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/*
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* QEMU float support
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*
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* Derived from SoftFloat.
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*/
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/*============================================================================
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This C source file is part of the SoftFloat IEC/IEEE Floating-point 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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/* softfloat (and in particular the code in softfloat-specialize.h) is
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* target-dependent and needs the TARGET_* macros.
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*/
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#include "config.h" |
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#include "fpu/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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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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/*----------------------------------------------------------------------------
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| Returns the fraction bits of the half-precision floating-point value `a'.
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*----------------------------------------------------------------------------*/
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INLINE uint32_t extractFloat16Frac(float16 a) |
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{ |
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return float16_val(a) & 0x3ff; |
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} |
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/*----------------------------------------------------------------------------
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| Returns the exponent bits of the half-precision floating-point value `a'.
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*----------------------------------------------------------------------------*/
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INLINE int_fast16_t extractFloat16Exp(float16 a) |
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{ |
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return (float16_val(a) >> 10) & 0x1f; |
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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 extractFloat16Sign(float16 a) |
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{ |
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return float16_val(a)>>15; |
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} |
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/*----------------------------------------------------------------------------
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| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
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| and 7, and returns the properly rounded 32-bit integer corresponding to the
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| input. If `zSign' is 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, uint64_t 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_t 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 ? (int32_t) 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, uint64_t absZ0, uint64_t 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_t 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 = ( (int64_t) 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 &= ~ ( ( (uint64_t) ( 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 ? (int64_t) 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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| 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 unsigned integer corresponding to the
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| input. Ordinarily, the fixed-point input is simply rounded to an integer,
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| with the inexact exception raised if the input cannot be represented exactly
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| as an integer. However, if the fixed-point input is too large, the invalid
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| exception is raised and the largest unsigned integer is returned.
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*----------------------------------------------------------------------------*/
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static int64 roundAndPackUint64(flag zSign, uint64_t absZ0,
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uint64_t absZ1 STATUS_PARAM) |
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{ |
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int8 roundingMode; |
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flag roundNearestEven, increment; |
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roundingMode = STATUS(float_rounding_mode); |
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roundNearestEven = (roundingMode == float_round_nearest_even); |
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increment = ((int64_t)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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} else if (absZ1) { |
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if (zSign) {
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increment = (roundingMode == float_round_down) && absZ1; |
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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) { |
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float_raise(float_flag_invalid STATUS_VAR); |
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return LIT64(0xFFFFFFFFFFFFFFFF); |
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} |
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absZ0 &= ~(((uint64_t)(absZ1<<1) == 0) & roundNearestEven); |
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} |
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if (zSign && absZ0) {
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float_raise(float_flag_invalid STATUS_VAR); |
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return 0; |
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} |
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if (absZ1) {
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STATUS(float_exception_flags) |= float_flag_inexact; |
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} |
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return absZ0;
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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 uint32_t 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 int_fast16_t 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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| If `a' is denormal and we are in flush-to-zero mode then set the
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| input-denormal exception and return zero. Otherwise just return the value.
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*----------------------------------------------------------------------------*/
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static float32 float32_squash_input_denormal(float32 a STATUS_PARAM)
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{ |
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if (STATUS(flush_inputs_to_zero)) {
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if (extractFloat32Exp(a) == 0 && extractFloat32Frac(a) != 0) { |
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float_raise(float_flag_input_denormal STATUS_VAR); |
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return make_float32(float32_val(a) & 0x80000000); |
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} |
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} |
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return a;
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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(uint32_t aSig, int_fast16_t *zExpPtr, uint32_t *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, int_fast16_t zExp, uint32_t zSig) |
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{ |
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return make_float32(
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( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) 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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359 |
| The handling of underflow and overflow follows the IEC/IEEE Standard for
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360 |
| Binary Floating-Point Arithmetic.
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*----------------------------------------------------------------------------*/
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362 |
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363 |
static float32 roundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM)
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{ |
365 |
int8 roundingMode; |
366 |
flag roundNearestEven; |
367 |
int8 roundIncrement, roundBits; |
368 |
flag isTiny; |
369 |
|
370 |
roundingMode = STATUS(float_rounding_mode); |
371 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
372 |
roundIncrement = 0x40;
|
373 |
if ( ! roundNearestEven ) {
|
374 |
if ( roundingMode == float_round_to_zero ) {
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375 |
roundIncrement = 0;
|
376 |
} |
377 |
else {
|
378 |
roundIncrement = 0x7F;
|
379 |
if ( zSign ) {
|
380 |
if ( roundingMode == float_round_up ) roundIncrement = 0; |
381 |
} |
382 |
else {
|
383 |
if ( roundingMode == float_round_down ) roundIncrement = 0; |
384 |
} |
385 |
} |
386 |
} |
387 |
roundBits = zSig & 0x7F;
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388 |
if ( 0xFD <= (uint16_t) zExp ) { |
389 |
if ( ( 0xFD < zExp ) |
390 |
|| ( ( zExp == 0xFD )
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391 |
&& ( (int32_t) ( zSig + roundIncrement ) < 0 ) )
|
392 |
) { |
393 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
394 |
return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 )); |
395 |
} |
396 |
if ( zExp < 0 ) { |
397 |
if (STATUS(flush_to_zero)) {
|
398 |
float_raise(float_flag_output_denormal STATUS_VAR); |
399 |
return packFloat32(zSign, 0, 0); |
400 |
} |
401 |
isTiny = |
402 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
403 |
|| ( zExp < -1 )
|
404 |
|| ( zSig + roundIncrement < 0x80000000 );
|
405 |
shift32RightJamming( zSig, - zExp, &zSig ); |
406 |
zExp = 0;
|
407 |
roundBits = zSig & 0x7F;
|
408 |
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
|
409 |
} |
410 |
} |
411 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
412 |
zSig = ( zSig + roundIncrement )>>7;
|
413 |
zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); |
414 |
if ( zSig == 0 ) zExp = 0; |
415 |
return packFloat32( zSign, zExp, zSig );
|
416 |
|
417 |
} |
418 |
|
419 |
/*----------------------------------------------------------------------------
|
420 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
421 |
| and significand `zSig', and returns the proper single-precision floating-
|
422 |
| point value corresponding to the abstract input. This routine is just like
|
423 |
| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
|
424 |
| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
|
425 |
| floating-point exponent.
|
426 |
*----------------------------------------------------------------------------*/
|
427 |
|
428 |
static float32
|
429 |
normalizeRoundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM) |
430 |
{ |
431 |
int8 shiftCount; |
432 |
|
433 |
shiftCount = countLeadingZeros32( zSig ) - 1;
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434 |
return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
|
435 |
|
436 |
} |
437 |
|
438 |
/*----------------------------------------------------------------------------
|
439 |
| Returns the fraction bits of the double-precision floating-point value `a'.
|
440 |
*----------------------------------------------------------------------------*/
|
441 |
|
442 |
INLINE uint64_t extractFloat64Frac( float64 a ) |
443 |
{ |
444 |
|
445 |
return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF ); |
446 |
|
447 |
} |
448 |
|
449 |
/*----------------------------------------------------------------------------
|
450 |
| Returns the exponent bits of the double-precision floating-point value `a'.
|
451 |
*----------------------------------------------------------------------------*/
|
452 |
|
453 |
INLINE int_fast16_t extractFloat64Exp(float64 a) |
454 |
{ |
455 |
|
456 |
return ( float64_val(a)>>52 ) & 0x7FF; |
457 |
|
458 |
} |
459 |
|
460 |
/*----------------------------------------------------------------------------
|
461 |
| Returns the sign bit of the double-precision floating-point value `a'.
|
462 |
*----------------------------------------------------------------------------*/
|
463 |
|
464 |
INLINE flag extractFloat64Sign( float64 a ) |
465 |
{ |
466 |
|
467 |
return float64_val(a)>>63; |
468 |
|
469 |
} |
470 |
|
471 |
/*----------------------------------------------------------------------------
|
472 |
| If `a' is denormal and we are in flush-to-zero mode then set the
|
473 |
| input-denormal exception and return zero. Otherwise just return the value.
|
474 |
*----------------------------------------------------------------------------*/
|
475 |
static float64 float64_squash_input_denormal(float64 a STATUS_PARAM)
|
476 |
{ |
477 |
if (STATUS(flush_inputs_to_zero)) {
|
478 |
if (extractFloat64Exp(a) == 0 && extractFloat64Frac(a) != 0) { |
479 |
float_raise(float_flag_input_denormal STATUS_VAR); |
480 |
return make_float64(float64_val(a) & (1ULL << 63)); |
481 |
} |
482 |
} |
483 |
return a;
|
484 |
} |
485 |
|
486 |
/*----------------------------------------------------------------------------
|
487 |
| Normalizes the subnormal double-precision floating-point value represented
|
488 |
| by the denormalized significand `aSig'. The normalized exponent and
|
489 |
| significand are stored at the locations pointed to by `zExpPtr' and
|
490 |
| `zSigPtr', respectively.
|
491 |
*----------------------------------------------------------------------------*/
|
492 |
|
493 |
static void |
494 |
normalizeFloat64Subnormal(uint64_t aSig, int_fast16_t *zExpPtr, uint64_t *zSigPtr) |
495 |
{ |
496 |
int8 shiftCount; |
497 |
|
498 |
shiftCount = countLeadingZeros64( aSig ) - 11;
|
499 |
*zSigPtr = aSig<<shiftCount; |
500 |
*zExpPtr = 1 - shiftCount;
|
501 |
|
502 |
} |
503 |
|
504 |
/*----------------------------------------------------------------------------
|
505 |
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
|
506 |
| double-precision floating-point value, returning the result. After being
|
507 |
| shifted into the proper positions, the three fields are simply added
|
508 |
| together to form the result. This means that any integer portion of `zSig'
|
509 |
| will be added into the exponent. Since a properly normalized significand
|
510 |
| will have an integer portion equal to 1, the `zExp' input should be 1 less
|
511 |
| than the desired result exponent whenever `zSig' is a complete, normalized
|
512 |
| significand.
|
513 |
*----------------------------------------------------------------------------*/
|
514 |
|
515 |
INLINE float64 packFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig) |
516 |
{ |
517 |
|
518 |
return make_float64(
|
519 |
( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig); |
520 |
|
521 |
} |
522 |
|
523 |
/*----------------------------------------------------------------------------
|
524 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
525 |
| and significand `zSig', and returns the proper double-precision floating-
|
526 |
| point value corresponding to the abstract input. Ordinarily, the abstract
|
527 |
| value is simply rounded and packed into the double-precision format, with
|
528 |
| the inexact exception raised if the abstract input cannot be represented
|
529 |
| exactly. However, if the abstract value is too large, the overflow and
|
530 |
| inexact exceptions are raised and an infinity or maximal finite value is
|
531 |
| returned. If the abstract value is too small, the input value is rounded
|
532 |
| to a subnormal number, and the underflow and inexact exceptions are raised
|
533 |
| if the abstract input cannot be represented exactly as a subnormal double-
|
534 |
| precision floating-point number.
|
535 |
| The input significand `zSig' has its binary point between bits 62
|
536 |
| and 61, which is 10 bits to the left of the usual location. This shifted
|
537 |
| significand must be normalized or smaller. If `zSig' is not normalized,
|
538 |
| `zExp' must be 0; in that case, the result returned is a subnormal number,
|
539 |
| and it must not require rounding. In the usual case that `zSig' is
|
540 |
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
|
541 |
| The handling of underflow and overflow follows the IEC/IEEE Standard for
|
542 |
| Binary Floating-Point Arithmetic.
|
543 |
*----------------------------------------------------------------------------*/
|
544 |
|
545 |
static float64 roundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM)
|
546 |
{ |
547 |
int8 roundingMode; |
548 |
flag roundNearestEven; |
549 |
int_fast16_t roundIncrement, roundBits; |
550 |
flag isTiny; |
551 |
|
552 |
roundingMode = STATUS(float_rounding_mode); |
553 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
554 |
roundIncrement = 0x200;
|
555 |
if ( ! roundNearestEven ) {
|
556 |
if ( roundingMode == float_round_to_zero ) {
|
557 |
roundIncrement = 0;
|
558 |
} |
559 |
else {
|
560 |
roundIncrement = 0x3FF;
|
561 |
if ( zSign ) {
|
562 |
if ( roundingMode == float_round_up ) roundIncrement = 0; |
563 |
} |
564 |
else {
|
565 |
if ( roundingMode == float_round_down ) roundIncrement = 0; |
566 |
} |
567 |
} |
568 |
} |
569 |
roundBits = zSig & 0x3FF;
|
570 |
if ( 0x7FD <= (uint16_t) zExp ) { |
571 |
if ( ( 0x7FD < zExp ) |
572 |
|| ( ( zExp == 0x7FD )
|
573 |
&& ( (int64_t) ( zSig + roundIncrement ) < 0 ) )
|
574 |
) { |
575 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
576 |
return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 )); |
577 |
} |
578 |
if ( zExp < 0 ) { |
579 |
if (STATUS(flush_to_zero)) {
|
580 |
float_raise(float_flag_output_denormal STATUS_VAR); |
581 |
return packFloat64(zSign, 0, 0); |
582 |
} |
583 |
isTiny = |
584 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
585 |
|| ( zExp < -1 )
|
586 |
|| ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
|
587 |
shift64RightJamming( zSig, - zExp, &zSig ); |
588 |
zExp = 0;
|
589 |
roundBits = zSig & 0x3FF;
|
590 |
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
|
591 |
} |
592 |
} |
593 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
594 |
zSig = ( zSig + roundIncrement )>>10;
|
595 |
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); |
596 |
if ( zSig == 0 ) zExp = 0; |
597 |
return packFloat64( zSign, zExp, zSig );
|
598 |
|
599 |
} |
600 |
|
601 |
/*----------------------------------------------------------------------------
|
602 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
603 |
| and significand `zSig', and returns the proper double-precision floating-
|
604 |
| point value corresponding to the abstract input. This routine is just like
|
605 |
| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
|
606 |
| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
|
607 |
| floating-point exponent.
|
608 |
*----------------------------------------------------------------------------*/
|
609 |
|
610 |
static float64
|
611 |
normalizeRoundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM) |
612 |
{ |
613 |
int8 shiftCount; |
614 |
|
615 |
shiftCount = countLeadingZeros64( zSig ) - 1;
|
616 |
return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
|
617 |
|
618 |
} |
619 |
|
620 |
/*----------------------------------------------------------------------------
|
621 |
| Returns the fraction bits of the extended double-precision floating-point
|
622 |
| value `a'.
|
623 |
*----------------------------------------------------------------------------*/
|
624 |
|
625 |
INLINE uint64_t extractFloatx80Frac( floatx80 a ) |
626 |
{ |
627 |
|
628 |
return a.low;
|
629 |
|
630 |
} |
631 |
|
632 |
/*----------------------------------------------------------------------------
|
633 |
| Returns the exponent bits of the extended double-precision floating-point
|
634 |
| value `a'.
|
635 |
*----------------------------------------------------------------------------*/
|
636 |
|
637 |
INLINE int32 extractFloatx80Exp( floatx80 a ) |
638 |
{ |
639 |
|
640 |
return a.high & 0x7FFF; |
641 |
|
642 |
} |
643 |
|
644 |
/*----------------------------------------------------------------------------
|
645 |
| Returns the sign bit of the extended double-precision floating-point value
|
646 |
| `a'.
|
647 |
*----------------------------------------------------------------------------*/
|
648 |
|
649 |
INLINE flag extractFloatx80Sign( floatx80 a ) |
650 |
{ |
651 |
|
652 |
return a.high>>15; |
653 |
|
654 |
} |
655 |
|
656 |
/*----------------------------------------------------------------------------
|
657 |
| Normalizes the subnormal extended double-precision floating-point value
|
658 |
| represented by the denormalized significand `aSig'. The normalized exponent
|
659 |
| and significand are stored at the locations pointed to by `zExpPtr' and
|
660 |
| `zSigPtr', respectively.
|
661 |
*----------------------------------------------------------------------------*/
|
662 |
|
663 |
static void |
664 |
normalizeFloatx80Subnormal( uint64_t aSig, int32 *zExpPtr, uint64_t *zSigPtr ) |
665 |
{ |
666 |
int8 shiftCount; |
667 |
|
668 |
shiftCount = countLeadingZeros64( aSig ); |
669 |
*zSigPtr = aSig<<shiftCount; |
670 |
*zExpPtr = 1 - shiftCount;
|
671 |
|
672 |
} |
673 |
|
674 |
/*----------------------------------------------------------------------------
|
675 |
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
|
676 |
| extended double-precision floating-point value, returning the result.
|
677 |
*----------------------------------------------------------------------------*/
|
678 |
|
679 |
INLINE floatx80 packFloatx80( flag zSign, int32 zExp, uint64_t zSig ) |
680 |
{ |
681 |
floatx80 z; |
682 |
|
683 |
z.low = zSig; |
684 |
z.high = ( ( (uint16_t) zSign )<<15 ) + zExp;
|
685 |
return z;
|
686 |
|
687 |
} |
688 |
|
689 |
/*----------------------------------------------------------------------------
|
690 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
691 |
| and extended significand formed by the concatenation of `zSig0' and `zSig1',
|
692 |
| and returns the proper extended double-precision floating-point value
|
693 |
| corresponding to the abstract input. Ordinarily, the abstract value is
|
694 |
| rounded and packed into the extended double-precision format, with the
|
695 |
| inexact exception raised if the abstract input cannot be represented
|
696 |
| exactly. However, if the abstract value is too large, the overflow and
|
697 |
| inexact exceptions are raised and an infinity or maximal finite value is
|
698 |
| returned. If the abstract value is too small, the input value is rounded to
|
699 |
| a subnormal number, and the underflow and inexact exceptions are raised if
|
700 |
| the abstract input cannot be represented exactly as a subnormal extended
|
701 |
| double-precision floating-point number.
|
702 |
| If `roundingPrecision' is 32 or 64, the result is rounded to the same
|
703 |
| number of bits as single or double precision, respectively. Otherwise, the
|
704 |
| result is rounded to the full precision of the extended double-precision
|
705 |
| format.
|
706 |
| The input significand must be normalized or smaller. If the input
|
707 |
| significand is not normalized, `zExp' must be 0; in that case, the result
|
708 |
| returned is a subnormal number, and it must not require rounding. The
|
709 |
| handling of underflow and overflow follows the IEC/IEEE Standard for Binary
|
710 |
| Floating-Point Arithmetic.
|
711 |
*----------------------------------------------------------------------------*/
|
712 |
|
713 |
static floatx80
|
714 |
roundAndPackFloatx80( |
715 |
int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 |
716 |
STATUS_PARAM) |
717 |
{ |
718 |
int8 roundingMode; |
719 |
flag roundNearestEven, increment, isTiny; |
720 |
int64 roundIncrement, roundMask, roundBits; |
721 |
|
722 |
roundingMode = STATUS(float_rounding_mode); |
723 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
724 |
if ( roundingPrecision == 80 ) goto precision80; |
725 |
if ( roundingPrecision == 64 ) { |
726 |
roundIncrement = LIT64( 0x0000000000000400 );
|
727 |
roundMask = LIT64( 0x00000000000007FF );
|
728 |
} |
729 |
else if ( roundingPrecision == 32 ) { |
730 |
roundIncrement = LIT64( 0x0000008000000000 );
|
731 |
roundMask = LIT64( 0x000000FFFFFFFFFF );
|
732 |
} |
733 |
else {
|
734 |
goto precision80;
|
735 |
} |
736 |
zSig0 |= ( zSig1 != 0 );
|
737 |
if ( ! roundNearestEven ) {
|
738 |
if ( roundingMode == float_round_to_zero ) {
|
739 |
roundIncrement = 0;
|
740 |
} |
741 |
else {
|
742 |
roundIncrement = roundMask; |
743 |
if ( zSign ) {
|
744 |
if ( roundingMode == float_round_up ) roundIncrement = 0; |
745 |
} |
746 |
else {
|
747 |
if ( roundingMode == float_round_down ) roundIncrement = 0; |
748 |
} |
749 |
} |
750 |
} |
751 |
roundBits = zSig0 & roundMask; |
752 |
if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { |
753 |
if ( ( 0x7FFE < zExp ) |
754 |
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
|
755 |
) { |
756 |
goto overflow;
|
757 |
} |
758 |
if ( zExp <= 0 ) { |
759 |
if (STATUS(flush_to_zero)) {
|
760 |
float_raise(float_flag_output_denormal STATUS_VAR); |
761 |
return packFloatx80(zSign, 0, 0); |
762 |
} |
763 |
isTiny = |
764 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
765 |
|| ( zExp < 0 )
|
766 |
|| ( zSig0 <= zSig0 + roundIncrement ); |
767 |
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
|
768 |
zExp = 0;
|
769 |
roundBits = zSig0 & roundMask; |
770 |
if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
|
771 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
772 |
zSig0 += roundIncrement; |
773 |
if ( (int64_t) zSig0 < 0 ) zExp = 1; |
774 |
roundIncrement = roundMask + 1;
|
775 |
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { |
776 |
roundMask |= roundIncrement; |
777 |
} |
778 |
zSig0 &= ~ roundMask; |
779 |
return packFloatx80( zSign, zExp, zSig0 );
|
780 |
} |
781 |
} |
782 |
if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
|
783 |
zSig0 += roundIncrement; |
784 |
if ( zSig0 < roundIncrement ) {
|
785 |
++zExp; |
786 |
zSig0 = LIT64( 0x8000000000000000 );
|
787 |
} |
788 |
roundIncrement = roundMask + 1;
|
789 |
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { |
790 |
roundMask |= roundIncrement; |
791 |
} |
792 |
zSig0 &= ~ roundMask; |
793 |
if ( zSig0 == 0 ) zExp = 0; |
794 |
return packFloatx80( zSign, zExp, zSig0 );
|
795 |
precision80:
|
796 |
increment = ( (int64_t) zSig1 < 0 );
|
797 |
if ( ! roundNearestEven ) {
|
798 |
if ( roundingMode == float_round_to_zero ) {
|
799 |
increment = 0;
|
800 |
} |
801 |
else {
|
802 |
if ( zSign ) {
|
803 |
increment = ( roundingMode == float_round_down ) && zSig1; |
804 |
} |
805 |
else {
|
806 |
increment = ( roundingMode == float_round_up ) && zSig1; |
807 |
} |
808 |
} |
809 |
} |
810 |
if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { |
811 |
if ( ( 0x7FFE < zExp ) |
812 |
|| ( ( zExp == 0x7FFE )
|
813 |
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
|
814 |
&& increment |
815 |
) |
816 |
) { |
817 |
roundMask = 0;
|
818 |
overflow:
|
819 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
820 |
if ( ( roundingMode == float_round_to_zero )
|
821 |
|| ( zSign && ( roundingMode == float_round_up ) ) |
822 |
|| ( ! zSign && ( roundingMode == float_round_down ) ) |
823 |
) { |
824 |
return packFloatx80( zSign, 0x7FFE, ~ roundMask ); |
825 |
} |
826 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
827 |
} |
828 |
if ( zExp <= 0 ) { |
829 |
isTiny = |
830 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
831 |
|| ( zExp < 0 )
|
832 |
|| ! increment |
833 |
|| ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
|
834 |
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
|
835 |
zExp = 0;
|
836 |
if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR);
|
837 |
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
838 |
if ( roundNearestEven ) {
|
839 |
increment = ( (int64_t) zSig1 < 0 );
|
840 |
} |
841 |
else {
|
842 |
if ( zSign ) {
|
843 |
increment = ( roundingMode == float_round_down ) && zSig1; |
844 |
} |
845 |
else {
|
846 |
increment = ( roundingMode == float_round_up ) && zSig1; |
847 |
} |
848 |
} |
849 |
if ( increment ) {
|
850 |
++zSig0; |
851 |
zSig0 &= |
852 |
~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
853 |
if ( (int64_t) zSig0 < 0 ) zExp = 1; |
854 |
} |
855 |
return packFloatx80( zSign, zExp, zSig0 );
|
856 |
} |
857 |
} |
858 |
if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
859 |
if ( increment ) {
|
860 |
++zSig0; |
861 |
if ( zSig0 == 0 ) { |
862 |
++zExp; |
863 |
zSig0 = LIT64( 0x8000000000000000 );
|
864 |
} |
865 |
else {
|
866 |
zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); |
867 |
} |
868 |
} |
869 |
else {
|
870 |
if ( zSig0 == 0 ) zExp = 0; |
871 |
} |
872 |
return packFloatx80( zSign, zExp, zSig0 );
|
873 |
|
874 |
} |
875 |
|
876 |
/*----------------------------------------------------------------------------
|
877 |
| Takes an abstract floating-point value having sign `zSign', exponent
|
878 |
| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
|
879 |
| and returns the proper extended double-precision floating-point value
|
880 |
| corresponding to the abstract input. This routine is just like
|
881 |
| `roundAndPackFloatx80' except that the input significand does not have to be
|
882 |
| normalized.
|
883 |
*----------------------------------------------------------------------------*/
|
884 |
|
885 |
static floatx80
|
886 |
normalizeRoundAndPackFloatx80( |
887 |
int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 |
888 |
STATUS_PARAM) |
889 |
{ |
890 |
int8 shiftCount; |
891 |
|
892 |
if ( zSig0 == 0 ) { |
893 |
zSig0 = zSig1; |
894 |
zSig1 = 0;
|
895 |
zExp -= 64;
|
896 |
} |
897 |
shiftCount = countLeadingZeros64( zSig0 ); |
898 |
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
899 |
zExp -= shiftCount; |
900 |
return
|
901 |
roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); |
902 |
|
903 |
} |
904 |
|
905 |
/*----------------------------------------------------------------------------
|
906 |
| Returns the least-significant 64 fraction bits of the quadruple-precision
|
907 |
| floating-point value `a'.
|
908 |
*----------------------------------------------------------------------------*/
|
909 |
|
910 |
INLINE uint64_t extractFloat128Frac1( float128 a ) |
911 |
{ |
912 |
|
913 |
return a.low;
|
914 |
|
915 |
} |
916 |
|
917 |
/*----------------------------------------------------------------------------
|
918 |
| Returns the most-significant 48 fraction bits of the quadruple-precision
|
919 |
| floating-point value `a'.
|
920 |
*----------------------------------------------------------------------------*/
|
921 |
|
922 |
INLINE uint64_t extractFloat128Frac0( float128 a ) |
923 |
{ |
924 |
|
925 |
return a.high & LIT64( 0x0000FFFFFFFFFFFF ); |
926 |
|
927 |
} |
928 |
|
929 |
/*----------------------------------------------------------------------------
|
930 |
| Returns the exponent bits of the quadruple-precision floating-point value
|
931 |
| `a'.
|
932 |
*----------------------------------------------------------------------------*/
|
933 |
|
934 |
INLINE int32 extractFloat128Exp( float128 a ) |
935 |
{ |
936 |
|
937 |
return ( a.high>>48 ) & 0x7FFF; |
938 |
|
939 |
} |
940 |
|
941 |
/*----------------------------------------------------------------------------
|
942 |
| Returns the sign bit of the quadruple-precision floating-point value `a'.
|
943 |
*----------------------------------------------------------------------------*/
|
944 |
|
945 |
INLINE flag extractFloat128Sign( float128 a ) |
946 |
{ |
947 |
|
948 |
return a.high>>63; |
949 |
|
950 |
} |
951 |
|
952 |
/*----------------------------------------------------------------------------
|
953 |
| Normalizes the subnormal quadruple-precision floating-point value
|
954 |
| represented by the denormalized significand formed by the concatenation of
|
955 |
| `aSig0' and `aSig1'. The normalized exponent is stored at the location
|
956 |
| pointed to by `zExpPtr'. The most significant 49 bits of the normalized
|
957 |
| significand are stored at the location pointed to by `zSig0Ptr', and the
|
958 |
| least significant 64 bits of the normalized significand are stored at the
|
959 |
| location pointed to by `zSig1Ptr'.
|
960 |
*----------------------------------------------------------------------------*/
|
961 |
|
962 |
static void |
963 |
normalizeFloat128Subnormal( |
964 |
uint64_t aSig0, |
965 |
uint64_t aSig1, |
966 |
int32 *zExpPtr, |
967 |
uint64_t *zSig0Ptr, |
968 |
uint64_t *zSig1Ptr |
969 |
) |
970 |
{ |
971 |
int8 shiftCount; |
972 |
|
973 |
if ( aSig0 == 0 ) { |
974 |
shiftCount = countLeadingZeros64( aSig1 ) - 15;
|
975 |
if ( shiftCount < 0 ) { |
976 |
*zSig0Ptr = aSig1>>( - shiftCount ); |
977 |
*zSig1Ptr = aSig1<<( shiftCount & 63 );
|
978 |
} |
979 |
else {
|
980 |
*zSig0Ptr = aSig1<<shiftCount; |
981 |
*zSig1Ptr = 0;
|
982 |
} |
983 |
*zExpPtr = - shiftCount - 63;
|
984 |
} |
985 |
else {
|
986 |
shiftCount = countLeadingZeros64( aSig0 ) - 15;
|
987 |
shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); |
988 |
*zExpPtr = 1 - shiftCount;
|
989 |
} |
990 |
|
991 |
} |
992 |
|
993 |
/*----------------------------------------------------------------------------
|
994 |
| Packs the sign `zSign', the exponent `zExp', and the significand formed
|
995 |
| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
|
996 |
| floating-point value, returning the result. After being shifted into the
|
997 |
| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
|
998 |
| added together to form the most significant 32 bits of the result. This
|
999 |
| means that any integer portion of `zSig0' will be added into the exponent.
|
1000 |
| Since a properly normalized significand will have an integer portion equal
|
1001 |
| to 1, the `zExp' input should be 1 less than the desired result exponent
|
1002 |
| whenever `zSig0' and `zSig1' concatenated form a complete, normalized
|
1003 |
| significand.
|
1004 |
*----------------------------------------------------------------------------*/
|
1005 |
|
1006 |
INLINE float128 |
1007 |
packFloat128( flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 ) |
1008 |
{ |
1009 |
float128 z; |
1010 |
|
1011 |
z.low = zSig1; |
1012 |
z.high = ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<48 ) + zSig0; |
1013 |
return z;
|
1014 |
|
1015 |
} |
1016 |
|
1017 |
/*----------------------------------------------------------------------------
|
1018 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
1019 |
| and extended significand formed by the concatenation of `zSig0', `zSig1',
|
1020 |
| and `zSig2', and returns the proper quadruple-precision floating-point value
|
1021 |
| corresponding to the abstract input. Ordinarily, the abstract value is
|
1022 |
| simply rounded and packed into the quadruple-precision format, with the
|
1023 |
| inexact exception raised if the abstract input cannot be represented
|
1024 |
| exactly. However, if the abstract value is too large, the overflow and
|
1025 |
| inexact exceptions are raised and an infinity or maximal finite value is
|
1026 |
| returned. If the abstract value is too small, the input value is rounded to
|
1027 |
| a subnormal number, and the underflow and inexact exceptions are raised if
|
1028 |
| the abstract input cannot be represented exactly as a subnormal quadruple-
|
1029 |
| precision floating-point number.
|
1030 |
| The input significand must be normalized or smaller. If the input
|
1031 |
| significand is not normalized, `zExp' must be 0; in that case, the result
|
1032 |
| returned is a subnormal number, and it must not require rounding. In the
|
1033 |
| usual case that the input significand is normalized, `zExp' must be 1 less
|
1034 |
| than the ``true'' floating-point exponent. The handling of underflow and
|
1035 |
| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1036 |
*----------------------------------------------------------------------------*/
|
1037 |
|
1038 |
static float128
|
1039 |
roundAndPackFloat128( |
1040 |
flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1, uint64_t zSig2 STATUS_PARAM) |
1041 |
{ |
1042 |
int8 roundingMode; |
1043 |
flag roundNearestEven, increment, isTiny; |
1044 |
|
1045 |
roundingMode = STATUS(float_rounding_mode); |
1046 |
roundNearestEven = ( roundingMode == float_round_nearest_even ); |
1047 |
increment = ( (int64_t) zSig2 < 0 );
|
1048 |
if ( ! roundNearestEven ) {
|
1049 |
if ( roundingMode == float_round_to_zero ) {
|
1050 |
increment = 0;
|
1051 |
} |
1052 |
else {
|
1053 |
if ( zSign ) {
|
1054 |
increment = ( roundingMode == float_round_down ) && zSig2; |
1055 |
} |
1056 |
else {
|
1057 |
increment = ( roundingMode == float_round_up ) && zSig2; |
1058 |
} |
1059 |
} |
1060 |
} |
1061 |
if ( 0x7FFD <= (uint32_t) zExp ) { |
1062 |
if ( ( 0x7FFD < zExp ) |
1063 |
|| ( ( zExp == 0x7FFD )
|
1064 |
&& eq128( |
1065 |
LIT64( 0x0001FFFFFFFFFFFF ),
|
1066 |
LIT64( 0xFFFFFFFFFFFFFFFF ),
|
1067 |
zSig0, |
1068 |
zSig1 |
1069 |
) |
1070 |
&& increment |
1071 |
) |
1072 |
) { |
1073 |
float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); |
1074 |
if ( ( roundingMode == float_round_to_zero )
|
1075 |
|| ( zSign && ( roundingMode == float_round_up ) ) |
1076 |
|| ( ! zSign && ( roundingMode == float_round_down ) ) |
1077 |
) { |
1078 |
return
|
1079 |
packFloat128( |
1080 |
zSign, |
1081 |
0x7FFE,
|
1082 |
LIT64( 0x0000FFFFFFFFFFFF ),
|
1083 |
LIT64( 0xFFFFFFFFFFFFFFFF )
|
1084 |
); |
1085 |
} |
1086 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
1087 |
} |
1088 |
if ( zExp < 0 ) { |
1089 |
if (STATUS(flush_to_zero)) {
|
1090 |
float_raise(float_flag_output_denormal STATUS_VAR); |
1091 |
return packFloat128(zSign, 0, 0, 0); |
1092 |
} |
1093 |
isTiny = |
1094 |
( STATUS(float_detect_tininess) == float_tininess_before_rounding ) |
1095 |
|| ( zExp < -1 )
|
1096 |
|| ! increment |
1097 |
|| lt128( |
1098 |
zSig0, |
1099 |
zSig1, |
1100 |
LIT64( 0x0001FFFFFFFFFFFF ),
|
1101 |
LIT64( 0xFFFFFFFFFFFFFFFF )
|
1102 |
); |
1103 |
shift128ExtraRightJamming( |
1104 |
zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); |
1105 |
zExp = 0;
|
1106 |
if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR);
|
1107 |
if ( roundNearestEven ) {
|
1108 |
increment = ( (int64_t) zSig2 < 0 );
|
1109 |
} |
1110 |
else {
|
1111 |
if ( zSign ) {
|
1112 |
increment = ( roundingMode == float_round_down ) && zSig2; |
1113 |
} |
1114 |
else {
|
1115 |
increment = ( roundingMode == float_round_up ) && zSig2; |
1116 |
} |
1117 |
} |
1118 |
} |
1119 |
} |
1120 |
if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1121 |
if ( increment ) {
|
1122 |
add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); |
1123 |
zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
|
1124 |
} |
1125 |
else {
|
1126 |
if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; |
1127 |
} |
1128 |
return packFloat128( zSign, zExp, zSig0, zSig1 );
|
1129 |
|
1130 |
} |
1131 |
|
1132 |
/*----------------------------------------------------------------------------
|
1133 |
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
1134 |
| and significand formed by the concatenation of `zSig0' and `zSig1', and
|
1135 |
| returns the proper quadruple-precision floating-point value corresponding
|
1136 |
| to the abstract input. This routine is just like `roundAndPackFloat128'
|
1137 |
| except that the input significand has fewer bits and does not have to be
|
1138 |
| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
|
1139 |
| point exponent.
