatx80( |
3885 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
3886 |
|
3887 |
} |
3888 |
|
3889 |
/*----------------------------------------------------------------------------
|
3890 |
| Returns the remainder of the extended double-precision floating-point value
|
3891 |
| `a' with respect to the corresponding value `b'. The operation is performed
|
3892 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3893 |
*----------------------------------------------------------------------------*/
|
3894 |
|
3895 |
floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) |
3896 |
{ |
3897 |
flag aSign, bSign, zSign; |
3898 |
int32 aExp, bExp, expDiff; |
3899 |
bits64 aSig0, aSig1, bSig; |
3900 |
bits64 q, term0, term1, alternateASig0, alternateASig1; |
3901 |
floatx80 z; |
3902 |
|
3903 |
aSig0 = extractFloatx80Frac( a ); |
3904 |
aExp = extractFloatx80Exp( a ); |
3905 |
aSign = extractFloatx80Sign( a ); |
3906 |
bSig = extractFloatx80Frac( b ); |
3907 |
bExp = extractFloatx80Exp( b ); |
3908 |
bSign = extractFloatx80Sign( b ); |
3909 |
if ( aExp == 0x7FFF ) { |
3910 |
if ( (bits64) ( aSig0<<1 ) |
3911 |
|| ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { |
3912 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
3913 |
} |
3914 |
goto invalid;
|
3915 |
} |
3916 |
if ( bExp == 0x7FFF ) { |
3917 |
if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
3918 |
return a;
|
3919 |
} |
3920 |
if ( bExp == 0 ) { |
3921 |
if ( bSig == 0 ) { |
3922 |
invalid:
|
3923 |
float_raise( float_flag_invalid STATUS_VAR); |
3924 |
z.low = floatx80_default_nan_low; |
3925 |
z.high = floatx80_default_nan_high; |
3926 |
return z;
|
3927 |
} |
3928 |
normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
3929 |
} |
3930 |
if ( aExp == 0 ) { |
3931 |
if ( (bits64) ( aSig0<<1 ) == 0 ) return a; |
3932 |
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
3933 |
} |
3934 |
bSig |= LIT64( 0x8000000000000000 );
|
3935 |
zSign = aSign; |
3936 |
expDiff = aExp - bExp; |
3937 |
aSig1 = 0;
|
3938 |
if ( expDiff < 0 ) { |
3939 |
if ( expDiff < -1 ) return a; |
3940 |
shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); |
3941 |
expDiff = 0;
|
3942 |
} |
3943 |
q = ( bSig <= aSig0 ); |
3944 |
if ( q ) aSig0 -= bSig;
|
3945 |
expDiff -= 64;
|
3946 |
while ( 0 < expDiff ) { |
3947 |
q = estimateDiv128To64( aSig0, aSig1, bSig ); |
3948 |
q = ( 2 < q ) ? q - 2 : 0; |
3949 |
mul64To128( bSig, q, &term0, &term1 ); |
3950 |
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
3951 |
shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
|
3952 |
expDiff -= 62;
|
3953 |
} |
3954 |
expDiff += 64;
|
3955 |
if ( 0 < expDiff ) { |
3956 |
q = estimateDiv128To64( aSig0, aSig1, bSig ); |
3957 |
q = ( 2 < q ) ? q - 2 : 0; |
3958 |
q >>= 64 - expDiff;
|
3959 |
mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
|
3960 |
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
3961 |
shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); |
3962 |
while ( le128( term0, term1, aSig0, aSig1 ) ) {
|
3963 |
++q; |
3964 |
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
3965 |
} |
3966 |
} |
3967 |
else {
|
3968 |
term1 = 0;
|
3969 |
term0 = bSig; |
3970 |
} |
3971 |
sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); |
3972 |
if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
3973 |
|| ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) |
3974 |
&& ( q & 1 ) )
|
3975 |
) { |
3976 |
aSig0 = alternateASig0; |
3977 |
aSig1 = alternateASig1; |
3978 |
zSign = ! zSign; |
3979 |
} |
3980 |
return
|
3981 |
normalizeRoundAndPackFloatx80( |
3982 |
80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR );
|
3983 |
|
3984 |
} |
3985 |
|
3986 |
/*----------------------------------------------------------------------------
|
3987 |
| Returns the square root of the extended double-precision floating-point
|
3988 |
| value `a'. The operation is performed according to the IEC/IEEE Standard
|
3989 |
| for Binary Floating-Point Arithmetic.
|
3990 |
*----------------------------------------------------------------------------*/
|
3991 |
|
3992 |
floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) |
3993 |
{ |
3994 |
flag aSign; |
3995 |
int32 aExp, zExp; |
3996 |
bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0; |
3997 |
bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
3998 |
floatx80 z; |
3999 |
|
4000 |
aSig0 = extractFloatx80Frac( a ); |
4001 |
aExp = extractFloatx80Exp( a ); |
4002 |
aSign = extractFloatx80Sign( a ); |
4003 |
if ( aExp == 0x7FFF ) { |
4004 |
if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); |
4005 |
if ( ! aSign ) return a; |
4006 |
goto invalid;
|
4007 |
} |
4008 |
if ( aSign ) {
|
4009 |
if ( ( aExp | aSig0 ) == 0 ) return a; |
4010 |
invalid:
|
4011 |
float_raise( float_flag_invalid STATUS_VAR); |
4012 |
z.low = floatx80_default_nan_low; |
4013 |
z.high = floatx80_default_nan_high; |
4014 |
return z;
|
4015 |
} |
4016 |
if ( aExp == 0 ) { |
4017 |
if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); |
4018 |
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
4019 |
} |
4020 |
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; |
4021 |
zSig0 = estimateSqrt32( aExp, aSig0>>32 );
|
4022 |
shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); |
4023 |
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); |
4024 |
doubleZSig0 = zSig0<<1;
|
4025 |
mul64To128( zSig0, zSig0, &term0, &term1 ); |
4026 |
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); |
4027 |
while ( (sbits64) rem0 < 0 ) { |
4028 |
--zSig0; |
4029 |
doubleZSig0 -= 2;
|
4030 |
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); |
4031 |
} |
4032 |
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
4033 |
if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { |
4034 |
if ( zSig1 == 0 ) zSig1 = 1; |
4035 |
mul64To128( doubleZSig0, zSig1, &term1, &term2 ); |
4036 |
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
4037 |
mul64To128( zSig1, zSig1, &term2, &term3 ); |
4038 |
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); |
4039 |
while ( (sbits64) rem1 < 0 ) { |
4040 |
--zSig1; |
4041 |
shortShift128Left( 0, zSig1, 1, &term2, &term3 ); |
4042 |
term3 |= 1;
|
4043 |
term2 |= doubleZSig0; |
4044 |
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
4045 |
} |
4046 |
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
4047 |
} |
4048 |
shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); |
4049 |
zSig0 |= doubleZSig0; |
4050 |
return
|
4051 |
roundAndPackFloatx80( |
4052 |
STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR );
|
4053 |
|
4054 |
} |
4055 |
|
4056 |
/*----------------------------------------------------------------------------
|
4057 |
| Returns 1 if the extended double-precision floating-point value `a' is
|
4058 |
| equal to the corresponding value `b', and 0 otherwise. The comparison is
|
4059 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4060 |
| Arithmetic.
|
4061 |
*----------------------------------------------------------------------------*/
|
4062 |
|
4063 |
int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
|
4064 |
{ |
4065 |
|
4066 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
4067 |
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
4068 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
4069 |
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
4070 |
) { |
4071 |
if ( floatx80_is_signaling_nan( a )
|
4072 |
|| floatx80_is_signaling_nan( b ) ) { |
4073 |
float_raise( float_flag_invalid STATUS_VAR); |
4074 |
} |
4075 |
return 0; |
4076 |
} |
4077 |
return
|
4078 |
( a.low == b.low ) |
4079 |
&& ( ( a.high == b.high ) |
4080 |
|| ( ( a.low == 0 )
|
4081 |
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) |
4082 |
); |
4083 |
|
4084 |
} |
4085 |
|
4086 |
/*----------------------------------------------------------------------------
|
4087 |
| Returns 1 if the extended double-precision floating-point value `a' is
|
4088 |
| less than or equal to the corresponding value `b', and 0 otherwise. The
|
4089 |
| comparison is performed according to the IEC/IEEE Standard for Binary
|
4090 |
| Floating-Point Arithmetic.
|
4091 |
*----------------------------------------------------------------------------*/
|
4092 |
|
4093 |
int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
|
4094 |
{ |
4095 |
flag aSign, bSign; |
4096 |
|
4097 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
4098 |
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
4099 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
4100 |
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
4101 |
) { |
4102 |
float_raise( float_flag_invalid STATUS_VAR); |
4103 |
return 0; |
4104 |
} |
4105 |
aSign = extractFloatx80Sign( a ); |
4106 |
bSign = extractFloatx80Sign( b ); |
4107 |
if ( aSign != bSign ) {
|
4108 |
return
|
4109 |
aSign |
4110 |
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
4111 |
== 0 );
|
4112 |
} |
4113 |
return
|
4114 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
4115 |
: le128( a.high, a.low, b.high, b.low ); |
4116 |
|
4117 |
} |
4118 |
|
4119 |
/*----------------------------------------------------------------------------
|
4120 |
| Returns 1 if the extended double-precision floating-point value `a' is
|
4121 |
| less than the corresponding value `b', and 0 otherwise. The comparison
|
4122 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4123 |
| Arithmetic.
|
4124 |
*----------------------------------------------------------------------------*/
|
4125 |
|
4126 |
int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
|
4127 |
{ |
4128 |
flag aSign, bSign; |
4129 |
|
4130 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
4131 |
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
4132 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
4133 |
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
4134 |
) { |
4135 |
float_raise( float_flag_invalid STATUS_VAR); |
4136 |
return 0; |
4137 |
} |
4138 |
aSign = extractFloatx80Sign( a ); |
4139 |
bSign = extractFloatx80Sign( b ); |
4140 |
if ( aSign != bSign ) {
|
4141 |
return
|
4142 |
aSign |
4143 |
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
4144 |
!= 0 );
|
4145 |
} |
4146 |
return
|
4147 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
4148 |
: lt128( a.high, a.low, b.high, b.low ); |
4149 |
|
4150 |
} |
4151 |
|
4152 |
/*----------------------------------------------------------------------------
|
4153 |
| Returns 1 if the extended double-precision floating-point value `a' is equal
|
4154 |
| to the corresponding value `b', and 0 otherwise. The invalid exception is
|
4155 |
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
4156 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4157 |
*----------------------------------------------------------------------------*/
|
4158 |
|
4159 |
int floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM )
|
4160 |
{ |
4161 |
|
4162 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
4163 |
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
4164 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
4165 |
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
4166 |
) { |
4167 |
float_raise( float_flag_invalid STATUS_VAR); |
4168 |
return 0; |
4169 |
} |
4170 |
return
|
4171 |
( a.low == b.low ) |
4172 |
&& ( ( a.high == b.high ) |
4173 |
|| ( ( a.low == 0 )
|
4174 |
&& ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) |
4175 |
); |
4176 |
|
4177 |
} |
4178 |
|
4179 |
/*----------------------------------------------------------------------------
|
4180 |
| Returns 1 if the extended double-precision floating-point value `a' is less
|
4181 |
| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs
|
4182 |
| do not cause an exception. Otherwise, the comparison is performed according
|
4183 |
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4184 |
*----------------------------------------------------------------------------*/
|
4185 |
|
4186 |
int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
4187 |
{ |
4188 |
flag aSign, bSign; |
4189 |
|
4190 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
4191 |
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
4192 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
4193 |
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
4194 |
) { |
4195 |
if ( floatx80_is_signaling_nan( a )
|
4196 |
|| floatx80_is_signaling_nan( b ) ) { |
4197 |
float_raise( float_flag_invalid STATUS_VAR); |
4198 |
} |
4199 |
return 0; |
4200 |
} |
4201 |
aSign = extractFloatx80Sign( a ); |
4202 |
bSign = extractFloatx80Sign( b ); |
4203 |
if ( aSign != bSign ) {
|
4204 |
return
|
4205 |
aSign |
4206 |
|| ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
4207 |
== 0 );
|
4208 |
} |
4209 |
return
|
4210 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
4211 |
: le128( a.high, a.low, b.high, b.low ); |
4212 |
|
4213 |
} |
4214 |
|
4215 |
/*----------------------------------------------------------------------------
|
4216 |
| Returns 1 if the extended double-precision floating-point value `a' is less
|
4217 |
| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
|
4218 |
| an exception. Otherwise, the comparison is performed according to the
|
4219 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4220 |
*----------------------------------------------------------------------------*/
|
4221 |
|
4222 |
int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
4223 |
{ |
4224 |
flag aSign, bSign; |
4225 |
|
4226 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
4227 |
&& (bits64) ( extractFloatx80Frac( a )<<1 ) )
|
4228 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
4229 |
&& (bits64) ( extractFloatx80Frac( b )<<1 ) )
|
4230 |
) { |
4231 |
if ( floatx80_is_signaling_nan( a )
|
4232 |
|| floatx80_is_signaling_nan( b ) ) { |
4233 |
float_raise( float_flag_invalid STATUS_VAR); |
4234 |
} |
4235 |
return 0; |
4236 |
} |
4237 |
aSign = extractFloatx80Sign( a ); |
4238 |
bSign = extractFloatx80Sign( b ); |
4239 |
if ( aSign != bSign ) {
|
4240 |
return
|
4241 |
aSign |
4242 |
&& ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
4243 |
!= 0 );
|
4244 |
} |
4245 |
return
|
4246 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
4247 |
: lt128( a.high, a.low, b.high, b.low ); |
4248 |
|
4249 |
} |
4250 |
|
4251 |
#endif
|
4252 |
|
4253 |
#ifdef FLOAT128
|
4254 |
|
4255 |
/*----------------------------------------------------------------------------
|
4256 |
| Returns the result of converting the quadruple-precision floating-point
|
4257 |
| value `a' to the 32-bit two's complement integer format. The conversion
|
4258 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4259 |
| Arithmetic---which means in particular that the conversion is rounded
|
4260 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
4261 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
4262 |
| largest integer with the same sign as `a' is returned.
|
4263 |
*----------------------------------------------------------------------------*/
|
4264 |
|
4265 |
int32 float128_to_int32( float128 a STATUS_PARAM ) |
4266 |
{ |
4267 |
flag aSign; |
4268 |
int32 aExp, shiftCount; |
4269 |
bits64 aSig0, aSig1; |
4270 |
|
4271 |
aSig1 = extractFloat128Frac1( a ); |
4272 |
aSig0 = extractFloat128Frac0( a ); |
4273 |
aExp = extractFloat128Exp( a ); |
4274 |
aSign = extractFloat128Sign( a ); |
4275 |
if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; |
4276 |
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
4277 |
aSig0 |= ( aSig1 != 0 );
|
4278 |
shiftCount = 0x4028 - aExp;
|
4279 |
if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); |
4280 |
return roundAndPackInt32( aSign, aSig0 STATUS_VAR );
|
4281 |
|
4282 |
} |
4283 |
|
4284 |
/*----------------------------------------------------------------------------
|
4285 |
| Returns the result of converting the quadruple-precision floating-point
|
4286 |
| value `a' to the 32-bit two's complement integer format. The conversion
|
4287 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4288 |
| Arithmetic, except that the conversion is always rounded toward zero. If
|
4289 |
| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
4290 |
| conversion overflows, the largest integer with the same sign as `a' is
|
4291 |
| returned.
|
4292 |
*----------------------------------------------------------------------------*/
|
4293 |
|
4294 |
int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) |
4295 |
{ |
4296 |
flag aSign; |
4297 |
int32 aExp, shiftCount; |
4298 |
bits64 aSig0, aSig1, savedASig; |
4299 |
int32 z; |
4300 |
|
4301 |
aSig1 = extractFloat128Frac1( a ); |
4302 |
aSig0 = extractFloat128Frac0( a ); |
4303 |
aExp = extractFloat128Exp( a ); |
4304 |
aSign = extractFloat128Sign( a ); |
4305 |
aSig0 |= ( aSig1 != 0 );
|
4306 |
if ( 0x401E < aExp ) { |
4307 |
if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; |
4308 |
goto invalid;
|
4309 |
} |
4310 |
else if ( aExp < 0x3FFF ) { |
4311 |
if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
4312 |
return 0; |
4313 |
} |
4314 |
aSig0 |= LIT64( 0x0001000000000000 );
|
4315 |
shiftCount = 0x402F - aExp;
|
4316 |
savedASig = aSig0; |
4317 |
aSig0 >>= shiftCount; |
4318 |
z = aSig0; |
4319 |
if ( aSign ) z = - z;
|
4320 |
if ( ( z < 0 ) ^ aSign ) { |
4321 |
invalid:
|
4322 |
float_raise( float_flag_invalid STATUS_VAR); |
4323 |
return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; |
4324 |
} |
4325 |
if ( ( aSig0<<shiftCount ) != savedASig ) {
|
4326 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4327 |
} |
4328 |
return z;
|
4329 |
|
4330 |
} |
4331 |
|
4332 |
/*----------------------------------------------------------------------------
|
4333 |
| Returns the result of converting the quadruple-precision floating-point
|
4334 |
| value `a' to the 64-bit two's complement integer format. The conversion
|
4335 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4336 |
| Arithmetic---which means in particular that the conversion is rounded
|
4337 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
4338 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
4339 |
| largest integer with the same sign as `a' is returned.