|
1140 |
*----------------------------------------------------------------------------*/
|
1141 |
|
1142 |
static float128
|
1143 |
normalizeRoundAndPackFloat128( |
1144 |
flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 STATUS_PARAM) |
1145 |
{ |
1146 |
int8 shiftCount; |
1147 |
uint64_t zSig2; |
1148 |
|
1149 |
if ( zSig0 == 0 ) { |
1150 |
zSig0 = zSig1; |
1151 |
zSig1 = 0;
|
1152 |
zExp -= 64;
|
1153 |
} |
1154 |
shiftCount = countLeadingZeros64( zSig0 ) - 15;
|
1155 |
if ( 0 <= shiftCount ) { |
1156 |
zSig2 = 0;
|
1157 |
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
1158 |
} |
1159 |
else {
|
1160 |
shift128ExtraRightJamming( |
1161 |
zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
|
1162 |
} |
1163 |
zExp -= shiftCount; |
1164 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR);
|
1165 |
|
1166 |
} |
1167 |
|
1168 |
/*----------------------------------------------------------------------------
|
1169 |
| Returns the result of converting the 32-bit two's complement integer `a'
|
1170 |
| to the single-precision floating-point format. The conversion is performed
|
1171 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1172 |
*----------------------------------------------------------------------------*/
|
1173 |
|
1174 |
float32 int32_to_float32(int32_t a STATUS_PARAM) |
1175 |
{ |
1176 |
flag zSign; |
1177 |
|
1178 |
if ( a == 0 ) return float32_zero; |
1179 |
if ( a == (int32_t) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); |
1180 |
zSign = ( a < 0 );
|
1181 |
return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); |
1182 |
|
1183 |
} |
1184 |
|
1185 |
/*----------------------------------------------------------------------------
|
1186 |
| Returns the result of converting the 32-bit two's complement integer `a'
|
1187 |
| to the double-precision floating-point format. The conversion is performed
|
1188 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1189 |
*----------------------------------------------------------------------------*/
|
1190 |
|
1191 |
float64 int32_to_float64(int32_t a STATUS_PARAM) |
1192 |
{ |
1193 |
flag zSign; |
1194 |
uint32 absA; |
1195 |
int8 shiftCount; |
1196 |
uint64_t zSig; |
1197 |
|
1198 |
if ( a == 0 ) return float64_zero; |
1199 |
zSign = ( a < 0 );
|
1200 |
absA = zSign ? - a : a; |
1201 |
shiftCount = countLeadingZeros32( absA ) + 21;
|
1202 |
zSig = absA; |
1203 |
return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); |
1204 |
|
1205 |
} |
1206 |
|
1207 |
/*----------------------------------------------------------------------------
|
1208 |
| Returns the result of converting the 32-bit two's complement integer `a'
|
1209 |
| to the extended double-precision floating-point format. The conversion
|
1210 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1211 |
| Arithmetic.
|
1212 |
*----------------------------------------------------------------------------*/
|
1213 |
|
1214 |
floatx80 int32_to_floatx80(int32_t a STATUS_PARAM) |
1215 |
{ |
1216 |
flag zSign; |
1217 |
uint32 absA; |
1218 |
int8 shiftCount; |
1219 |
uint64_t zSig; |
1220 |
|
1221 |
if ( a == 0 ) return packFloatx80( 0, 0, 0 ); |
1222 |
zSign = ( a < 0 );
|
1223 |
absA = zSign ? - a : a; |
1224 |
shiftCount = countLeadingZeros32( absA ) + 32;
|
1225 |
zSig = absA; |
1226 |
return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); |
1227 |
|
1228 |
} |
1229 |
|
1230 |
/*----------------------------------------------------------------------------
|
1231 |
| Returns the result of converting the 32-bit two's complement integer `a' to
|
1232 |
| the quadruple-precision floating-point format. The conversion is performed
|
1233 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1234 |
*----------------------------------------------------------------------------*/
|
1235 |
|
1236 |
float128 int32_to_float128(int32_t a STATUS_PARAM) |
1237 |
{ |
1238 |
flag zSign; |
1239 |
uint32 absA; |
1240 |
int8 shiftCount; |
1241 |
uint64_t zSig0; |
1242 |
|
1243 |
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); |
1244 |
zSign = ( a < 0 );
|
1245 |
absA = zSign ? - a : a; |
1246 |
shiftCount = countLeadingZeros32( absA ) + 17;
|
1247 |
zSig0 = absA; |
1248 |
return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); |
1249 |
|
1250 |
} |
1251 |
|
1252 |
/*----------------------------------------------------------------------------
|
1253 |
| Returns the result of converting the 64-bit two's complement integer `a'
|
1254 |
| to the single-precision floating-point format. The conversion is performed
|
1255 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1256 |
*----------------------------------------------------------------------------*/
|
1257 |
|
1258 |
float32 int64_to_float32(int64_t a STATUS_PARAM) |
1259 |
{ |
1260 |
flag zSign; |
1261 |
uint64 absA; |
1262 |
int8 shiftCount; |
1263 |
|
1264 |
if ( a == 0 ) return float32_zero; |
1265 |
zSign = ( a < 0 );
|
1266 |
absA = zSign ? - a : a; |
1267 |
shiftCount = countLeadingZeros64( absA ) - 40;
|
1268 |
if ( 0 <= shiftCount ) { |
1269 |
return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); |
1270 |
} |
1271 |
else {
|
1272 |
shiftCount += 7;
|
1273 |
if ( shiftCount < 0 ) { |
1274 |
shift64RightJamming( absA, - shiftCount, &absA ); |
1275 |
} |
1276 |
else {
|
1277 |
absA <<= shiftCount; |
1278 |
} |
1279 |
return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); |
1280 |
} |
1281 |
|
1282 |
} |
1283 |
|
1284 |
float32 uint64_to_float32(uint64_t a STATUS_PARAM) |
1285 |
{ |
1286 |
int8 shiftCount; |
1287 |
|
1288 |
if ( a == 0 ) return float32_zero; |
1289 |
shiftCount = countLeadingZeros64( a ) - 40;
|
1290 |
if ( 0 <= shiftCount ) { |
1291 |
return packFloat32(0, 0x95 - shiftCount, a<<shiftCount); |
1292 |
} |
1293 |
else {
|
1294 |
shiftCount += 7;
|
1295 |
if ( shiftCount < 0 ) { |
1296 |
shift64RightJamming( a, - shiftCount, &a ); |
1297 |
} |
1298 |
else {
|
1299 |
a <<= shiftCount; |
1300 |
} |
1301 |
return roundAndPackFloat32(0, 0x9C - shiftCount, a STATUS_VAR); |
1302 |
} |
1303 |
} |
1304 |
|
1305 |
/*----------------------------------------------------------------------------
|
1306 |
| Returns the result of converting the 64-bit two's complement integer `a'
|
1307 |
| to the double-precision floating-point format. The conversion is performed
|
1308 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1309 |
*----------------------------------------------------------------------------*/
|
1310 |
|
1311 |
float64 int64_to_float64(int64_t a STATUS_PARAM) |
1312 |
{ |
1313 |
flag zSign; |
1314 |
|
1315 |
if ( a == 0 ) return float64_zero; |
1316 |
if ( a == (int64_t) LIT64( 0x8000000000000000 ) ) { |
1317 |
return packFloat64( 1, 0x43E, 0 ); |
1318 |
} |
1319 |
zSign = ( a < 0 );
|
1320 |
return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); |
1321 |
|
1322 |
} |
1323 |
|
1324 |
float64 uint64_to_float64(uint64_t a STATUS_PARAM) |
1325 |
{ |
1326 |
int exp = 0x43C; |
1327 |
|
1328 |
if (a == 0) { |
1329 |
return float64_zero;
|
1330 |
} |
1331 |
if ((int64_t)a < 0) { |
1332 |
shift64RightJamming(a, 1, &a);
|
1333 |
exp += 1;
|
1334 |
} |
1335 |
return normalizeRoundAndPackFloat64(0, exp, a STATUS_VAR); |
1336 |
} |
1337 |
|
1338 |
/*----------------------------------------------------------------------------
|
1339 |
| Returns the result of converting the 64-bit two's complement integer `a'
|
1340 |
| to the extended double-precision floating-point format. The conversion
|
1341 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1342 |
| Arithmetic.
|
1343 |
*----------------------------------------------------------------------------*/
|
1344 |
|
1345 |
floatx80 int64_to_floatx80(int64_t a STATUS_PARAM) |
1346 |
{ |
1347 |
flag zSign; |
1348 |
uint64 absA; |
1349 |
int8 shiftCount; |
1350 |
|
1351 |
if ( a == 0 ) return packFloatx80( 0, 0, 0 ); |
1352 |
zSign = ( a < 0 );
|
1353 |
absA = zSign ? - a : a; |
1354 |
shiftCount = countLeadingZeros64( absA ); |
1355 |
return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); |
1356 |
|
1357 |
} |
1358 |
|
1359 |
/*----------------------------------------------------------------------------
|
1360 |
| Returns the result of converting the 64-bit two's complement integer `a' to
|
1361 |
| the quadruple-precision floating-point format. The conversion is performed
|
1362 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
1363 |
*----------------------------------------------------------------------------*/
|
1364 |
|
1365 |
float128 int64_to_float128(int64_t a STATUS_PARAM) |
1366 |
{ |
1367 |
flag zSign; |
1368 |
uint64 absA; |
1369 |
int8 shiftCount; |
1370 |
int32 zExp; |
1371 |
uint64_t zSig0, zSig1; |
1372 |
|
1373 |
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); |
1374 |
zSign = ( a < 0 );
|
1375 |
absA = zSign ? - a : a; |
1376 |
shiftCount = countLeadingZeros64( absA ) + 49;
|
1377 |
zExp = 0x406E - shiftCount;
|
1378 |
if ( 64 <= shiftCount ) { |
1379 |
zSig1 = 0;
|
1380 |
zSig0 = absA; |
1381 |
shiftCount -= 64;
|
1382 |
} |
1383 |
else {
|
1384 |
zSig1 = absA; |
1385 |
zSig0 = 0;
|
1386 |
} |
1387 |
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); |
1388 |
return packFloat128( zSign, zExp, zSig0, zSig1 );
|
1389 |
|
1390 |
} |
1391 |
|
1392 |
float128 uint64_to_float128(uint64_t a STATUS_PARAM) |
1393 |
{ |
1394 |
if (a == 0) { |
1395 |
return float128_zero;
|
1396 |
} |
1397 |
return normalizeRoundAndPackFloat128(0, 0x406E, a, 0 STATUS_VAR); |
1398 |
} |
1399 |
|
1400 |
/*----------------------------------------------------------------------------
|
1401 |
| Returns the result of converting the single-precision floating-point value
|
1402 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
1403 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1404 |
| Arithmetic---which means in particular that the conversion is rounded
|
1405 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
1406 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
1407 |
| largest integer with the same sign as `a' is returned.
|
1408 |
*----------------------------------------------------------------------------*/
|
1409 |
|
1410 |
int32 float32_to_int32( float32 a STATUS_PARAM ) |
1411 |
{ |
1412 |
flag aSign; |
1413 |
int_fast16_t aExp, shiftCount; |
1414 |
uint32_t aSig; |
1415 |
uint64_t aSig64; |
1416 |
|
1417 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1418 |
aSig = extractFloat32Frac( a ); |
1419 |
aExp = extractFloat32Exp( a ); |
1420 |
aSign = extractFloat32Sign( a ); |
1421 |
if ( ( aExp == 0xFF ) && aSig ) aSign = 0; |
1422 |
if ( aExp ) aSig |= 0x00800000; |
1423 |
shiftCount = 0xAF - aExp;
|
1424 |
aSig64 = aSig; |
1425 |
aSig64 <<= 32;
|
1426 |
if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); |
1427 |
return roundAndPackInt32( aSign, aSig64 STATUS_VAR );
|
1428 |
|
1429 |
} |
1430 |
|
1431 |
/*----------------------------------------------------------------------------
|
1432 |
| Returns the result of converting the single-precision floating-point value
|
1433 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
1434 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1435 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
1436 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
1437 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
1438 |
| returned.
|
1439 |
*----------------------------------------------------------------------------*/
|
1440 |
|
1441 |
int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) |
1442 |
{ |
1443 |
flag aSign; |
1444 |
int_fast16_t aExp, shiftCount; |
1445 |
uint32_t aSig; |
1446 |
int32_t z; |
1447 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1448 |
|
1449 |
aSig = extractFloat32Frac( a ); |
1450 |
aExp = extractFloat32Exp( a ); |
1451 |
aSign = extractFloat32Sign( a ); |
1452 |
shiftCount = aExp - 0x9E;
|
1453 |
if ( 0 <= shiftCount ) { |
1454 |
if ( float32_val(a) != 0xCF000000 ) { |
1455 |
float_raise( float_flag_invalid STATUS_VAR); |
1456 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; |
1457 |
} |
1458 |
return (int32_t) 0x80000000; |
1459 |
} |
1460 |
else if ( aExp <= 0x7E ) { |
1461 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1462 |
return 0; |
1463 |
} |
1464 |
aSig = ( aSig | 0x00800000 )<<8; |
1465 |
z = aSig>>( - shiftCount ); |
1466 |
if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { |
1467 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1468 |
} |
1469 |
if ( aSign ) z = - z;
|
1470 |
return z;
|
1471 |
|
1472 |
} |
1473 |
|
1474 |
/*----------------------------------------------------------------------------
|
1475 |
| Returns the result of converting the single-precision floating-point value
|
1476 |
| `a' to the 16-bit two's complement integer format. The conversion is
|
1477 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1478 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
1479 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
1480 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
1481 |
| returned.
|
1482 |
*----------------------------------------------------------------------------*/
|
1483 |
|
1484 |
int_fast16_t float32_to_int16_round_to_zero(float32 a STATUS_PARAM) |
1485 |
{ |
1486 |
flag aSign; |
1487 |
int_fast16_t aExp, shiftCount; |
1488 |
uint32_t aSig; |
1489 |
int32 z; |
1490 |
|
1491 |
aSig = extractFloat32Frac( a ); |
1492 |
aExp = extractFloat32Exp( a ); |
1493 |
aSign = extractFloat32Sign( a ); |
1494 |
shiftCount = aExp - 0x8E;
|
1495 |
if ( 0 <= shiftCount ) { |
1496 |
if ( float32_val(a) != 0xC7000000 ) { |
1497 |
float_raise( float_flag_invalid STATUS_VAR); |
1498 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
1499 |
return 0x7FFF; |
1500 |
} |
1501 |
} |
1502 |
return (int32_t) 0xffff8000; |
1503 |
} |
1504 |
else if ( aExp <= 0x7E ) { |
1505 |
if ( aExp | aSig ) {
|
1506 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1507 |
} |
1508 |
return 0; |
1509 |
} |
1510 |
shiftCount -= 0x10;
|
1511 |
aSig = ( aSig | 0x00800000 )<<8; |
1512 |
z = aSig>>( - shiftCount ); |
1513 |
if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { |
1514 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1515 |
} |
1516 |
if ( aSign ) {
|
1517 |
z = - z; |
1518 |
} |
1519 |
return z;
|
1520 |
|
1521 |
} |
1522 |
|
1523 |
/*----------------------------------------------------------------------------
|
1524 |
| Returns the result of converting the single-precision floating-point value
|
1525 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
1526 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1527 |
| Arithmetic---which means in particular that the conversion is rounded
|
1528 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
1529 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
1530 |
| largest integer with the same sign as `a' is returned.
|
1531 |
*----------------------------------------------------------------------------*/
|
1532 |
|
1533 |
int64 float32_to_int64( float32 a STATUS_PARAM ) |
1534 |
{ |
1535 |
flag aSign; |
1536 |
int_fast16_t aExp, shiftCount; |
1537 |
uint32_t aSig; |
1538 |
uint64_t aSig64, aSigExtra; |
1539 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1540 |
|
1541 |
aSig = extractFloat32Frac( a ); |
1542 |
aExp = extractFloat32Exp( a ); |
1543 |
aSign = extractFloat32Sign( a ); |
1544 |
shiftCount = 0xBE - aExp;
|
1545 |
if ( shiftCount < 0 ) { |
1546 |
float_raise( float_flag_invalid STATUS_VAR); |
1547 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
1548 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
1549 |
} |
1550 |
return (int64_t) LIT64( 0x8000000000000000 ); |
1551 |
} |
1552 |
if ( aExp ) aSig |= 0x00800000; |
1553 |
aSig64 = aSig; |
1554 |
aSig64 <<= 40;
|
1555 |
shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra );
|
1556 |
return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR );
|
1557 |
|
1558 |
} |
1559 |
|
1560 |
/*----------------------------------------------------------------------------
|
1561 |
| Returns the result of converting the single-precision floating-point value
|
1562 |
| `a' to the 64-bit unsigned integer format. The conversion is
|
1563 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1564 |
| Arithmetic---which means in particular that the conversion is rounded
|
1565 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
1566 |
| unsigned integer is returned. Otherwise, if the conversion overflows, the
|
1567 |
| largest unsigned integer is returned. If the 'a' is negative, the result
|
1568 |
| is rounded and zero is returned; values that do not round to zero will
|
1569 |
| raise the inexact exception flag.
|
1570 |
*----------------------------------------------------------------------------*/
|
1571 |
|
1572 |
uint64 float32_to_uint64(float32 a STATUS_PARAM) |
1573 |
{ |
1574 |
flag aSign; |
1575 |
int_fast16_t aExp, shiftCount; |
1576 |
uint32_t aSig; |
1577 |
uint64_t aSig64, aSigExtra; |
1578 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1579 |
|
1580 |
aSig = extractFloat32Frac(a); |
1581 |
aExp = extractFloat32Exp(a); |
1582 |
aSign = extractFloat32Sign(a); |
1583 |
if ((aSign) && (aExp > 126)) { |
1584 |
float_raise(float_flag_invalid STATUS_VAR); |
1585 |
if (float32_is_any_nan(a)) {
|
1586 |
return LIT64(0xFFFFFFFFFFFFFFFF); |
1587 |
} else {
|
1588 |
return 0; |
1589 |
} |
1590 |
} |
1591 |
shiftCount = 0xBE - aExp;
|
1592 |
if (aExp) {
|
1593 |
aSig |= 0x00800000;
|
1594 |
} |
1595 |
if (shiftCount < 0) { |
1596 |
float_raise(float_flag_invalid STATUS_VAR); |
1597 |
return LIT64(0xFFFFFFFFFFFFFFFF); |
1598 |
} |
1599 |
|
1600 |
aSig64 = aSig; |
1601 |
aSig64 <<= 40;
|
1602 |
shift64ExtraRightJamming(aSig64, 0, shiftCount, &aSig64, &aSigExtra);
|
1603 |
return roundAndPackUint64(aSign, aSig64, aSigExtra STATUS_VAR);
|
1604 |
} |
1605 |
|
1606 |
/*----------------------------------------------------------------------------
|
1607 |
| Returns the result of converting the single-precision floating-point value
|
1608 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
1609 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1610 |
| Arithmetic, except that the conversion is always rounded toward zero. If
|
1611 |
| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
1612 |
| conversion overflows, the largest integer with the same sign as `a' is
|
1613 |
| returned.
|
1614 |
*----------------------------------------------------------------------------*/
|
1615 |
|
1616 |
int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) |
1617 |
{ |
1618 |
flag aSign; |
1619 |
int_fast16_t aExp, shiftCount; |
1620 |
uint32_t aSig; |
1621 |
uint64_t aSig64; |
1622 |
int64 z; |
1623 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1624 |
|
1625 |
aSig = extractFloat32Frac( a ); |
1626 |
aExp = extractFloat32Exp( a ); |
1627 |
aSign = extractFloat32Sign( a ); |
1628 |
shiftCount = aExp - 0xBE;
|
1629 |
if ( 0 <= shiftCount ) { |
1630 |
if ( float32_val(a) != 0xDF000000 ) { |
1631 |
float_raise( float_flag_invalid STATUS_VAR); |
1632 |
if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { |
1633 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
1634 |
} |
1635 |
} |
1636 |
return (int64_t) LIT64( 0x8000000000000000 ); |
1637 |
} |
1638 |
else if ( aExp <= 0x7E ) { |
1639 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1640 |
return 0; |
1641 |
} |
1642 |
aSig64 = aSig | 0x00800000;
|
1643 |
aSig64 <<= 40;
|
1644 |
z = aSig64>>( - shiftCount ); |
1645 |
if ( (uint64_t) ( aSig64<<( shiftCount & 63 ) ) ) { |
1646 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1647 |
} |
1648 |
if ( aSign ) z = - z;
|
1649 |
return z;
|
1650 |
|
1651 |
} |
1652 |
|
1653 |
/*----------------------------------------------------------------------------
|
1654 |
| Returns the result of converting the single-precision floating-point value
|
1655 |
| `a' to the double-precision floating-point format. The conversion is
|
1656 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1657 |
| Arithmetic.
|
1658 |
*----------------------------------------------------------------------------*/
|
1659 |
|
1660 |
float64 float32_to_float64( float32 a STATUS_PARAM ) |
1661 |
{ |
1662 |
flag aSign; |
1663 |
int_fast16_t aExp; |
1664 |
uint32_t aSig; |
1665 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1666 |
|
1667 |
aSig = extractFloat32Frac( a ); |
1668 |
aExp = extractFloat32Exp( a ); |
1669 |
aSign = extractFloat32Sign( a ); |
1670 |
if ( aExp == 0xFF ) { |
1671 |
if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
1672 |
return packFloat64( aSign, 0x7FF, 0 ); |
1673 |
} |
1674 |
if ( aExp == 0 ) { |
1675 |
if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); |
1676 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1677 |
--aExp; |
1678 |
} |
1679 |
return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 ); |
1680 |
|
1681 |
} |
1682 |
|
1683 |
/*----------------------------------------------------------------------------
|
1684 |
| Returns the result of converting the single-precision floating-point value
|
1685 |
| `a' to the extended double-precision floating-point format. The conversion
|
1686 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1687 |
| Arithmetic.
|
1688 |
*----------------------------------------------------------------------------*/
|
1689 |
|
1690 |
floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) |
1691 |
{ |
1692 |
flag aSign; |
1693 |
int_fast16_t aExp; |
1694 |
uint32_t aSig; |
1695 |
|
1696 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1697 |
aSig = extractFloat32Frac( a ); |
1698 |
aExp = extractFloat32Exp( a ); |
1699 |
aSign = extractFloat32Sign( a ); |
1700 |
if ( aExp == 0xFF ) { |
1701 |
if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
1702 |
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
1703 |
} |
1704 |
if ( aExp == 0 ) { |
1705 |
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); |
1706 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1707 |
} |
1708 |
aSig |= 0x00800000;
|
1709 |
return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 ); |
1710 |
|
1711 |
} |
1712 |
|
1713 |
/*----------------------------------------------------------------------------
|
1714 |
| Returns the result of converting the single-precision floating-point value
|
1715 |
| `a' to the double-precision floating-point format. The conversion is
|
1716 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
1717 |
| Arithmetic.
|
1718 |
*----------------------------------------------------------------------------*/
|
1719 |
|
1720 |
float128 float32_to_float128( float32 a STATUS_PARAM ) |
1721 |
{ |
1722 |
flag aSign; |
1723 |
int_fast16_t aExp; |
1724 |
uint32_t aSig; |
1725 |
|
1726 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1727 |
aSig = extractFloat32Frac( a ); |
1728 |
aExp = extractFloat32Exp( a ); |
1729 |
aSign = extractFloat32Sign( a ); |
1730 |
if ( aExp == 0xFF ) { |
1731 |
if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
1732 |
return packFloat128( aSign, 0x7FFF, 0, 0 ); |
1733 |
} |
1734 |
if ( aExp == 0 ) { |
1735 |
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); |
1736 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
1737 |
--aExp; |
1738 |
} |
1739 |
return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 ); |
1740 |
|
1741 |
} |
1742 |
|
1743 |
/*----------------------------------------------------------------------------
|
1744 |
| Rounds the single-precision floating-point value `a' to an integer, and
|
1745 |
| returns the result as a single-precision floating-point value. The
|
1746 |
| operation is performed according to the IEC/IEEE Standard for Binary
|
1747 |
| Floating-Point Arithmetic.
|
1748 |
*----------------------------------------------------------------------------*/
|
1749 |
|
1750 |
float32 float32_round_to_int( float32 a STATUS_PARAM) |
1751 |
{ |
1752 |
flag aSign; |
1753 |
int_fast16_t aExp; |
1754 |
uint32_t lastBitMask, roundBitsMask; |
1755 |
int8 roundingMode; |
1756 |
uint32_t z; |
1757 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1758 |
|
1759 |
aExp = extractFloat32Exp( a ); |
1760 |
if ( 0x96 <= aExp ) { |
1761 |
if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { |
1762 |
return propagateFloat32NaN( a, a STATUS_VAR );
|
1763 |
} |
1764 |
return a;
|
1765 |
} |
1766 |
if ( aExp <= 0x7E ) { |
1767 |
if ( (uint32_t) ( float32_val(a)<<1 ) == 0 ) return a; |
1768 |
STATUS(float_exception_flags) |= float_flag_inexact; |
1769 |
aSign = extractFloat32Sign( a ); |
1770 |
switch ( STATUS(float_rounding_mode) ) {
|
1771 |
case float_round_nearest_even:
|
1772 |
if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { |
1773 |
return packFloat32( aSign, 0x7F, 0 ); |
1774 |
} |
1775 |
break;
|
1776 |
case float_round_down:
|
1777 |
return make_float32(aSign ? 0xBF800000 : 0); |
1778 |
case float_round_up:
|
1779 |
return make_float32(aSign ? 0x80000000 : 0x3F800000); |
1780 |
} |
1781 |
return packFloat32( aSign, 0, 0 ); |
1782 |
} |
1783 |
lastBitMask = 1;
|
1784 |
lastBitMask <<= 0x96 - aExp;
|
1785 |
roundBitsMask = lastBitMask - 1;
|
1786 |
z = float32_val(a); |
1787 |
roundingMode = STATUS(float_rounding_mode); |
1788 |
if ( roundingMode == float_round_nearest_even ) {
|
1789 |
z += lastBitMask>>1;
|
1790 |
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; |
1791 |
} |
1792 |
else if ( roundingMode != float_round_to_zero ) { |
1793 |
if ( extractFloat32Sign( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) {
|
1794 |
z += roundBitsMask; |
1795 |
} |
1796 |
} |
1797 |
z &= ~ roundBitsMask; |
1798 |
if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact;
|
1799 |
return make_float32(z);
|
1800 |
|
1801 |
} |
1802 |
|
1803 |
/*----------------------------------------------------------------------------
|
1804 |
| Returns the result of adding the absolute values of the single-precision
|
1805 |
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
1806 |
| before being returned. `zSign' is ignored if the result is a NaN.
|
1807 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
1808 |
| Floating-Point Arithmetic.
|
1809 |
*----------------------------------------------------------------------------*/
|
1810 |
|
1811 |
static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
|
1812 |
{ |
1813 |
int_fast16_t aExp, bExp, zExp; |
1814 |
uint32_t aSig, bSig, zSig; |
1815 |
int_fast16_t expDiff; |
1816 |
|
1817 |
aSig = extractFloat32Frac( a ); |
1818 |
aExp = extractFloat32Exp( a ); |
1819 |
bSig = extractFloat32Frac( b ); |
1820 |
bExp = extractFloat32Exp( b ); |
1821 |
expDiff = aExp - bExp; |
1822 |
aSig <<= 6;
|
1823 |
bSig <<= 6;
|
1824 |
if ( 0 < expDiff ) { |
1825 |
if ( aExp == 0xFF ) { |
1826 |
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1827 |
return a;
|
1828 |
} |
1829 |
if ( bExp == 0 ) { |
1830 |
--expDiff; |
1831 |
} |
1832 |
else {
|
1833 |
bSig |= 0x20000000;
|
1834 |
} |
1835 |
shift32RightJamming( bSig, expDiff, &bSig ); |
1836 |
zExp = aExp; |
1837 |
} |
1838 |
else if ( expDiff < 0 ) { |
1839 |
if ( bExp == 0xFF ) { |
1840 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1841 |
return packFloat32( zSign, 0xFF, 0 ); |
1842 |
} |
1843 |
if ( aExp == 0 ) { |
1844 |
++expDiff; |
1845 |
} |
1846 |
else {
|
1847 |
aSig |= 0x20000000;
|
1848 |
} |
1849 |
shift32RightJamming( aSig, - expDiff, &aSig ); |
1850 |
zExp = bExp; |
1851 |
} |
1852 |
else {
|
1853 |
if ( aExp == 0xFF ) { |
1854 |
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1855 |
return a;
|
1856 |
} |
1857 |
if ( aExp == 0 ) { |
1858 |
if (STATUS(flush_to_zero)) {
|
1859 |
if (aSig | bSig) {
|
1860 |
float_raise(float_flag_output_denormal STATUS_VAR); |
1861 |
} |
1862 |
return packFloat32(zSign, 0, 0); |
1863 |
} |
1864 |
return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); |
1865 |
} |
1866 |
zSig = 0x40000000 + aSig + bSig;
|
1867 |
zExp = aExp; |
1868 |
goto roundAndPack;
|
1869 |
} |
1870 |
aSig |= 0x20000000;
|
1871 |
zSig = ( aSig + bSig )<<1;
|
1872 |
--zExp; |
1873 |
if ( (int32_t) zSig < 0 ) { |
1874 |
zSig = aSig + bSig; |
1875 |
++zExp; |
1876 |
} |
1877 |
roundAndPack:
|
1878 |
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
1879 |
|
1880 |
} |
1881 |
|
1882 |
/*----------------------------------------------------------------------------
|
1883 |
| Returns the result of subtracting the absolute values of the single-
|
1884 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
1885 |
| difference is negated before being returned. `zSign' is ignored if the
|
1886 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
1887 |
| Standard for Binary Floating-Point Arithmetic.
|
1888 |
*----------------------------------------------------------------------------*/
|
1889 |
|
1890 |
static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
|
1891 |
{ |
1892 |
int_fast16_t aExp, bExp, zExp; |
1893 |
uint32_t aSig, bSig, zSig; |
1894 |
int_fast16_t expDiff; |
1895 |
|
1896 |
aSig = extractFloat32Frac( a ); |
1897 |
aExp = extractFloat32Exp( a ); |
1898 |
bSig = extractFloat32Frac( b ); |
1899 |
bExp = extractFloat32Exp( b ); |
1900 |
expDiff = aExp - bExp; |
1901 |
aSig <<= 7;
|
1902 |
bSig <<= 7;
|
1903 |
if ( 0 < expDiff ) goto aExpBigger; |
1904 |
if ( expDiff < 0 ) goto bExpBigger; |
1905 |
if ( aExp == 0xFF ) { |
1906 |
if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1907 |
float_raise( float_flag_invalid STATUS_VAR); |
1908 |
return float32_default_nan;
|
1909 |
} |
1910 |
if ( aExp == 0 ) { |
1911 |
aExp = 1;
|
1912 |
bExp = 1;
|
1913 |
} |
1914 |
if ( bSig < aSig ) goto aBigger; |
1915 |
if ( aSig < bSig ) goto bBigger; |
1916 |
return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
1917 |
bExpBigger:
|
1918 |
if ( bExp == 0xFF ) { |
1919 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1920 |
return packFloat32( zSign ^ 1, 0xFF, 0 ); |
1921 |
} |
1922 |
if ( aExp == 0 ) { |
1923 |
++expDiff; |
1924 |
} |
1925 |
else {
|
1926 |
aSig |= 0x40000000;
|
1927 |
} |
1928 |
shift32RightJamming( aSig, - expDiff, &aSig ); |
1929 |
bSig |= 0x40000000;
|
1930 |
bBigger:
|
1931 |
zSig = bSig - aSig; |
1932 |
zExp = bExp; |
1933 |
zSign ^= 1;
|
1934 |
goto normalizeRoundAndPack;
|
1935 |
aExpBigger:
|
1936 |
if ( aExp == 0xFF ) { |
1937 |
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
1938 |
return a;
|
1939 |
} |
1940 |
if ( bExp == 0 ) { |
1941 |
--expDiff; |
1942 |
} |
1943 |
else {
|
1944 |
bSig |= 0x40000000;
|
1945 |
} |
1946 |
shift32RightJamming( bSig, expDiff, &bSig ); |
1947 |
aSig |= 0x40000000;
|
1948 |
aBigger:
|
1949 |
zSig = aSig - bSig; |
1950 |
zExp = aExp; |
1951 |
normalizeRoundAndPack:
|
1952 |
--zExp; |
1953 |
return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
1954 |
|
1955 |
} |
1956 |
|
1957 |
/*----------------------------------------------------------------------------
|
1958 |
| Returns the result of adding the single-precision floating-point values `a'
|
1959 |
| and `b'. The operation is performed according to the IEC/IEEE Standard for
|
1960 |
| Binary Floating-Point Arithmetic.
|
1961 |
*----------------------------------------------------------------------------*/
|
1962 |
|
1963 |
float32 float32_add( float32 a, float32 b STATUS_PARAM ) |
1964 |
{ |
1965 |
flag aSign, bSign; |
1966 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1967 |
b = float32_squash_input_denormal(b STATUS_VAR); |
1968 |
|
1969 |
aSign = extractFloat32Sign( a ); |
1970 |
bSign = extractFloat32Sign( b ); |
1971 |
if ( aSign == bSign ) {
|
1972 |
return addFloat32Sigs( a, b, aSign STATUS_VAR);
|
1973 |
} |
1974 |
else {
|
1975 |
return subFloat32Sigs( a, b, aSign STATUS_VAR );
|
1976 |
} |
1977 |
|
1978 |
} |
1979 |
|
1980 |
/*----------------------------------------------------------------------------
|
1981 |
| Returns the result of subtracting the single-precision floating-point values
|
1982 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
1983 |
| for Binary Floating-Point Arithmetic.