|
4340 |
*----------------------------------------------------------------------------*/
|
4341 |
|
4342 |
int64 float128_to_int64( float128 a STATUS_PARAM ) |
4343 |
{ |
4344 |
flag aSign; |
4345 |
int32 aExp, shiftCount; |
4346 |
bits64 aSig0, aSig1; |
4347 |
|
4348 |
aSig1 = extractFloat128Frac1( a ); |
4349 |
aSig0 = extractFloat128Frac0( a ); |
4350 |
aExp = extractFloat128Exp( a ); |
4351 |
aSign = extractFloat128Sign( a ); |
4352 |
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
4353 |
shiftCount = 0x402F - aExp;
|
4354 |
if ( shiftCount <= 0 ) { |
4355 |
if ( 0x403E < aExp ) { |
4356 |
float_raise( float_flag_invalid STATUS_VAR); |
4357 |
if ( ! aSign
|
4358 |
|| ( ( aExp == 0x7FFF )
|
4359 |
&& ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) )
|
4360 |
) |
4361 |
) { |
4362 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
4363 |
} |
4364 |
return (sbits64) LIT64( 0x8000000000000000 ); |
4365 |
} |
4366 |
shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); |
4367 |
} |
4368 |
else {
|
4369 |
shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); |
4370 |
} |
4371 |
return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR );
|
4372 |
|
4373 |
} |
4374 |
|
4375 |
/*----------------------------------------------------------------------------
|
4376 |
| Returns the result of converting the quadruple-precision floating-point
|
4377 |
| value `a' to the 64-bit two's complement integer format. The conversion
|
4378 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4379 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
4380 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
4381 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
4382 |
| returned.
|
4383 |
*----------------------------------------------------------------------------*/
|
4384 |
|
4385 |
int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) |
4386 |
{ |
4387 |
flag aSign; |
4388 |
int32 aExp, shiftCount; |
4389 |
bits64 aSig0, aSig1; |
4390 |
int64 z; |
4391 |
|
4392 |
aSig1 = extractFloat128Frac1( a ); |
4393 |
aSig0 = extractFloat128Frac0( a ); |
4394 |
aExp = extractFloat128Exp( a ); |
4395 |
aSign = extractFloat128Sign( a ); |
4396 |
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
4397 |
shiftCount = aExp - 0x402F;
|
4398 |
if ( 0 < shiftCount ) { |
4399 |
if ( 0x403E <= aExp ) { |
4400 |
aSig0 &= LIT64( 0x0000FFFFFFFFFFFF );
|
4401 |
if ( ( a.high == LIT64( 0xC03E000000000000 ) ) |
4402 |
&& ( aSig1 < LIT64( 0x0002000000000000 ) ) ) {
|
4403 |
if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
4404 |
} |
4405 |
else {
|
4406 |
float_raise( float_flag_invalid STATUS_VAR); |
4407 |
if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { |
4408 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
4409 |
} |
4410 |
} |
4411 |
return (sbits64) LIT64( 0x8000000000000000 ); |
4412 |
} |
4413 |
z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
|
4414 |
if ( (bits64) ( aSig1<<shiftCount ) ) {
|
4415 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4416 |
} |
4417 |
} |
4418 |
else {
|
4419 |
if ( aExp < 0x3FFF ) { |
4420 |
if ( aExp | aSig0 | aSig1 ) {
|
4421 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4422 |
} |
4423 |
return 0; |
4424 |
} |
4425 |
z = aSig0>>( - shiftCount ); |
4426 |
if ( aSig1
|
4427 |
|| ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) {
|
4428 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4429 |
} |
4430 |
} |
4431 |
if ( aSign ) z = - z;
|
4432 |
return z;
|
4433 |
|
4434 |
} |
4435 |
|
4436 |
/*----------------------------------------------------------------------------
|
4437 |
| Returns the result of converting the quadruple-precision floating-point
|
4438 |
| value `a' to the single-precision floating-point format. The conversion
|
4439 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4440 |
| Arithmetic.
|
4441 |
*----------------------------------------------------------------------------*/
|
4442 |
|
4443 |
float32 float128_to_float32( float128 a STATUS_PARAM ) |
4444 |
{ |
4445 |
flag aSign; |
4446 |
int32 aExp; |
4447 |
bits64 aSig0, aSig1; |
4448 |
bits32 zSig; |
4449 |
|
4450 |
aSig1 = extractFloat128Frac1( a ); |
4451 |
aSig0 = extractFloat128Frac0( a ); |
4452 |
aExp = extractFloat128Exp( a ); |
4453 |
aSign = extractFloat128Sign( a ); |
4454 |
if ( aExp == 0x7FFF ) { |
4455 |
if ( aSig0 | aSig1 ) {
|
4456 |
return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) );
|
4457 |
} |
4458 |
return packFloat32( aSign, 0xFF, 0 ); |
4459 |
} |
4460 |
aSig0 |= ( aSig1 != 0 );
|
4461 |
shift64RightJamming( aSig0, 18, &aSig0 );
|
4462 |
zSig = aSig0; |
4463 |
if ( aExp || zSig ) {
|
4464 |
zSig |= 0x40000000;
|
4465 |
aExp -= 0x3F81;
|
4466 |
} |
4467 |
return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
|
4468 |
|
4469 |
} |
4470 |
|
4471 |
/*----------------------------------------------------------------------------
|
4472 |
| Returns the result of converting the quadruple-precision floating-point
|
4473 |
| value `a' to the double-precision floating-point format. The conversion
|
4474 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
4475 |
| Arithmetic.
|
4476 |
*----------------------------------------------------------------------------*/
|
4477 |
|
4478 |
float64 float128_to_float64( float128 a STATUS_PARAM ) |
4479 |
{ |
4480 |
flag aSign; |
4481 |
int32 aExp; |
4482 |
bits64 aSig0, aSig1; |
4483 |
|
4484 |
aSig1 = extractFloat128Frac1( a ); |
4485 |
aSig0 = extractFloat128Frac0( a ); |
4486 |
aExp = extractFloat128Exp( a ); |
4487 |
aSign = extractFloat128Sign( a ); |
4488 |
if ( aExp == 0x7FFF ) { |
4489 |
if ( aSig0 | aSig1 ) {
|
4490 |
return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) );
|
4491 |
} |
4492 |
return packFloat64( aSign, 0x7FF, 0 ); |
4493 |
} |
4494 |
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
4495 |
aSig0 |= ( aSig1 != 0 );
|
4496 |
if ( aExp || aSig0 ) {
|
4497 |
aSig0 |= LIT64( 0x4000000000000000 );
|
4498 |
aExp -= 0x3C01;
|
4499 |
} |
4500 |
return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR );
|
4501 |
|
4502 |
} |
4503 |
|
4504 |
#ifdef FLOATX80
|
4505 |
|
4506 |
/*----------------------------------------------------------------------------
|
4507 |
| Returns the result of converting the quadruple-precision floating-point
|
4508 |
| value `a' to the extended double-precision floating-point format. The
|
4509 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4510 |
| Floating-Point Arithmetic.
|
4511 |
*----------------------------------------------------------------------------*/
|
4512 |
|
4513 |
floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) |
4514 |
{ |
4515 |
flag aSign; |
4516 |
int32 aExp; |
4517 |
bits64 aSig0, aSig1; |
4518 |
|
4519 |
aSig1 = extractFloat128Frac1( a ); |
4520 |
aSig0 = extractFloat128Frac0( a ); |
4521 |
aExp = extractFloat128Exp( a ); |
4522 |
aSign = extractFloat128Sign( a ); |
4523 |
if ( aExp == 0x7FFF ) { |
4524 |
if ( aSig0 | aSig1 ) {
|
4525 |
return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) );
|
4526 |
} |
4527 |
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4528 |
} |
4529 |
if ( aExp == 0 ) { |
4530 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); |
4531 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
4532 |
} |
4533 |
else {
|
4534 |
aSig0 |= LIT64( 0x0001000000000000 );
|
4535 |
} |
4536 |
shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
|
4537 |
return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); |
4538 |
|
4539 |
} |
4540 |
|
4541 |
#endif
|
4542 |
|
4543 |
/*----------------------------------------------------------------------------
|
4544 |
| Rounds the quadruple-precision floating-point value `a' to an integer, and
|
4545 |
| returns the result as a quadruple-precision floating-point value. The
|
4546 |
| operation is performed according to the IEC/IEEE Standard for Binary
|
4547 |
| Floating-Point Arithmetic.
|
4548 |
*----------------------------------------------------------------------------*/
|
4549 |
|
4550 |
float128 float128_round_to_int( float128 a STATUS_PARAM ) |
4551 |
{ |
4552 |
flag aSign; |
4553 |
int32 aExp; |
4554 |
bits64 lastBitMask, roundBitsMask; |
4555 |
int8 roundingMode; |
4556 |
float128 z; |
4557 |
|
4558 |
aExp = extractFloat128Exp( a ); |
4559 |
if ( 0x402F <= aExp ) { |
4560 |
if ( 0x406F <= aExp ) { |
4561 |
if ( ( aExp == 0x7FFF ) |
4562 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) |
4563 |
) { |
4564 |
return propagateFloat128NaN( a, a STATUS_VAR );
|
4565 |
} |
4566 |
return a;
|
4567 |
} |
4568 |
lastBitMask = 1;
|
4569 |
lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; |
4570 |
roundBitsMask = lastBitMask - 1;
|
4571 |
z = a; |
4572 |
roundingMode = STATUS(float_rounding_mode); |
4573 |
if ( roundingMode == float_round_nearest_even ) {
|
4574 |
if ( lastBitMask ) {
|
4575 |
add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); |
4576 |
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; |
4577 |
} |
4578 |
else {
|
4579 |
if ( (sbits64) z.low < 0 ) { |
4580 |
++z.high; |
4581 |
if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1; |
4582 |
} |
4583 |
} |
4584 |
} |
4585 |
else if ( roundingMode != float_round_to_zero ) { |
4586 |
if ( extractFloat128Sign( z )
|
4587 |
^ ( roundingMode == float_round_up ) ) { |
4588 |
add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low );
|
4589 |
} |
4590 |
} |
4591 |
z.low &= ~ roundBitsMask; |
4592 |
} |
4593 |
else {
|
4594 |
if ( aExp < 0x3FFF ) { |
4595 |
if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a; |
4596 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4597 |
aSign = extractFloat128Sign( a ); |
4598 |
switch ( STATUS(float_rounding_mode) ) {
|
4599 |
case float_round_nearest_even:
|
4600 |
if ( ( aExp == 0x3FFE ) |
4601 |
&& ( extractFloat128Frac0( a ) |
4602 |
| extractFloat128Frac1( a ) ) |
4603 |
) { |
4604 |
return packFloat128( aSign, 0x3FFF, 0, 0 ); |
4605 |
} |
4606 |
break;
|
4607 |
case float_round_down:
|
4608 |
return
|
4609 |
aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) |
4610 |
: packFloat128( 0, 0, 0, 0 ); |
4611 |
case float_round_up:
|
4612 |
return
|
4613 |
aSign ? packFloat128( 1, 0, 0, 0 ) |
4614 |
: packFloat128( 0, 0x3FFF, 0, 0 ); |
4615 |
} |
4616 |
return packFloat128( aSign, 0, 0, 0 ); |
4617 |
} |
4618 |
lastBitMask = 1;
|
4619 |
lastBitMask <<= 0x402F - aExp;
|
4620 |
roundBitsMask = lastBitMask - 1;
|
4621 |
z.low = 0;
|
4622 |
z.high = a.high; |
4623 |
roundingMode = STATUS(float_rounding_mode); |
4624 |
if ( roundingMode == float_round_nearest_even ) {
|
4625 |
z.high += lastBitMask>>1;
|
4626 |
if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { |
4627 |
z.high &= ~ lastBitMask; |
4628 |
} |
4629 |
} |
4630 |
else if ( roundingMode != float_round_to_zero ) { |
4631 |
if ( extractFloat128Sign( z )
|
4632 |
^ ( roundingMode == float_round_up ) ) { |
4633 |
z.high |= ( a.low != 0 );
|
4634 |
z.high += roundBitsMask; |
4635 |
} |
4636 |
} |
4637 |
z.high &= ~ roundBitsMask; |
4638 |
} |
4639 |
if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
|
4640 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4641 |
} |
4642 |
return z;
|
4643 |
|
4644 |
} |
4645 |
|
4646 |
/*----------------------------------------------------------------------------
|
4647 |
| Returns the result of adding the absolute values of the quadruple-precision
|
4648 |
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
4649 |
| before being returned. `zSign' is ignored if the result is a NaN.
|
4650 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
4651 |
| Floating-Point Arithmetic.
|
4652 |
*----------------------------------------------------------------------------*/
|
4653 |
|
4654 |
static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
|
4655 |
{ |
4656 |
int32 aExp, bExp, zExp; |
4657 |
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
4658 |
int32 expDiff; |
4659 |
|
4660 |
aSig1 = extractFloat128Frac1( a ); |
4661 |
aSig0 = extractFloat128Frac0( a ); |
4662 |
aExp = extractFloat128Exp( a ); |
4663 |
bSig1 = extractFloat128Frac1( b ); |
4664 |
bSig0 = extractFloat128Frac0( b ); |
4665 |
bExp = extractFloat128Exp( b ); |
4666 |
expDiff = aExp - bExp; |
4667 |
if ( 0 < expDiff ) { |
4668 |
if ( aExp == 0x7FFF ) { |
4669 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4670 |
return a;
|
4671 |
} |
4672 |
if ( bExp == 0 ) { |
4673 |
--expDiff; |
4674 |
} |
4675 |
else {
|
4676 |
bSig0 |= LIT64( 0x0001000000000000 );
|
4677 |
} |
4678 |
shift128ExtraRightJamming( |
4679 |
bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
|
4680 |
zExp = aExp; |
4681 |
} |
4682 |
else if ( expDiff < 0 ) { |
4683 |
if ( bExp == 0x7FFF ) { |
4684 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4685 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
4686 |
} |
4687 |
if ( aExp == 0 ) { |
4688 |
++expDiff; |
4689 |
} |
4690 |
else {
|
4691 |
aSig0 |= LIT64( 0x0001000000000000 );
|
4692 |
} |
4693 |
shift128ExtraRightJamming( |
4694 |
aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
|
4695 |
zExp = bExp; |
4696 |
} |
4697 |
else {
|
4698 |
if ( aExp == 0x7FFF ) { |
4699 |
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
4700 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
4701 |
} |
4702 |
return a;
|
4703 |
} |
4704 |
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
4705 |
if ( aExp == 0 ) { |
4706 |
if ( STATUS(flush_to_zero) ) return packFloat128( zSign, 0, 0, 0 ); |
4707 |
return packFloat128( zSign, 0, zSig0, zSig1 ); |
4708 |
} |
4709 |
zSig2 = 0;
|
4710 |
zSig0 |= LIT64( 0x0002000000000000 );
|
4711 |
zExp = aExp; |
4712 |
goto shiftRight1;
|
4713 |
} |
4714 |
aSig0 |= LIT64( 0x0001000000000000 );
|
4715 |
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
4716 |
--zExp; |
4717 |
if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; |
4718 |
++zExp; |
4719 |
shiftRight1:
|
4720 |
shift128ExtraRightJamming( |
4721 |
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
4722 |
roundAndPack:
|
4723 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
|
4724 |
|
4725 |
} |
4726 |
|
4727 |
/*----------------------------------------------------------------------------
|
4728 |
| Returns the result of subtracting the absolute values of the quadruple-
|
4729 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
4730 |
| difference is negated before being returned. `zSign' is ignored if the
|
4731 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
4732 |
| Standard for Binary Floating-Point Arithmetic.