|
1984 |
*----------------------------------------------------------------------------*/
|
1985 |
|
1986 |
float32 float32_sub( float32 a, float32 b STATUS_PARAM ) |
1987 |
{ |
1988 |
flag aSign, bSign; |
1989 |
a = float32_squash_input_denormal(a STATUS_VAR); |
1990 |
b = float32_squash_input_denormal(b STATUS_VAR); |
1991 |
|
1992 |
aSign = extractFloat32Sign( a ); |
1993 |
bSign = extractFloat32Sign( b ); |
1994 |
if ( aSign == bSign ) {
|
1995 |
return subFloat32Sigs( a, b, aSign STATUS_VAR );
|
1996 |
} |
1997 |
else {
|
1998 |
return addFloat32Sigs( a, b, aSign STATUS_VAR );
|
1999 |
} |
2000 |
|
2001 |
} |
2002 |
|
2003 |
/*----------------------------------------------------------------------------
|
2004 |
| Returns the result of multiplying the single-precision floating-point values
|
2005 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
2006 |
| for Binary Floating-Point Arithmetic.
|
2007 |
*----------------------------------------------------------------------------*/
|
2008 |
|
2009 |
float32 float32_mul( float32 a, float32 b STATUS_PARAM ) |
2010 |
{ |
2011 |
flag aSign, bSign, zSign; |
2012 |
int_fast16_t aExp, bExp, zExp; |
2013 |
uint32_t aSig, bSig; |
2014 |
uint64_t zSig64; |
2015 |
uint32_t zSig; |
2016 |
|
2017 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2018 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2019 |
|
2020 |
aSig = extractFloat32Frac( a ); |
2021 |
aExp = extractFloat32Exp( a ); |
2022 |
aSign = extractFloat32Sign( a ); |
2023 |
bSig = extractFloat32Frac( b ); |
2024 |
bExp = extractFloat32Exp( b ); |
2025 |
bSign = extractFloat32Sign( b ); |
2026 |
zSign = aSign ^ bSign; |
2027 |
if ( aExp == 0xFF ) { |
2028 |
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { |
2029 |
return propagateFloat32NaN( a, b STATUS_VAR );
|
2030 |
} |
2031 |
if ( ( bExp | bSig ) == 0 ) { |
2032 |
float_raise( float_flag_invalid STATUS_VAR); |
2033 |
return float32_default_nan;
|
2034 |
} |
2035 |
return packFloat32( zSign, 0xFF, 0 ); |
2036 |
} |
2037 |
if ( bExp == 0xFF ) { |
2038 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
2039 |
if ( ( aExp | aSig ) == 0 ) { |
2040 |
float_raise( float_flag_invalid STATUS_VAR); |
2041 |
return float32_default_nan;
|
2042 |
} |
2043 |
return packFloat32( zSign, 0xFF, 0 ); |
2044 |
} |
2045 |
if ( aExp == 0 ) { |
2046 |
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); |
2047 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2048 |
} |
2049 |
if ( bExp == 0 ) { |
2050 |
if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); |
2051 |
normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
2052 |
} |
2053 |
zExp = aExp + bExp - 0x7F;
|
2054 |
aSig = ( aSig | 0x00800000 )<<7; |
2055 |
bSig = ( bSig | 0x00800000 )<<8; |
2056 |
shift64RightJamming( ( (uint64_t) aSig ) * bSig, 32, &zSig64 );
|
2057 |
zSig = zSig64; |
2058 |
if ( 0 <= (int32_t) ( zSig<<1 ) ) { |
2059 |
zSig <<= 1;
|
2060 |
--zExp; |
2061 |
} |
2062 |
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
2063 |
|
2064 |
} |
2065 |
|
2066 |
/*----------------------------------------------------------------------------
|
2067 |
| Returns the result of dividing the single-precision floating-point value `a'
|
2068 |
| by the corresponding value `b'. The operation is performed according to the
|
2069 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2070 |
*----------------------------------------------------------------------------*/
|
2071 |
|
2072 |
float32 float32_div( float32 a, float32 b STATUS_PARAM ) |
2073 |
{ |
2074 |
flag aSign, bSign, zSign; |
2075 |
int_fast16_t aExp, bExp, zExp; |
2076 |
uint32_t aSig, bSig, zSig; |
2077 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2078 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2079 |
|
2080 |
aSig = extractFloat32Frac( a ); |
2081 |
aExp = extractFloat32Exp( a ); |
2082 |
aSign = extractFloat32Sign( a ); |
2083 |
bSig = extractFloat32Frac( b ); |
2084 |
bExp = extractFloat32Exp( b ); |
2085 |
bSign = extractFloat32Sign( b ); |
2086 |
zSign = aSign ^ bSign; |
2087 |
if ( aExp == 0xFF ) { |
2088 |
if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
2089 |
if ( bExp == 0xFF ) { |
2090 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
2091 |
float_raise( float_flag_invalid STATUS_VAR); |
2092 |
return float32_default_nan;
|
2093 |
} |
2094 |
return packFloat32( zSign, 0xFF, 0 ); |
2095 |
} |
2096 |
if ( bExp == 0xFF ) { |
2097 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
2098 |
return packFloat32( zSign, 0, 0 ); |
2099 |
} |
2100 |
if ( bExp == 0 ) { |
2101 |
if ( bSig == 0 ) { |
2102 |
if ( ( aExp | aSig ) == 0 ) { |
2103 |
float_raise( float_flag_invalid STATUS_VAR); |
2104 |
return float32_default_nan;
|
2105 |
} |
2106 |
float_raise( float_flag_divbyzero STATUS_VAR); |
2107 |
return packFloat32( zSign, 0xFF, 0 ); |
2108 |
} |
2109 |
normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
2110 |
} |
2111 |
if ( aExp == 0 ) { |
2112 |
if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); |
2113 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2114 |
} |
2115 |
zExp = aExp - bExp + 0x7D;
|
2116 |
aSig = ( aSig | 0x00800000 )<<7; |
2117 |
bSig = ( bSig | 0x00800000 )<<8; |
2118 |
if ( bSig <= ( aSig + aSig ) ) {
|
2119 |
aSig >>= 1;
|
2120 |
++zExp; |
2121 |
} |
2122 |
zSig = ( ( (uint64_t) aSig )<<32 ) / bSig;
|
2123 |
if ( ( zSig & 0x3F ) == 0 ) { |
2124 |
zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 );
|
2125 |
} |
2126 |
return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
|
2127 |
|
2128 |
} |
2129 |
|
2130 |
/*----------------------------------------------------------------------------
|
2131 |
| Returns the remainder of the single-precision floating-point value `a'
|
2132 |
| with respect to the corresponding value `b'. The operation is performed
|
2133 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2134 |
*----------------------------------------------------------------------------*/
|
2135 |
|
2136 |
float32 float32_rem( float32 a, float32 b STATUS_PARAM ) |
2137 |
{ |
2138 |
flag aSign, zSign; |
2139 |
int_fast16_t aExp, bExp, expDiff; |
2140 |
uint32_t aSig, bSig; |
2141 |
uint32_t q; |
2142 |
uint64_t aSig64, bSig64, q64; |
2143 |
uint32_t alternateASig; |
2144 |
int32_t sigMean; |
2145 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2146 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2147 |
|
2148 |
aSig = extractFloat32Frac( a ); |
2149 |
aExp = extractFloat32Exp( a ); |
2150 |
aSign = extractFloat32Sign( a ); |
2151 |
bSig = extractFloat32Frac( b ); |
2152 |
bExp = extractFloat32Exp( b ); |
2153 |
if ( aExp == 0xFF ) { |
2154 |
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { |
2155 |
return propagateFloat32NaN( a, b STATUS_VAR );
|
2156 |
} |
2157 |
float_raise( float_flag_invalid STATUS_VAR); |
2158 |
return float32_default_nan;
|
2159 |
} |
2160 |
if ( bExp == 0xFF ) { |
2161 |
if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); |
2162 |
return a;
|
2163 |
} |
2164 |
if ( bExp == 0 ) { |
2165 |
if ( bSig == 0 ) { |
2166 |
float_raise( float_flag_invalid STATUS_VAR); |
2167 |
return float32_default_nan;
|
2168 |
} |
2169 |
normalizeFloat32Subnormal( bSig, &bExp, &bSig ); |
2170 |
} |
2171 |
if ( aExp == 0 ) { |
2172 |
if ( aSig == 0 ) return a; |
2173 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2174 |
} |
2175 |
expDiff = aExp - bExp; |
2176 |
aSig |= 0x00800000;
|
2177 |
bSig |= 0x00800000;
|
2178 |
if ( expDiff < 32 ) { |
2179 |
aSig <<= 8;
|
2180 |
bSig <<= 8;
|
2181 |
if ( expDiff < 0 ) { |
2182 |
if ( expDiff < -1 ) return a; |
2183 |
aSig >>= 1;
|
2184 |
} |
2185 |
q = ( bSig <= aSig ); |
2186 |
if ( q ) aSig -= bSig;
|
2187 |
if ( 0 < expDiff ) { |
2188 |
q = ( ( (uint64_t) aSig )<<32 ) / bSig;
|
2189 |
q >>= 32 - expDiff;
|
2190 |
bSig >>= 2;
|
2191 |
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; |
2192 |
} |
2193 |
else {
|
2194 |
aSig >>= 2;
|
2195 |
bSig >>= 2;
|
2196 |
} |
2197 |
} |
2198 |
else {
|
2199 |
if ( bSig <= aSig ) aSig -= bSig;
|
2200 |
aSig64 = ( (uint64_t) aSig )<<40;
|
2201 |
bSig64 = ( (uint64_t) bSig )<<40;
|
2202 |
expDiff -= 64;
|
2203 |
while ( 0 < expDiff ) { |
2204 |
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
2205 |
q64 = ( 2 < q64 ) ? q64 - 2 : 0; |
2206 |
aSig64 = - ( ( bSig * q64 )<<38 );
|
2207 |
expDiff -= 62;
|
2208 |
} |
2209 |
expDiff += 64;
|
2210 |
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
2211 |
q64 = ( 2 < q64 ) ? q64 - 2 : 0; |
2212 |
q = q64>>( 64 - expDiff );
|
2213 |
bSig <<= 6;
|
2214 |
aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; |
2215 |
} |
2216 |
do {
|
2217 |
alternateASig = aSig; |
2218 |
++q; |
2219 |
aSig -= bSig; |
2220 |
} while ( 0 <= (int32_t) aSig ); |
2221 |
sigMean = aSig + alternateASig; |
2222 |
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { |
2223 |
aSig = alternateASig; |
2224 |
} |
2225 |
zSign = ( (int32_t) aSig < 0 );
|
2226 |
if ( zSign ) aSig = - aSig;
|
2227 |
return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR );
|
2228 |
|
2229 |
} |
2230 |
|
2231 |
/*----------------------------------------------------------------------------
|
2232 |
| Returns the result of multiplying the single-precision floating-point values
|
2233 |
| `a' and `b' then adding 'c', with no intermediate rounding step after the
|
2234 |
| multiplication. The operation is performed according to the IEC/IEEE
|
2235 |
| Standard for Binary Floating-Point Arithmetic 754-2008.
|
2236 |
| The flags argument allows the caller to select negation of the
|
2237 |
| addend, the intermediate product, or the final result. (The difference
|
2238 |
| between this and having the caller do a separate negation is that negating
|
2239 |
| externally will flip the sign bit on NaNs.)
|
2240 |
*----------------------------------------------------------------------------*/
|
2241 |
|
2242 |
float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM)
|
2243 |
{ |
2244 |
flag aSign, bSign, cSign, zSign; |
2245 |
int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; |
2246 |
uint32_t aSig, bSig, cSig; |
2247 |
flag pInf, pZero, pSign; |
2248 |
uint64_t pSig64, cSig64, zSig64; |
2249 |
uint32_t pSig; |
2250 |
int shiftcount;
|
2251 |
flag signflip, infzero; |
2252 |
|
2253 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2254 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2255 |
c = float32_squash_input_denormal(c STATUS_VAR); |
2256 |
aSig = extractFloat32Frac(a); |
2257 |
aExp = extractFloat32Exp(a); |
2258 |
aSign = extractFloat32Sign(a); |
2259 |
bSig = extractFloat32Frac(b); |
2260 |
bExp = extractFloat32Exp(b); |
2261 |
bSign = extractFloat32Sign(b); |
2262 |
cSig = extractFloat32Frac(c); |
2263 |
cExp = extractFloat32Exp(c); |
2264 |
cSign = extractFloat32Sign(c); |
2265 |
|
2266 |
infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) || |
2267 |
(aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0)); |
2268 |
|
2269 |
/* It is implementation-defined whether the cases of (0,inf,qnan)
|
2270 |
* and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
|
2271 |
* they return if they do), so we have to hand this information
|
2272 |
* off to the target-specific pick-a-NaN routine.
|
2273 |
*/
|
2274 |
if (((aExp == 0xff) && aSig) || |
2275 |
((bExp == 0xff) && bSig) ||
|
2276 |
((cExp == 0xff) && cSig)) {
|
2277 |
return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR);
|
2278 |
} |
2279 |
|
2280 |
if (infzero) {
|
2281 |
float_raise(float_flag_invalid STATUS_VAR); |
2282 |
return float32_default_nan;
|
2283 |
} |
2284 |
|
2285 |
if (flags & float_muladd_negate_c) {
|
2286 |
cSign ^= 1;
|
2287 |
} |
2288 |
|
2289 |
signflip = (flags & float_muladd_negate_result) ? 1 : 0; |
2290 |
|
2291 |
/* Work out the sign and type of the product */
|
2292 |
pSign = aSign ^ bSign; |
2293 |
if (flags & float_muladd_negate_product) {
|
2294 |
pSign ^= 1;
|
2295 |
} |
2296 |
pInf = (aExp == 0xff) || (bExp == 0xff); |
2297 |
pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); |
2298 |
|
2299 |
if (cExp == 0xff) { |
2300 |
if (pInf && (pSign ^ cSign)) {
|
2301 |
/* addition of opposite-signed infinities => InvalidOperation */
|
2302 |
float_raise(float_flag_invalid STATUS_VAR); |
2303 |
return float32_default_nan;
|
2304 |
} |
2305 |
/* Otherwise generate an infinity of the same sign */
|
2306 |
return packFloat32(cSign ^ signflip, 0xff, 0); |
2307 |
} |
2308 |
|
2309 |
if (pInf) {
|
2310 |
return packFloat32(pSign ^ signflip, 0xff, 0); |
2311 |
} |
2312 |
|
2313 |
if (pZero) {
|
2314 |
if (cExp == 0) { |
2315 |
if (cSig == 0) { |
2316 |
/* Adding two exact zeroes */
|
2317 |
if (pSign == cSign) {
|
2318 |
zSign = pSign; |
2319 |
} else if (STATUS(float_rounding_mode) == float_round_down) { |
2320 |
zSign = 1;
|
2321 |
} else {
|
2322 |
zSign = 0;
|
2323 |
} |
2324 |
return packFloat32(zSign ^ signflip, 0, 0); |
2325 |
} |
2326 |
/* Exact zero plus a denorm */
|
2327 |
if (STATUS(flush_to_zero)) {
|
2328 |
float_raise(float_flag_output_denormal STATUS_VAR); |
2329 |
return packFloat32(cSign ^ signflip, 0, 0); |
2330 |
} |
2331 |
} |
2332 |
/* Zero plus something non-zero : just return the something */
|
2333 |
return packFloat32(cSign ^ signflip, cExp, cSig);
|
2334 |
} |
2335 |
|
2336 |
if (aExp == 0) { |
2337 |
normalizeFloat32Subnormal(aSig, &aExp, &aSig); |
2338 |
} |
2339 |
if (bExp == 0) { |
2340 |
normalizeFloat32Subnormal(bSig, &bExp, &bSig); |
2341 |
} |
2342 |
|
2343 |
/* Calculate the actual result a * b + c */
|
2344 |
|
2345 |
/* Multiply first; this is easy. */
|
2346 |
/* NB: we subtract 0x7e where float32_mul() subtracts 0x7f
|
2347 |
* because we want the true exponent, not the "one-less-than"
|
2348 |
* flavour that roundAndPackFloat32() takes.
|
2349 |
*/
|
2350 |
pExp = aExp + bExp - 0x7e;
|
2351 |
aSig = (aSig | 0x00800000) << 7; |
2352 |
bSig = (bSig | 0x00800000) << 8; |
2353 |
pSig64 = (uint64_t)aSig * bSig; |
2354 |
if ((int64_t)(pSig64 << 1) >= 0) { |
2355 |
pSig64 <<= 1;
|
2356 |
pExp--; |
2357 |
} |
2358 |
|
2359 |
zSign = pSign ^ signflip; |
2360 |
|
2361 |
/* Now pSig64 is the significand of the multiply, with the explicit bit in
|
2362 |
* position 62.
|
2363 |
*/
|
2364 |
if (cExp == 0) { |
2365 |
if (!cSig) {
|
2366 |
/* Throw out the special case of c being an exact zero now */
|
2367 |
shift64RightJamming(pSig64, 32, &pSig64);
|
2368 |
pSig = pSig64; |
2369 |
return roundAndPackFloat32(zSign, pExp - 1, |
2370 |
pSig STATUS_VAR); |
2371 |
} |
2372 |
normalizeFloat32Subnormal(cSig, &cExp, &cSig); |
2373 |
} |
2374 |
|
2375 |
cSig64 = (uint64_t)cSig << (62 - 23); |
2376 |
cSig64 |= LIT64(0x4000000000000000);
|
2377 |
expDiff = pExp - cExp; |
2378 |
|
2379 |
if (pSign == cSign) {
|
2380 |
/* Addition */
|
2381 |
if (expDiff > 0) { |
2382 |
/* scale c to match p */
|
2383 |
shift64RightJamming(cSig64, expDiff, &cSig64); |
2384 |
zExp = pExp; |
2385 |
} else if (expDiff < 0) { |
2386 |
/* scale p to match c */
|
2387 |
shift64RightJamming(pSig64, -expDiff, &pSig64); |
2388 |
zExp = cExp; |
2389 |
} else {
|
2390 |
/* no scaling needed */
|
2391 |
zExp = cExp; |
2392 |
} |
2393 |
/* Add significands and make sure explicit bit ends up in posn 62 */
|
2394 |
zSig64 = pSig64 + cSig64; |
2395 |
if ((int64_t)zSig64 < 0) { |
2396 |
shift64RightJamming(zSig64, 1, &zSig64);
|
2397 |
} else {
|
2398 |
zExp--; |
2399 |
} |
2400 |
} else {
|
2401 |
/* Subtraction */
|
2402 |
if (expDiff > 0) { |
2403 |
shift64RightJamming(cSig64, expDiff, &cSig64); |
2404 |
zSig64 = pSig64 - cSig64; |
2405 |
zExp = pExp; |
2406 |
} else if (expDiff < 0) { |
2407 |
shift64RightJamming(pSig64, -expDiff, &pSig64); |
2408 |
zSig64 = cSig64 - pSig64; |
2409 |
zExp = cExp; |
2410 |
zSign ^= 1;
|
2411 |
} else {
|
2412 |
zExp = pExp; |
2413 |
if (cSig64 < pSig64) {
|
2414 |
zSig64 = pSig64 - cSig64; |
2415 |
} else if (pSig64 < cSig64) { |
2416 |
zSig64 = cSig64 - pSig64; |
2417 |
zSign ^= 1;
|
2418 |
} else {
|
2419 |
/* Exact zero */
|
2420 |
zSign = signflip; |
2421 |
if (STATUS(float_rounding_mode) == float_round_down) {
|
2422 |
zSign ^= 1;
|
2423 |
} |
2424 |
return packFloat32(zSign, 0, 0); |
2425 |
} |
2426 |
} |
2427 |
--zExp; |
2428 |
/* Normalize to put the explicit bit back into bit 62. */
|
2429 |
shiftcount = countLeadingZeros64(zSig64) - 1;
|
2430 |
zSig64 <<= shiftcount; |
2431 |
zExp -= shiftcount; |
2432 |
} |
2433 |
shift64RightJamming(zSig64, 32, &zSig64);
|
2434 |
return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR);
|
2435 |
} |
2436 |
|
2437 |
|
2438 |
/*----------------------------------------------------------------------------
|
2439 |
| Returns the square root of the single-precision floating-point value `a'.
|
2440 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
2441 |
| Floating-Point Arithmetic.
|
2442 |
*----------------------------------------------------------------------------*/
|
2443 |
|
2444 |
float32 float32_sqrt( float32 a STATUS_PARAM ) |
2445 |
{ |
2446 |
flag aSign; |
2447 |
int_fast16_t aExp, zExp; |
2448 |
uint32_t aSig, zSig; |
2449 |
uint64_t rem, term; |
2450 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2451 |
|
2452 |
aSig = extractFloat32Frac( a ); |
2453 |
aExp = extractFloat32Exp( a ); |
2454 |
aSign = extractFloat32Sign( a ); |
2455 |
if ( aExp == 0xFF ) { |
2456 |
if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
2457 |
if ( ! aSign ) return a; |
2458 |
float_raise( float_flag_invalid STATUS_VAR); |
2459 |
return float32_default_nan;
|
2460 |
} |
2461 |
if ( aSign ) {
|
2462 |
if ( ( aExp | aSig ) == 0 ) return a; |
2463 |
float_raise( float_flag_invalid STATUS_VAR); |
2464 |
return float32_default_nan;
|
2465 |
} |
2466 |
if ( aExp == 0 ) { |
2467 |
if ( aSig == 0 ) return float32_zero; |
2468 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2469 |
} |
2470 |
zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; |
2471 |
aSig = ( aSig | 0x00800000 )<<8; |
2472 |
zSig = estimateSqrt32( aExp, aSig ) + 2;
|
2473 |
if ( ( zSig & 0x7F ) <= 5 ) { |
2474 |
if ( zSig < 2 ) { |
2475 |
zSig = 0x7FFFFFFF;
|
2476 |
goto roundAndPack;
|
2477 |
} |
2478 |
aSig >>= aExp & 1;
|
2479 |
term = ( (uint64_t) zSig ) * zSig; |
2480 |
rem = ( ( (uint64_t) aSig )<<32 ) - term;
|
2481 |
while ( (int64_t) rem < 0 ) { |
2482 |
--zSig; |
2483 |
rem += ( ( (uint64_t) zSig )<<1 ) | 1; |
2484 |
} |
2485 |
zSig |= ( rem != 0 );
|
2486 |
} |
2487 |
shift32RightJamming( zSig, 1, &zSig );
|
2488 |
roundAndPack:
|
2489 |
return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); |
2490 |
|
2491 |
} |
2492 |
|
2493 |
/*----------------------------------------------------------------------------
|
2494 |
| Returns the binary exponential of the single-precision floating-point value
|
2495 |
| `a'. The operation is performed according to the IEC/IEEE Standard for
|
2496 |
| Binary Floating-Point Arithmetic.
|
2497 |
|
|
2498 |
| Uses the following identities:
|
2499 |
|
|
2500 |
| 1. -------------------------------------------------------------------------
|
2501 |
| x x*ln(2)
|
2502 |
| 2 = e
|
2503 |
|
|
2504 |
| 2. -------------------------------------------------------------------------
|
2505 |
| 2 3 4 5 n
|
2506 |
| x x x x x x x
|
2507 |
| e = 1 + --- + --- + --- + --- + --- + ... + --- + ...
|
2508 |
| 1! 2! 3! 4! 5! n!
|
2509 |
*----------------------------------------------------------------------------*/
|
2510 |
|
2511 |
static const float64 float32_exp2_coefficients[15] = |
2512 |
{ |
2513 |
const_float64( 0x3ff0000000000000ll ), /* 1 */ |
2514 |
const_float64( 0x3fe0000000000000ll ), /* 2 */ |
2515 |
const_float64( 0x3fc5555555555555ll ), /* 3 */ |
2516 |
const_float64( 0x3fa5555555555555ll ), /* 4 */ |
2517 |
const_float64( 0x3f81111111111111ll ), /* 5 */ |
2518 |
const_float64( 0x3f56c16c16c16c17ll ), /* 6 */ |
2519 |
const_float64( 0x3f2a01a01a01a01all ), /* 7 */ |
2520 |
const_float64( 0x3efa01a01a01a01all ), /* 8 */ |
2521 |
const_float64( 0x3ec71de3a556c734ll ), /* 9 */ |
2522 |
const_float64( 0x3e927e4fb7789f5cll ), /* 10 */ |
2523 |
const_float64( 0x3e5ae64567f544e4ll ), /* 11 */ |
2524 |
const_float64( 0x3e21eed8eff8d898ll ), /* 12 */ |
2525 |
const_float64( 0x3de6124613a86d09ll ), /* 13 */ |
2526 |
const_float64( 0x3da93974a8c07c9dll ), /* 14 */ |
2527 |
const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */ |
2528 |
}; |
2529 |
|
2530 |
float32 float32_exp2( float32 a STATUS_PARAM ) |
2531 |
{ |
2532 |
flag aSign; |
2533 |
int_fast16_t aExp; |
2534 |
uint32_t aSig; |
2535 |
float64 r, x, xn; |
2536 |
int i;
|
2537 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2538 |
|
2539 |
aSig = extractFloat32Frac( a ); |
2540 |
aExp = extractFloat32Exp( a ); |
2541 |
aSign = extractFloat32Sign( a ); |
2542 |
|
2543 |
if ( aExp == 0xFF) { |
2544 |
if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
2545 |
return (aSign) ? float32_zero : a;
|
2546 |
} |
2547 |
if (aExp == 0) { |
2548 |
if (aSig == 0) return float32_one; |
2549 |
} |
2550 |
|
2551 |
float_raise( float_flag_inexact STATUS_VAR); |
2552 |
|
2553 |
/* ******************************* */
|
2554 |
/* using float64 for approximation */
|
2555 |
/* ******************************* */
|
2556 |
x = float32_to_float64(a STATUS_VAR); |
2557 |
x = float64_mul(x, float64_ln2 STATUS_VAR); |
2558 |
|
2559 |
xn = x; |
2560 |
r = float64_one; |
2561 |
for (i = 0 ; i < 15 ; i++) { |
2562 |
float64 f; |
2563 |
|
2564 |
f = float64_mul(xn, float32_exp2_coefficients[i] STATUS_VAR); |
2565 |
r = float64_add(r, f STATUS_VAR); |
2566 |
|
2567 |
xn = float64_mul(xn, x STATUS_VAR); |
2568 |
} |
2569 |
|
2570 |
return float64_to_float32(r, status);
|
2571 |
} |
2572 |
|
2573 |
/*----------------------------------------------------------------------------
|
2574 |
| Returns the binary log of the single-precision floating-point value `a'.
|
2575 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
2576 |
| Floating-Point Arithmetic.
|
2577 |
*----------------------------------------------------------------------------*/
|
2578 |
float32 float32_log2( float32 a STATUS_PARAM ) |
2579 |
{ |
2580 |
flag aSign, zSign; |
2581 |
int_fast16_t aExp; |
2582 |
uint32_t aSig, zSig, i; |
2583 |
|
2584 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2585 |
aSig = extractFloat32Frac( a ); |
2586 |
aExp = extractFloat32Exp( a ); |
2587 |
aSign = extractFloat32Sign( a ); |
2588 |
|
2589 |
if ( aExp == 0 ) { |
2590 |
if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 ); |
2591 |
normalizeFloat32Subnormal( aSig, &aExp, &aSig ); |
2592 |
} |
2593 |
if ( aSign ) {
|
2594 |
float_raise( float_flag_invalid STATUS_VAR); |
2595 |
return float32_default_nan;
|
2596 |
} |
2597 |
if ( aExp == 0xFF ) { |
2598 |
if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); |
2599 |
return a;
|
2600 |
} |
2601 |
|
2602 |
aExp -= 0x7F;
|
2603 |
aSig |= 0x00800000;
|
2604 |
zSign = aExp < 0;
|
2605 |
zSig = aExp << 23;
|
2606 |
|
2607 |
for (i = 1 << 22; i > 0; i >>= 1) { |
2608 |
aSig = ( (uint64_t)aSig * aSig ) >> 23;
|
2609 |
if ( aSig & 0x01000000 ) { |
2610 |
aSig >>= 1;
|
2611 |
zSig |= i; |
2612 |
} |
2613 |
} |
2614 |
|
2615 |
if ( zSign )
|
2616 |
zSig = -zSig; |
2617 |
|
2618 |
return normalizeRoundAndPackFloat32( zSign, 0x85, zSig STATUS_VAR ); |
2619 |
} |
2620 |
|
2621 |
/*----------------------------------------------------------------------------
|
2622 |
| Returns 1 if the single-precision floating-point value `a' is equal to
|
2623 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
2624 |
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
2625 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2626 |
*----------------------------------------------------------------------------*/
|
2627 |
|
2628 |
int float32_eq( float32 a, float32 b STATUS_PARAM )
|
2629 |
{ |
2630 |
uint32_t av, bv; |
2631 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2632 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2633 |
|
2634 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2635 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2636 |
) { |
2637 |
float_raise( float_flag_invalid STATUS_VAR); |
2638 |
return 0; |
2639 |
} |
2640 |
av = float32_val(a); |
2641 |
bv = float32_val(b); |
2642 |
return ( av == bv ) || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
2643 |
} |
2644 |
|
2645 |
/*----------------------------------------------------------------------------
|
2646 |
| Returns 1 if the single-precision floating-point value `a' is less than
|
2647 |
| or equal to the corresponding value `b', and 0 otherwise. The invalid
|
2648 |
| exception is raised if either operand is a NaN. The comparison is performed
|
2649 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2650 |
*----------------------------------------------------------------------------*/
|
2651 |
|
2652 |
int float32_le( float32 a, float32 b STATUS_PARAM )
|
2653 |
{ |
2654 |
flag aSign, bSign; |
2655 |
uint32_t av, bv; |
2656 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2657 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2658 |
|
2659 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2660 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2661 |
) { |
2662 |
float_raise( float_flag_invalid STATUS_VAR); |
2663 |
return 0; |
2664 |
} |
2665 |
aSign = extractFloat32Sign( a ); |
2666 |
bSign = extractFloat32Sign( b ); |
2667 |
av = float32_val(a); |
2668 |
bv = float32_val(b); |
2669 |
if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
2670 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
2671 |
|
2672 |
} |
2673 |
|
2674 |
/*----------------------------------------------------------------------------
|
2675 |
| Returns 1 if the single-precision floating-point value `a' is less than
|
2676 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
2677 |
| raised if either operand is a NaN. The comparison is performed according
|
2678 |
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2679 |
*----------------------------------------------------------------------------*/
|
2680 |
|
2681 |
int float32_lt( float32 a, float32 b STATUS_PARAM )
|
2682 |
{ |
2683 |
flag aSign, bSign; |
2684 |
uint32_t av, bv; |
2685 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2686 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2687 |
|
2688 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2689 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2690 |
) { |
2691 |
float_raise( float_flag_invalid STATUS_VAR); |
2692 |
return 0; |
2693 |
} |
2694 |
aSign = extractFloat32Sign( a ); |
2695 |
bSign = extractFloat32Sign( b ); |
2696 |
av = float32_val(a); |
2697 |
bv = float32_val(b); |
2698 |
if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); |
2699 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
2700 |
|
2701 |
} |
2702 |
|
2703 |
/*----------------------------------------------------------------------------
|
2704 |
| Returns 1 if the single-precision floating-point values `a' and `b' cannot
|
2705 |
| be compared, and 0 otherwise. The invalid exception is raised if either
|
2706 |
| operand is a NaN. The comparison is performed according to the IEC/IEEE
|
2707 |
| Standard for Binary Floating-Point Arithmetic.
|
2708 |
*----------------------------------------------------------------------------*/
|
2709 |
|
2710 |
int float32_unordered( float32 a, float32 b STATUS_PARAM )
|
2711 |
{ |
2712 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2713 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2714 |
|
2715 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2716 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2717 |
) { |
2718 |
float_raise( float_flag_invalid STATUS_VAR); |
2719 |
return 1; |
2720 |
} |
2721 |
return 0; |
2722 |
} |
2723 |
|
2724 |
/*----------------------------------------------------------------------------
|
2725 |
| Returns 1 if the single-precision floating-point value `a' is equal to
|
2726 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
2727 |
| exception. The comparison is performed according to the IEC/IEEE Standard
|
2728 |
| for Binary Floating-Point Arithmetic.
|
2729 |
*----------------------------------------------------------------------------*/
|
2730 |
|
2731 |
int float32_eq_quiet( float32 a, float32 b STATUS_PARAM )
|
2732 |
{ |
2733 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2734 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2735 |
|
2736 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2737 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2738 |
) { |
2739 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2740 |
float_raise( float_flag_invalid STATUS_VAR); |
2741 |
} |
2742 |
return 0; |
2743 |
} |
2744 |
return ( float32_val(a) == float32_val(b) ) ||
|
2745 |
( (uint32_t) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 ); |
2746 |
} |
2747 |
|
2748 |
/*----------------------------------------------------------------------------
|
2749 |
| Returns 1 if the single-precision floating-point value `a' is less than or
|
2750 |
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
2751 |
| cause an exception. Otherwise, the comparison is performed according to the
|
2752 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
2753 |
*----------------------------------------------------------------------------*/
|
2754 |
|
2755 |
int float32_le_quiet( float32 a, float32 b STATUS_PARAM )
|
2756 |
{ |
2757 |
flag aSign, bSign; |
2758 |
uint32_t av, bv; |
2759 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2760 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2761 |
|
2762 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2763 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2764 |
) { |
2765 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2766 |
float_raise( float_flag_invalid STATUS_VAR); |
2767 |
} |
2768 |
return 0; |
2769 |
} |
2770 |
aSign = extractFloat32Sign( a ); |
2771 |
bSign = extractFloat32Sign( b ); |
2772 |
av = float32_val(a); |
2773 |
bv = float32_val(b); |
2774 |
if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); |
2775 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
2776 |
|
2777 |
} |
2778 |
|
2779 |
/*----------------------------------------------------------------------------
|
2780 |
| Returns 1 if the single-precision floating-point value `a' is less than
|
2781 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
2782 |
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
2783 |
| Standard for Binary Floating-Point Arithmetic.