|
4733 |
*----------------------------------------------------------------------------*/
|
4734 |
|
4735 |
static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
|
4736 |
{ |
4737 |
int32 aExp, bExp, zExp; |
4738 |
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; |
4739 |
int32 expDiff; |
4740 |
float128 z; |
4741 |
|
4742 |
aSig1 = extractFloat128Frac1( a ); |
4743 |
aSig0 = extractFloat128Frac0( a ); |
4744 |
aExp = extractFloat128Exp( a ); |
4745 |
bSig1 = extractFloat128Frac1( b ); |
4746 |
bSig0 = extractFloat128Frac0( b ); |
4747 |
bExp = extractFloat128Exp( b ); |
4748 |
expDiff = aExp - bExp; |
4749 |
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
4750 |
shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 );
|
4751 |
if ( 0 < expDiff ) goto aExpBigger; |
4752 |
if ( expDiff < 0 ) goto bExpBigger; |
4753 |
if ( aExp == 0x7FFF ) { |
4754 |
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
4755 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
4756 |
} |
4757 |
float_raise( float_flag_invalid STATUS_VAR); |
4758 |
z.low = float128_default_nan_low; |
4759 |
z.high = float128_default_nan_high; |
4760 |
return z;
|
4761 |
} |
4762 |
if ( aExp == 0 ) { |
4763 |
aExp = 1;
|
4764 |
bExp = 1;
|
4765 |
} |
4766 |
if ( bSig0 < aSig0 ) goto aBigger; |
4767 |
if ( aSig0 < bSig0 ) goto bBigger; |
4768 |
if ( bSig1 < aSig1 ) goto aBigger; |
4769 |
if ( aSig1 < bSig1 ) goto bBigger; |
4770 |
return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); |
4771 |
bExpBigger:
|
4772 |
if ( bExp == 0x7FFF ) { |
4773 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4774 |
return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); |
4775 |
} |
4776 |
if ( aExp == 0 ) { |
4777 |
++expDiff; |
4778 |
} |
4779 |
else {
|
4780 |
aSig0 |= LIT64( 0x4000000000000000 );
|
4781 |
} |
4782 |
shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); |
4783 |
bSig0 |= LIT64( 0x4000000000000000 );
|
4784 |
bBigger:
|
4785 |
sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); |
4786 |
zExp = bExp; |
4787 |
zSign ^= 1;
|
4788 |
goto normalizeRoundAndPack;
|
4789 |
aExpBigger:
|
4790 |
if ( aExp == 0x7FFF ) { |
4791 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4792 |
return a;
|
4793 |
} |
4794 |
if ( bExp == 0 ) { |
4795 |
--expDiff; |
4796 |
} |
4797 |
else {
|
4798 |
bSig0 |= LIT64( 0x4000000000000000 );
|
4799 |
} |
4800 |
shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); |
4801 |
aSig0 |= LIT64( 0x4000000000000000 );
|
4802 |
aBigger:
|
4803 |
sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
4804 |
zExp = aExp; |
4805 |
normalizeRoundAndPack:
|
4806 |
--zExp; |
4807 |
return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); |
4808 |
|
4809 |
} |
4810 |
|
4811 |
/*----------------------------------------------------------------------------
|
4812 |
| Returns the result of adding the quadruple-precision floating-point values
|
4813 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
4814 |
| for Binary Floating-Point Arithmetic.
|
4815 |
*----------------------------------------------------------------------------*/
|
4816 |
|
4817 |
float128 float128_add( float128 a, float128 b STATUS_PARAM ) |
4818 |
{ |
4819 |
flag aSign, bSign; |
4820 |
|
4821 |
aSign = extractFloat128Sign( a ); |
4822 |
bSign = extractFloat128Sign( b ); |
4823 |
if ( aSign == bSign ) {
|
4824 |
return addFloat128Sigs( a, b, aSign STATUS_VAR );
|
4825 |
} |
4826 |
else {
|
4827 |
return subFloat128Sigs( a, b, aSign STATUS_VAR );
|
4828 |
} |
4829 |
|
4830 |
} |
4831 |
|
4832 |
/*----------------------------------------------------------------------------
|
4833 |
| Returns the result of subtracting the quadruple-precision floating-point
|
4834 |
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
4835 |
| Standard for Binary Floating-Point Arithmetic.
|
4836 |
*----------------------------------------------------------------------------*/
|
4837 |
|
4838 |
float128 float128_sub( float128 a, float128 b STATUS_PARAM ) |
4839 |
{ |
4840 |
flag aSign, bSign; |
4841 |
|
4842 |
aSign = extractFloat128Sign( a ); |
4843 |
bSign = extractFloat128Sign( b ); |
4844 |
if ( aSign == bSign ) {
|
4845 |
return subFloat128Sigs( a, b, aSign STATUS_VAR );
|
4846 |
} |
4847 |
else {
|
4848 |
return addFloat128Sigs( a, b, aSign STATUS_VAR );
|
4849 |
} |
4850 |
|
4851 |
} |
4852 |
|
4853 |
/*----------------------------------------------------------------------------
|
4854 |
| Returns the result of multiplying the quadruple-precision floating-point
|
4855 |
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
4856 |
| Standard for Binary Floating-Point Arithmetic.
|
4857 |
*----------------------------------------------------------------------------*/
|
4858 |
|
4859 |
float128 float128_mul( float128 a, float128 b STATUS_PARAM ) |
4860 |
{ |
4861 |
flag aSign, bSign, zSign; |
4862 |
int32 aExp, bExp, zExp; |
4863 |
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; |
4864 |
float128 z; |
4865 |
|
4866 |
aSig1 = extractFloat128Frac1( a ); |
4867 |
aSig0 = extractFloat128Frac0( a ); |
4868 |
aExp = extractFloat128Exp( a ); |
4869 |
aSign = extractFloat128Sign( a ); |
4870 |
bSig1 = extractFloat128Frac1( b ); |
4871 |
bSig0 = extractFloat128Frac0( b ); |
4872 |
bExp = extractFloat128Exp( b ); |
4873 |
bSign = extractFloat128Sign( b ); |
4874 |
zSign = aSign ^ bSign; |
4875 |
if ( aExp == 0x7FFF ) { |
4876 |
if ( ( aSig0 | aSig1 )
|
4877 |
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
4878 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
4879 |
} |
4880 |
if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; |
4881 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
4882 |
} |
4883 |
if ( bExp == 0x7FFF ) { |
4884 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4885 |
if ( ( aExp | aSig0 | aSig1 ) == 0 ) { |
4886 |
invalid:
|
4887 |
float_raise( float_flag_invalid STATUS_VAR); |
4888 |
z.low = float128_default_nan_low; |
4889 |
z.high = float128_default_nan_high; |
4890 |
return z;
|
4891 |
} |
4892 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
4893 |
} |
4894 |
if ( aExp == 0 ) { |
4895 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
4896 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
4897 |
} |
4898 |
if ( bExp == 0 ) { |
4899 |
if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
4900 |
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
4901 |
} |
4902 |
zExp = aExp + bExp - 0x4000;
|
4903 |
aSig0 |= LIT64( 0x0001000000000000 );
|
4904 |
shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 );
|
4905 |
mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); |
4906 |
add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); |
4907 |
zSig2 |= ( zSig3 != 0 );
|
4908 |
if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { |
4909 |
shift128ExtraRightJamming( |
4910 |
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
4911 |
++zExp; |
4912 |
} |
4913 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
|
4914 |
|
4915 |
} |
4916 |
|
4917 |
/*----------------------------------------------------------------------------
|
4918 |
| Returns the result of dividing the quadruple-precision floating-point value
|
4919 |
| `a' by the corresponding value `b'. The operation is performed according to
|
4920 |
| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4921 |
*----------------------------------------------------------------------------*/
|
4922 |
|
4923 |
float128 float128_div( float128 a, float128 b STATUS_PARAM ) |
4924 |
{ |
4925 |
flag aSign, bSign, zSign; |
4926 |
int32 aExp, bExp, zExp; |
4927 |
bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
4928 |
bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
4929 |
float128 z; |
4930 |
|
4931 |
aSig1 = extractFloat128Frac1( a ); |
4932 |
aSig0 = extractFloat128Frac0( a ); |
4933 |
aExp = extractFloat128Exp( a ); |
4934 |
aSign = extractFloat128Sign( a ); |
4935 |
bSig1 = extractFloat128Frac1( b ); |
4936 |
bSig0 = extractFloat128Frac0( b ); |
4937 |
bExp = extractFloat128Exp( b ); |
4938 |
bSign = extractFloat128Sign( b ); |
4939 |
zSign = aSign ^ bSign; |
4940 |
if ( aExp == 0x7FFF ) { |
4941 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4942 |
if ( bExp == 0x7FFF ) { |
4943 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4944 |
goto invalid;
|
4945 |
} |
4946 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
4947 |
} |
4948 |
if ( bExp == 0x7FFF ) { |
4949 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
4950 |
return packFloat128( zSign, 0, 0, 0 ); |
4951 |
} |
4952 |
if ( bExp == 0 ) { |
4953 |
if ( ( bSig0 | bSig1 ) == 0 ) { |
4954 |
if ( ( aExp | aSig0 | aSig1 ) == 0 ) { |
4955 |
invalid:
|
4956 |
float_raise( float_flag_invalid STATUS_VAR); |
4957 |
z.low = float128_default_nan_low; |
4958 |
z.high = float128_default_nan_high; |
4959 |
return z;
|
4960 |
} |
4961 |
float_raise( float_flag_divbyzero STATUS_VAR); |
4962 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
4963 |
} |
4964 |
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
4965 |
} |
4966 |
if ( aExp == 0 ) { |
4967 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
4968 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
4969 |
} |
4970 |
zExp = aExp - bExp + 0x3FFD;
|
4971 |
shortShift128Left( |
4972 |
aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); |
4973 |
shortShift128Left( |
4974 |
bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); |
4975 |
if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) {
|
4976 |
shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
|
4977 |
++zExp; |
4978 |
} |
4979 |
zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
4980 |
mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); |
4981 |
sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
|
4982 |
while ( (sbits64) rem0 < 0 ) { |
4983 |
--zSig0; |
4984 |
add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
|
4985 |
} |
4986 |
zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); |
4987 |
if ( ( zSig1 & 0x3FFF ) <= 4 ) { |
4988 |
mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); |
4989 |
sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
|
4990 |
while ( (sbits64) rem1 < 0 ) { |
4991 |
--zSig1; |
4992 |
add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
|
4993 |
} |
4994 |
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
4995 |
} |
4996 |
shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); |
4997 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
|
4998 |
|
4999 |
} |
5000 |
|
5001 |
/*----------------------------------------------------------------------------
|
5002 |
| Returns the remainder of the quadruple-precision floating-point value `a'
|
5003 |
| with respect to the corresponding value `b'. The operation is performed
|
5004 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5005 |
*----------------------------------------------------------------------------*/
|
5006 |
|
5007 |
float128 float128_rem( float128 a, float128 b STATUS_PARAM ) |
5008 |
{ |
5009 |
flag aSign, bSign, zSign; |
5010 |
int32 aExp, bExp, expDiff; |
5011 |
bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; |
5012 |
bits64 allZero, alternateASig0, alternateASig1, sigMean1; |
5013 |
sbits64 sigMean0; |
5014 |
float128 z; |
5015 |
|
5016 |
aSig1 = extractFloat128Frac1( a ); |
5017 |
aSig0 = extractFloat128Frac0( a ); |
5018 |
aExp = extractFloat128Exp( a ); |
5019 |
aSign = extractFloat128Sign( a ); |
5020 |
bSig1 = extractFloat128Frac1( b ); |
5021 |
bSig0 = extractFloat128Frac0( b ); |
5022 |
bExp = extractFloat128Exp( b ); |
5023 |
bSign = extractFloat128Sign( b ); |
5024 |
if ( aExp == 0x7FFF ) { |
5025 |
if ( ( aSig0 | aSig1 )
|
5026 |
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
5027 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
5028 |
} |
5029 |
goto invalid;
|
5030 |
} |
5031 |
if ( bExp == 0x7FFF ) { |
5032 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
5033 |
return a;
|
5034 |
} |
5035 |
if ( bExp == 0 ) { |
5036 |
if ( ( bSig0 | bSig1 ) == 0 ) { |
5037 |
invalid:
|
5038 |
float_raise( float_flag_invalid STATUS_VAR); |
5039 |
z.low = float128_default_nan_low; |
5040 |
z.high = float128_default_nan_high; |
5041 |
return z;
|
5042 |
} |
5043 |
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
5044 |
} |
5045 |
if ( aExp == 0 ) { |
5046 |
if ( ( aSig0 | aSig1 ) == 0 ) return a; |
5047 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
5048 |
} |
5049 |
expDiff = aExp - bExp; |
5050 |
if ( expDiff < -1 ) return a; |
5051 |
shortShift128Left( |
5052 |
aSig0 | LIT64( 0x0001000000000000 ),
|
5053 |
aSig1, |
5054 |
15 - ( expDiff < 0 ), |
5055 |
&aSig0, |
5056 |
&aSig1 |
5057 |
); |
5058 |
shortShift128Left( |
5059 |
bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); |
5060 |
q = le128( bSig0, bSig1, aSig0, aSig1 ); |
5061 |
if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
|
5062 |
expDiff -= 64;
|
5063 |
while ( 0 < expDiff ) { |
5064 |
q = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
5065 |
q = ( 4 < q ) ? q - 4 : 0; |
5066 |
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); |
5067 |
shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
|
5068 |
shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
|
5069 |
sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
|
5070 |
expDiff -= 61;
|
5071 |
} |
5072 |
if ( -64 < expDiff ) { |
5073 |
q = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
5074 |
q = ( 4 < q ) ? q - 4 : 0; |
5075 |
q >>= - expDiff; |
5076 |
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
5077 |
expDiff += 52;
|
5078 |
if ( expDiff < 0 ) { |
5079 |
shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); |
5080 |
} |
5081 |
else {
|
5082 |
shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); |
5083 |
} |
5084 |
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); |
5085 |
sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); |
5086 |
} |
5087 |
else {
|
5088 |
shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
|
5089 |
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
5090 |
} |
5091 |
do {
|
5092 |
alternateASig0 = aSig0; |
5093 |
alternateASig1 = aSig1; |
5094 |
++q; |
5095 |
sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); |
5096 |
} while ( 0 <= (sbits64) aSig0 ); |
5097 |
add128( |
5098 |
aSig0, aSig1, alternateASig0, alternateASig1, (bits64 *)&sigMean0, &sigMean1 ); |
5099 |
if ( ( sigMean0 < 0 ) |
5100 |
|| ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { |
5101 |
aSig0 = alternateASig0; |
5102 |
aSig1 = alternateASig1; |
5103 |
} |
5104 |
zSign = ( (sbits64) aSig0 < 0 );
|
5105 |
if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); |
5106 |
return
|
5107 |
normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR );
|
5108 |
|
5109 |
} |
5110 |
|
5111 |
/*----------------------------------------------------------------------------
|
5112 |
| Returns the square root of the quadruple-precision floating-point value `a'.
|
5113 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
5114 |
| Floating-Point Arithmetic.
|
5115 |
*----------------------------------------------------------------------------*/
|
5116 |
|
5117 |
float128 float128_sqrt( float128 a STATUS_PARAM ) |
5118 |
{ |
5119 |
flag aSign; |
5120 |
int32 aExp, zExp; |
5121 |
bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; |
5122 |
bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
5123 |
float128 z; |
5124 |
|
5125 |
aSig1 = extractFloat128Frac1( a ); |
5126 |
aSig0 = extractFloat128Frac0( a ); |
5127 |
aExp = extractFloat128Exp( a ); |
5128 |
aSign = extractFloat128Sign( a ); |
5129 |
if ( aExp == 0x7FFF ) { |
5130 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); |
5131 |
if ( ! aSign ) return a; |
5132 |
goto invalid;
|
5133 |
} |
5134 |
if ( aSign ) {
|
5135 |
if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; |
5136 |
invalid:
|
5137 |
float_raise( float_flag_invalid STATUS_VAR); |
5138 |
z.low = float128_default_nan_low; |
5139 |
z.high = float128_default_nan_high; |
5140 |
return z;
|
5141 |
} |
5142 |
if ( aExp == 0 ) { |
5143 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); |
5144 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
5145 |
} |
5146 |
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; |
5147 |
aSig0 |= LIT64( 0x0001000000000000 );
|
5148 |
zSig0 = estimateSqrt32( aExp, aSig0>>17 );
|
5149 |
shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); |
5150 |
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); |
5151 |
doubleZSig0 = zSig0<<1;
|
5152 |
mul64To128( zSig0, zSig0, &term0, &term1 ); |
5153 |
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); |
5154 |
while ( (sbits64) rem0 < 0 ) { |
5155 |
--zSig0; |
5156 |
doubleZSig0 -= 2;
|
5157 |
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); |
5158 |
} |
5159 |
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
5160 |
if ( ( zSig1 & 0x1FFF ) <= 5 ) { |
5161 |
if ( zSig1 == 0 ) zSig1 = 1; |
5162 |
mul64To128( doubleZSig0, zSig1, &term1, &term2 ); |
5163 |
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
5164 |
mul64To128( zSig1, zSig1, &term2, &term3 ); |
5165 |
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); |
5166 |
while ( (sbits64) rem1 < 0 ) { |
5167 |
--zSig1; |
5168 |
shortShift128Left( 0, zSig1, 1, &term2, &term3 ); |
5169 |
term3 |= 1;
|
5170 |
term2 |= doubleZSig0; |
5171 |
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
5172 |
} |
5173 |
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
5174 |
} |
5175 |
shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); |
5176 |
return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); |
5177 |
|
5178 |
} |
5179 |
|
5180 |
/*----------------------------------------------------------------------------
|
5181 |
| Returns 1 if the quadruple-precision floating-point value `a' is equal to
|
5182 |
| the corresponding value `b', and 0 otherwise. The comparison is performed
|
5183 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5184 |
*----------------------------------------------------------------------------*/
|
5185 |
|
5186 |
int float128_eq( float128 a, float128 b STATUS_PARAM )
|
5187 |
{ |
5188 |
|
5189 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
5190 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
5191 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
5192 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
5193 |
) { |
5194 |
if ( float128_is_signaling_nan( a )
|
5195 |
|| float128_is_signaling_nan( b ) ) { |
5196 |
float_raise( float_flag_invalid STATUS_VAR); |
5197 |
} |
5198 |
return 0; |
5199 |
} |
5200 |
return
|
5201 |
( a.low == b.low ) |
5202 |
&& ( ( a.high == b.high ) |
5203 |
|| ( ( a.low == 0 )
|
5204 |
&& ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) |
5205 |
); |
5206 |
|
5207 |
} |
5208 |
|
5209 |
/*----------------------------------------------------------------------------
|
5210 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
5211 |
| or equal to the corresponding value `b', and 0 otherwise. The comparison
|
5212 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5213 |
| Arithmetic.