|
2784 |
*----------------------------------------------------------------------------*/
|
2785 |
|
2786 |
int float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
|
2787 |
{ |
2788 |
flag aSign, bSign; |
2789 |
uint32_t av, bv; |
2790 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2791 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2792 |
|
2793 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2794 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2795 |
) { |
2796 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2797 |
float_raise( float_flag_invalid STATUS_VAR); |
2798 |
} |
2799 |
return 0; |
2800 |
} |
2801 |
aSign = extractFloat32Sign( a ); |
2802 |
bSign = extractFloat32Sign( b ); |
2803 |
av = float32_val(a); |
2804 |
bv = float32_val(b); |
2805 |
if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); |
2806 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
2807 |
|
2808 |
} |
2809 |
|
2810 |
/*----------------------------------------------------------------------------
|
2811 |
| Returns 1 if the single-precision floating-point values `a' and `b' cannot
|
2812 |
| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The
|
2813 |
| comparison is performed according to the IEC/IEEE Standard for Binary
|
2814 |
| Floating-Point Arithmetic.
|
2815 |
*----------------------------------------------------------------------------*/
|
2816 |
|
2817 |
int float32_unordered_quiet( float32 a, float32 b STATUS_PARAM )
|
2818 |
{ |
2819 |
a = float32_squash_input_denormal(a STATUS_VAR); |
2820 |
b = float32_squash_input_denormal(b STATUS_VAR); |
2821 |
|
2822 |
if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) |
2823 |
|| ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
|
2824 |
) { |
2825 |
if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
|
2826 |
float_raise( float_flag_invalid STATUS_VAR); |
2827 |
} |
2828 |
return 1; |
2829 |
} |
2830 |
return 0; |
2831 |
} |
2832 |
|
2833 |
/*----------------------------------------------------------------------------
|
2834 |
| Returns the result of converting the double-precision floating-point value
|
2835 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
2836 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2837 |
| Arithmetic---which means in particular that the conversion is rounded
|
2838 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
2839 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
2840 |
| largest integer with the same sign as `a' is returned.
|
2841 |
*----------------------------------------------------------------------------*/
|
2842 |
|
2843 |
int32 float64_to_int32( float64 a STATUS_PARAM ) |
2844 |
{ |
2845 |
flag aSign; |
2846 |
int_fast16_t aExp, shiftCount; |
2847 |
uint64_t aSig; |
2848 |
a = float64_squash_input_denormal(a STATUS_VAR); |
2849 |
|
2850 |
aSig = extractFloat64Frac( a ); |
2851 |
aExp = extractFloat64Exp( a ); |
2852 |
aSign = extractFloat64Sign( a ); |
2853 |
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; |
2854 |
if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
2855 |
shiftCount = 0x42C - aExp;
|
2856 |
if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); |
2857 |
return roundAndPackInt32( aSign, aSig STATUS_VAR );
|
2858 |
|
2859 |
} |
2860 |
|
2861 |
/*----------------------------------------------------------------------------
|
2862 |
| Returns the result of converting the double-precision floating-point value
|
2863 |
| `a' to the 32-bit two's complement integer format. The conversion is
|
2864 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2865 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
2866 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
2867 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
2868 |
| returned.
|
2869 |
*----------------------------------------------------------------------------*/
|
2870 |
|
2871 |
int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) |
2872 |
{ |
2873 |
flag aSign; |
2874 |
int_fast16_t aExp, shiftCount; |
2875 |
uint64_t aSig, savedASig; |
2876 |
int32_t z; |
2877 |
a = float64_squash_input_denormal(a STATUS_VAR); |
2878 |
|
2879 |
aSig = extractFloat64Frac( a ); |
2880 |
aExp = extractFloat64Exp( a ); |
2881 |
aSign = extractFloat64Sign( a ); |
2882 |
if ( 0x41E < aExp ) { |
2883 |
if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; |
2884 |
goto invalid;
|
2885 |
} |
2886 |
else if ( aExp < 0x3FF ) { |
2887 |
if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
2888 |
return 0; |
2889 |
} |
2890 |
aSig |= LIT64( 0x0010000000000000 );
|
2891 |
shiftCount = 0x433 - aExp;
|
2892 |
savedASig = aSig; |
2893 |
aSig >>= shiftCount; |
2894 |
z = aSig; |
2895 |
if ( aSign ) z = - z;
|
2896 |
if ( ( z < 0 ) ^ aSign ) { |
2897 |
invalid:
|
2898 |
float_raise( float_flag_invalid STATUS_VAR); |
2899 |
return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
2900 |
} |
2901 |
if ( ( aSig<<shiftCount ) != savedASig ) {
|
2902 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2903 |
} |
2904 |
return z;
|
2905 |
|
2906 |
} |
2907 |
|
2908 |
/*----------------------------------------------------------------------------
|
2909 |
| Returns the result of converting the double-precision floating-point value
|
2910 |
| `a' to the 16-bit two's complement integer format. The conversion is
|
2911 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2912 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
2913 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
2914 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
2915 |
| returned.
|
2916 |
*----------------------------------------------------------------------------*/
|
2917 |
|
2918 |
int_fast16_t float64_to_int16_round_to_zero(float64 a STATUS_PARAM) |
2919 |
{ |
2920 |
flag aSign; |
2921 |
int_fast16_t aExp, shiftCount; |
2922 |
uint64_t aSig, savedASig; |
2923 |
int32 z; |
2924 |
|
2925 |
aSig = extractFloat64Frac( a ); |
2926 |
aExp = extractFloat64Exp( a ); |
2927 |
aSign = extractFloat64Sign( a ); |
2928 |
if ( 0x40E < aExp ) { |
2929 |
if ( ( aExp == 0x7FF ) && aSig ) { |
2930 |
aSign = 0;
|
2931 |
} |
2932 |
goto invalid;
|
2933 |
} |
2934 |
else if ( aExp < 0x3FF ) { |
2935 |
if ( aExp || aSig ) {
|
2936 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2937 |
} |
2938 |
return 0; |
2939 |
} |
2940 |
aSig |= LIT64( 0x0010000000000000 );
|
2941 |
shiftCount = 0x433 - aExp;
|
2942 |
savedASig = aSig; |
2943 |
aSig >>= shiftCount; |
2944 |
z = aSig; |
2945 |
if ( aSign ) {
|
2946 |
z = - z; |
2947 |
} |
2948 |
if ( ( (int16_t)z < 0 ) ^ aSign ) { |
2949 |
invalid:
|
2950 |
float_raise( float_flag_invalid STATUS_VAR); |
2951 |
return aSign ? (int32_t) 0xffff8000 : 0x7FFF; |
2952 |
} |
2953 |
if ( ( aSig<<shiftCount ) != savedASig ) {
|
2954 |
STATUS(float_exception_flags) |= float_flag_inexact; |
2955 |
} |
2956 |
return z;
|
2957 |
} |
2958 |
|
2959 |
/*----------------------------------------------------------------------------
|
2960 |
| Returns the result of converting the double-precision floating-point value
|
2961 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
2962 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
2963 |
| Arithmetic---which means in particular that the conversion is rounded
|
2964 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
2965 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
2966 |
| largest integer with the same sign as `a' is returned.
|
2967 |
*----------------------------------------------------------------------------*/
|
2968 |
|
2969 |
int64 float64_to_int64( float64 a STATUS_PARAM ) |
2970 |
{ |
2971 |
flag aSign; |
2972 |
int_fast16_t aExp, shiftCount; |
2973 |
uint64_t aSig, aSigExtra; |
2974 |
a = float64_squash_input_denormal(a STATUS_VAR); |
2975 |
|
2976 |
aSig = extractFloat64Frac( a ); |
2977 |
aExp = extractFloat64Exp( a ); |
2978 |
aSign = extractFloat64Sign( a ); |
2979 |
if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
2980 |
shiftCount = 0x433 - aExp;
|
2981 |
if ( shiftCount <= 0 ) { |
2982 |
if ( 0x43E < aExp ) { |
2983 |
float_raise( float_flag_invalid STATUS_VAR); |
2984 |
if ( ! aSign
|
2985 |
|| ( ( aExp == 0x7FF )
|
2986 |
&& ( aSig != LIT64( 0x0010000000000000 ) ) )
|
2987 |
) { |
2988 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
2989 |
} |
2990 |
return (int64_t) LIT64( 0x8000000000000000 ); |
2991 |
} |
2992 |
aSigExtra = 0;
|
2993 |
aSig <<= - shiftCount; |
2994 |
} |
2995 |
else {
|
2996 |
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
|
2997 |
} |
2998 |
return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
|
2999 |
|
3000 |
} |
3001 |
|
3002 |
/*----------------------------------------------------------------------------
|
3003 |
| Returns the result of converting the double-precision floating-point value
|
3004 |
| `a' to the 64-bit two's complement integer format. The conversion is
|
3005 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
3006 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
3007 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
3008 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
3009 |
| returned.
|
3010 |
*----------------------------------------------------------------------------*/
|
3011 |
|
3012 |
int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) |
3013 |
{ |
3014 |
flag aSign; |
3015 |
int_fast16_t aExp, shiftCount; |
3016 |
uint64_t aSig; |
3017 |
int64 z; |
3018 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3019 |
|
3020 |
aSig = extractFloat64Frac( a ); |
3021 |
aExp = extractFloat64Exp( a ); |
3022 |
aSign = extractFloat64Sign( a ); |
3023 |
if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); |
3024 |
shiftCount = aExp - 0x433;
|
3025 |
if ( 0 <= shiftCount ) { |
3026 |
if ( 0x43E <= aExp ) { |
3027 |
if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) { |
3028 |
float_raise( float_flag_invalid STATUS_VAR); |
3029 |
if ( ! aSign
|
3030 |
|| ( ( aExp == 0x7FF )
|
3031 |
&& ( aSig != LIT64( 0x0010000000000000 ) ) )
|
3032 |
) { |
3033 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
3034 |
} |
3035 |
} |
3036 |
return (int64_t) LIT64( 0x8000000000000000 ); |
3037 |
} |
3038 |
z = aSig<<shiftCount; |
3039 |
} |
3040 |
else {
|
3041 |
if ( aExp < 0x3FE ) { |
3042 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
3043 |
return 0; |
3044 |
} |
3045 |
z = aSig>>( - shiftCount ); |
3046 |
if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { |
3047 |
STATUS(float_exception_flags) |= float_flag_inexact; |
3048 |
} |
3049 |
} |
3050 |
if ( aSign ) z = - z;
|
3051 |
return z;
|
3052 |
|
3053 |
} |
3054 |
|
3055 |
/*----------------------------------------------------------------------------
|
3056 |
| Returns the result of converting the double-precision floating-point value
|
3057 |
| `a' to the single-precision floating-point format. The conversion is
|
3058 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
3059 |
| Arithmetic.
|
3060 |
*----------------------------------------------------------------------------*/
|
3061 |
|
3062 |
float32 float64_to_float32( float64 a STATUS_PARAM ) |
3063 |
{ |
3064 |
flag aSign; |
3065 |
int_fast16_t aExp; |
3066 |
uint64_t aSig; |
3067 |
uint32_t zSig; |
3068 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3069 |
|
3070 |
aSig = extractFloat64Frac( a ); |
3071 |
aExp = extractFloat64Exp( a ); |
3072 |
aSign = extractFloat64Sign( a ); |
3073 |
if ( aExp == 0x7FF ) { |
3074 |
if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
3075 |
return packFloat32( aSign, 0xFF, 0 ); |
3076 |
} |
3077 |
shift64RightJamming( aSig, 22, &aSig );
|
3078 |
zSig = aSig; |
3079 |
if ( aExp || zSig ) {
|
3080 |
zSig |= 0x40000000;
|
3081 |
aExp -= 0x381;
|
3082 |
} |
3083 |
return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
|
3084 |
|
3085 |
} |
3086 |
|
3087 |
|
3088 |
/*----------------------------------------------------------------------------
|
3089 |
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
|
3090 |
| half-precision floating-point value, returning the result. After being
|
3091 |
| shifted into the proper positions, the three fields are simply added
|
3092 |
| together to form the result. This means that any integer portion of `zSig'
|
3093 |
| will be added into the exponent. Since a properly normalized significand
|
3094 |
| will have an integer portion equal to 1, the `zExp' input should be 1 less
|
3095 |
| than the desired result exponent whenever `zSig' is a complete, normalized
|
3096 |
| significand.
|
3097 |
*----------------------------------------------------------------------------*/
|
3098 |
static float16 packFloat16(flag zSign, int_fast16_t zExp, uint16_t zSig)
|
3099 |
{ |
3100 |
return make_float16(
|
3101 |
(((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig); |
3102 |
} |
3103 |
|
3104 |
/* Half precision floats come in two formats: standard IEEE and "ARM" format.
|
3105 |
The latter gains extra exponent range by omitting the NaN/Inf encodings. */
|
3106 |
|
3107 |
float32 float16_to_float32(float16 a, flag ieee STATUS_PARAM) |
3108 |
{ |
3109 |
flag aSign; |
3110 |
int_fast16_t aExp; |
3111 |
uint32_t aSig; |
3112 |
|
3113 |
aSign = extractFloat16Sign(a); |
3114 |
aExp = extractFloat16Exp(a); |
3115 |
aSig = extractFloat16Frac(a); |
3116 |
|
3117 |
if (aExp == 0x1f && ieee) { |
3118 |
if (aSig) {
|
3119 |
return commonNaNToFloat32(float16ToCommonNaN(a STATUS_VAR) STATUS_VAR);
|
3120 |
} |
3121 |
return packFloat32(aSign, 0xff, 0); |
3122 |
} |
3123 |
if (aExp == 0) { |
3124 |
int8 shiftCount; |
3125 |
|
3126 |
if (aSig == 0) { |
3127 |
return packFloat32(aSign, 0, 0); |
3128 |
} |
3129 |
|
3130 |
shiftCount = countLeadingZeros32( aSig ) - 21;
|
3131 |
aSig = aSig << shiftCount; |
3132 |
aExp = -shiftCount; |
3133 |
} |
3134 |
return packFloat32( aSign, aExp + 0x70, aSig << 13); |
3135 |
} |
3136 |
|
3137 |
float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM) |
3138 |
{ |
3139 |
flag aSign; |
3140 |
int_fast16_t aExp; |
3141 |
uint32_t aSig; |
3142 |
uint32_t mask; |
3143 |
uint32_t increment; |
3144 |
int8 roundingMode; |
3145 |
int maxexp = ieee ? 15 : 16; |
3146 |
bool rounding_bumps_exp;
|
3147 |
bool is_tiny = false; |
3148 |
|
3149 |
a = float32_squash_input_denormal(a STATUS_VAR); |
3150 |
|
3151 |
aSig = extractFloat32Frac( a ); |
3152 |
aExp = extractFloat32Exp( a ); |
3153 |
aSign = extractFloat32Sign( a ); |
3154 |
if ( aExp == 0xFF ) { |
3155 |
if (aSig) {
|
3156 |
/* Input is a NaN */
|
3157 |
if (!ieee) {
|
3158 |
float_raise(float_flag_invalid STATUS_VAR); |
3159 |
return packFloat16(aSign, 0, 0); |
3160 |
} |
3161 |
return commonNaNToFloat16(
|
3162 |
float32ToCommonNaN(a STATUS_VAR) STATUS_VAR); |
3163 |
} |
3164 |
/* Infinity */
|
3165 |
if (!ieee) {
|
3166 |
float_raise(float_flag_invalid STATUS_VAR); |
3167 |
return packFloat16(aSign, 0x1f, 0x3ff); |
3168 |
} |
3169 |
return packFloat16(aSign, 0x1f, 0); |
3170 |
} |
3171 |
if (aExp == 0 && aSig == 0) { |
3172 |
return packFloat16(aSign, 0, 0); |
3173 |
} |
3174 |
/* Decimal point between bits 22 and 23. Note that we add the 1 bit
|
3175 |
* even if the input is denormal; however this is harmless because
|
3176 |
* the largest possible single-precision denormal is still smaller
|
3177 |
* than the smallest representable half-precision denormal, and so we
|
3178 |
* will end up ignoring aSig and returning via the "always return zero"
|
3179 |
* codepath.
|
3180 |
*/
|
3181 |
aSig |= 0x00800000;
|
3182 |
aExp -= 0x7f;
|
3183 |
/* Calculate the mask of bits of the mantissa which are not
|
3184 |
* representable in half-precision and will be lost.
|
3185 |
*/
|
3186 |
if (aExp < -14) { |
3187 |
/* Will be denormal in halfprec */
|
3188 |
mask = 0x00ffffff;
|
3189 |
if (aExp >= -24) { |
3190 |
mask >>= 25 + aExp;
|
3191 |
} |
3192 |
} else {
|
3193 |
/* Normal number in halfprec */
|
3194 |
mask = 0x00001fff;
|
3195 |
} |
3196 |
|
3197 |
roundingMode = STATUS(float_rounding_mode); |
3198 |
switch (roundingMode) {
|
3199 |
case float_round_nearest_even:
|
3200 |
increment = (mask + 1) >> 1; |
3201 |
if ((aSig & mask) == increment) {
|
3202 |
increment = aSig & (increment << 1);
|
3203 |
} |
3204 |
break;
|
3205 |
case float_round_up:
|
3206 |
increment = aSign ? 0 : mask;
|
3207 |
break;
|
3208 |
case float_round_down:
|
3209 |
increment = aSign ? mask : 0;
|
3210 |
break;
|
3211 |
default: /* round_to_zero */ |
3212 |
increment = 0;
|
3213 |
break;
|
3214 |
} |
3215 |
|
3216 |
rounding_bumps_exp = (aSig + increment >= 0x01000000);
|
3217 |
|
3218 |
if (aExp > maxexp || (aExp == maxexp && rounding_bumps_exp)) {
|
3219 |
if (ieee) {
|
3220 |
float_raise(float_flag_overflow | float_flag_inexact STATUS_VAR); |
3221 |
return packFloat16(aSign, 0x1f, 0); |
3222 |
} else {
|
3223 |
float_raise(float_flag_invalid STATUS_VAR); |
3224 |
return packFloat16(aSign, 0x1f, 0x3ff); |
3225 |
} |
3226 |
} |
3227 |
|
3228 |
if (aExp < -14) { |
3229 |
/* Note that flush-to-zero does not affect half-precision results */
|
3230 |
is_tiny = |
3231 |
(STATUS(float_detect_tininess) == float_tininess_before_rounding) |
3232 |
|| (aExp < -15)
|
3233 |
|| (!rounding_bumps_exp); |
3234 |
} |
3235 |
if (aSig & mask) {
|
3236 |
float_raise(float_flag_inexact STATUS_VAR); |
3237 |
if (is_tiny) {
|
3238 |
float_raise(float_flag_underflow STATUS_VAR); |
3239 |
} |
3240 |
} |
3241 |
|
3242 |
aSig += increment; |
3243 |
if (rounding_bumps_exp) {
|
3244 |
aSig >>= 1;
|
3245 |
aExp++; |
3246 |
} |
3247 |
|
3248 |
if (aExp < -24) { |
3249 |
return packFloat16(aSign, 0, 0); |
3250 |
} |
3251 |
if (aExp < -14) { |
3252 |
aSig >>= -14 - aExp;
|
3253 |
aExp = -14;
|
3254 |
} |
3255 |
return packFloat16(aSign, aExp + 14, aSig >> 13); |
3256 |
} |
3257 |
|
3258 |
/*----------------------------------------------------------------------------
|
3259 |
| Returns the result of converting the double-precision floating-point value
|
3260 |
| `a' to the extended double-precision floating-point format. The conversion
|
3261 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
3262 |
| Arithmetic.
|
3263 |
*----------------------------------------------------------------------------*/
|
3264 |
|
3265 |
floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) |
3266 |
{ |
3267 |
flag aSign; |
3268 |
int_fast16_t aExp; |
3269 |
uint64_t aSig; |
3270 |
|
3271 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3272 |
aSig = extractFloat64Frac( a ); |
3273 |
aExp = extractFloat64Exp( a ); |
3274 |
aSign = extractFloat64Sign( a ); |
3275 |
if ( aExp == 0x7FF ) { |
3276 |
if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
3277 |
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3278 |
} |
3279 |
if ( aExp == 0 ) { |
3280 |
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); |
3281 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3282 |
} |
3283 |
return
|
3284 |
packFloatx80( |
3285 |
aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); |
3286 |
|
3287 |
} |
3288 |
|
3289 |
/*----------------------------------------------------------------------------
|
3290 |
| Returns the result of converting the double-precision floating-point value
|
3291 |
| `a' to the quadruple-precision floating-point format. The conversion is
|
3292 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
3293 |
| Arithmetic.
|
3294 |
*----------------------------------------------------------------------------*/
|
3295 |
|
3296 |
float128 float64_to_float128( float64 a STATUS_PARAM ) |
3297 |
{ |
3298 |
flag aSign; |
3299 |
int_fast16_t aExp; |
3300 |
uint64_t aSig, zSig0, zSig1; |
3301 |
|
3302 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3303 |
aSig = extractFloat64Frac( a ); |
3304 |
aExp = extractFloat64Exp( a ); |
3305 |
aSign = extractFloat64Sign( a ); |
3306 |
if ( aExp == 0x7FF ) { |
3307 |
if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); |
3308 |
return packFloat128( aSign, 0x7FFF, 0, 0 ); |
3309 |
} |
3310 |
if ( aExp == 0 ) { |
3311 |
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); |
3312 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3313 |
--aExp; |
3314 |
} |
3315 |
shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); |
3316 |
return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); |
3317 |
|
3318 |
} |
3319 |
|
3320 |
/*----------------------------------------------------------------------------
|
3321 |
| Rounds the double-precision floating-point value `a' to an integer, and
|
3322 |
| returns the result as a double-precision floating-point value. The
|
3323 |
| operation is performed according to the IEC/IEEE Standard for Binary
|
3324 |
| Floating-Point Arithmetic.
|
3325 |
*----------------------------------------------------------------------------*/
|
3326 |
|
3327 |
float64 float64_round_to_int( float64 a STATUS_PARAM ) |
3328 |
{ |
3329 |
flag aSign; |
3330 |
int_fast16_t aExp; |
3331 |
uint64_t lastBitMask, roundBitsMask; |
3332 |
int8 roundingMode; |
3333 |
uint64_t z; |
3334 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3335 |
|
3336 |
aExp = extractFloat64Exp( a ); |
3337 |
if ( 0x433 <= aExp ) { |
3338 |
if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { |
3339 |
return propagateFloat64NaN( a, a STATUS_VAR );
|
3340 |
} |
3341 |
return a;
|
3342 |
} |
3343 |
if ( aExp < 0x3FF ) { |
3344 |
if ( (uint64_t) ( float64_val(a)<<1 ) == 0 ) return a; |
3345 |
STATUS(float_exception_flags) |= float_flag_inexact; |
3346 |
aSign = extractFloat64Sign( a ); |
3347 |
switch ( STATUS(float_rounding_mode) ) {
|
3348 |
case float_round_nearest_even:
|
3349 |
if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { |
3350 |
return packFloat64( aSign, 0x3FF, 0 ); |
3351 |
} |
3352 |
break;
|
3353 |
case float_round_down:
|
3354 |
return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0); |
3355 |
case float_round_up:
|
3356 |
return make_float64(
|
3357 |
aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 )); |
3358 |
} |
3359 |
return packFloat64( aSign, 0, 0 ); |
3360 |
} |
3361 |
lastBitMask = 1;
|
3362 |
lastBitMask <<= 0x433 - aExp;
|
3363 |
roundBitsMask = lastBitMask - 1;
|
3364 |
z = float64_val(a); |
3365 |
roundingMode = STATUS(float_rounding_mode); |
3366 |
if ( roundingMode == float_round_nearest_even ) {
|
3367 |
z += lastBitMask>>1;
|
3368 |
if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; |
3369 |
} |
3370 |
else if ( roundingMode != float_round_to_zero ) { |
3371 |
if ( extractFloat64Sign( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) {
|
3372 |
z += roundBitsMask; |
3373 |
} |
3374 |
} |
3375 |
z &= ~ roundBitsMask; |
3376 |
if ( z != float64_val(a) )
|
3377 |
STATUS(float_exception_flags) |= float_flag_inexact; |
3378 |
return make_float64(z);
|
3379 |
|
3380 |
} |
3381 |
|
3382 |
float64 float64_trunc_to_int( float64 a STATUS_PARAM) |
3383 |
{ |
3384 |
int oldmode;
|
3385 |
float64 res; |
3386 |
oldmode = STATUS(float_rounding_mode); |
3387 |
STATUS(float_rounding_mode) = float_round_to_zero; |
3388 |
res = float64_round_to_int(a STATUS_VAR); |
3389 |
STATUS(float_rounding_mode) = oldmode; |
3390 |
return res;
|
3391 |
} |
3392 |
|
3393 |
/*----------------------------------------------------------------------------
|
3394 |
| Returns the result of adding the absolute values of the double-precision
|
3395 |
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
3396 |
| before being returned. `zSign' is ignored if the result is a NaN.
|
3397 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
3398 |
| Floating-Point Arithmetic.
|
3399 |
*----------------------------------------------------------------------------*/
|
3400 |
|
3401 |
static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
|
3402 |
{ |
3403 |
int_fast16_t aExp, bExp, zExp; |
3404 |
uint64_t aSig, bSig, zSig; |
3405 |
int_fast16_t expDiff; |
3406 |
|
3407 |
aSig = extractFloat64Frac( a ); |
3408 |
aExp = extractFloat64Exp( a ); |
3409 |
bSig = extractFloat64Frac( b ); |
3410 |
bExp = extractFloat64Exp( b ); |
3411 |
expDiff = aExp - bExp; |
3412 |
aSig <<= 9;
|
3413 |
bSig <<= 9;
|
3414 |
if ( 0 < expDiff ) { |
3415 |
if ( aExp == 0x7FF ) { |
3416 |
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3417 |
return a;
|
3418 |
} |
3419 |
if ( bExp == 0 ) { |
3420 |
--expDiff; |
3421 |
} |
3422 |
else {
|
3423 |
bSig |= LIT64( 0x2000000000000000 );
|
3424 |
} |
3425 |
shift64RightJamming( bSig, expDiff, &bSig ); |
3426 |
zExp = aExp; |
3427 |
} |
3428 |
else if ( expDiff < 0 ) { |
3429 |
if ( bExp == 0x7FF ) { |
3430 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3431 |
return packFloat64( zSign, 0x7FF, 0 ); |
3432 |
} |
3433 |
if ( aExp == 0 ) { |
3434 |
++expDiff; |
3435 |
} |
3436 |
else {
|
3437 |
aSig |= LIT64( 0x2000000000000000 );
|
3438 |
} |
3439 |
shift64RightJamming( aSig, - expDiff, &aSig ); |
3440 |
zExp = bExp; |
3441 |
} |
3442 |
else {
|
3443 |
if ( aExp == 0x7FF ) { |
3444 |
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3445 |
return a;
|
3446 |
} |
3447 |
if ( aExp == 0 ) { |
3448 |
if (STATUS(flush_to_zero)) {
|
3449 |
if (aSig | bSig) {
|
3450 |
float_raise(float_flag_output_denormal STATUS_VAR); |
3451 |
} |
3452 |
return packFloat64(zSign, 0, 0); |
3453 |
} |
3454 |
return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); |
3455 |
} |
3456 |
zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
|
3457 |
zExp = aExp; |
3458 |
goto roundAndPack;
|
3459 |
} |
3460 |
aSig |= LIT64( 0x2000000000000000 );
|
3461 |
zSig = ( aSig + bSig )<<1;
|
3462 |
--zExp; |
3463 |
if ( (int64_t) zSig < 0 ) { |
3464 |
zSig = aSig + bSig; |
3465 |
++zExp; |
3466 |
} |
3467 |
roundAndPack:
|
3468 |
return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
|
3469 |
|
3470 |
} |
3471 |
|
3472 |
/*----------------------------------------------------------------------------
|
3473 |
| Returns the result of subtracting the absolute values of the double-
|
3474 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
3475 |
| difference is negated before being returned. `zSign' is ignored if the
|
3476 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
3477 |
| Standard for Binary Floating-Point Arithmetic.
|
3478 |
*----------------------------------------------------------------------------*/
|
3479 |
|
3480 |
static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
|
3481 |
{ |
3482 |
int_fast16_t aExp, bExp, zExp; |
3483 |
uint64_t aSig, bSig, zSig; |
3484 |
int_fast16_t expDiff; |
3485 |
|
3486 |
aSig = extractFloat64Frac( a ); |
3487 |
aExp = extractFloat64Exp( a ); |
3488 |
bSig = extractFloat64Frac( b ); |
3489 |
bExp = extractFloat64Exp( b ); |
3490 |
expDiff = aExp - bExp; |
3491 |
aSig <<= 10;
|
3492 |
bSig <<= 10;
|
3493 |
if ( 0 < expDiff ) goto aExpBigger; |
3494 |
if ( expDiff < 0 ) goto bExpBigger; |
3495 |
if ( aExp == 0x7FF ) { |
3496 |
if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3497 |
float_raise( float_flag_invalid STATUS_VAR); |
3498 |
return float64_default_nan;
|
3499 |
} |
3500 |
if ( aExp == 0 ) { |
3501 |
aExp = 1;
|
3502 |
bExp = 1;
|
3503 |
} |
3504 |
if ( bSig < aSig ) goto aBigger; |
3505 |
if ( aSig < bSig ) goto bBigger; |
3506 |
return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
3507 |
bExpBigger:
|
3508 |
if ( bExp == 0x7FF ) { |
3509 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3510 |
return packFloat64( zSign ^ 1, 0x7FF, 0 ); |
3511 |
} |
3512 |
if ( aExp == 0 ) { |
3513 |
++expDiff; |
3514 |
} |
3515 |
else {
|
3516 |
aSig |= LIT64( 0x4000000000000000 );
|
3517 |
} |
3518 |
shift64RightJamming( aSig, - expDiff, &aSig ); |
3519 |
bSig |= LIT64( 0x4000000000000000 );
|
3520 |
bBigger:
|
3521 |
zSig = bSig - aSig; |
3522 |
zExp = bExp; |
3523 |
zSign ^= 1;
|
3524 |
goto normalizeRoundAndPack;
|
3525 |
aExpBigger:
|
3526 |
if ( aExp == 0x7FF ) { |
3527 |
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3528 |
return a;
|
3529 |
} |
3530 |
if ( bExp == 0 ) { |
3531 |
--expDiff; |
3532 |
} |
3533 |
else {
|
3534 |
bSig |= LIT64( 0x4000000000000000 );
|
3535 |
} |
3536 |
shift64RightJamming( bSig, expDiff, &bSig ); |
3537 |
aSig |= LIT64( 0x4000000000000000 );
|
3538 |
aBigger:
|
3539 |
zSig = aSig - bSig; |
3540 |
zExp = aExp; |
3541 |
normalizeRoundAndPack:
|
3542 |
--zExp; |
3543 |
return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
|
3544 |
|
3545 |
} |
3546 |
|
3547 |
/*----------------------------------------------------------------------------
|
3548 |
| Returns the result of adding the double-precision floating-point values `a'
|
3549 |
| and `b'. The operation is performed according to the IEC/IEEE Standard for
|
3550 |
| Binary Floating-Point Arithmetic.
|
3551 |
*----------------------------------------------------------------------------*/
|
3552 |
|
3553 |
float64 float64_add( float64 a, float64 b STATUS_PARAM ) |
3554 |
{ |
3555 |
flag aSign, bSign; |
3556 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3557 |
b = float64_squash_input_denormal(b STATUS_VAR); |
3558 |
|
3559 |
aSign = extractFloat64Sign( a ); |
3560 |
bSign = extractFloat64Sign( b ); |
3561 |
if ( aSign == bSign ) {
|
3562 |
return addFloat64Sigs( a, b, aSign STATUS_VAR );
|
3563 |
} |
3564 |
else {
|
3565 |
return subFloat64Sigs( a, b, aSign STATUS_VAR );
|
3566 |
} |
3567 |
|
3568 |
} |
3569 |
|
3570 |
/*----------------------------------------------------------------------------
|
3571 |
| Returns the result of subtracting the double-precision floating-point values
|
3572 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
3573 |
| for Binary Floating-Point Arithmetic.
|
3574 |
*----------------------------------------------------------------------------*/
|
3575 |
|
3576 |
float64 float64_sub( float64 a, float64 b STATUS_PARAM ) |
3577 |
{ |
3578 |
flag aSign, bSign; |
3579 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3580 |
b = float64_squash_input_denormal(b STATUS_VAR); |
3581 |
|
3582 |
aSign = extractFloat64Sign( a ); |
3583 |
bSign = extractFloat64Sign( b ); |
3584 |
if ( aSign == bSign ) {
|
3585 |
return subFloat64Sigs( a, b, aSign STATUS_VAR );
|
3586 |
} |
3587 |
else {
|
3588 |
return addFloat64Sigs( a, b, aSign STATUS_VAR );
|
3589 |
} |
3590 |
|
3591 |
} |
3592 |
|
3593 |
/*----------------------------------------------------------------------------
|
3594 |
| Returns the result of multiplying the double-precision floating-point values
|
3595 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
3596 |
| for Binary Floating-Point Arithmetic.