|
5214 |
*----------------------------------------------------------------------------*/
|
5215 |
|
5216 |
int float128_le( float128 a, float128 b STATUS_PARAM )
|
5217 |
{ |
5218 |
flag aSign, bSign; |
5219 |
|
5220 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
5221 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
5222 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
5223 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
5224 |
) { |
5225 |
float_raise( float_flag_invalid STATUS_VAR); |
5226 |
return 0; |
5227 |
} |
5228 |
aSign = extractFloat128Sign( a ); |
5229 |
bSign = extractFloat128Sign( b ); |
5230 |
if ( aSign != bSign ) {
|
5231 |
return
|
5232 |
aSign |
5233 |
|| ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5234 |
== 0 );
|
5235 |
} |
5236 |
return
|
5237 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
5238 |
: le128( a.high, a.low, b.high, b.low ); |
5239 |
|
5240 |
} |
5241 |
|
5242 |
/*----------------------------------------------------------------------------
|
5243 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
5244 |
| the corresponding value `b', and 0 otherwise. The comparison is performed
|
5245 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5246 |
*----------------------------------------------------------------------------*/
|
5247 |
|
5248 |
int float128_lt( float128 a, float128 b STATUS_PARAM )
|
5249 |
{ |
5250 |
flag aSign, bSign; |
5251 |
|
5252 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
5253 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
5254 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
5255 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
5256 |
) { |
5257 |
float_raise( float_flag_invalid STATUS_VAR); |
5258 |
return 0; |
5259 |
} |
5260 |
aSign = extractFloat128Sign( a ); |
5261 |
bSign = extractFloat128Sign( b ); |
5262 |
if ( aSign != bSign ) {
|
5263 |
return
|
5264 |
aSign |
5265 |
&& ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5266 |
!= 0 );
|
5267 |
} |
5268 |
return
|
5269 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
5270 |
: lt128( a.high, a.low, b.high, b.low ); |
5271 |
|
5272 |
} |
5273 |
|
5274 |
/*----------------------------------------------------------------------------
|
5275 |
| Returns 1 if the quadruple-precision floating-point value `a' is equal to
|
5276 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
5277 |
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
5278 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5279 |
*----------------------------------------------------------------------------*/
|
5280 |
|
5281 |
int float128_eq_signaling( float128 a, float128 b STATUS_PARAM )
|
5282 |
{ |
5283 |
|
5284 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
5285 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
5286 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
5287 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
5288 |
) { |
5289 |
float_raise( float_flag_invalid STATUS_VAR); |
5290 |
return 0; |
5291 |
} |
5292 |
return
|
5293 |
( a.low == b.low ) |
5294 |
&& ( ( a.high == b.high ) |
5295 |
|| ( ( a.low == 0 )
|
5296 |
&& ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) |
5297 |
); |
5298 |
|
5299 |
} |
5300 |
|
5301 |
/*----------------------------------------------------------------------------
|
5302 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
5303 |
| or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
5304 |
| cause an exception. Otherwise, the comparison is performed according to the
|
5305 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5306 |
*----------------------------------------------------------------------------*/
|
5307 |
|
5308 |
int float128_le_quiet( float128 a, float128 b STATUS_PARAM )
|
5309 |
{ |
5310 |
flag aSign, bSign; |
5311 |
|
5312 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
5313 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
5314 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
5315 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
5316 |
) { |
5317 |
if ( float128_is_signaling_nan( a )
|
5318 |
|| float128_is_signaling_nan( b ) ) { |
5319 |
float_raise( float_flag_invalid STATUS_VAR); |
5320 |
} |
5321 |
return 0; |
5322 |
} |
5323 |
aSign = extractFloat128Sign( a ); |
5324 |
bSign = extractFloat128Sign( b ); |
5325 |
if ( aSign != bSign ) {
|
5326 |
return
|
5327 |
aSign |
5328 |
|| ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5329 |
== 0 );
|
5330 |
} |
5331 |
return
|
5332 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
5333 |
: le128( a.high, a.low, b.high, b.low ); |
5334 |
|
5335 |
} |
5336 |
|
5337 |
/*----------------------------------------------------------------------------
|
5338 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
5339 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
5340 |
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
5341 |
| Standard for Binary Floating-Point Arithmetic.
|
5342 |
*----------------------------------------------------------------------------*/
|
5343 |
|
5344 |
int float128_lt_quiet( float128 a, float128 b STATUS_PARAM )
|
5345 |
{ |
5346 |
flag aSign, bSign; |
5347 |
|
5348 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
5349 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
5350 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
5351 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
5352 |
) { |
5353 |
if ( float128_is_signaling_nan( a )
|
5354 |
|| float128_is_signaling_nan( b ) ) { |
5355 |
float_raise( float_flag_invalid STATUS_VAR); |
5356 |
} |
5357 |
return 0; |
5358 |
} |
5359 |
aSign = extractFloat128Sign( a ); |
5360 |
bSign = extractFloat128Sign( b ); |
5361 |
if ( aSign != bSign ) {
|
5362 |
return
|
5363 |
aSign |
5364 |
&& ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5365 |
!= 0 );
|
5366 |
} |
5367 |
return
|
5368 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
5369 |
: lt128( a.high, a.low, b.high, b.low ); |
5370 |
|
5371 |
} |
5372 |
|
5373 |
#endif
|
5374 |
|
5375 |
/* misc functions */
|
5376 |
float32 uint32_to_float32( unsigned int a STATUS_PARAM ) |
5377 |
{ |
5378 |
return int64_to_float32(a STATUS_VAR);
|
5379 |
} |
5380 |
|
5381 |
float64 uint32_to_float64( unsigned int a STATUS_PARAM ) |
5382 |
{ |
5383 |
return int64_to_float64(a STATUS_VAR);
|
5384 |
} |
5385 |
|
5386 |
unsigned int float32_to_uint32( float32 a STATUS_PARAM ) |
5387 |
{ |
5388 |
int64_t v; |
5389 |
unsigned int res; |
5390 |
|
5391 |
v = float32_to_int64(a STATUS_VAR); |
5392 |
if (v < 0) { |
5393 |
res = 0;
|
5394 |
float_raise( float_flag_invalid STATUS_VAR); |
5395 |
} else if (v > 0xffffffff) { |
5396 |
res = 0xffffffff;
|
5397 |
float_raise( float_flag_invalid STATUS_VAR); |
5398 |
} else {
|
5399 |
res = v; |
5400 |
} |
5401 |
return res;
|
5402 |
} |
5403 |
|
5404 |
unsigned int float32_to_uint32_round_to_zero( float32 a STATUS_PARAM ) |
5405 |
{ |
5406 |
int64_t v; |
5407 |
unsigned int res; |
5408 |
|
5409 |
v = float32_to_int64_round_to_zero(a STATUS_VAR); |
5410 |
if (v < 0) { |
5411 |
res = 0;
|
5412 |
float_raise( float_flag_invalid STATUS_VAR); |
5413 |
} else if (v > 0xffffffff) { |
5414 |
res = 0xffffffff;
|
5415 |
float_raise( float_flag_invalid STATUS_VAR); |
5416 |
} else {
|
5417 |
res = v; |
5418 |
} |
5419 |
return res;
|
5420 |
} |
5421 |
|
5422 |
unsigned int float64_to_uint32( float64 a STATUS_PARAM ) |
5423 |