|
3597 |
*----------------------------------------------------------------------------*/
|
3598 |
|
3599 |
float64 float64_mul( float64 a, float64 b STATUS_PARAM ) |
3600 |
{ |
3601 |
flag aSign, bSign, zSign; |
3602 |
int_fast16_t aExp, bExp, zExp; |
3603 |
uint64_t aSig, bSig, zSig0, zSig1; |
3604 |
|
3605 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3606 |
b = float64_squash_input_denormal(b STATUS_VAR); |
3607 |
|
3608 |
aSig = extractFloat64Frac( a ); |
3609 |
aExp = extractFloat64Exp( a ); |
3610 |
aSign = extractFloat64Sign( a ); |
3611 |
bSig = extractFloat64Frac( b ); |
3612 |
bExp = extractFloat64Exp( b ); |
3613 |
bSign = extractFloat64Sign( b ); |
3614 |
zSign = aSign ^ bSign; |
3615 |
if ( aExp == 0x7FF ) { |
3616 |
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { |
3617 |
return propagateFloat64NaN( a, b STATUS_VAR );
|
3618 |
} |
3619 |
if ( ( bExp | bSig ) == 0 ) { |
3620 |
float_raise( float_flag_invalid STATUS_VAR); |
3621 |
return float64_default_nan;
|
3622 |
} |
3623 |
return packFloat64( zSign, 0x7FF, 0 ); |
3624 |
} |
3625 |
if ( bExp == 0x7FF ) { |
3626 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3627 |
if ( ( aExp | aSig ) == 0 ) { |
3628 |
float_raise( float_flag_invalid STATUS_VAR); |
3629 |
return float64_default_nan;
|
3630 |
} |
3631 |
return packFloat64( zSign, 0x7FF, 0 ); |
3632 |
} |
3633 |
if ( aExp == 0 ) { |
3634 |
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); |
3635 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3636 |
} |
3637 |
if ( bExp == 0 ) { |
3638 |
if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); |
3639 |
normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
3640 |
} |
3641 |
zExp = aExp + bExp - 0x3FF;
|
3642 |
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; |
3643 |
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
3644 |
mul64To128( aSig, bSig, &zSig0, &zSig1 ); |
3645 |
zSig0 |= ( zSig1 != 0 );
|
3646 |
if ( 0 <= (int64_t) ( zSig0<<1 ) ) { |
3647 |
zSig0 <<= 1;
|
3648 |
--zExp; |
3649 |
} |
3650 |
return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR );
|
3651 |
|
3652 |
} |
3653 |
|
3654 |
/*----------------------------------------------------------------------------
|
3655 |
| Returns the result of dividing the double-precision floating-point value `a'
|
3656 |
| by the corresponding value `b'. The operation is performed according to
|
3657 |
| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3658 |
*----------------------------------------------------------------------------*/
|
3659 |
|
3660 |
float64 float64_div( float64 a, float64 b STATUS_PARAM ) |
3661 |
{ |
3662 |
flag aSign, bSign, zSign; |
3663 |
int_fast16_t aExp, bExp, zExp; |
3664 |
uint64_t aSig, bSig, zSig; |
3665 |
uint64_t rem0, rem1; |
3666 |
uint64_t term0, term1; |
3667 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3668 |
b = float64_squash_input_denormal(b STATUS_VAR); |
3669 |
|
3670 |
aSig = extractFloat64Frac( a ); |
3671 |
aExp = extractFloat64Exp( a ); |
3672 |
aSign = extractFloat64Sign( a ); |
3673 |
bSig = extractFloat64Frac( b ); |
3674 |
bExp = extractFloat64Exp( b ); |
3675 |
bSign = extractFloat64Sign( b ); |
3676 |
zSign = aSign ^ bSign; |
3677 |
if ( aExp == 0x7FF ) { |
3678 |
if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3679 |
if ( bExp == 0x7FF ) { |
3680 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3681 |
float_raise( float_flag_invalid STATUS_VAR); |
3682 |
return float64_default_nan;
|
3683 |
} |
3684 |
return packFloat64( zSign, 0x7FF, 0 ); |
3685 |
} |
3686 |
if ( bExp == 0x7FF ) { |
3687 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3688 |
return packFloat64( zSign, 0, 0 ); |
3689 |
} |
3690 |
if ( bExp == 0 ) { |
3691 |
if ( bSig == 0 ) { |
3692 |
if ( ( aExp | aSig ) == 0 ) { |
3693 |
float_raise( float_flag_invalid STATUS_VAR); |
3694 |
return float64_default_nan;
|
3695 |
} |
3696 |
float_raise( float_flag_divbyzero STATUS_VAR); |
3697 |
return packFloat64( zSign, 0x7FF, 0 ); |
3698 |
} |
3699 |
normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
3700 |
} |
3701 |
if ( aExp == 0 ) { |
3702 |
if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); |
3703 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3704 |
} |
3705 |
zExp = aExp - bExp + 0x3FD;
|
3706 |
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; |
3707 |
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
3708 |
if ( bSig <= ( aSig + aSig ) ) {
|
3709 |
aSig >>= 1;
|
3710 |
++zExp; |
3711 |
} |
3712 |
zSig = estimateDiv128To64( aSig, 0, bSig );
|
3713 |
if ( ( zSig & 0x1FF ) <= 2 ) { |
3714 |
mul64To128( bSig, zSig, &term0, &term1 ); |
3715 |
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
3716 |
while ( (int64_t) rem0 < 0 ) { |
3717 |
--zSig; |
3718 |
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
3719 |
} |
3720 |
zSig |= ( rem1 != 0 );
|
3721 |
} |
3722 |
return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
|
3723 |
|
3724 |
} |
3725 |
|
3726 |
/*----------------------------------------------------------------------------
|
3727 |
| Returns the remainder of the double-precision floating-point value `a'
|
3728 |
| with respect to the corresponding value `b'. The operation is performed
|
3729 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
3730 |
*----------------------------------------------------------------------------*/
|
3731 |
|
3732 |
float64 float64_rem( float64 a, float64 b STATUS_PARAM ) |
3733 |
{ |
3734 |
flag aSign, zSign; |
3735 |
int_fast16_t aExp, bExp, expDiff; |
3736 |
uint64_t aSig, bSig; |
3737 |
uint64_t q, alternateASig; |
3738 |
int64_t sigMean; |
3739 |
|
3740 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3741 |
b = float64_squash_input_denormal(b STATUS_VAR); |
3742 |
aSig = extractFloat64Frac( a ); |
3743 |
aExp = extractFloat64Exp( a ); |
3744 |
aSign = extractFloat64Sign( a ); |
3745 |
bSig = extractFloat64Frac( b ); |
3746 |
bExp = extractFloat64Exp( b ); |
3747 |
if ( aExp == 0x7FF ) { |
3748 |
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { |
3749 |
return propagateFloat64NaN( a, b STATUS_VAR );
|
3750 |
} |
3751 |
float_raise( float_flag_invalid STATUS_VAR); |
3752 |
return float64_default_nan;
|
3753 |
} |
3754 |
if ( bExp == 0x7FF ) { |
3755 |
if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); |
3756 |
return a;
|
3757 |
} |
3758 |
if ( bExp == 0 ) { |
3759 |
if ( bSig == 0 ) { |
3760 |
float_raise( float_flag_invalid STATUS_VAR); |
3761 |
return float64_default_nan;
|
3762 |
} |
3763 |
normalizeFloat64Subnormal( bSig, &bExp, &bSig ); |
3764 |
} |
3765 |
if ( aExp == 0 ) { |
3766 |
if ( aSig == 0 ) return a; |
3767 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
3768 |
} |
3769 |
expDiff = aExp - bExp; |
3770 |
aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; |
3771 |
bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; |
3772 |
if ( expDiff < 0 ) { |
3773 |
if ( expDiff < -1 ) return a; |
3774 |
aSig >>= 1;
|
3775 |
} |
3776 |
q = ( bSig <= aSig ); |
3777 |
if ( q ) aSig -= bSig;
|
3778 |
expDiff -= 64;
|
3779 |
while ( 0 < expDiff ) { |
3780 |
q = estimateDiv128To64( aSig, 0, bSig );
|
3781 |
q = ( 2 < q ) ? q - 2 : 0; |
3782 |
aSig = - ( ( bSig>>2 ) * q );
|
3783 |
expDiff -= 62;
|
3784 |
} |
3785 |
expDiff += 64;
|
3786 |
if ( 0 < expDiff ) { |
3787 |
q = estimateDiv128To64( aSig, 0, bSig );
|
3788 |
q = ( 2 < q ) ? q - 2 : 0; |
3789 |
q >>= 64 - expDiff;
|
3790 |
bSig >>= 2;
|
3791 |
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; |
3792 |
} |
3793 |
else {
|
3794 |
aSig >>= 2;
|
3795 |
bSig >>= 2;
|
3796 |
} |
3797 |
do {
|
3798 |
alternateASig = aSig; |
3799 |
++q; |
3800 |
aSig -= bSig; |
3801 |
} while ( 0 <= (int64_t) aSig ); |
3802 |
sigMean = aSig + alternateASig; |
3803 |
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { |
3804 |
aSig = alternateASig; |
3805 |
} |
3806 |
zSign = ( (int64_t) aSig < 0 );
|
3807 |
if ( zSign ) aSig = - aSig;
|
3808 |
return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR );
|
3809 |
|
3810 |
} |
3811 |
|
3812 |
/*----------------------------------------------------------------------------
|
3813 |
| Returns the result of multiplying the double-precision floating-point values
|
3814 |
| `a' and `b' then adding 'c', with no intermediate rounding step after the
|
3815 |
| multiplication. The operation is performed according to the IEC/IEEE
|
3816 |
| Standard for Binary Floating-Point Arithmetic 754-2008.
|
3817 |
| The flags argument allows the caller to select negation of the
|
3818 |
| addend, the intermediate product, or the final result. (The difference
|
3819 |
| between this and having the caller do a separate negation is that negating
|
3820 |
| externally will flip the sign bit on NaNs.)
|
3821 |
*----------------------------------------------------------------------------*/
|
3822 |
|
3823 |
float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM)
|
3824 |
{ |
3825 |
flag aSign, bSign, cSign, zSign; |
3826 |
int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; |
3827 |
uint64_t aSig, bSig, cSig; |
3828 |
flag pInf, pZero, pSign; |
3829 |
uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1; |
3830 |
int shiftcount;
|
3831 |
flag signflip, infzero; |
3832 |
|
3833 |
a = float64_squash_input_denormal(a STATUS_VAR); |
3834 |
b = float64_squash_input_denormal(b STATUS_VAR); |
3835 |
c = float64_squash_input_denormal(c STATUS_VAR); |
3836 |
aSig = extractFloat64Frac(a); |
3837 |
aExp = extractFloat64Exp(a); |
3838 |
aSign = extractFloat64Sign(a); |
3839 |
bSig = extractFloat64Frac(b); |
3840 |
bExp = extractFloat64Exp(b); |
3841 |
bSign = extractFloat64Sign(b); |
3842 |
cSig = extractFloat64Frac(c); |
3843 |
cExp = extractFloat64Exp(c); |
3844 |
cSign = extractFloat64Sign(c); |
3845 |
|
3846 |
infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) || |
3847 |
(aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0)); |
3848 |
|
3849 |
/* It is implementation-defined whether the cases of (0,inf,qnan)
|
3850 |
* and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
|
3851 |
* they return if they do), so we have to hand this information
|
3852 |
* off to the target-specific pick-a-NaN routine.
|
3853 |
*/
|
3854 |
if (((aExp == 0x7ff) && aSig) || |
3855 |
((bExp == 0x7ff) && bSig) ||
|
3856 |
((cExp == 0x7ff) && cSig)) {
|
3857 |
return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR);
|
3858 |
} |
3859 |
|
3860 |
if (infzero) {
|
3861 |
float_raise(float_flag_invalid STATUS_VAR); |
3862 |
return float64_default_nan;
|
3863 |
} |
3864 |
|
3865 |
if (flags & float_muladd_negate_c) {
|
3866 |
cSign ^= 1;
|
3867 |
} |
3868 |
|
3869 |
signflip = (flags & float_muladd_negate_result) ? 1 : 0; |
3870 |
|
3871 |
/* Work out the sign and type of the product */
|
3872 |
pSign = aSign ^ bSign; |
3873 |
if (flags & float_muladd_negate_product) {
|
3874 |
pSign ^= 1;
|
3875 |
} |
3876 |
pInf = (aExp == 0x7ff) || (bExp == 0x7ff); |
3877 |
pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); |
3878 |
|
3879 |
if (cExp == 0x7ff) { |
3880 |
if (pInf && (pSign ^ cSign)) {
|
3881 |
/* addition of opposite-signed infinities => InvalidOperation */
|
3882 |
float_raise(float_flag_invalid STATUS_VAR); |
3883 |
return float64_default_nan;
|
3884 |
} |
3885 |
/* Otherwise generate an infinity of the same sign */
|
3886 |
return packFloat64(cSign ^ signflip, 0x7ff, 0); |
3887 |
} |
3888 |
|
3889 |
if (pInf) {
|
3890 |
return packFloat64(pSign ^ signflip, 0x7ff, 0); |
3891 |
} |
3892 |
|
3893 |
if (pZero) {
|
3894 |
if (cExp == 0) { |
3895 |
if (cSig == 0) { |
3896 |
/* Adding two exact zeroes */
|
3897 |
if (pSign == cSign) {
|
3898 |
zSign = pSign; |
3899 |
} else if (STATUS(float_rounding_mode) == float_round_down) { |
3900 |
zSign = 1;
|
3901 |
} else {
|
3902 |
zSign = 0;
|
3903 |
} |
3904 |
return packFloat64(zSign ^ signflip, 0, 0); |
3905 |
} |
3906 |
/* Exact zero plus a denorm */
|
3907 |
if (STATUS(flush_to_zero)) {
|
3908 |
float_raise(float_flag_output_denormal STATUS_VAR); |
3909 |
return packFloat64(cSign ^ signflip, 0, 0); |
3910 |
} |
3911 |
} |
3912 |
/* Zero plus something non-zero : just return the something */
|
3913 |
return packFloat64(cSign ^ signflip, cExp, cSig);
|
3914 |
} |
3915 |
|
3916 |
if (aExp == 0) { |
3917 |
normalizeFloat64Subnormal(aSig, &aExp, &aSig); |
3918 |
} |
3919 |
if (bExp == 0) { |
3920 |
normalizeFloat64Subnormal(bSig, &bExp, &bSig); |
3921 |
} |
3922 |
|
3923 |
/* Calculate the actual result a * b + c */
|
3924 |
|
3925 |
/* Multiply first; this is easy. */
|
3926 |
/* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff
|
3927 |
* because we want the true exponent, not the "one-less-than"
|
3928 |
* flavour that roundAndPackFloat64() takes.
|
3929 |
*/
|
3930 |
pExp = aExp + bExp - 0x3fe;
|
3931 |
aSig = (aSig | LIT64(0x0010000000000000))<<10; |
3932 |
bSig = (bSig | LIT64(0x0010000000000000))<<11; |
3933 |
mul64To128(aSig, bSig, &pSig0, &pSig1); |
3934 |
if ((int64_t)(pSig0 << 1) >= 0) { |
3935 |
shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1);
|
3936 |
pExp--; |
3937 |
} |
3938 |
|
3939 |
zSign = pSign ^ signflip; |
3940 |
|
3941 |
/* Now [pSig0:pSig1] is the significand of the multiply, with the explicit
|
3942 |
* bit in position 126.
|
3943 |
*/
|
3944 |
if (cExp == 0) { |
3945 |
if (!cSig) {
|
3946 |
/* Throw out the special case of c being an exact zero now */
|
3947 |
shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1);
|
3948 |
return roundAndPackFloat64(zSign, pExp - 1, |
3949 |
pSig1 STATUS_VAR); |
3950 |
} |
3951 |
normalizeFloat64Subnormal(cSig, &cExp, &cSig); |
3952 |
} |
3953 |
|
3954 |
/* Shift cSig and add the explicit bit so [cSig0:cSig1] is the
|
3955 |
* significand of the addend, with the explicit bit in position 126.
|
3956 |
*/
|
3957 |
cSig0 = cSig << (126 - 64 - 52); |
3958 |
cSig1 = 0;
|
3959 |
cSig0 |= LIT64(0x4000000000000000);
|
3960 |
expDiff = pExp - cExp; |
3961 |
|
3962 |
if (pSign == cSign) {
|
3963 |
/* Addition */
|
3964 |
if (expDiff > 0) { |
3965 |
/* scale c to match p */
|
3966 |
shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); |
3967 |
zExp = pExp; |
3968 |
} else if (expDiff < 0) { |
3969 |
/* scale p to match c */
|
3970 |
shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); |
3971 |
zExp = cExp; |
3972 |
} else {
|
3973 |
/* no scaling needed */
|
3974 |
zExp = cExp; |
3975 |
} |
3976 |
/* Add significands and make sure explicit bit ends up in posn 126 */
|
3977 |
add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); |
3978 |
if ((int64_t)zSig0 < 0) { |
3979 |
shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1);
|
3980 |
} else {
|
3981 |
zExp--; |
3982 |
} |
3983 |
shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1);
|
3984 |
return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR);
|
3985 |
} else {
|
3986 |
/* Subtraction */
|
3987 |
if (expDiff > 0) { |
3988 |
shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); |
3989 |
sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); |
3990 |
zExp = pExp; |
3991 |
} else if (expDiff < 0) { |
3992 |
shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); |
3993 |
sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); |
3994 |
zExp = cExp; |
3995 |
zSign ^= 1;
|
3996 |
} else {
|
3997 |
zExp = pExp; |
3998 |
if (lt128(cSig0, cSig1, pSig0, pSig1)) {
|
3999 |
sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); |
4000 |
} else if (lt128(pSig0, pSig1, cSig0, cSig1)) { |
4001 |
sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); |
4002 |
zSign ^= 1;
|
4003 |
} else {
|
4004 |
/* Exact zero */
|
4005 |
zSign = signflip; |
4006 |
if (STATUS(float_rounding_mode) == float_round_down) {
|
4007 |
zSign ^= 1;
|
4008 |
} |
4009 |
return packFloat64(zSign, 0, 0); |
4010 |
} |
4011 |
} |
4012 |
--zExp; |
4013 |
/* Do the equivalent of normalizeRoundAndPackFloat64() but
|
4014 |
* starting with the significand in a pair of uint64_t.
|
4015 |
*/
|
4016 |
if (zSig0) {
|
4017 |
shiftcount = countLeadingZeros64(zSig0) - 1;
|
4018 |
shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1); |
4019 |
if (zSig1) {
|
4020 |
zSig0 |= 1;
|
4021 |
} |
4022 |
zExp -= shiftcount; |
4023 |
} else {
|
4024 |
shiftcount = countLeadingZeros64(zSig1); |
4025 |
if (shiftcount == 0) { |
4026 |
zSig0 = (zSig1 >> 1) | (zSig1 & 1); |
4027 |
zExp -= 63;
|
4028 |
} else {
|
4029 |
shiftcount--; |
4030 |
zSig0 = zSig1 << shiftcount; |
4031 |
zExp -= (shiftcount + 64);
|
4032 |
} |
4033 |
} |
4034 |
return roundAndPackFloat64(zSign, zExp, zSig0 STATUS_VAR);
|
4035 |
} |
4036 |
} |
4037 |
|
4038 |
/*----------------------------------------------------------------------------
|
4039 |
| Returns the square root of the double-precision floating-point value `a'.
|
4040 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
4041 |
| Floating-Point Arithmetic.
|
4042 |
*----------------------------------------------------------------------------*/
|
4043 |
|
4044 |
float64 float64_sqrt( float64 a STATUS_PARAM ) |
4045 |
{ |
4046 |
flag aSign; |
4047 |
int_fast16_t aExp, zExp; |
4048 |
uint64_t aSig, zSig, doubleZSig; |
4049 |
uint64_t rem0, rem1, term0, term1; |
4050 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4051 |
|
4052 |
aSig = extractFloat64Frac( a ); |
4053 |
aExp = extractFloat64Exp( a ); |
4054 |
aSign = extractFloat64Sign( a ); |
4055 |
if ( aExp == 0x7FF ) { |
4056 |
if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); |
4057 |
if ( ! aSign ) return a; |
4058 |
float_raise( float_flag_invalid STATUS_VAR); |
4059 |
return float64_default_nan;
|
4060 |
} |
4061 |
if ( aSign ) {
|
4062 |
if ( ( aExp | aSig ) == 0 ) return a; |
4063 |
float_raise( float_flag_invalid STATUS_VAR); |
4064 |
return float64_default_nan;
|
4065 |
} |
4066 |
if ( aExp == 0 ) { |
4067 |
if ( aSig == 0 ) return float64_zero; |
4068 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
4069 |
} |
4070 |
zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; |
4071 |
aSig |= LIT64( 0x0010000000000000 );
|
4072 |
zSig = estimateSqrt32( aExp, aSig>>21 );
|
4073 |
aSig <<= 9 - ( aExp & 1 ); |
4074 |
zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); |
4075 |
if ( ( zSig & 0x1FF ) <= 5 ) { |
4076 |
doubleZSig = zSig<<1;
|
4077 |
mul64To128( zSig, zSig, &term0, &term1 ); |
4078 |
sub128( aSig, 0, term0, term1, &rem0, &rem1 );
|
4079 |
while ( (int64_t) rem0 < 0 ) { |
4080 |
--zSig; |
4081 |
doubleZSig -= 2;
|
4082 |
add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); |
4083 |
} |
4084 |
zSig |= ( ( rem0 | rem1 ) != 0 );
|
4085 |
} |
4086 |
return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); |
4087 |
|
4088 |
} |
4089 |
|
4090 |
/*----------------------------------------------------------------------------
|
4091 |
| Returns the binary log of the double-precision floating-point value `a'.
|
4092 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
4093 |
| Floating-Point Arithmetic.
|
4094 |
*----------------------------------------------------------------------------*/
|
4095 |
float64 float64_log2( float64 a STATUS_PARAM ) |
4096 |
{ |
4097 |
flag aSign, zSign; |
4098 |
int_fast16_t aExp; |
4099 |
uint64_t aSig, aSig0, aSig1, zSig, i; |
4100 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4101 |
|
4102 |
aSig = extractFloat64Frac( a ); |
4103 |
aExp = extractFloat64Exp( a ); |
4104 |
aSign = extractFloat64Sign( a ); |
4105 |
|
4106 |
if ( aExp == 0 ) { |
4107 |
if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 ); |
4108 |
normalizeFloat64Subnormal( aSig, &aExp, &aSig ); |
4109 |
} |
4110 |
if ( aSign ) {
|
4111 |
float_raise( float_flag_invalid STATUS_VAR); |
4112 |
return float64_default_nan;
|
4113 |
} |
4114 |
if ( aExp == 0x7FF ) { |
4115 |
if ( aSig ) return propagateFloat64NaN( a, float64_zero STATUS_VAR ); |
4116 |
return a;
|
4117 |
} |
4118 |
|
4119 |
aExp -= 0x3FF;
|
4120 |
aSig |= LIT64( 0x0010000000000000 );
|
4121 |
zSign = aExp < 0;
|
4122 |
zSig = (uint64_t)aExp << 52;
|
4123 |
for (i = 1LL << 51; i > 0; i >>= 1) { |
4124 |
mul64To128( aSig, aSig, &aSig0, &aSig1 ); |
4125 |
aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 ); |
4126 |
if ( aSig & LIT64( 0x0020000000000000 ) ) { |
4127 |
aSig >>= 1;
|
4128 |
zSig |= i; |
4129 |
} |
4130 |
} |
4131 |
|
4132 |
if ( zSign )
|
4133 |
zSig = -zSig; |
4134 |
return normalizeRoundAndPackFloat64( zSign, 0x408, zSig STATUS_VAR ); |
4135 |
} |
4136 |
|
4137 |
/*----------------------------------------------------------------------------
|
4138 |
| Returns 1 if the double-precision floating-point value `a' is equal to the
|
4139 |
| corresponding value `b', and 0 otherwise. The invalid exception is raised
|
4140 |
| if either operand is a NaN. Otherwise, the comparison is performed
|
4141 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4142 |
*----------------------------------------------------------------------------*/
|
4143 |
|
4144 |
int float64_eq( float64 a, float64 b STATUS_PARAM )
|
4145 |
{ |
4146 |
uint64_t av, bv; |
4147 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4148 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4149 |
|
4150 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4151 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4152 |
) { |
4153 |
float_raise( float_flag_invalid STATUS_VAR); |
4154 |
return 0; |
4155 |
} |
4156 |
av = float64_val(a); |
4157 |
bv = float64_val(b); |
4158 |
return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
4159 |
|
4160 |
} |
4161 |
|
4162 |
/*----------------------------------------------------------------------------
|
4163 |
| Returns 1 if the double-precision floating-point value `a' is less than or
|
4164 |
| equal to the corresponding value `b', and 0 otherwise. The invalid
|
4165 |
| exception is raised if either operand is a NaN. The comparison is performed
|
4166 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4167 |
*----------------------------------------------------------------------------*/
|
4168 |
|
4169 |
int float64_le( float64 a, float64 b STATUS_PARAM )
|
4170 |
{ |
4171 |
flag aSign, bSign; |
4172 |
uint64_t av, bv; |
4173 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4174 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4175 |
|
4176 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4177 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4178 |
) { |
4179 |
float_raise( float_flag_invalid STATUS_VAR); |
4180 |
return 0; |
4181 |
} |
4182 |
aSign = extractFloat64Sign( a ); |
4183 |
bSign = extractFloat64Sign( b ); |
4184 |
av = float64_val(a); |
4185 |
bv = float64_val(b); |
4186 |
if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
4187 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
4188 |
|
4189 |
} |
4190 |
|
4191 |
/*----------------------------------------------------------------------------
|
4192 |
| Returns 1 if the double-precision floating-point value `a' is less than
|
4193 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
4194 |
| raised if either operand is a NaN. The comparison is performed according
|
4195 |
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4196 |
*----------------------------------------------------------------------------*/
|
4197 |
|
4198 |
int float64_lt( float64 a, float64 b STATUS_PARAM )
|
4199 |
{ |
4200 |
flag aSign, bSign; |
4201 |
uint64_t av, bv; |
4202 |
|
4203 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4204 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4205 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4206 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4207 |
) { |
4208 |
float_raise( float_flag_invalid STATUS_VAR); |
4209 |
return 0; |
4210 |
} |
4211 |
aSign = extractFloat64Sign( a ); |
4212 |
bSign = extractFloat64Sign( b ); |
4213 |
av = float64_val(a); |
4214 |
bv = float64_val(b); |
4215 |
if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); |
4216 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
4217 |
|
4218 |
} |
4219 |
|
4220 |
/*----------------------------------------------------------------------------
|
4221 |
| Returns 1 if the double-precision floating-point values `a' and `b' cannot
|
4222 |
| be compared, and 0 otherwise. The invalid exception is raised if either
|
4223 |
| operand is a NaN. The comparison is performed according to the IEC/IEEE
|
4224 |
| Standard for Binary Floating-Point Arithmetic.
|
4225 |
*----------------------------------------------------------------------------*/
|
4226 |
|
4227 |
int float64_unordered( float64 a, float64 b STATUS_PARAM )
|
4228 |
{ |
4229 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4230 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4231 |
|
4232 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4233 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4234 |
) { |
4235 |
float_raise( float_flag_invalid STATUS_VAR); |
4236 |
return 1; |
4237 |
} |
4238 |
return 0; |
4239 |
} |
4240 |
|
4241 |
/*----------------------------------------------------------------------------
|
4242 |
| Returns 1 if the double-precision floating-point value `a' is equal to the
|
4243 |
| corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
4244 |
| exception.The comparison is performed according to the IEC/IEEE Standard
|
4245 |
| for Binary Floating-Point Arithmetic.
|
4246 |
*----------------------------------------------------------------------------*/
|
4247 |
|
4248 |
int float64_eq_quiet( float64 a, float64 b STATUS_PARAM )
|
4249 |
{ |
4250 |
uint64_t av, bv; |
4251 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4252 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4253 |
|
4254 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4255 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4256 |
) { |
4257 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
4258 |
float_raise( float_flag_invalid STATUS_VAR); |
4259 |
} |
4260 |
return 0; |
4261 |
} |
4262 |
av = float64_val(a); |
4263 |
bv = float64_val(b); |
4264 |
return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
4265 |
|
4266 |
} |
4267 |
|
4268 |
/*----------------------------------------------------------------------------
|
4269 |
| Returns 1 if the double-precision floating-point value `a' is less than or
|
4270 |
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
4271 |
| cause an exception. Otherwise, the comparison is performed according to the
|
4272 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4273 |
*----------------------------------------------------------------------------*/
|
4274 |
|
4275 |
int float64_le_quiet( float64 a, float64 b STATUS_PARAM )
|
4276 |
{ |
4277 |
flag aSign, bSign; |
4278 |
uint64_t av, bv; |
4279 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4280 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4281 |
|
4282 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4283 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4284 |
) { |
4285 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
4286 |
float_raise( float_flag_invalid STATUS_VAR); |
4287 |
} |
4288 |
return 0; |
4289 |
} |
4290 |
aSign = extractFloat64Sign( a ); |
4291 |
bSign = extractFloat64Sign( b ); |
4292 |
av = float64_val(a); |
4293 |
bv = float64_val(b); |
4294 |
if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); |
4295 |
return ( av == bv ) || ( aSign ^ ( av < bv ) );
|
4296 |
|
4297 |
} |
4298 |
|
4299 |
/*----------------------------------------------------------------------------
|
4300 |
| Returns 1 if the double-precision floating-point value `a' is less than
|
4301 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
4302 |
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
4303 |
| Standard for Binary Floating-Point Arithmetic.
|
4304 |
*----------------------------------------------------------------------------*/
|
4305 |
|
4306 |
int float64_lt_quiet( float64 a, float64 b STATUS_PARAM )
|
4307 |
{ |
4308 |
flag aSign, bSign; |
4309 |
uint64_t av, bv; |
4310 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4311 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4312 |
|
4313 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4314 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4315 |
) { |
4316 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
4317 |
float_raise( float_flag_invalid STATUS_VAR); |
4318 |
} |
4319 |
return 0; |
4320 |
} |
4321 |
aSign = extractFloat64Sign( a ); |
4322 |
bSign = extractFloat64Sign( b ); |
4323 |
av = float64_val(a); |
4324 |
bv = float64_val(b); |
4325 |
if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); |
4326 |
return ( av != bv ) && ( aSign ^ ( av < bv ) );
|
4327 |
|
4328 |
} |
4329 |
|
4330 |
/*----------------------------------------------------------------------------
|
4331 |
| Returns 1 if the double-precision floating-point values `a' and `b' cannot
|
4332 |
| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The
|
4333 |
| comparison is performed according to the IEC/IEEE Standard for Binary
|
4334 |
| Floating-Point Arithmetic.
|
4335 |
*----------------------------------------------------------------------------*/
|
4336 |
|
4337 |
int float64_unordered_quiet( float64 a, float64 b STATUS_PARAM )
|
4338 |
{ |
4339 |
a = float64_squash_input_denormal(a STATUS_VAR); |
4340 |
b = float64_squash_input_denormal(b STATUS_VAR); |
4341 |
|
4342 |
if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) |
4343 |
|| ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
|
4344 |
) { |
4345 |
if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
|
4346 |
float_raise( float_flag_invalid STATUS_VAR); |
4347 |
} |
4348 |
return 1; |
4349 |
} |
4350 |
return 0; |
4351 |
} |
4352 |
|
4353 |
/*----------------------------------------------------------------------------
|
4354 |
| Returns the result of converting the extended double-precision floating-
|
4355 |
| point value `a' to the 32-bit two's complement integer format. The
|
4356 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4357 |
| Floating-Point Arithmetic---which means in particular that the conversion
|
4358 |
| is rounded according to the current rounding mode. If `a' is a NaN, the
|
4359 |
| largest positive integer is returned. Otherwise, if the conversion
|
4360 |
| overflows, the largest integer with the same sign as `a' is returned.
|
4361 |
*----------------------------------------------------------------------------*/
|
4362 |
|
4363 |
int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) |
4364 |
{ |
4365 |
flag aSign; |
4366 |
int32 aExp, shiftCount; |
4367 |
uint64_t aSig; |
4368 |
|
4369 |
aSig = extractFloatx80Frac( a ); |
4370 |
aExp = extractFloatx80Exp( a ); |
4371 |
aSign = extractFloatx80Sign( a ); |
4372 |
if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; |
4373 |
shiftCount = 0x4037 - aExp;
|
4374 |
if ( shiftCount <= 0 ) shiftCount = 1; |
4375 |
shift64RightJamming( aSig, shiftCount, &aSig ); |
4376 |
return roundAndPackInt32( aSign, aSig STATUS_VAR );
|
4377 |
|
4378 |
} |
4379 |
|
4380 |
/*----------------------------------------------------------------------------
|
4381 |
| Returns the result of converting the extended double-precision floating-
|
4382 |
| point value `a' to the 32-bit two's complement integer format. The
|
4383 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4384 |
| Floating-Point Arithmetic, except that the conversion is always rounded
|
4385 |
| toward zero. If `a' is a NaN, the largest positive integer is returned.
|
4386 |
| Otherwise, if the conversion overflows, the largest integer with the same
|
4387 |
| sign as `a' is returned.
|
4388 |
*----------------------------------------------------------------------------*/
|
4389 |
|
4390 |
int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) |
4391 |
{ |
4392 |
flag aSign; |
4393 |
int32 aExp, shiftCount; |
4394 |
uint64_t aSig, savedASig; |
4395 |
int32_t z; |
4396 |
|
4397 |
aSig = extractFloatx80Frac( a ); |
4398 |
aExp = extractFloatx80Exp( a ); |
4399 |
aSign = extractFloatx80Sign( a ); |
4400 |
if ( 0x401E < aExp ) { |
4401 |
if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; |
4402 |
goto invalid;
|
4403 |
} |
4404 |
else if ( aExp < 0x3FFF ) { |
4405 |
if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
4406 |
return 0; |
4407 |
} |
4408 |
shiftCount = 0x403E - aExp;
|
4409 |
savedASig = aSig; |
4410 |
aSig >>= shiftCount; |
4411 |
z = aSig; |
4412 |
if ( aSign ) z = - z;
|
4413 |
if ( ( z < 0 ) ^ aSign ) { |
4414 |
invalid:
|
4415 |
float_raise( float_flag_invalid STATUS_VAR); |
4416 |
return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
4417 |
} |
4418 |
if ( ( aSig<<shiftCount ) != savedASig ) {
|
4419 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4420 |
} |
4421 |
return z;
|
4422 |
|
4423 |
} |
4424 |
|
4425 |
/*----------------------------------------------------------------------------
|
4426 |
| Returns the result of converting the extended double-precision floating-
|
4427 |
| point value `a' to the 64-bit two's complement integer format. The
|
4428 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4429 |
| Floating-Point Arithmetic---which means in particular that the conversion
|
4430 |
| is rounded according to the current rounding mode. If `a' is a NaN,
|
4431 |
| the largest positive integer is returned. Otherwise, if the conversion
|
4432 |
| overflows, the largest integer with the same sign as `a' is returned.
|
4433 |
*----------------------------------------------------------------------------*/
|
4434 |
|
4435 |
int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) |
4436 |
{ |
4437 |
flag aSign; |
4438 |
int32 aExp, shiftCount; |
4439 |
uint64_t aSig, aSigExtra; |
4440 |
|
4441 |
aSig = extractFloatx80Frac( a ); |
4442 |
aExp = extractFloatx80Exp( a ); |
4443 |
aSign = extractFloatx80Sign( a ); |
4444 |
shiftCount = 0x403E - aExp;
|
4445 |
if ( shiftCount <= 0 ) { |
4446 |
if ( shiftCount ) {
|
4447 |
float_raise( float_flag_invalid STATUS_VAR); |
4448 |
if ( ! aSign
|
4449 |
|| ( ( aExp == 0x7FFF )
|
4450 |
&& ( aSig != LIT64( 0x8000000000000000 ) ) )
|
4451 |
) { |
4452 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
4453 |
} |
4454 |
return (int64_t) LIT64( 0x8000000000000000 ); |
4455 |
} |
4456 |
aSigExtra = 0;
|
4457 |
} |
4458 |
else {
|
4459 |
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
|
4460 |
} |
4461 |
return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
|
4462 |
|
4463 |
} |
4464 |
|
4465 |
/*----------------------------------------------------------------------------
|
4466 |
| Returns the result of converting the extended double-precision floating-
|
4467 |
| point value `a' to the 64-bit two's complement integer format. The
|
4468 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4469 |
| Floating-Point Arithmetic, except that the conversion is always rounded
|
4470 |
| toward zero. If `a' is a NaN, the largest positive integer is returned.
|
4471 |
| Otherwise, if the conversion overflows, the largest integer with the same
|
4472 |
| sign as `a' is returned.
|
4473 |
*----------------------------------------------------------------------------*/
|
4474 |
|
4475 |
int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) |
4476 |
{ |
4477 |
flag aSign; |
4478 |
int32 aExp, shiftCount; |
4479 |
uint64_t aSig; |
4480 |
int64 z; |
4481 |
|
4482 |
aSig = extractFloatx80Frac( a ); |
4483 |
aExp = extractFloatx80Exp( a ); |
4484 |
aSign = extractFloatx80Sign( a ); |
4485 |
shiftCount = aExp - 0x403E;
|
4486 |
if ( 0 <= shiftCount ) { |
4487 |
aSig &= LIT64( 0x7FFFFFFFFFFFFFFF );
|
4488 |
if ( ( a.high != 0xC03E ) || aSig ) { |
4489 |
float_raise( float_flag_invalid STATUS_VAR); |
4490 |
if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { |
4491 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
4492 |
} |
4493 |
} |
4494 |
return (int64_t) LIT64( 0x8000000000000000 ); |
4495 |
} |
4496 |
else if ( aExp < 0x3FFF ) { |
4497 |
if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
|
4498 |
return 0; |
4499 |
} |
4500 |
z = aSig>>( - shiftCount ); |
4501 |
if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { |
4502 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4503 |
} |
4504 |
if ( aSign ) z = - z;
|
4505 |
return z;
|
4506 |
|
4507 |
} |
4508 |
|
4509 |
/*----------------------------------------------------------------------------
|
4510 |
| Returns the result of converting the extended double-precision floating-
|
4511 |
| point value `a' to the single-precision floating-point format. The
|
4512 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4513 |
| Floating-Point Arithmetic.
|
4514 |
*----------------------------------------------------------------------------*/
|
4515 |
|
4516 |
float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) |
4517 |
{ |
4518 |
flag aSign; |
4519 |
int32 aExp; |
4520 |
uint64_t aSig; |
4521 |
|
4522 |
aSig = extractFloatx80Frac( a ); |
4523 |
aExp = extractFloatx80Exp( a ); |
4524 |
aSign = extractFloatx80Sign( a ); |
4525 |
if ( aExp == 0x7FFF ) { |
4526 |
if ( (uint64_t) ( aSig<<1 ) ) { |
4527 |
return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
|
4528 |
} |
4529 |
return packFloat32( aSign, 0xFF, 0 ); |
4530 |
} |
4531 |
shift64RightJamming( aSig, 33, &aSig );
|
4532 |
if ( aExp || aSig ) aExp -= 0x3F81; |
4533 |
return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
|
4534 |
|
4535 |
} |
4536 |
|
4537 |
/*----------------------------------------------------------------------------
|
4538 |
| Returns the result of converting the extended double-precision floating-
|
4539 |
| point value `a' to the double-precision floating-point format. The
|
4540 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4541 |
| Floating-Point Arithmetic.
|
4542 |
*----------------------------------------------------------------------------*/
|
4543 |
|
4544 |
float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) |
4545 |
{ |
4546 |
flag aSign; |
4547 |
int32 aExp; |
4548 |
uint64_t aSig, zSig; |
4549 |
|
4550 |
aSig = extractFloatx80Frac( a ); |
4551 |
aExp = extractFloatx80Exp( a ); |
4552 |
aSign = extractFloatx80Sign( a ); |
4553 |
if ( aExp == 0x7FFF ) { |
4554 |
if ( (uint64_t) ( aSig<<1 ) ) { |
4555 |
return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
|
4556 |
} |
4557 |
return packFloat64( aSign, 0x7FF, 0 ); |
4558 |
} |
4559 |
shift64RightJamming( aSig, 1, &zSig );
|
4560 |
if ( aExp || aSig ) aExp -= 0x3C01; |
4561 |
return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR );
|
4562 |
|
4563 |
} |
4564 |
|
4565 |
/*----------------------------------------------------------------------------
|
4566 |
| Returns the result of converting the extended double-precision floating-
|
4567 |
| point value `a' to the quadruple-precision floating-point format. The
|
4568 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
4569 |
| Floating-Point Arithmetic.
|
4570 |
*----------------------------------------------------------------------------*/
|
4571 |
|
4572 |
float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) |
4573 |
{ |
4574 |
flag aSign; |
4575 |
int_fast16_t aExp; |
4576 |
uint64_t aSig, zSig0, zSig1; |
4577 |
|
4578 |
aSig = extractFloatx80Frac( a ); |
4579 |
aExp = extractFloatx80Exp( a ); |
4580 |
aSign = extractFloatx80Sign( a ); |
4581 |
if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) { |
4582 |
return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
|
4583 |
} |
4584 |
shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); |
4585 |
return packFloat128( aSign, aExp, zSig0, zSig1 );
|
4586 |
|
4587 |
} |
4588 |
|
4589 |
/*----------------------------------------------------------------------------
|
4590 |
| Rounds the extended double-precision floating-point value `a' to an integer,
|
4591 |
| and returns the result as an extended quadruple-precision floating-point
|
4592 |
| value. The operation is performed according to the IEC/IEEE Standard for
|
4593 |
| Binary Floating-Point Arithmetic.
|
4594 |
*----------------------------------------------------------------------------*/
|
4595 |
|
4596 |
floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) |
4597 |
{ |
4598 |
flag aSign; |
4599 |
int32 aExp; |
4600 |
uint64_t lastBitMask, roundBitsMask; |
4601 |
int8 roundingMode; |
4602 |
floatx80 z; |
4603 |
|
4604 |
aExp = extractFloatx80Exp( a ); |
4605 |
if ( 0x403E <= aExp ) { |
4606 |
if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) { |
4607 |
return propagateFloatx80NaN( a, a STATUS_VAR );
|
4608 |
} |
4609 |
return a;
|
4610 |
} |
4611 |
if ( aExp < 0x3FFF ) { |
4612 |
if ( ( aExp == 0 ) |
4613 |
&& ( (uint64_t) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { |
4614 |
return a;
|
4615 |
} |
4616 |
STATUS(float_exception_flags) |= float_flag_inexact; |
4617 |
aSign = extractFloatx80Sign( a ); |
4618 |
switch ( STATUS(float_rounding_mode) ) {
|
4619 |
case float_round_nearest_even:
|
4620 |
if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) |
4621 |
) { |
4622 |
return
|
4623 |
packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); |
4624 |
} |
4625 |
break;
|
4626 |
case float_round_down:
|
4627 |
return
|
4628 |
aSign ? |
4629 |
packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) |
4630 |
: packFloatx80( 0, 0, 0 ); |
4631 |
case float_round_up:
|
4632 |
return
|
4633 |
aSign ? packFloatx80( 1, 0, 0 ) |
4634 |
: packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); |
4635 |
} |
4636 |
return packFloatx80( aSign, 0, 0 ); |
4637 |
} |
4638 |
lastBitMask = 1;
|
4639 |
lastBitMask <<= 0x403E - aExp;
|
4640 |
roundBitsMask = lastBitMask - 1;
|
4641 |
z = a; |
4642 |
roundingMode = STATUS(float_rounding_mode); |
4643 |
if ( roundingMode == float_round_nearest_even ) {
|
4644 |
z.low += lastBitMask>>1;
|
4645 |
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; |
4646 |
} |
4647 |
else if ( roundingMode != float_round_to_zero ) { |
4648 |
if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
|
4649 |
z.low += roundBitsMask; |
4650 |
} |
4651 |
} |
4652 |
z.low &= ~ roundBitsMask; |
4653 |
if ( z.low == 0 ) { |
4654 |
++z.high; |
4655 |
z.low = LIT64( 0x8000000000000000 );
|
4656 |
} |
4657 |
if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact;
|
4658 |
return z;
|
4659 |
|
4660 |
} |
4661 |
|
4662 |
/*----------------------------------------------------------------------------
|
4663 |
| Returns the result of adding the absolute values of the extended double-
|
4664 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the sum is
|
4665 |
| negated before being returned. `zSign' is ignored if the result is a NaN.
|
4666 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
4667 |
| Floating-Point Arithmetic.
|
4668 |
*----------------------------------------------------------------------------*/
|
4669 |
|
4670 |
static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM)
|
4671 |
{ |
4672 |
int32 aExp, bExp, zExp; |
4673 |
uint64_t aSig, bSig, zSig0, zSig1; |
4674 |
int32 expDiff; |
4675 |
|
4676 |
aSig = extractFloatx80Frac( a ); |
4677 |
aExp = extractFloatx80Exp( a ); |
4678 |
bSig = extractFloatx80Frac( b ); |
4679 |
bExp = extractFloatx80Exp( b ); |
4680 |
expDiff = aExp - bExp; |
4681 |
if ( 0 < expDiff ) { |
4682 |
if ( aExp == 0x7FFF ) { |
4683 |
if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4684 |
return a;
|
4685 |
} |
4686 |
if ( bExp == 0 ) --expDiff; |
4687 |
shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
4688 |
zExp = aExp; |
4689 |
} |
4690 |
else if ( expDiff < 0 ) { |
4691 |
if ( bExp == 0x7FFF ) { |
4692 |
if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4693 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4694 |
} |
4695 |
if ( aExp == 0 ) ++expDiff; |
4696 |
shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
4697 |
zExp = bExp; |
4698 |
} |
4699 |
else {
|
4700 |
if ( aExp == 0x7FFF ) { |
4701 |
if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { |
4702 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
4703 |
} |
4704 |
return a;
|
4705 |
} |
4706 |
zSig1 = 0;
|
4707 |
zSig0 = aSig + bSig; |
4708 |
if ( aExp == 0 ) { |
4709 |
normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); |
4710 |
goto roundAndPack;
|
4711 |
} |
4712 |
zExp = aExp; |
4713 |
goto shiftRight1;
|
4714 |
} |
4715 |
zSig0 = aSig + bSig; |
4716 |
if ( (int64_t) zSig0 < 0 ) goto roundAndPack; |
4717 |
shiftRight1:
|
4718 |
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
4719 |
zSig0 |= LIT64( 0x8000000000000000 );
|
4720 |
++zExp; |
4721 |
roundAndPack:
|
4722 |
return
|
4723 |
roundAndPackFloatx80( |
4724 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
4725 |
|
4726 |
} |
4727 |
|
4728 |
/*----------------------------------------------------------------------------
|
4729 |
| Returns the result of subtracting the absolute values of the extended
|
4730 |
| double-precision floating-point values `a' and `b'. If `zSign' is 1, the
|
4731 |
| difference is negated before being returned. `zSign' is ignored if the
|
4732 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
4733 |
| Standard for Binary Floating-Point Arithmetic.
|
4734 |
*----------------------------------------------------------------------------*/
|
4735 |
|
4736 |
static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM )
|
4737 |
{ |
4738 |
int32 aExp, bExp, zExp; |
4739 |
uint64_t aSig, bSig, zSig0, zSig1; |
4740 |
int32 expDiff; |
4741 |
floatx80 z; |
4742 |
|
4743 |
aSig = extractFloatx80Frac( a ); |
4744 |
aExp = extractFloatx80Exp( a ); |
4745 |
bSig = extractFloatx80Frac( b ); |
4746 |
bExp = extractFloatx80Exp( b ); |
4747 |
expDiff = aExp - bExp; |
4748 |
if ( 0 < expDiff ) goto aExpBigger; |
4749 |
if ( expDiff < 0 ) goto bExpBigger; |
4750 |
if ( aExp == 0x7FFF ) { |
4751 |
if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { |
4752 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
4753 |
} |
4754 |
float_raise( float_flag_invalid STATUS_VAR); |
4755 |
z.low = floatx80_default_nan_low; |
4756 |
z.high = floatx80_default_nan_high; |
4757 |
return z;
|
4758 |
} |
4759 |
if ( aExp == 0 ) { |
4760 |
aExp = 1;
|
4761 |
bExp = 1;
|
4762 |
} |
4763 |
zSig1 = 0;
|
4764 |
if ( bSig < aSig ) goto aBigger; |
4765 |
if ( aSig < bSig ) goto bBigger; |
4766 |
return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); |
4767 |
bExpBigger:
|
4768 |
if ( bExp == 0x7FFF ) { |
4769 |
if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4770 |
return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4771 |
} |
4772 |
if ( aExp == 0 ) ++expDiff; |
4773 |
shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
4774 |
bBigger:
|
4775 |
sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
|
4776 |
zExp = bExp; |
4777 |
zSign ^= 1;
|
4778 |
goto normalizeRoundAndPack;
|
4779 |
aExpBigger:
|
4780 |
if ( aExp == 0x7FFF ) { |
4781 |
if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4782 |
return a;
|
4783 |
} |
4784 |
if ( bExp == 0 ) --expDiff; |
4785 |
shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
4786 |
aBigger:
|
4787 |
sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
|
4788 |
zExp = aExp; |
4789 |
normalizeRoundAndPack:
|
4790 |
return
|
4791 |
normalizeRoundAndPackFloatx80( |
4792 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
4793 |
|
4794 |
} |
4795 |
|
4796 |
/*----------------------------------------------------------------------------
|
4797 |
| Returns the result of adding the extended double-precision floating-point
|
4798 |
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
4799 |
| Standard for Binary Floating-Point Arithmetic.
|
4800 |
*----------------------------------------------------------------------------*/
|
4801 |
|
4802 |
floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) |
4803 |
{ |
4804 |
flag aSign, bSign; |
4805 |
|
4806 |
aSign = extractFloatx80Sign( a ); |
4807 |
bSign = extractFloatx80Sign( b ); |
4808 |
if ( aSign == bSign ) {
|
4809 |
return addFloatx80Sigs( a, b, aSign STATUS_VAR );
|
4810 |
} |
4811 |
else {
|
4812 |
return subFloatx80Sigs( a, b, aSign STATUS_VAR );
|
4813 |
} |
4814 |
|
4815 |
} |
4816 |
|
4817 |
/*----------------------------------------------------------------------------
|
4818 |
| Returns the result of subtracting the extended double-precision floating-
|
4819 |
| point values `a' and `b'. The operation is performed according to the
|
4820 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4821 |
*----------------------------------------------------------------------------*/
|
4822 |
|
4823 |
floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) |
4824 |
{ |
4825 |
flag aSign, bSign; |
4826 |
|
4827 |
aSign = extractFloatx80Sign( a ); |
4828 |
bSign = extractFloatx80Sign( b ); |
4829 |
if ( aSign == bSign ) {
|
4830 |
return subFloatx80Sigs( a, b, aSign STATUS_VAR );
|
4831 |
} |
4832 |
else {
|
4833 |
return addFloatx80Sigs( a, b, aSign STATUS_VAR );
|
4834 |
} |
4835 |
|
4836 |
} |
4837 |
|
4838 |
/*----------------------------------------------------------------------------
|
4839 |
| Returns the result of multiplying the extended double-precision floating-
|
4840 |
| point values `a' and `b'. The operation is performed according to the
|
4841 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4842 |
*----------------------------------------------------------------------------*/
|
4843 |
|
4844 |
floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) |
4845 |
{ |
4846 |
flag aSign, bSign, zSign; |
4847 |
int32 aExp, bExp, zExp; |
4848 |
uint64_t aSig, bSig, zSig0, zSig1; |
4849 |
floatx80 z; |
4850 |
|
4851 |
aSig = extractFloatx80Frac( a ); |
4852 |
aExp = extractFloatx80Exp( a ); |
4853 |
aSign = extractFloatx80Sign( a ); |
4854 |
bSig = extractFloatx80Frac( b ); |
4855 |
bExp = extractFloatx80Exp( b ); |
4856 |
bSign = extractFloatx80Sign( b ); |
4857 |
zSign = aSign ^ bSign; |
4858 |
if ( aExp == 0x7FFF ) { |
4859 |
if ( (uint64_t) ( aSig<<1 ) |
4860 |
|| ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { |
4861 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
4862 |
} |
4863 |
if ( ( bExp | bSig ) == 0 ) goto invalid; |
4864 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4865 |
} |
4866 |
if ( bExp == 0x7FFF ) { |
4867 |
if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4868 |
if ( ( aExp | aSig ) == 0 ) { |
4869 |
invalid:
|
4870 |
float_raise( float_flag_invalid STATUS_VAR); |
4871 |
z.low = floatx80_default_nan_low; |
4872 |
z.high = floatx80_default_nan_high; |
4873 |
return z;
|
4874 |
} |
4875 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4876 |
} |
4877 |
if ( aExp == 0 ) { |
4878 |
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
4879 |
normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); |
4880 |
} |
4881 |
if ( bExp == 0 ) { |
4882 |
if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
4883 |
normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
4884 |
} |
4885 |
zExp = aExp + bExp - 0x3FFE;
|
4886 |
mul64To128( aSig, bSig, &zSig0, &zSig1 ); |
4887 |
if ( 0 < (int64_t) zSig0 ) { |
4888 |
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
4889 |
--zExp; |
4890 |
} |
4891 |
return
|
4892 |
roundAndPackFloatx80( |
4893 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
4894 |
|
4895 |
} |
4896 |
|
4897 |
/*----------------------------------------------------------------------------
|
4898 |
| Returns the result of dividing the extended double-precision floating-point
|
4899 |
| value `a' by the corresponding value `b'. The operation is performed
|
4900 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4901 |
*----------------------------------------------------------------------------*/
|
4902 |
|
4903 |
floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) |
4904 |
{ |
4905 |
flag aSign, bSign, zSign; |
4906 |
int32 aExp, bExp, zExp; |
4907 |
uint64_t aSig, bSig, zSig0, zSig1; |
4908 |
uint64_t rem0, rem1, rem2, term0, term1, term2; |
4909 |
floatx80 z; |
4910 |
|
4911 |
aSig = extractFloatx80Frac( a ); |
4912 |
aExp = extractFloatx80Exp( a ); |
4913 |
aSign = extractFloatx80Sign( a ); |
4914 |
bSig = extractFloatx80Frac( b ); |
4915 |
bExp = extractFloatx80Exp( b ); |
4916 |
bSign = extractFloatx80Sign( b ); |
4917 |
zSign = aSign ^ bSign; |
4918 |
if ( aExp == 0x7FFF ) { |
4919 |
if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4920 |
if ( bExp == 0x7FFF ) { |
4921 |
if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4922 |
goto invalid;
|
4923 |
} |
4924 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4925 |
} |
4926 |
if ( bExp == 0x7FFF ) { |
4927 |
if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
4928 |
return packFloatx80( zSign, 0, 0 ); |
4929 |
} |
4930 |
if ( bExp == 0 ) { |
4931 |
if ( bSig == 0 ) { |
4932 |
if ( ( aExp | aSig ) == 0 ) { |
4933 |
invalid:
|
4934 |
float_raise( float_flag_invalid STATUS_VAR); |
4935 |
z.low = floatx80_default_nan_low; |
4936 |
z.high = floatx80_default_nan_high; |
4937 |
return z;
|
4938 |
} |
4939 |
float_raise( float_flag_divbyzero STATUS_VAR); |
4940 |
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
4941 |
} |
4942 |
normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
4943 |
} |
4944 |
if ( aExp == 0 ) { |
4945 |
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); |
4946 |
normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); |
4947 |
} |
4948 |
zExp = aExp - bExp + 0x3FFE;
|
4949 |
rem1 = 0;
|
4950 |
if ( bSig <= aSig ) {
|
4951 |
shift128Right( aSig, 0, 1, &aSig, &rem1 ); |
4952 |
++zExp; |
4953 |
} |
4954 |
zSig0 = estimateDiv128To64( aSig, rem1, bSig ); |
4955 |
mul64To128( bSig, zSig0, &term0, &term1 ); |
4956 |
sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); |
4957 |
while ( (int64_t) rem0 < 0 ) { |
4958 |
--zSig0; |
4959 |
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
4960 |
} |
4961 |
zSig1 = estimateDiv128To64( rem1, 0, bSig );
|
4962 |
if ( (uint64_t) ( zSig1<<1 ) <= 8 ) { |
4963 |
mul64To128( bSig, zSig1, &term1, &term2 ); |
4964 |
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
4965 |
while ( (int64_t) rem1 < 0 ) { |
4966 |
--zSig1; |
4967 |
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
|
4968 |
} |
4969 |
zSig1 |= ( ( rem1 | rem2 ) != 0 );
|
4970 |
} |
4971 |
return
|
4972 |
roundAndPackFloatx80( |
4973 |
STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); |
4974 |
|
4975 |
} |
4976 |
|
4977 |
/*----------------------------------------------------------------------------
|
4978 |
| Returns the remainder of the extended double-precision floating-point value
|
4979 |
| `a' with respect to the corresponding value `b'. The operation is performed
|
4980 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
4981 |
*----------------------------------------------------------------------------*/
|
4982 |
|
4983 |
floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) |
4984 |
{ |
4985 |
flag aSign, zSign; |
4986 |
int32 aExp, bExp, expDiff; |
4987 |
uint64_t aSig0, aSig1, bSig; |
4988 |
uint64_t q, term0, term1, alternateASig0, alternateASig1; |
4989 |
floatx80 z; |
4990 |
|
4991 |
aSig0 = extractFloatx80Frac( a ); |
4992 |
aExp = extractFloatx80Exp( a ); |
4993 |
aSign = extractFloatx80Sign( a ); |
4994 |
bSig = extractFloatx80Frac( b ); |
4995 |
bExp = extractFloatx80Exp( b ); |
4996 |
if ( aExp == 0x7FFF ) { |
4997 |
if ( (uint64_t) ( aSig0<<1 ) |
4998 |
|| ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { |
4999 |
return propagateFloatx80NaN( a, b STATUS_VAR );
|
5000 |
} |
5001 |
goto invalid;
|
5002 |
} |
5003 |
if ( bExp == 0x7FFF ) { |
5004 |
if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); |
5005 |
return a;
|
5006 |
} |
5007 |
if ( bExp == 0 ) { |
5008 |
if ( bSig == 0 ) { |
5009 |
invalid:
|
5010 |
float_raise( float_flag_invalid STATUS_VAR); |
5011 |
z.low = floatx80_default_nan_low; |
5012 |
z.high = floatx80_default_nan_high; |
5013 |
return z;
|
5014 |
} |
5015 |
normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); |
5016 |
} |
5017 |
if ( aExp == 0 ) { |
5018 |
if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a; |
5019 |
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
5020 |
} |
5021 |
bSig |= LIT64( 0x8000000000000000 );
|
5022 |
zSign = aSign; |
5023 |
expDiff = aExp - bExp; |
5024 |
aSig1 = 0;
|
5025 |
if ( expDiff < 0 ) { |
5026 |
if ( expDiff < -1 ) return a; |
5027 |
shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); |
5028 |
expDiff = 0;
|
5029 |
} |
5030 |
q = ( bSig <= aSig0 ); |
5031 |
if ( q ) aSig0 -= bSig;
|
5032 |
expDiff -= 64;
|
5033 |
while ( 0 < expDiff ) { |
5034 |
q = estimateDiv128To64( aSig0, aSig1, bSig ); |
5035 |
q = ( 2 < q ) ? q - 2 : 0; |
5036 |
mul64To128( bSig, q, &term0, &term1 ); |
5037 |
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
5038 |
shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
|
5039 |
expDiff -= 62;
|
5040 |
} |
5041 |
expDiff += 64;
|
5042 |
if ( 0 < expDiff ) { |
5043 |
q = estimateDiv128To64( aSig0, aSig1, bSig ); |
5044 |
q = ( 2 < q ) ? q - 2 : 0; |
5045 |
q >>= 64 - expDiff;
|
5046 |
mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
|
5047 |
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
5048 |
shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); |
5049 |
while ( le128( term0, term1, aSig0, aSig1 ) ) {
|
5050 |
++q; |
5051 |
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); |
5052 |
} |
5053 |
} |
5054 |
else {
|
5055 |
term1 = 0;
|
5056 |
term0 = bSig; |
5057 |
} |
5058 |
sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); |
5059 |
if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
5060 |
|| ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) |
5061 |
&& ( q & 1 ) )
|
5062 |
) { |
5063 |
aSig0 = alternateASig0; |
5064 |
aSig1 = alternateASig1; |
5065 |
zSign = ! zSign; |
5066 |
} |
5067 |
return
|
5068 |
normalizeRoundAndPackFloatx80( |
5069 |
80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR );
|
5070 |
|
5071 |
} |
5072 |
|
5073 |
/*----------------------------------------------------------------------------
|
5074 |
| Returns the square root of the extended double-precision floating-point
|
5075 |
| value `a'. The operation is performed according to the IEC/IEEE Standard
|
5076 |
| for Binary Floating-Point Arithmetic.
|
5077 |
*----------------------------------------------------------------------------*/
|
5078 |
|
5079 |
floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) |
5080 |
{ |
5081 |
flag aSign; |
5082 |
int32 aExp, zExp; |
5083 |
uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0; |
5084 |
uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
5085 |
floatx80 z; |
5086 |
|
5087 |
aSig0 = extractFloatx80Frac( a ); |
5088 |
aExp = extractFloatx80Exp( a ); |
5089 |
aSign = extractFloatx80Sign( a ); |
5090 |
if ( aExp == 0x7FFF ) { |
5091 |
if ( (uint64_t) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); |
5092 |
if ( ! aSign ) return a; |
5093 |
goto invalid;
|
5094 |
} |
5095 |
if ( aSign ) {
|
5096 |
if ( ( aExp | aSig0 ) == 0 ) return a; |
5097 |
invalid:
|
5098 |
float_raise( float_flag_invalid STATUS_VAR); |
5099 |
z.low = floatx80_default_nan_low; |
5100 |
z.high = floatx80_default_nan_high; |
5101 |
return z;
|
5102 |
} |
5103 |
if ( aExp == 0 ) { |
5104 |
if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); |
5105 |
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); |
5106 |
} |
5107 |
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; |
5108 |
zSig0 = estimateSqrt32( aExp, aSig0>>32 );
|
5109 |
shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); |
5110 |
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); |
5111 |
doubleZSig0 = zSig0<<1;
|
5112 |
mul64To128( zSig0, zSig0, &term0, &term1 ); |
5113 |
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); |
5114 |
while ( (int64_t) rem0 < 0 ) { |
5115 |
--zSig0; |
5116 |
doubleZSig0 -= 2;
|
5117 |
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); |
5118 |
} |
5119 |
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
5120 |
if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { |
5121 |
if ( zSig1 == 0 ) zSig1 = 1; |
5122 |
mul64To128( doubleZSig0, zSig1, &term1, &term2 ); |
5123 |
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
5124 |
mul64To128( zSig1, zSig1, &term2, &term3 ); |
5125 |
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); |
5126 |
while ( (int64_t) rem1 < 0 ) { |
5127 |
--zSig1; |
5128 |
shortShift128Left( 0, zSig1, 1, &term2, &term3 ); |
5129 |
term3 |= 1;
|
5130 |
term2 |= doubleZSig0; |
5131 |
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
5132 |
} |
5133 |
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
5134 |
} |
5135 |
shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); |
5136 |
zSig0 |= doubleZSig0; |
5137 |
return
|
5138 |
roundAndPackFloatx80( |
5139 |
STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR );
|
5140 |
|
5141 |
} |
5142 |
|
5143 |
/*----------------------------------------------------------------------------
|
5144 |
| Returns 1 if the extended double-precision floating-point value `a' is equal
|
5145 |
| to the corresponding value `b', and 0 otherwise. The invalid exception is
|
5146 |
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
5147 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5148 |
*----------------------------------------------------------------------------*/
|
5149 |
|
5150 |
int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
|
5151 |
{ |
5152 |
|
5153 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5154 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5155 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5156 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5157 |
) { |
5158 |
float_raise( float_flag_invalid STATUS_VAR); |
5159 |
return 0; |
5160 |
} |
5161 |
return
|
5162 |
( a.low == b.low ) |
5163 |
&& ( ( a.high == b.high ) |
5164 |
|| ( ( a.low == 0 )
|
5165 |
&& ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
5166 |
); |
5167 |
|
5168 |
} |
5169 |
|
5170 |
/*----------------------------------------------------------------------------
|
5171 |
| Returns 1 if the extended double-precision floating-point value `a' is
|
5172 |
| less than or equal to the corresponding value `b', and 0 otherwise. The
|
5173 |
| invalid exception is raised if either operand is a NaN. The comparison is
|
5174 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5175 |
| Arithmetic.
|
5176 |
*----------------------------------------------------------------------------*/
|
5177 |
|
5178 |
int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
|
5179 |
{ |
5180 |
flag aSign, bSign; |
5181 |
|
5182 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5183 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5184 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5185 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5186 |
) { |
5187 |
float_raise( float_flag_invalid STATUS_VAR); |
5188 |
return 0; |
5189 |
} |
5190 |
aSign = extractFloatx80Sign( a ); |
5191 |
bSign = extractFloatx80Sign( b ); |
5192 |
if ( aSign != bSign ) {
|
5193 |
return
|
5194 |
aSign |
5195 |
|| ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5196 |
== 0 );
|
5197 |
} |
5198 |
return
|
5199 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
5200 |
: le128( a.high, a.low, b.high, b.low ); |
5201 |
|
5202 |
} |
5203 |
|
5204 |
/*----------------------------------------------------------------------------
|
5205 |
| Returns 1 if the extended double-precision floating-point value `a' is
|
5206 |
| less than the corresponding value `b', and 0 otherwise. The invalid
|
5207 |
| exception is raised if either operand is a NaN. The comparison is performed
|
5208 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5209 |
*----------------------------------------------------------------------------*/
|
5210 |
|
5211 |
int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
|
5212 |
{ |
5213 |
flag aSign, bSign; |
5214 |
|
5215 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5216 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5217 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5218 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5219 |
) { |
5220 |
float_raise( float_flag_invalid STATUS_VAR); |
5221 |
return 0; |
5222 |
} |
5223 |
aSign = extractFloatx80Sign( a ); |
5224 |
bSign = extractFloatx80Sign( b ); |
5225 |
if ( aSign != bSign ) {
|
5226 |
return
|
5227 |
aSign |
5228 |
&& ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5229 |
!= 0 );
|
5230 |
} |
5231 |
return
|
5232 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
5233 |
: lt128( a.high, a.low, b.high, b.low ); |
5234 |
|
5235 |
} |
5236 |
|
5237 |
/*----------------------------------------------------------------------------
|
5238 |
| Returns 1 if the extended double-precision floating-point values `a' and `b'
|
5239 |
| cannot be compared, and 0 otherwise. The invalid exception is raised if
|
5240 |
| either operand is a NaN. The comparison is performed according to the
|
5241 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5242 |
*----------------------------------------------------------------------------*/
|
5243 |
int floatx80_unordered( floatx80 a, floatx80 b STATUS_PARAM )
|
5244 |
{ |
5245 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5246 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5247 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5248 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5249 |
) { |
5250 |
float_raise( float_flag_invalid STATUS_VAR); |
5251 |
return 1; |
5252 |
} |
5253 |
return 0; |
5254 |
} |
5255 |
|
5256 |
/*----------------------------------------------------------------------------
|
5257 |
| Returns 1 if the extended double-precision floating-point value `a' is
|
5258 |
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
5259 |
| cause an exception. The comparison is performed according to the IEC/IEEE
|
5260 |
| Standard for Binary Floating-Point Arithmetic.
|
5261 |
*----------------------------------------------------------------------------*/
|
5262 |
|
5263 |
int floatx80_eq_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
5264 |
{ |
5265 |
|
5266 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5267 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5268 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5269 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5270 |
) { |
5271 |
if ( floatx80_is_signaling_nan( a )
|
5272 |
|| floatx80_is_signaling_nan( b ) ) { |
5273 |
float_raise( float_flag_invalid STATUS_VAR); |
5274 |
} |
5275 |
return 0; |
5276 |
} |
5277 |
return
|
5278 |
( a.low == b.low ) |
5279 |
&& ( ( a.high == b.high ) |
5280 |
|| ( ( a.low == 0 )
|
5281 |
&& ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
5282 |
); |
5283 |
|
5284 |
} |
5285 |
|
5286 |
/*----------------------------------------------------------------------------
|
5287 |
| Returns 1 if the extended double-precision floating-point value `a' is less
|
5288 |
| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs
|
5289 |
| do not cause an exception. Otherwise, the comparison is performed according
|
5290 |
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5291 |
*----------------------------------------------------------------------------*/
|
5292 |
|
5293 |
int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
5294 |
{ |
5295 |
flag aSign, bSign; |
5296 |
|
5297 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5298 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5299 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5300 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5301 |
) { |
5302 |
if ( floatx80_is_signaling_nan( a )
|
5303 |
|| floatx80_is_signaling_nan( b ) ) { |
5304 |
float_raise( float_flag_invalid STATUS_VAR); |
5305 |
} |
5306 |
return 0; |
5307 |
} |
5308 |
aSign = extractFloatx80Sign( a ); |
5309 |
bSign = extractFloatx80Sign( b ); |
5310 |
if ( aSign != bSign ) {
|
5311 |
return
|
5312 |
aSign |
5313 |
|| ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5314 |
== 0 );
|
5315 |
} |
5316 |
return
|
5317 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
5318 |
: le128( a.high, a.low, b.high, b.low ); |
5319 |
|
5320 |
} |
5321 |
|
5322 |
/*----------------------------------------------------------------------------
|
5323 |
| Returns 1 if the extended double-precision floating-point value `a' is less
|
5324 |
| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
|
5325 |
| an exception. Otherwise, the comparison is performed according to the
|
5326 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
5327 |
*----------------------------------------------------------------------------*/
|
5328 |
|
5329 |
int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
5330 |
{ |
5331 |
flag aSign, bSign; |
5332 |
|
5333 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5334 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5335 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5336 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5337 |
) { |
5338 |
if ( floatx80_is_signaling_nan( a )
|
5339 |
|| floatx80_is_signaling_nan( b ) ) { |
5340 |
float_raise( float_flag_invalid STATUS_VAR); |
5341 |
} |
5342 |
return 0; |
5343 |
} |
5344 |
aSign = extractFloatx80Sign( a ); |
5345 |
bSign = extractFloatx80Sign( b ); |
5346 |
if ( aSign != bSign ) {
|
5347 |
return
|
5348 |
aSign |
5349 |
&& ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
5350 |
!= 0 );
|
5351 |
} |
5352 |
return
|
5353 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
5354 |
: lt128( a.high, a.low, b.high, b.low ); |
5355 |
|
5356 |
} |
5357 |
|
5358 |
/*----------------------------------------------------------------------------
|
5359 |
| Returns 1 if the extended double-precision floating-point values `a' and `b'
|
5360 |
| cannot be compared, and 0 otherwise. Quiet NaNs do not cause an exception.