{ |
5424 |
int64_t v; |
5425 |
unsigned int res; |
5426 |
|
5427 |
v = float64_to_int64(a STATUS_VAR); |
5428 |
if (v < 0) { |
5429 |
res = 0;
|
5430 |
float_raise( float_flag_invalid STATUS_VAR); |
5431 |
} else if (v > 0xffffffff) { |
5432 |
res = 0xffffffff;
|
5433 |
float_raise( float_flag_invalid STATUS_VAR); |
5434 |
} else {
|
5435 |
res = v; |
5436 |
} |
5437 |
return res;
|
5438 |
} |
5439 |
|
5440 |
unsigned int float64_to_uint32_round_to_zero( float64 a STATUS_PARAM ) |
5441 |
{ |
5442 |
int64_t v; |
5443 |
unsigned int res; |
5444 |
|
5445 |
v = float64_to_int64_round_to_zero(a STATUS_VAR); |
5446 |
if (v < 0) { |
5447 |
res = 0;
|
5448 |
float_raise( float_flag_invalid STATUS_VAR); |
5449 |
} else if (v > 0xffffffff) { |
5450 |
res = 0xffffffff;
|
5451 |
float_raise( float_flag_invalid STATUS_VAR); |
5452 |
} else {
|
5453 |
res = v; |
5454 |
} |
5455 |
return res;
|
5456 |
} |
5457 |
|
5458 |
/* FIXME: This looks broken. */
|
5459 |
uint64_t float64_to_uint64 (float64 a STATUS_PARAM) |
5460 |
{ |
5461 |
int64_t v; |
5462 |
|
5463 |
v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); |
5464 |
v += float64_val(a); |
5465 |
v = float64_to_int64(make_float64(v) STATUS_VAR); |
5466 |
|
5467 |
return v - INT64_MIN;
|
5468 |
} |
5469 |
|
5470 |
uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM) |
5471 |
{ |
5472 |
int64_t v; |
5473 |
|
5474 |
v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); |
5475 |
v += float64_val(a); |
5476 |
v = float64_to_int64_round_to_zero(make_float64(v) STATUS_VAR); |
5477 |
|
5478 |
return v - INT64_MIN;
|
5479 |
} |
5480 |
|
5481 |
#define COMPARE(s, nan_exp) \
|
5482 |
INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \ |
5483 |
int is_quiet STATUS_PARAM ) \
|
5484 |
{ \ |
5485 |
flag aSign, bSign; \ |
5486 |
bits ## s av, bv; \ |
5487 |
\ |
5488 |
if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ |
5489 |
extractFloat ## s ## Frac( a ) ) || \ |
5490 |
( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ |
5491 |
extractFloat ## s ## Frac( b ) )) { \ |
5492 |
if (!is_quiet || \
|
5493 |
float ## s ## _is_signaling_nan( a ) || \ |
5494 |
float ## s ## _is_signaling_nan( b ) ) { \ |
5495 |
float_raise( float_flag_invalid STATUS_VAR); \ |
5496 |
} \ |
5497 |
return float_relation_unordered; \
|
5498 |
} \ |
5499 |
aSign = extractFloat ## s ## Sign( a ); \ |
5500 |
bSign = extractFloat ## s ## Sign( b ); \ |
5501 |
av = float ## s ## _val(a); \ |
5502 |
bv = float ## s ## _val(b); \ |
5503 |
if ( aSign != bSign ) { \
|
5504 |
if ( (bits ## s) ( ( av | bv )<<1 ) == 0 ) { \ |
5505 |
/* zero case */ \
|
5506 |
return float_relation_equal; \
|
5507 |
} else { \
|
5508 |
return 1 - (2 * aSign); \ |
5509 |
} \ |
5510 |
} else { \
|
5511 |
if (av == bv) { \
|
5512 |
return float_relation_equal; \
|
5513 |
} else { \
|
5514 |
return 1 - 2 * (aSign ^ ( av < bv )); \ |
5515 |
} \ |
5516 |
} \ |
5517 |
} \ |
5518 |
\ |
5519 |
int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \ |
5520 |
{ \ |
5521 |
return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \ |
5522 |
} \ |
5523 |
\ |
5524 |
int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \ |
5525 |
{ \ |
5526 |
return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \ |
5527 |
} |
5528 |
|
5529 |
COMPARE(32, 0xff) |
5530 |
COMPARE(64, 0x7ff) |
5531 |
|
5532 |
INLINE int float128_compare_internal( float128 a, float128 b,
|
5533 |
int is_quiet STATUS_PARAM )
|
5534 |
{ |
5535 |
flag aSign, bSign; |
5536 |
|
5537 |
if (( ( extractFloat128Exp( a ) == 0x7fff ) && |
5538 |
( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) || |
5539 |
( ( extractFloat128Exp( b ) == 0x7fff ) &&
|
5540 |
( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) { |
5541 |
if (!is_quiet ||
|
5542 |
float128_is_signaling_nan( a ) || |
5543 |
float128_is_signaling_nan( b ) ) { |
5544 |
float_raise( float_flag_invalid STATUS_VAR); |
5545 |
} |
5546 |
return float_relation_unordered;
|
5547 |
} |
5548 |
aSign = extractFloat128Sign( a ); |
5549 |
bSign = extractFloat128Sign( b ); |
5550 |
if ( aSign != bSign ) {
|
5551 |
if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) { |
5552 |
/* zero case */
|
5553 |
return float_relation_equal;
|
5554 |
} else {
|
5555 |
return 1 - (2 * aSign); |
5556 |
} |
5557 |
} else {
|
5558 |
if (a.low == b.low && a.high == b.high) {
|
5559 |
return float_relation_equal;
|
5560 |
} else {
|
5561 |
return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); |
5562 |
} |
5563 |
} |
5564 |
} |
5565 |
|
5566 |
int float128_compare( float128 a, float128 b STATUS_PARAM )
|
5567 |
{ |
5568 |
return float128_compare_internal(a, b, 0 STATUS_VAR); |
5569 |
} |
5570 |
|
5571 |
int float128_compare_quiet( float128 a, float128 b STATUS_PARAM )
|
5572 |
{ |
5573 |
return float128_compare_internal(a, b, 1 STATUS_VAR); |
5574 |
} |
5575 |
|
5576 |
/* Multiply A by 2 raised to the power N. */
|
5577 |
float32 float32_scalbn( float32 a, int n STATUS_PARAM )
|
5578 |
{ |
5579 |
flag aSign; |
5580 |
int16 aExp; |
5581 |
bits32 aSig; |
5582 |
|
5583 |
aSig = extractFloat32Frac( a ); |
5584 |
aExp = extractFloat32Exp( a ); |
5585 |
aSign = extractFloat32Sign( a ); |
5586 |
|
5587 |
if ( aExp == 0xFF ) { |
5588 |
return a;
|
5589 |
} |
5590 |
if ( aExp != 0 ) |
5591 |
aSig |= 0x00800000;
|
5592 |
else if ( aSig == 0 ) |
5593 |
return a;
|
5594 |
|
5595 |
aExp += n - 1;
|
5596 |
aSig <<= 7;
|
5597 |
return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
|
5598 |
} |
5599 |
|
5600 |
float64 float64_scalbn( float64 a, int n STATUS_PARAM )
|
5601 |
{ |
5602 |
flag aSign; |
5603 |
int16 aExp; |
5604 |
bits64 aSig; |
5605 |
|
5606 |
aSig = extractFloat64Frac( a ); |
5607 |
aExp = extractFloat64Exp( a ); |
5608 |
aSign = extractFloat64Sign( a ); |
5609 |
|
5610 |
if ( aExp == 0x7FF ) { |
5611 |
return a;
|
5612 |
} |
5613 |
if ( aExp != 0 ) |
5614 |
aSig |= LIT64( 0x0010000000000000 );
|
5615 |
else if ( aSig == 0 ) |
5616 |
return a;
|
5617 |
|
5618 |
aExp += n - 1;
|
5619 |
aSig <<= 10;
|
5620 |
return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR );
|
5621 |
} |
5622 |
|
5623 |
#ifdef FLOATX80
|
5624 |
floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM )
|
5625 |
{ |
5626 |
flag aSign; |
5627 |
int16 aExp; |
5628 |
bits64 aSig; |
5629 |
|
5630 |
aSig = extractFloatx80Frac( a ); |
5631 |
aExp = extractFloatx80Exp( a ); |
5632 |
aSign = extractFloatx80Sign( a ); |
5633 |
|
5634 |
if ( aExp == 0x7FF ) { |
5635 |
return a;
|
5636 |
} |
5637 |
if (aExp == 0 && aSig == 0) |
5638 |
return a;
|
5639 |
|
5640 |
aExp += n; |
5641 |
return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision),
|
5642 |
aSign, aExp, aSig, 0 STATUS_VAR );
|
5643 |
} |
5644 |
#endif
|
5645 |
|
5646 |
#ifdef FLOAT128
|
5647 |
float128 float128_scalbn( float128 a, int n STATUS_PARAM )
|
5648 |
{ |
5649 |
flag aSign; |
5650 |
int32 aExp; |
5651 |
bits64 aSig0, aSig1; |
5652 |
|
5653 |
aSig1 = extractFloat128Frac1( a ); |
5654 |
aSig0 = extractFloat128Frac0( a ); |
5655 |
aExp = extractFloat128Exp( a ); |
5656 |
aSign = extractFloat128Sign( a ); |
5657 |
if ( aExp == 0x7FFF ) { |
5658 |
return a;
|
5659 |
} |
5660 |
if ( aExp != 0 ) |
5661 |
aSig0 |= LIT64( 0x0001000000000000 );
|
5662 |
else if ( aSig0 == 0 && aSig1 == 0 ) |
5663 |
return a;
|
5664 |
|
5665 |
aExp += n - 1;
|
5666 |
return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
|
5667 |
STATUS_VAR ); |
5668 |
|
5669 |
} |
5670 |
#endif
|