|
5361 |
| The comparison is performed according to the IEC/IEEE Standard for Binary
|
5362 |
| Floating-Point Arithmetic.
|
5363 |
*----------------------------------------------------------------------------*/
|
5364 |
int floatx80_unordered_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
5365 |
{ |
5366 |
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) |
5367 |
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
5368 |
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
5369 |
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
5370 |
) { |
5371 |
if ( floatx80_is_signaling_nan( a )
|
5372 |
|| floatx80_is_signaling_nan( b ) ) { |
5373 |
float_raise( float_flag_invalid STATUS_VAR); |
5374 |
} |
5375 |
return 1; |
5376 |
} |
5377 |
return 0; |
5378 |
} |
5379 |
|
5380 |
/*----------------------------------------------------------------------------
|
5381 |
| Returns the result of converting the quadruple-precision floating-point
|
5382 |
| value `a' to the 32-bit two's complement integer format. The conversion
|
5383 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5384 |
| Arithmetic---which means in particular that the conversion is rounded
|
5385 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
5386 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
5387 |
| largest integer with the same sign as `a' is returned.
|
5388 |
*----------------------------------------------------------------------------*/
|
5389 |
|
5390 |
int32 float128_to_int32( float128 a STATUS_PARAM ) |
5391 |
{ |
5392 |
flag aSign; |
5393 |
int32 aExp, shiftCount; |
5394 |
uint64_t aSig0, aSig1; |
5395 |
|
5396 |
aSig1 = extractFloat128Frac1( a ); |
5397 |
aSig0 = extractFloat128Frac0( a ); |
5398 |
aExp = extractFloat128Exp( a ); |
5399 |
aSign = extractFloat128Sign( a ); |
5400 |
if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; |
5401 |
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
5402 |
aSig0 |= ( aSig1 != 0 );
|
5403 |
shiftCount = 0x4028 - aExp;
|
5404 |
if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); |
5405 |
return roundAndPackInt32( aSign, aSig0 STATUS_VAR );
|
5406 |
|
5407 |
} |
5408 |
|
5409 |
/*----------------------------------------------------------------------------
|
5410 |
| Returns the result of converting the quadruple-precision floating-point
|
5411 |
| value `a' to the 32-bit two's complement integer format. The conversion
|
5412 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5413 |
| Arithmetic, except that the conversion is always rounded toward zero. If
|
5414 |
| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
5415 |
| conversion overflows, the largest integer with the same sign as `a' is
|
5416 |
| returned.
|
5417 |
*----------------------------------------------------------------------------*/
|
5418 |
|
5419 |
int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) |
5420 |
{ |
5421 |
flag aSign; |
5422 |
int32 aExp, shiftCount; |
5423 |
uint64_t aSig0, aSig1, savedASig; |
5424 |
int32_t z; |
5425 |
|
5426 |
aSig1 = extractFloat128Frac1( a ); |
5427 |
aSig0 = extractFloat128Frac0( a ); |
5428 |
aExp = extractFloat128Exp( a ); |
5429 |
aSign = extractFloat128Sign( a ); |
5430 |
aSig0 |= ( aSig1 != 0 );
|
5431 |
if ( 0x401E < aExp ) { |
5432 |
if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; |
5433 |
goto invalid;
|
5434 |
} |
5435 |
else if ( aExp < 0x3FFF ) { |
5436 |
if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
5437 |
return 0; |
5438 |
} |
5439 |
aSig0 |= LIT64( 0x0001000000000000 );
|
5440 |
shiftCount = 0x402F - aExp;
|
5441 |
savedASig = aSig0; |
5442 |
aSig0 >>= shiftCount; |
5443 |
z = aSig0; |
5444 |
if ( aSign ) z = - z;
|
5445 |
if ( ( z < 0 ) ^ aSign ) { |
5446 |
invalid:
|
5447 |
float_raise( float_flag_invalid STATUS_VAR); |
5448 |
return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; |
5449 |
} |
5450 |
if ( ( aSig0<<shiftCount ) != savedASig ) {
|
5451 |
STATUS(float_exception_flags) |= float_flag_inexact; |
5452 |
} |
5453 |
return z;
|
5454 |
|
5455 |
} |
5456 |
|
5457 |
/*----------------------------------------------------------------------------
|
5458 |
| Returns the result of converting the quadruple-precision floating-point
|
5459 |
| value `a' to the 64-bit two's complement integer format. The conversion
|
5460 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5461 |
| Arithmetic---which means in particular that the conversion is rounded
|
5462 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
5463 |
| positive integer is returned. Otherwise, if the conversion overflows, the
|
5464 |
| largest integer with the same sign as `a' is returned.
|
5465 |
*----------------------------------------------------------------------------*/
|
5466 |
|
5467 |
int64 float128_to_int64( float128 a STATUS_PARAM ) |
5468 |
{ |
5469 |
flag aSign; |
5470 |
int32 aExp, shiftCount; |
5471 |
uint64_t aSig0, aSig1; |
5472 |
|
5473 |
aSig1 = extractFloat128Frac1( a ); |
5474 |
aSig0 = extractFloat128Frac0( a ); |
5475 |
aExp = extractFloat128Exp( a ); |
5476 |
aSign = extractFloat128Sign( a ); |
5477 |
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
5478 |
shiftCount = 0x402F - aExp;
|
5479 |
if ( shiftCount <= 0 ) { |
5480 |
if ( 0x403E < aExp ) { |
5481 |
float_raise( float_flag_invalid STATUS_VAR); |
5482 |
if ( ! aSign
|
5483 |
|| ( ( aExp == 0x7FFF )
|
5484 |
&& ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) )
|
5485 |
) |
5486 |
) { |
5487 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
5488 |
} |
5489 |
return (int64_t) LIT64( 0x8000000000000000 ); |
5490 |
} |
5491 |
shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); |
5492 |
} |
5493 |
else {
|
5494 |
shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); |
5495 |
} |
5496 |
return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR );
|
5497 |
|
5498 |
} |
5499 |
|
5500 |
/*----------------------------------------------------------------------------
|
5501 |
| Returns the result of converting the quadruple-precision floating-point
|
5502 |
| value `a' to the 64-bit two's complement integer format. The conversion
|
5503 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5504 |
| Arithmetic, except that the conversion is always rounded toward zero.
|
5505 |
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
5506 |
| the conversion overflows, the largest integer with the same sign as `a' is
|
5507 |
| returned.
|
5508 |
*----------------------------------------------------------------------------*/
|
5509 |
|
5510 |
int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) |
5511 |
{ |
5512 |
flag aSign; |
5513 |
int32 aExp, shiftCount; |
5514 |
uint64_t aSig0, aSig1; |
5515 |
int64 z; |
5516 |
|
5517 |
aSig1 = extractFloat128Frac1( a ); |
5518 |
aSig0 = extractFloat128Frac0( a ); |
5519 |
aExp = extractFloat128Exp( a ); |
5520 |
aSign = extractFloat128Sign( a ); |
5521 |
if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); |
5522 |
shiftCount = aExp - 0x402F;
|
5523 |
if ( 0 < shiftCount ) { |
5524 |
if ( 0x403E <= aExp ) { |
5525 |
aSig0 &= LIT64( 0x0000FFFFFFFFFFFF );
|
5526 |
if ( ( a.high == LIT64( 0xC03E000000000000 ) ) |
5527 |
&& ( aSig1 < LIT64( 0x0002000000000000 ) ) ) {
|
5528 |
if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
|
5529 |
} |
5530 |
else {
|
5531 |
float_raise( float_flag_invalid STATUS_VAR); |
5532 |
if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { |
5533 |
return LIT64( 0x7FFFFFFFFFFFFFFF ); |
5534 |
} |
5535 |
} |
5536 |
return (int64_t) LIT64( 0x8000000000000000 ); |
5537 |
} |
5538 |
z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
|
5539 |
if ( (uint64_t) ( aSig1<<shiftCount ) ) {
|
5540 |
STATUS(float_exception_flags) |= float_flag_inexact; |
5541 |
} |
5542 |
} |
5543 |
else {
|
5544 |
if ( aExp < 0x3FFF ) { |
5545 |
if ( aExp | aSig0 | aSig1 ) {
|
5546 |
STATUS(float_exception_flags) |= float_flag_inexact; |
5547 |
} |
5548 |
return 0; |
5549 |
} |
5550 |
z = aSig0>>( - shiftCount ); |
5551 |
if ( aSig1
|
5552 |
|| ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) {
|
5553 |
STATUS(float_exception_flags) |= float_flag_inexact; |
5554 |
} |
5555 |
} |
5556 |
if ( aSign ) z = - z;
|
5557 |
return z;
|
5558 |
|
5559 |
} |
5560 |
|
5561 |
/*----------------------------------------------------------------------------
|
5562 |
| Returns the result of converting the quadruple-precision floating-point
|
5563 |
| value `a' to the single-precision floating-point format. The conversion
|
5564 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5565 |
| Arithmetic.
|
5566 |
*----------------------------------------------------------------------------*/
|
5567 |
|
5568 |
float32 float128_to_float32( float128 a STATUS_PARAM ) |
5569 |
{ |
5570 |
flag aSign; |
5571 |
int32 aExp; |
5572 |
uint64_t aSig0, aSig1; |
5573 |
uint32_t zSig; |
5574 |
|
5575 |
aSig1 = extractFloat128Frac1( a ); |
5576 |
aSig0 = extractFloat128Frac0( a ); |
5577 |
aExp = extractFloat128Exp( a ); |
5578 |
aSign = extractFloat128Sign( a ); |
5579 |
if ( aExp == 0x7FFF ) { |
5580 |
if ( aSig0 | aSig1 ) {
|
5581 |
return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
|
5582 |
} |
5583 |
return packFloat32( aSign, 0xFF, 0 ); |
5584 |
} |
5585 |
aSig0 |= ( aSig1 != 0 );
|
5586 |
shift64RightJamming( aSig0, 18, &aSig0 );
|
5587 |
zSig = aSig0; |
5588 |
if ( aExp || zSig ) {
|
5589 |
zSig |= 0x40000000;
|
5590 |
aExp -= 0x3F81;
|
5591 |
} |
5592 |
return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
|
5593 |
|
5594 |
} |
5595 |
|
5596 |
/*----------------------------------------------------------------------------
|
5597 |
| Returns the result of converting the quadruple-precision floating-point
|
5598 |
| value `a' to the double-precision floating-point format. The conversion
|
5599 |
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
5600 |
| Arithmetic.
|
5601 |
*----------------------------------------------------------------------------*/
|
5602 |
|
5603 |
float64 float128_to_float64( float128 a STATUS_PARAM ) |
5604 |
{ |
5605 |
flag aSign; |
5606 |
int32 aExp; |
5607 |
uint64_t aSig0, aSig1; |
5608 |
|
5609 |
aSig1 = extractFloat128Frac1( a ); |
5610 |
aSig0 = extractFloat128Frac0( a ); |
5611 |
aExp = extractFloat128Exp( a ); |
5612 |
aSign = extractFloat128Sign( a ); |
5613 |
if ( aExp == 0x7FFF ) { |
5614 |
if ( aSig0 | aSig1 ) {
|
5615 |
return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
|
5616 |
} |
5617 |
return packFloat64( aSign, 0x7FF, 0 ); |
5618 |
} |
5619 |
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
5620 |
aSig0 |= ( aSig1 != 0 );
|
5621 |
if ( aExp || aSig0 ) {
|
5622 |
aSig0 |= LIT64( 0x4000000000000000 );
|
5623 |
aExp -= 0x3C01;
|
5624 |
} |
5625 |
return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR );
|
5626 |
|
5627 |
} |
5628 |
|
5629 |
/*----------------------------------------------------------------------------
|
5630 |
| Returns the result of converting the quadruple-precision floating-point
|
5631 |
| value `a' to the extended double-precision floating-point format. The
|
5632 |
| conversion is performed according to the IEC/IEEE Standard for Binary
|
5633 |
| Floating-Point Arithmetic.
|
5634 |
*----------------------------------------------------------------------------*/
|
5635 |
|
5636 |
floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) |
5637 |
{ |
5638 |
flag aSign; |
5639 |
int32 aExp; |
5640 |
uint64_t aSig0, aSig1; |
5641 |
|
5642 |
aSig1 = extractFloat128Frac1( a ); |
5643 |
aSig0 = extractFloat128Frac0( a ); |
5644 |
aExp = extractFloat128Exp( a ); |
5645 |
aSign = extractFloat128Sign( a ); |
5646 |
if ( aExp == 0x7FFF ) { |
5647 |
if ( aSig0 | aSig1 ) {
|
5648 |
return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR );
|
5649 |
} |
5650 |
return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
5651 |
} |
5652 |
if ( aExp == 0 ) { |
5653 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); |
5654 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
5655 |
} |
5656 |
else {
|
5657 |
aSig0 |= LIT64( 0x0001000000000000 );
|
5658 |
} |
5659 |
shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
|
5660 |
return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); |
5661 |
|
5662 |
} |
5663 |
|
5664 |
/*----------------------------------------------------------------------------
|
5665 |
| Rounds the quadruple-precision floating-point value `a' to an integer, and
|
5666 |
| returns the result as a quadruple-precision floating-point value. The
|
5667 |
| operation is performed according to the IEC/IEEE Standard for Binary
|
5668 |
| Floating-Point Arithmetic.
|
5669 |
*----------------------------------------------------------------------------*/
|
5670 |
|
5671 |
float128 float128_round_to_int( float128 a STATUS_PARAM ) |
5672 |
{ |
5673 |
flag aSign; |
5674 |
int32 aExp; |
5675 |
uint64_t lastBitMask, roundBitsMask; |
5676 |
int8 roundingMode; |
5677 |
float128 z; |
5678 |
|
5679 |
aExp = extractFloat128Exp( a ); |
5680 |
if ( 0x402F <= aExp ) { |
5681 |
if ( 0x406F <= aExp ) { |
5682 |
if ( ( aExp == 0x7FFF ) |
5683 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) |
5684 |
) { |
5685 |
return propagateFloat128NaN( a, a STATUS_VAR );
|
5686 |
} |
5687 |
return a;
|
5688 |
} |
5689 |
lastBitMask = 1;
|
5690 |
lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; |
5691 |
roundBitsMask = lastBitMask - 1;
|
5692 |
z = a; |
5693 |
roundingMode = STATUS(float_rounding_mode); |
5694 |
if ( roundingMode == float_round_nearest_even ) {
|
5695 |
if ( lastBitMask ) {
|
5696 |
add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); |
5697 |
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; |
5698 |
} |
5699 |
else {
|
5700 |
if ( (int64_t) z.low < 0 ) { |
5701 |
++z.high; |
5702 |
if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1; |
5703 |
} |
5704 |
} |
5705 |
} |
5706 |
else if ( roundingMode != float_round_to_zero ) { |
5707 |
if ( extractFloat128Sign( z )
|
5708 |
^ ( roundingMode == float_round_up ) ) { |
5709 |
add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low );
|
5710 |
} |
5711 |
} |
5712 |
z.low &= ~ roundBitsMask; |
5713 |
} |
5714 |
else {
|
5715 |
if ( aExp < 0x3FFF ) { |
5716 |
if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a; |
5717 |
STATUS(float_exception_flags) |= float_flag_inexact; |
5718 |
aSign = extractFloat128Sign( a ); |
5719 |
switch ( STATUS(float_rounding_mode) ) {
|
5720 |
case float_round_nearest_even:
|
5721 |
if ( ( aExp == 0x3FFE ) |
5722 |
&& ( extractFloat128Frac0( a ) |
5723 |
| extractFloat128Frac1( a ) ) |
5724 |
) { |
5725 |
return packFloat128( aSign, 0x3FFF, 0, 0 ); |
5726 |
} |
5727 |
break;
|
5728 |
case float_round_down:
|
5729 |
return
|
5730 |
aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) |
5731 |
: packFloat128( 0, 0, 0, 0 ); |
5732 |
case float_round_up:
|
5733 |
return
|
5734 |
aSign ? packFloat128( 1, 0, 0, 0 ) |
5735 |
: packFloat128( 0, 0x3FFF, 0, 0 ); |
5736 |
} |
5737 |
return packFloat128( aSign, 0, 0, 0 ); |
5738 |
} |
5739 |
lastBitMask = 1;
|
5740 |
lastBitMask <<= 0x402F - aExp;
|
5741 |
roundBitsMask = lastBitMask - 1;
|
5742 |
z.low = 0;
|
5743 |
z.high = a.high; |
5744 |
roundingMode = STATUS(float_rounding_mode); |
5745 |
if ( roundingMode == float_round_nearest_even ) {
|
5746 |
z.high += lastBitMask>>1;
|
5747 |
if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { |
5748 |
z.high &= ~ lastBitMask; |
5749 |
} |
5750 |
} |
5751 |
else if ( roundingMode != float_round_to_zero ) { |
5752 |
if ( extractFloat128Sign( z )
|
5753 |
^ ( roundingMode == float_round_up ) ) { |
5754 |
z.high |= ( a.low != 0 );
|
5755 |
z.high += roundBitsMask; |
5756 |
} |
5757 |
} |
5758 |
z.high &= ~ roundBitsMask; |
5759 |
} |
5760 |
if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
|
5761 |
STATUS(float_exception_flags) |= float_flag_inexact; |
5762 |
} |
5763 |
return z;
|
5764 |
|
5765 |
} |
5766 |
|
5767 |
/*----------------------------------------------------------------------------
|
5768 |
| Returns the result of adding the absolute values of the quadruple-precision
|
5769 |
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
5770 |
| before being returned. `zSign' is ignored if the result is a NaN.
|
5771 |
| The addition is performed according to the IEC/IEEE Standard for Binary
|
5772 |
| Floating-Point Arithmetic.
|
5773 |
*----------------------------------------------------------------------------*/
|
5774 |
|
5775 |
static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
|
5776 |
{ |
5777 |
int32 aExp, bExp, zExp; |
5778 |
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
5779 |
int32 expDiff; |
5780 |
|
5781 |
aSig1 = extractFloat128Frac1( a ); |
5782 |
aSig0 = extractFloat128Frac0( a ); |
5783 |
aExp = extractFloat128Exp( a ); |
5784 |
bSig1 = extractFloat128Frac1( b ); |
5785 |
bSig0 = extractFloat128Frac0( b ); |
5786 |
bExp = extractFloat128Exp( b ); |
5787 |
expDiff = aExp - bExp; |
5788 |
if ( 0 < expDiff ) { |
5789 |
if ( aExp == 0x7FFF ) { |
5790 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
5791 |
return a;
|
5792 |
} |
5793 |
if ( bExp == 0 ) { |
5794 |
--expDiff; |
5795 |
} |
5796 |
else {
|
5797 |
bSig0 |= LIT64( 0x0001000000000000 );
|
5798 |
} |
5799 |
shift128ExtraRightJamming( |
5800 |
bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
|
5801 |
zExp = aExp; |
5802 |
} |
5803 |
else if ( expDiff < 0 ) { |
5804 |
if ( bExp == 0x7FFF ) { |
5805 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
5806 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
5807 |
} |
5808 |
if ( aExp == 0 ) { |
5809 |
++expDiff; |
5810 |
} |
5811 |
else {
|
5812 |
aSig0 |= LIT64( 0x0001000000000000 );
|
5813 |
} |
5814 |
shift128ExtraRightJamming( |
5815 |
aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
|
5816 |
zExp = bExp; |
5817 |
} |
5818 |
else {
|
5819 |
if ( aExp == 0x7FFF ) { |
5820 |
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
5821 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
5822 |
} |
5823 |
return a;
|
5824 |
} |
5825 |
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
5826 |
if ( aExp == 0 ) { |
5827 |
if (STATUS(flush_to_zero)) {
|
5828 |
if (zSig0 | zSig1) {
|
5829 |
float_raise(float_flag_output_denormal STATUS_VAR); |
5830 |
} |
5831 |
return packFloat128(zSign, 0, 0, 0); |
5832 |
} |
5833 |
return packFloat128( zSign, 0, zSig0, zSig1 ); |
5834 |
} |
5835 |
zSig2 = 0;
|
5836 |
zSig0 |= LIT64( 0x0002000000000000 );
|
5837 |
zExp = aExp; |
5838 |
goto shiftRight1;
|
5839 |
} |
5840 |
aSig0 |= LIT64( 0x0001000000000000 );
|
5841 |
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
5842 |
--zExp; |
5843 |
if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; |
5844 |
++zExp; |
5845 |
shiftRight1:
|
5846 |
shift128ExtraRightJamming( |
5847 |
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
5848 |
roundAndPack:
|
5849 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
|
5850 |
|
5851 |
} |
5852 |
|
5853 |
/*----------------------------------------------------------------------------
|
5854 |
| Returns the result of subtracting the absolute values of the quadruple-
|
5855 |
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
5856 |
| difference is negated before being returned. `zSign' is ignored if the
|
5857 |
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
5858 |
| Standard for Binary Floating-Point Arithmetic.
|
5859 |
*----------------------------------------------------------------------------*/
|
5860 |
|
5861 |
static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
|
5862 |
{ |
5863 |
int32 aExp, bExp, zExp; |
5864 |
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; |
5865 |
int32 expDiff; |
5866 |
float128 z; |
5867 |
|
5868 |
aSig1 = extractFloat128Frac1( a ); |
5869 |
aSig0 = extractFloat128Frac0( a ); |
5870 |
aExp = extractFloat128Exp( a ); |
5871 |
bSig1 = extractFloat128Frac1( b ); |
5872 |
bSig0 = extractFloat128Frac0( b ); |
5873 |
bExp = extractFloat128Exp( b ); |
5874 |
expDiff = aExp - bExp; |
5875 |
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
5876 |
shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 );
|
5877 |
if ( 0 < expDiff ) goto aExpBigger; |
5878 |
if ( expDiff < 0 ) goto bExpBigger; |
5879 |
if ( aExp == 0x7FFF ) { |
5880 |
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
5881 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
5882 |
} |
5883 |
float_raise( float_flag_invalid STATUS_VAR); |
5884 |
z.low = float128_default_nan_low; |
5885 |
z.high = float128_default_nan_high; |
5886 |
return z;
|
5887 |
} |
5888 |
if ( aExp == 0 ) { |
5889 |
aExp = 1;
|
5890 |
bExp = 1;
|
5891 |
} |
5892 |
if ( bSig0 < aSig0 ) goto aBigger; |
5893 |
if ( aSig0 < bSig0 ) goto bBigger; |
5894 |
if ( bSig1 < aSig1 ) goto aBigger; |
5895 |
if ( aSig1 < bSig1 ) goto bBigger; |
5896 |
return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); |
5897 |
bExpBigger:
|
5898 |
if ( bExp == 0x7FFF ) { |
5899 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
5900 |
return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); |
5901 |
} |
5902 |
if ( aExp == 0 ) { |
5903 |
++expDiff; |
5904 |
} |
5905 |
else {
|
5906 |
aSig0 |= LIT64( 0x4000000000000000 );
|
5907 |
} |
5908 |
shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); |
5909 |
bSig0 |= LIT64( 0x4000000000000000 );
|
5910 |
bBigger:
|
5911 |
sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); |
5912 |
zExp = bExp; |
5913 |
zSign ^= 1;
|
5914 |
goto normalizeRoundAndPack;
|
5915 |
aExpBigger:
|
5916 |
if ( aExp == 0x7FFF ) { |
5917 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
5918 |
return a;
|
5919 |
} |
5920 |
if ( bExp == 0 ) { |
5921 |
--expDiff; |
5922 |
} |
5923 |
else {
|
5924 |
bSig0 |= LIT64( 0x4000000000000000 );
|
5925 |
} |
5926 |
shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); |
5927 |
aSig0 |= LIT64( 0x4000000000000000 );
|
5928 |
aBigger:
|
5929 |
sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); |
5930 |
zExp = aExp; |
5931 |
normalizeRoundAndPack:
|
5932 |
--zExp; |
5933 |
return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); |
5934 |
|
5935 |
} |
5936 |
|
5937 |
/*----------------------------------------------------------------------------
|
5938 |
| Returns the result of adding the quadruple-precision floating-point values
|
5939 |
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
5940 |
| for Binary Floating-Point Arithmetic.
|
5941 |
*----------------------------------------------------------------------------*/
|
5942 |
|
5943 |
float128 float128_add( float128 a, float128 b STATUS_PARAM ) |
5944 |
{ |
5945 |
flag aSign, bSign; |
5946 |
|
5947 |
aSign = extractFloat128Sign( a ); |
5948 |
bSign = extractFloat128Sign( b ); |
5949 |
if ( aSign == bSign ) {
|
5950 |
return addFloat128Sigs( a, b, aSign STATUS_VAR );
|
5951 |
} |
5952 |
else {
|
5953 |
return subFloat128Sigs( a, b, aSign STATUS_VAR );
|
5954 |
} |
5955 |
|
5956 |
} |
5957 |
|
5958 |
/*----------------------------------------------------------------------------
|
5959 |
| Returns the result of subtracting the quadruple-precision floating-point
|
5960 |
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
5961 |
| Standard for Binary Floating-Point Arithmetic.
|
5962 |
*----------------------------------------------------------------------------*/
|
5963 |
|
5964 |
float128 float128_sub( float128 a, float128 b STATUS_PARAM ) |
5965 |
{ |
5966 |
flag aSign, bSign; |
5967 |
|
5968 |
aSign = extractFloat128Sign( a ); |
5969 |
bSign = extractFloat128Sign( b ); |
5970 |
if ( aSign == bSign ) {
|
5971 |
return subFloat128Sigs( a, b, aSign STATUS_VAR );
|
5972 |
} |
5973 |
else {
|
5974 |
return addFloat128Sigs( a, b, aSign STATUS_VAR );
|
5975 |
} |
5976 |
|
5977 |
} |
5978 |
|
5979 |
/*----------------------------------------------------------------------------
|
5980 |
| Returns the result of multiplying the quadruple-precision floating-point
|
5981 |
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
5982 |
| Standard for Binary Floating-Point Arithmetic.
|
5983 |
*----------------------------------------------------------------------------*/
|
5984 |
|
5985 |
float128 float128_mul( float128 a, float128 b STATUS_PARAM ) |
5986 |
{ |
5987 |
flag aSign, bSign, zSign; |
5988 |
int32 aExp, bExp, zExp; |
5989 |
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; |
5990 |
float128 z; |
5991 |
|
5992 |
aSig1 = extractFloat128Frac1( a ); |
5993 |
aSig0 = extractFloat128Frac0( a ); |
5994 |
aExp = extractFloat128Exp( a ); |
5995 |
aSign = extractFloat128Sign( a ); |
5996 |
bSig1 = extractFloat128Frac1( b ); |
5997 |
bSig0 = extractFloat128Frac0( b ); |
5998 |
bExp = extractFloat128Exp( b ); |
5999 |
bSign = extractFloat128Sign( b ); |
6000 |
zSign = aSign ^ bSign; |
6001 |
if ( aExp == 0x7FFF ) { |
6002 |
if ( ( aSig0 | aSig1 )
|
6003 |
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
6004 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
6005 |
} |
6006 |
if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; |
6007 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
6008 |
} |
6009 |
if ( bExp == 0x7FFF ) { |
6010 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
6011 |
if ( ( aExp | aSig0 | aSig1 ) == 0 ) { |
6012 |
invalid:
|
6013 |
float_raise( float_flag_invalid STATUS_VAR); |
6014 |
z.low = float128_default_nan_low; |
6015 |
z.high = float128_default_nan_high; |
6016 |
return z;
|
6017 |
} |
6018 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
6019 |
} |
6020 |
if ( aExp == 0 ) { |
6021 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
6022 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
6023 |
} |
6024 |
if ( bExp == 0 ) { |
6025 |
if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
6026 |
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
6027 |
} |
6028 |
zExp = aExp + bExp - 0x4000;
|
6029 |
aSig0 |= LIT64( 0x0001000000000000 );
|
6030 |
shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 );
|
6031 |
mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); |
6032 |
add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); |
6033 |
zSig2 |= ( zSig3 != 0 );
|
6034 |
if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { |
6035 |
shift128ExtraRightJamming( |
6036 |
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
6037 |
++zExp; |
6038 |
} |
6039 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
|
6040 |
|
6041 |
} |
6042 |
|
6043 |
/*----------------------------------------------------------------------------
|
6044 |
| Returns the result of dividing the quadruple-precision floating-point value
|
6045 |
| `a' by the corresponding value `b'. The operation is performed according to
|
6046 |
| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
6047 |
*----------------------------------------------------------------------------*/
|
6048 |
|
6049 |
float128 float128_div( float128 a, float128 b STATUS_PARAM ) |
6050 |
{ |
6051 |
flag aSign, bSign, zSign; |
6052 |
int32 aExp, bExp, zExp; |
6053 |
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; |
6054 |
uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
6055 |
float128 z; |
6056 |
|
6057 |
aSig1 = extractFloat128Frac1( a ); |
6058 |
aSig0 = extractFloat128Frac0( a ); |
6059 |
aExp = extractFloat128Exp( a ); |
6060 |
aSign = extractFloat128Sign( a ); |
6061 |
bSig1 = extractFloat128Frac1( b ); |
6062 |
bSig0 = extractFloat128Frac0( b ); |
6063 |
bExp = extractFloat128Exp( b ); |
6064 |
bSign = extractFloat128Sign( b ); |
6065 |
zSign = aSign ^ bSign; |
6066 |
if ( aExp == 0x7FFF ) { |
6067 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
6068 |
if ( bExp == 0x7FFF ) { |
6069 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
6070 |
goto invalid;
|
6071 |
} |
6072 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
6073 |
} |
6074 |
if ( bExp == 0x7FFF ) { |
6075 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
6076 |
return packFloat128( zSign, 0, 0, 0 ); |
6077 |
} |
6078 |
if ( bExp == 0 ) { |
6079 |
if ( ( bSig0 | bSig1 ) == 0 ) { |
6080 |
if ( ( aExp | aSig0 | aSig1 ) == 0 ) { |
6081 |
invalid:
|
6082 |
float_raise( float_flag_invalid STATUS_VAR); |
6083 |
z.low = float128_default_nan_low; |
6084 |
z.high = float128_default_nan_high; |
6085 |
return z;
|
6086 |
} |
6087 |
float_raise( float_flag_divbyzero STATUS_VAR); |
6088 |
return packFloat128( zSign, 0x7FFF, 0, 0 ); |
6089 |
} |
6090 |
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
6091 |
} |
6092 |
if ( aExp == 0 ) { |
6093 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); |
6094 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
6095 |
} |
6096 |
zExp = aExp - bExp + 0x3FFD;
|
6097 |
shortShift128Left( |
6098 |
aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); |
6099 |
shortShift128Left( |
6100 |
bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); |
6101 |
if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) {
|
6102 |
shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
|
6103 |
++zExp; |
6104 |
} |
6105 |
zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
6106 |
mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); |
6107 |
sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
|
6108 |
while ( (int64_t) rem0 < 0 ) { |
6109 |
--zSig0; |
6110 |
add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
|
6111 |
} |
6112 |
zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); |
6113 |
if ( ( zSig1 & 0x3FFF ) <= 4 ) { |
6114 |
mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); |
6115 |
sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
|
6116 |
while ( (int64_t) rem1 < 0 ) { |
6117 |
--zSig1; |
6118 |
add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
|
6119 |
} |
6120 |
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
6121 |
} |
6122 |
shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); |
6123 |
return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
|
6124 |
|
6125 |
} |
6126 |
|
6127 |
/*----------------------------------------------------------------------------
|
6128 |
| Returns the remainder of the quadruple-precision floating-point value `a'
|
6129 |
| with respect to the corresponding value `b'. The operation is performed
|
6130 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
6131 |
*----------------------------------------------------------------------------*/
|
6132 |
|
6133 |
float128 float128_rem( float128 a, float128 b STATUS_PARAM ) |
6134 |
{ |
6135 |
flag aSign, zSign; |
6136 |
int32 aExp, bExp, expDiff; |
6137 |
uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; |
6138 |
uint64_t allZero, alternateASig0, alternateASig1, sigMean1; |
6139 |
int64_t sigMean0; |
6140 |
float128 z; |
6141 |
|
6142 |
aSig1 = extractFloat128Frac1( a ); |
6143 |
aSig0 = extractFloat128Frac0( a ); |
6144 |
aExp = extractFloat128Exp( a ); |
6145 |
aSign = extractFloat128Sign( a ); |
6146 |
bSig1 = extractFloat128Frac1( b ); |
6147 |
bSig0 = extractFloat128Frac0( b ); |
6148 |
bExp = extractFloat128Exp( b ); |
6149 |
if ( aExp == 0x7FFF ) { |
6150 |
if ( ( aSig0 | aSig1 )
|
6151 |
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
6152 |
return propagateFloat128NaN( a, b STATUS_VAR );
|
6153 |
} |
6154 |
goto invalid;
|
6155 |
} |
6156 |
if ( bExp == 0x7FFF ) { |
6157 |
if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); |
6158 |
return a;
|
6159 |
} |
6160 |
if ( bExp == 0 ) { |
6161 |
if ( ( bSig0 | bSig1 ) == 0 ) { |
6162 |
invalid:
|
6163 |
float_raise( float_flag_invalid STATUS_VAR); |
6164 |
z.low = float128_default_nan_low; |
6165 |
z.high = float128_default_nan_high; |
6166 |
return z;
|
6167 |
} |
6168 |
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); |
6169 |
} |
6170 |
if ( aExp == 0 ) { |
6171 |
if ( ( aSig0 | aSig1 ) == 0 ) return a; |
6172 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
6173 |
} |
6174 |
expDiff = aExp - bExp; |
6175 |
if ( expDiff < -1 ) return a; |
6176 |
shortShift128Left( |
6177 |
aSig0 | LIT64( 0x0001000000000000 ),
|
6178 |
aSig1, |
6179 |
15 - ( expDiff < 0 ), |
6180 |
&aSig0, |
6181 |
&aSig1 |
6182 |
); |
6183 |
shortShift128Left( |
6184 |
bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); |
6185 |
q = le128( bSig0, bSig1, aSig0, aSig1 ); |
6186 |
if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
|
6187 |
expDiff -= 64;
|
6188 |
while ( 0 < expDiff ) { |
6189 |
q = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
6190 |
q = ( 4 < q ) ? q - 4 : 0; |
6191 |
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); |
6192 |
shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
|
6193 |
shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
|
6194 |
sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
|
6195 |
expDiff -= 61;
|
6196 |
} |
6197 |
if ( -64 < expDiff ) { |
6198 |
q = estimateDiv128To64( aSig0, aSig1, bSig0 ); |
6199 |
q = ( 4 < q ) ? q - 4 : 0; |
6200 |
q >>= - expDiff; |
6201 |
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
6202 |
expDiff += 52;
|
6203 |
if ( expDiff < 0 ) { |
6204 |
shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); |
6205 |
} |
6206 |
else {
|
6207 |
shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); |
6208 |
} |
6209 |
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); |
6210 |
sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); |
6211 |
} |
6212 |
else {
|
6213 |
shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
|
6214 |
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
6215 |
} |
6216 |
do {
|
6217 |
alternateASig0 = aSig0; |
6218 |
alternateASig1 = aSig1; |
6219 |
++q; |
6220 |
sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); |
6221 |
} while ( 0 <= (int64_t) aSig0 ); |
6222 |
add128( |
6223 |
aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 ); |
6224 |
if ( ( sigMean0 < 0 ) |
6225 |
|| ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { |
6226 |
aSig0 = alternateASig0; |
6227 |
aSig1 = alternateASig1; |
6228 |
} |
6229 |
zSign = ( (int64_t) aSig0 < 0 );
|
6230 |
if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); |
6231 |
return
|
6232 |
normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR );
|
6233 |
|
6234 |
} |
6235 |
|
6236 |
/*----------------------------------------------------------------------------
|
6237 |
| Returns the square root of the quadruple-precision floating-point value `a'.
|
6238 |
| The operation is performed according to the IEC/IEEE Standard for Binary
|
6239 |
| Floating-Point Arithmetic.
|
6240 |
*----------------------------------------------------------------------------*/
|
6241 |
|
6242 |
float128 float128_sqrt( float128 a STATUS_PARAM ) |
6243 |
{ |
6244 |
flag aSign; |
6245 |
int32 aExp, zExp; |
6246 |
uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; |
6247 |
uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; |
6248 |
float128 z; |
6249 |
|
6250 |
aSig1 = extractFloat128Frac1( a ); |
6251 |
aSig0 = extractFloat128Frac0( a ); |
6252 |
aExp = extractFloat128Exp( a ); |
6253 |
aSign = extractFloat128Sign( a ); |
6254 |
if ( aExp == 0x7FFF ) { |
6255 |
if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); |
6256 |
if ( ! aSign ) return a; |
6257 |
goto invalid;
|
6258 |
} |
6259 |
if ( aSign ) {
|
6260 |
if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; |
6261 |
invalid:
|
6262 |
float_raise( float_flag_invalid STATUS_VAR); |
6263 |
z.low = float128_default_nan_low; |
6264 |
z.high = float128_default_nan_high; |
6265 |
return z;
|
6266 |
} |
6267 |
if ( aExp == 0 ) { |
6268 |
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); |
6269 |
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); |
6270 |
} |
6271 |
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; |
6272 |
aSig0 |= LIT64( 0x0001000000000000 );
|
6273 |
zSig0 = estimateSqrt32( aExp, aSig0>>17 );
|
6274 |
shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); |
6275 |
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); |
6276 |
doubleZSig0 = zSig0<<1;
|
6277 |
mul64To128( zSig0, zSig0, &term0, &term1 ); |
6278 |
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); |
6279 |
while ( (int64_t) rem0 < 0 ) { |
6280 |
--zSig0; |
6281 |
doubleZSig0 -= 2;
|
6282 |
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); |
6283 |
} |
6284 |
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
6285 |
if ( ( zSig1 & 0x1FFF ) <= 5 ) { |
6286 |
if ( zSig1 == 0 ) zSig1 = 1; |
6287 |
mul64To128( doubleZSig0, zSig1, &term1, &term2 ); |
6288 |
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
6289 |
mul64To128( zSig1, zSig1, &term2, &term3 ); |
6290 |
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); |
6291 |
while ( (int64_t) rem1 < 0 ) { |
6292 |
--zSig1; |
6293 |
shortShift128Left( 0, zSig1, 1, &term2, &term3 ); |
6294 |
term3 |= 1;
|
6295 |
term2 |= doubleZSig0; |
6296 |
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
6297 |
} |
6298 |
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
6299 |
} |
6300 |
shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); |
6301 |
return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); |
6302 |
|
6303 |
} |
6304 |
|
6305 |
/*----------------------------------------------------------------------------
|
6306 |
| Returns 1 if the quadruple-precision floating-point value `a' is equal to
|
6307 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
6308 |
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
6309 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
6310 |
*----------------------------------------------------------------------------*/
|
6311 |
|
6312 |
int float128_eq( float128 a, float128 b STATUS_PARAM )
|
6313 |
{ |
6314 |
|
6315 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6316 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6317 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6318 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6319 |
) { |
6320 |
float_raise( float_flag_invalid STATUS_VAR); |
6321 |
return 0; |
6322 |
} |
6323 |
return
|
6324 |
( a.low == b.low ) |
6325 |
&& ( ( a.high == b.high ) |
6326 |
|| ( ( a.low == 0 )
|
6327 |
&& ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
6328 |
); |
6329 |
|
6330 |
} |
6331 |
|
6332 |
/*----------------------------------------------------------------------------
|
6333 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
6334 |
| or equal to the corresponding value `b', and 0 otherwise. The invalid
|
6335 |
| exception is raised if either operand is a NaN. The comparison is performed
|
6336 |
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
6337 |
*----------------------------------------------------------------------------*/
|
6338 |
|
6339 |
int float128_le( float128 a, float128 b STATUS_PARAM )
|
6340 |
{ |
6341 |
flag aSign, bSign; |
6342 |
|
6343 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6344 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6345 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6346 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6347 |
) { |
6348 |
float_raise( float_flag_invalid STATUS_VAR); |
6349 |
return 0; |
6350 |
} |
6351 |
aSign = extractFloat128Sign( a ); |
6352 |
bSign = extractFloat128Sign( b ); |
6353 |
if ( aSign != bSign ) {
|
6354 |
return
|
6355 |
aSign |
6356 |
|| ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
6357 |
== 0 );
|
6358 |
} |
6359 |
return
|
6360 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
6361 |
: le128( a.high, a.low, b.high, b.low ); |
6362 |
|
6363 |
} |
6364 |
|
6365 |
/*----------------------------------------------------------------------------
|
6366 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
6367 |
| the corresponding value `b', and 0 otherwise. The invalid exception is
|
6368 |
| raised if either operand is a NaN. The comparison is performed according
|
6369 |
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
6370 |
*----------------------------------------------------------------------------*/
|
6371 |
|
6372 |
int float128_lt( float128 a, float128 b STATUS_PARAM )
|
6373 |
{ |
6374 |
flag aSign, bSign; |
6375 |
|
6376 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6377 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6378 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6379 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6380 |
) { |
6381 |
float_raise( float_flag_invalid STATUS_VAR); |
6382 |
return 0; |
6383 |
} |
6384 |
aSign = extractFloat128Sign( a ); |
6385 |
bSign = extractFloat128Sign( b ); |
6386 |
if ( aSign != bSign ) {
|
6387 |
return
|
6388 |
aSign |
6389 |
&& ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
6390 |
!= 0 );
|
6391 |
} |
6392 |
return
|
6393 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
6394 |
: lt128( a.high, a.low, b.high, b.low ); |
6395 |
|
6396 |
} |
6397 |
|
6398 |
/*----------------------------------------------------------------------------
|
6399 |
| Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot
|
6400 |
| be compared, and 0 otherwise. The invalid exception is raised if either
|
6401 |
| operand is a NaN. The comparison is performed according to the IEC/IEEE
|
6402 |
| Standard for Binary Floating-Point Arithmetic.
|
6403 |
*----------------------------------------------------------------------------*/
|
6404 |
|
6405 |
int float128_unordered( float128 a, float128 b STATUS_PARAM )
|
6406 |
{ |
6407 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6408 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6409 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6410 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6411 |
) { |
6412 |
float_raise( float_flag_invalid STATUS_VAR); |
6413 |
return 1; |
6414 |
} |
6415 |
return 0; |
6416 |
} |
6417 |
|
6418 |
/*----------------------------------------------------------------------------
|
6419 |
| Returns 1 if the quadruple-precision floating-point value `a' is equal to
|
6420 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
6421 |
| exception. The comparison is performed according to the IEC/IEEE Standard
|
6422 |
| for Binary Floating-Point Arithmetic.
|
6423 |
*----------------------------------------------------------------------------*/
|
6424 |
|
6425 |
int float128_eq_quiet( float128 a, float128 b STATUS_PARAM )
|
6426 |
{ |
6427 |
|
6428 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6429 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6430 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6431 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6432 |
) { |
6433 |
if ( float128_is_signaling_nan( a )
|
6434 |
|| float128_is_signaling_nan( b ) ) { |
6435 |
float_raise( float_flag_invalid STATUS_VAR); |
6436 |
} |
6437 |
return 0; |
6438 |
} |
6439 |
return
|
6440 |
( a.low == b.low ) |
6441 |
&& ( ( a.high == b.high ) |
6442 |
|| ( ( a.low == 0 )
|
6443 |
&& ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) |
6444 |
); |
6445 |
|
6446 |
} |
6447 |
|
6448 |
/*----------------------------------------------------------------------------
|
6449 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
6450 |
| or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
6451 |
| cause an exception. Otherwise, the comparison is performed according to the
|
6452 |
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
6453 |
*----------------------------------------------------------------------------*/
|
6454 |
|
6455 |
int float128_le_quiet( float128 a, float128 b STATUS_PARAM )
|
6456 |
{ |
6457 |
flag aSign, bSign; |
6458 |
|
6459 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6460 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6461 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6462 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6463 |
) { |
6464 |
if ( float128_is_signaling_nan( a )
|
6465 |
|| float128_is_signaling_nan( b ) ) { |
6466 |
float_raise( float_flag_invalid STATUS_VAR); |
6467 |
} |
6468 |
return 0; |
6469 |
} |
6470 |
aSign = extractFloat128Sign( a ); |
6471 |
bSign = extractFloat128Sign( b ); |
6472 |
if ( aSign != bSign ) {
|
6473 |
return
|
6474 |
aSign |
6475 |
|| ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
6476 |
== 0 );
|
6477 |
} |
6478 |
return
|
6479 |
aSign ? le128( b.high, b.low, a.high, a.low ) |
6480 |
: le128( a.high, a.low, b.high, b.low ); |
6481 |
|
6482 |
} |
6483 |
|
6484 |
/*----------------------------------------------------------------------------
|
6485 |
| Returns 1 if the quadruple-precision floating-point value `a' is less than
|
6486 |
| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
|
6487 |
| exception. Otherwise, the comparison is performed according to the IEC/IEEE
|
6488 |
| Standard for Binary Floating-Point Arithmetic.
|
6489 |
*----------------------------------------------------------------------------*/
|
6490 |
|
6491 |
int float128_lt_quiet( float128 a, float128 b STATUS_PARAM )
|
6492 |
{ |
6493 |
flag aSign, bSign; |
6494 |
|
6495 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6496 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6497 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6498 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6499 |
) { |
6500 |
if ( float128_is_signaling_nan( a )
|
6501 |
|| float128_is_signaling_nan( b ) ) { |
6502 |
float_raise( float_flag_invalid STATUS_VAR); |
6503 |
} |
6504 |
return 0; |
6505 |
} |
6506 |
aSign = extractFloat128Sign( a ); |
6507 |
bSign = extractFloat128Sign( b ); |
6508 |
if ( aSign != bSign ) {
|
6509 |
return
|
6510 |
aSign |
6511 |
&& ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
6512 |
!= 0 );
|
6513 |
} |
6514 |
return
|
6515 |
aSign ? lt128( b.high, b.low, a.high, a.low ) |
6516 |
: lt128( a.high, a.low, b.high, b.low ); |
6517 |
|
6518 |
} |
6519 |
|
6520 |
/*----------------------------------------------------------------------------
|
6521 |
| Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot
|
6522 |
| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The
|
6523 |
| comparison is performed according to the IEC/IEEE Standard for Binary
|
6524 |
| Floating-Point Arithmetic.
|
6525 |
*----------------------------------------------------------------------------*/
|
6526 |
|
6527 |
int float128_unordered_quiet( float128 a, float128 b STATUS_PARAM )
|
6528 |
{ |
6529 |
if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) |
6530 |
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) |
6531 |
|| ( ( extractFloat128Exp( b ) == 0x7FFF )
|
6532 |
&& ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) |
6533 |
) { |
6534 |
if ( float128_is_signaling_nan( a )
|
6535 |
|| float128_is_signaling_nan( b ) ) { |
6536 |
float_raise( float_flag_invalid STATUS_VAR); |
6537 |
} |
6538 |
return 1; |
6539 |
} |
6540 |
return 0; |
6541 |
} |
6542 |
|
6543 |
/* misc functions */
|
6544 |
float32 uint32_to_float32(uint32_t a STATUS_PARAM) |
6545 |
{ |
6546 |
return int64_to_float32(a STATUS_VAR);
|
6547 |
} |
6548 |
|
6549 |
float64 uint32_to_float64(uint32_t a STATUS_PARAM) |
6550 |
{ |
6551 |
return int64_to_float64(a STATUS_VAR);
|
6552 |
} |
6553 |
|
6554 |
uint32 float32_to_uint32( float32 a STATUS_PARAM ) |
6555 |
{ |
6556 |
int64_t v; |
6557 |
uint32 res; |
6558 |
int old_exc_flags = get_float_exception_flags(status);
|
6559 |
|
6560 |
v = float32_to_int64(a STATUS_VAR); |
6561 |
if (v < 0) { |
6562 |
res = 0;
|
6563 |
} else if (v > 0xffffffff) { |
6564 |
res = 0xffffffff;
|
6565 |
} else {
|
6566 |
return v;
|
6567 |
} |
6568 |
set_float_exception_flags(old_exc_flags, status); |
6569 |
float_raise(float_flag_invalid STATUS_VAR); |
6570 |
return res;
|
6571 |
} |
6572 |
|
6573 |
uint32 float32_to_uint32_round_to_zero( float32 a STATUS_PARAM ) |
6574 |
{ |
6575 |
int64_t v; |
6576 |
uint32 res; |
6577 |
int old_exc_flags = get_float_exception_flags(status);
|
6578 |
|
6579 |
v = float32_to_int64_round_to_zero(a STATUS_VAR); |
6580 |
if (v < 0) { |
6581 |
res = 0;
|
6582 |
} else if (v > 0xffffffff) { |
6583 |
res = 0xffffffff;
|
6584 |
} else {
|
6585 |
return v;
|
6586 |
} |
6587 |
set_float_exception_flags(old_exc_flags, status); |
6588 |
float_raise(float_flag_invalid STATUS_VAR); |
6589 |
return res;
|
6590 |
} |
6591 |
|
6592 |
int_fast16_t float32_to_int16(float32 a STATUS_PARAM) |
6593 |
{ |
6594 |
int32_t v; |
6595 |
int_fast16_t res; |
6596 |
int old_exc_flags = get_float_exception_flags(status);
|
6597 |
|
6598 |
v = float32_to_int32(a STATUS_VAR); |
6599 |
if (v < -0x8000) { |
6600 |
res = -0x8000;
|
6601 |
} else if (v > 0x7fff) { |
6602 |
res = 0x7fff;
|
6603 |
} else {
|
6604 |
return v;
|
6605 |
} |
6606 |
|
6607 |
set_float_exception_flags(old_exc_flags, status); |
6608 |
float_raise(float_flag_invalid STATUS_VAR); |
6609 |
return res;
|
6610 |
} |
6611 |
|
6612 |
uint_fast16_t float32_to_uint16(float32 a STATUS_PARAM) |
6613 |
{ |
6614 |
int32_t v; |
6615 |
uint_fast16_t res; |
6616 |
int old_exc_flags = get_float_exception_flags(status);
|
6617 |
|
6618 |
v = float32_to_int32(a STATUS_VAR); |
6619 |
if (v < 0) { |
6620 |
res = 0;
|
6621 |
} else if (v > 0xffff) { |
6622 |
res = 0xffff;
|
6623 |
} else {
|
6624 |
return v;
|
6625 |
} |
6626 |
|
6627 |
set_float_exception_flags(old_exc_flags, status); |
6628 |
float_raise(float_flag_invalid STATUS_VAR); |
6629 |
return res;
|
6630 |
} |
6631 |
|
6632 |
uint_fast16_t float32_to_uint16_round_to_zero(float32 a STATUS_PARAM) |
6633 |
{ |
6634 |
int64_t v; |
6635 |
uint_fast16_t res; |
6636 |
int old_exc_flags = get_float_exception_flags(status);
|
6637 |
|
6638 |
v = float32_to_int64_round_to_zero(a STATUS_VAR); |
6639 |
if (v < 0) { |
6640 |
res = 0;
|
6641 |
} else if (v > 0xffff) { |
6642 |
res = 0xffff;
|
6643 |
} else {
|
6644 |
return v;
|
6645 |
} |
6646 |
set_float_exception_flags(old_exc_flags, status); |
6647 |
float_raise(float_flag_invalid STATUS_VAR); |
6648 |
return res;
|
6649 |
} |
6650 |
|
6651 |
uint32 float64_to_uint32( float64 a STATUS_PARAM ) |
6652 |
{ |
6653 |
uint64_t v; |
6654 |
uint32 res; |
6655 |
int old_exc_flags = get_float_exception_flags(status);
|
6656 |
|
6657 |
v = float64_to_uint64(a STATUS_VAR); |
6658 |
if (v > 0xffffffff) { |
6659 |
res = 0xffffffff;
|
6660 |
} else {
|
6661 |
return v;
|
6662 |
} |
6663 |
set_float_exception_flags(old_exc_flags, status); |
6664 |
float_raise(float_flag_invalid STATUS_VAR); |
6665 |
return res;
|
6666 |
} |
6667 |
|
6668 |
uint32 float64_to_uint32_round_to_zero( float64 a STATUS_PARAM ) |
6669 |
{ |
6670 |
uint64_t v; |
6671 |
uint32 res; |
6672 |
int old_exc_flags = get_float_exception_flags(status);
|
6673 |
|
6674 |
v = float64_to_uint64_round_to_zero(a STATUS_VAR); |
6675 |
if (v > 0xffffffff) { |
6676 |
res = 0xffffffff;
|
6677 |
} else {
|
6678 |
return v;
|
6679 |
} |
6680 |
set_float_exception_flags(old_exc_flags, status); |
6681 |
float_raise(float_flag_invalid STATUS_VAR); |
6682 |
return res;
|
6683 |
} |
6684 |
|
6685 |
int_fast16_t float64_to_int16(float64 a STATUS_PARAM) |
6686 |
{ |
6687 |
int64_t v; |
6688 |
int_fast16_t res; |
6689 |
int old_exc_flags = get_float_exception_flags(status);
|
6690 |
|
6691 |
v = float64_to_int32(a STATUS_VAR); |
6692 |
if (v < -0x8000) { |
6693 |
res = -0x8000;
|
6694 |
} else if (v > 0x7fff) { |
6695 |
res = 0x7fff;
|
6696 |
} else {
|
6697 |
return v;
|
6698 |
} |
6699 |
|
6700 |
set_float_exception_flags(old_exc_flags, status); |
6701 |
float_raise(float_flag_invalid STATUS_VAR); |
6702 |
return res;
|
6703 |
} |
6704 |
|
6705 |
uint_fast16_t float64_to_uint16(float64 a STATUS_PARAM) |
6706 |
{ |
6707 |
int64_t v; |
6708 |
uint_fast16_t res; |
6709 |
int old_exc_flags = get_float_exception_flags(status);
|
6710 |
|
6711 |
v = float64_to_int32(a STATUS_VAR); |
6712 |
if (v < 0) { |
6713 |
res = 0;
|
6714 |
} else if (v > 0xffff) { |
6715 |
res = 0xffff;
|
6716 |
} else {
|
6717 |
return v;
|
6718 |
} |
6719 |
|
6720 |
set_float_exception_flags(old_exc_flags, status); |
6721 |
float_raise(float_flag_invalid STATUS_VAR); |
6722 |
return res;
|
6723 |
} |
6724 |
|
6725 |
uint_fast16_t float64_to_uint16_round_to_zero(float64 a STATUS_PARAM) |
6726 |
{ |
6727 |
int64_t v; |
6728 |
uint_fast16_t res; |
6729 |
int old_exc_flags = get_float_exception_flags(status);
|
6730 |
|
6731 |
v = float64_to_int64_round_to_zero(a STATUS_VAR); |
6732 |
if (v < 0) { |
6733 |
res = 0;
|
6734 |
} else if (v > 0xffff) { |
6735 |
res = 0xffff;
|
6736 |
} else {
|
6737 |
return v;
|
6738 |
} |
6739 |
set_float_exception_flags(old_exc_flags, status); |
6740 |
float_raise(float_flag_invalid STATUS_VAR); |
6741 |
return res;
|
6742 |
} |
6743 |
|
6744 |
/*----------------------------------------------------------------------------
|
6745 |
| Returns the result of converting the double-precision floating-point value
|
6746 |
| `a' to the 64-bit unsigned integer format. The conversion is
|
6747 |
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
6748 |
| Arithmetic---which means in particular that the conversion is rounded
|
6749 |
| according to the current rounding mode. If `a' is a NaN, the largest
|
6750 |
| positive integer is returned. If the conversion overflows, the
|
6751 |
| largest unsigned integer is returned. If 'a' is negative, the value is
|
6752 |
| rounded and zero is returned; negative values that do not round to zero
|
6753 |
| will raise the inexact exception.
|
6754 |
*----------------------------------------------------------------------------*/
|
6755 |
|
6756 |
uint64_t float64_to_uint64(float64 a STATUS_PARAM) |
6757 |
{ |
6758 |
flag aSign; |
6759 |
int_fast16_t aExp, shiftCount; |
6760 |
uint64_t aSig, aSigExtra; |
6761 |
a = float64_squash_input_denormal(a STATUS_VAR); |
6762 |
|
6763 |
aSig = extractFloat64Frac(a); |
6764 |
aExp = extractFloat64Exp(a); |
6765 |
aSign = extractFloat64Sign(a); |
6766 |
if (aSign && (aExp > 1022)) { |
6767 |
float_raise(float_flag_invalid STATUS_VAR); |
6768 |
if (float64_is_any_nan(a)) {
|
6769 |
return LIT64(0xFFFFFFFFFFFFFFFF); |
6770 |
} else {
|
6771 |
return 0; |
6772 |
} |
6773 |
} |
6774 |
if (aExp) {
|
6775 |
aSig |= LIT64(0x0010000000000000);
|
6776 |
} |
6777 |
shiftCount = 0x433 - aExp;
|
6778 |
if (shiftCount <= 0) { |
6779 |
if (0x43E < aExp) { |
6780 |
float_raise(float_flag_invalid STATUS_VAR); |
6781 |
return LIT64(0xFFFFFFFFFFFFFFFF); |
6782 |
} |
6783 |
aSigExtra = 0;
|
6784 |
aSig <<= -shiftCount; |
6785 |
} else {
|
6786 |
shift64ExtraRightJamming(aSig, 0, shiftCount, &aSig, &aSigExtra);
|
6787 |
} |
6788 |
return roundAndPackUint64(aSign, aSig, aSigExtra STATUS_VAR);
|
6789 |
} |
6790 |
|
6791 |
uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM) |
6792 |
{ |
6793 |
signed char current_rounding_mode = STATUS(float_rounding_mode); |
6794 |
set_float_rounding_mode(float_round_to_zero STATUS_VAR); |
6795 |
int64_t v = float64_to_uint64(a STATUS_VAR); |
6796 |
set_float_rounding_mode(current_rounding_mode STATUS_VAR); |
6797 |
return v;
|
6798 |
} |
6799 |
|
6800 |
#define COMPARE(s, nan_exp) \
|
6801 |
INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \ |
6802 |
int is_quiet STATUS_PARAM ) \
|
6803 |
{ \ |
6804 |
flag aSign, bSign; \ |
6805 |
uint ## s ## _t av, bv; \ |
6806 |
a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ |
6807 |
b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ |
6808 |
\ |
6809 |
if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ |
6810 |
extractFloat ## s ## Frac( a ) ) || \ |
6811 |
( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ |
6812 |
extractFloat ## s ## Frac( b ) )) { \ |
6813 |
if (!is_quiet || \
|
6814 |
float ## s ## _is_signaling_nan( a ) || \ |
6815 |
float ## s ## _is_signaling_nan( b ) ) { \ |
6816 |
float_raise( float_flag_invalid STATUS_VAR); \ |
6817 |
} \ |
6818 |
return float_relation_unordered; \
|
6819 |
} \ |
6820 |
aSign = extractFloat ## s ## Sign( a ); \ |
6821 |
bSign = extractFloat ## s ## Sign( b ); \ |
6822 |
av = float ## s ## _val(a); \ |
6823 |
bv = float ## s ## _val(b); \ |
6824 |
if ( aSign != bSign ) { \
|
6825 |
if ( (uint ## s ## _t) ( ( av | bv )<<1 ) == 0 ) { \ |
6826 |
/* zero case */ \
|
6827 |
return float_relation_equal; \
|
6828 |
} else { \
|
6829 |
return 1 - (2 * aSign); \ |
6830 |
} \ |
6831 |
} else { \
|
6832 |
if (av == bv) { \
|
6833 |
return float_relation_equal; \
|
6834 |
} else { \
|
6835 |
return 1 - 2 * (aSign ^ ( av < bv )); \ |
6836 |
} \ |
6837 |
} \ |
6838 |
} \ |
6839 |
\ |
6840 |
int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \ |
6841 |
{ \ |
6842 |
return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \ |
6843 |
} \ |
6844 |
\ |
6845 |
int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \ |
6846 |
{ \ |
6847 |
return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \ |
6848 |
} |
6849 |
|
6850 |
COMPARE(32, 0xff) |
6851 |
COMPARE(64, 0x7ff) |
6852 |
|
6853 |
INLINE int floatx80_compare_internal( floatx80 a, floatx80 b,
|
6854 |
int is_quiet STATUS_PARAM )
|
6855 |
{ |
6856 |
flag aSign, bSign; |
6857 |
|
6858 |
if (( ( extractFloatx80Exp( a ) == 0x7fff ) && |
6859 |
( extractFloatx80Frac( a )<<1 ) ) ||
|
6860 |
( ( extractFloatx80Exp( b ) == 0x7fff ) &&
|
6861 |
( extractFloatx80Frac( b )<<1 ) )) {
|
6862 |
if (!is_quiet ||
|
6863 |
floatx80_is_signaling_nan( a ) || |
6864 |
floatx80_is_signaling_nan( b ) ) { |
6865 |
float_raise( float_flag_invalid STATUS_VAR); |
6866 |
} |
6867 |
return float_relation_unordered;
|
6868 |
} |
6869 |
aSign = extractFloatx80Sign( a ); |
6870 |
bSign = extractFloatx80Sign( b ); |
6871 |
if ( aSign != bSign ) {
|
6872 |
|
6873 |
if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) && |
6874 |
( ( a.low | b.low ) == 0 ) ) {
|
6875 |
/* zero case */
|
6876 |
return float_relation_equal;
|
6877 |
} else {
|
6878 |
return 1 - (2 * aSign); |
6879 |
} |
6880 |
} else {
|
6881 |
if (a.low == b.low && a.high == b.high) {
|
6882 |
return float_relation_equal;
|
6883 |
} else {
|
6884 |
return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); |
6885 |
} |
6886 |
} |
6887 |
} |
6888 |
|
6889 |
int floatx80_compare( floatx80 a, floatx80 b STATUS_PARAM )
|
6890 |
{ |
6891 |
return floatx80_compare_internal(a, b, 0 STATUS_VAR); |
6892 |
} |
6893 |
|
6894 |
int floatx80_compare_quiet( floatx80 a, floatx80 b STATUS_PARAM )
|
6895 |
{ |
6896 |
return floatx80_compare_internal(a, b, 1 STATUS_VAR); |
6897 |
} |
6898 |
|
6899 |
INLINE int float128_compare_internal( float128 a, float128 b,
|
6900 |
int is_quiet STATUS_PARAM )
|
6901 |
{ |
6902 |
flag aSign, bSign; |
6903 |
|
6904 |
if (( ( extractFloat128Exp( a ) == 0x7fff ) && |
6905 |
( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) || |
6906 |
( ( extractFloat128Exp( b ) == 0x7fff ) &&
|
6907 |
( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) { |
6908 |
if (!is_quiet ||
|
6909 |
float128_is_signaling_nan( a ) || |
6910 |
float128_is_signaling_nan( b ) ) { |
6911 |
float_raise( float_flag_invalid STATUS_VAR); |
6912 |
} |
6913 |
return float_relation_unordered;
|
6914 |
} |
6915 |
aSign = extractFloat128Sign( a ); |
6916 |
bSign = extractFloat128Sign( b ); |
6917 |
if ( aSign != bSign ) {
|
6918 |
if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) { |
6919 |
/* zero case */
|
6920 |
return float_relation_equal;
|
6921 |
} else {
|
6922 |
return 1 - (2 * aSign); |
6923 |
} |
6924 |
} else {
|
6925 |
if (a.low == b.low && a.high == b.high) {
|
6926 |
return float_relation_equal;
|
6927 |
} else {
|
6928 |
return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); |
6929 |
} |
6930 |
} |
6931 |
} |
6932 |
|
6933 |
int float128_compare( float128 a, float128 b STATUS_PARAM )
|
6934 |
{ |
6935 |
return float128_compare_internal(a, b, 0 STATUS_VAR); |
6936 |
} |
6937 |
|
6938 |
int float128_compare_quiet( float128 a, float128 b STATUS_PARAM )
|
6939 |
{ |
6940 |
return float128_compare_internal(a, b, 1 STATUS_VAR); |
6941 |
} |
6942 |
|
6943 |
/* min() and max() functions. These can't be implemented as
|
6944 |
* 'compare and pick one input' because that would mishandle
|
6945 |
* NaNs and +0 vs -0.
|
6946 |
*
|
6947 |
* minnum() and maxnum() functions. These are similar to the min()
|
6948 |
* and max() functions but if one of the arguments is a QNaN and
|
6949 |
* the other is numerical then the numerical argument is returned.
|
6950 |
* minnum() and maxnum correspond to the IEEE 754-2008 minNum()
|
6951 |
* and maxNum() operations. min() and max() are the typical min/max
|
6952 |
* semantics provided by many CPUs which predate that specification.
|
6953 |
*/
|
6954 |
#define MINMAX(s) \
|
6955 |
INLINE float ## s float ## s ## _minmax(float ## s a, float ## s b, \ |
6956 |
int ismin, int isieee STATUS_PARAM) \ |
6957 |
{ \ |
6958 |
flag aSign, bSign; \ |
6959 |
uint ## s ## _t av, bv; \ |
6960 |
a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ |
6961 |
b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ |
6962 |
if (float ## s ## _is_any_nan(a) || \ |
6963 |
float ## s ## _is_any_nan(b)) { \ |
6964 |
if (isieee) { \
|
6965 |
if (float ## s ## _is_quiet_nan(a) && \ |
6966 |
!float ## s ##_is_any_nan(b)) { \ |
6967 |
return b; \
|
6968 |
} else if (float ## s ## _is_quiet_nan(b) && \ |
6969 |
!float ## s ## _is_any_nan(a)) { \ |
6970 |
return a; \
|
6971 |
} \ |
6972 |
} \ |
6973 |
return propagateFloat ## s ## NaN(a, b STATUS_VAR); \ |
6974 |
} \ |
6975 |
aSign = extractFloat ## s ## Sign(a); \ |
6976 |
bSign = extractFloat ## s ## Sign(b); \ |
6977 |
av = float ## s ## _val(a); \ |
6978 |
bv = float ## s ## _val(b); \ |
6979 |
if (aSign != bSign) { \
|
6980 |
if (ismin) { \
|
6981 |
return aSign ? a : b; \
|
6982 |
} else { \
|
6983 |
return aSign ? b : a; \
|
6984 |
} \ |
6985 |
} else { \
|
6986 |
if (ismin) { \
|
6987 |
return (aSign ^ (av < bv)) ? a : b; \
|
6988 |
} else { \
|
6989 |
return (aSign ^ (av < bv)) ? b : a; \
|
6990 |
} \ |
6991 |
} \ |
6992 |
} \ |
6993 |
\ |
6994 |
float ## s float ## s ## _min(float ## s a, float ## s b STATUS_PARAM) \ |
6995 |
{ \ |
6996 |
return float ## s ## _minmax(a, b, 1, 0 STATUS_VAR); \ |
6997 |
} \ |
6998 |
\ |
6999 |
float ## s float ## s ## _max(float ## s a, float ## s b STATUS_PARAM) \ |
7000 |
{ \ |
7001 |
return float ## s ## _minmax(a, b, 0, 0 STATUS_VAR); \ |
7002 |
} \ |
7003 |
\ |
7004 |
float ## s float ## s ## _minnum(float ## s a, float ## s b STATUS_PARAM) \ |
7005 |
{ \ |
7006 |
return float ## s ## _minmax(a, b, 1, 1 STATUS_VAR); \ |
7007 |
} \ |
7008 |
\ |
7009 |
float ## s float ## s ## _maxnum(float ## s a, float ## s b STATUS_PARAM) \ |
7010 |
{ \ |
7011 |
return float ## s ## _minmax(a, b, 0, 1 STATUS_VAR); \ |
7012 |
} |
7013 |
|
7014 |
MINMAX(32)
|
7015 |
MINMAX(64)
|
7016 |
|
7017 |
|
7018 |
/* Multiply A by 2 raised to the power N. */
|
7019 |
float32 float32_scalbn( float32 a, int n STATUS_PARAM )
|
7020 |
{ |
7021 |
flag aSign; |
7022 |
int16_t aExp; |
7023 |
uint32_t aSig; |
7024 |
|
7025 |
a = float32_squash_input_denormal(a STATUS_VAR); |
7026 |
aSig = extractFloat32Frac( a ); |
7027 |
aExp = extractFloat32Exp( a ); |
7028 |
aSign = extractFloat32Sign( a ); |
7029 |
|
7030 |
if ( aExp == 0xFF ) { |
7031 |
if ( aSig ) {
|
7032 |
return propagateFloat32NaN( a, a STATUS_VAR );
|
7033 |
} |
7034 |
return a;
|
7035 |
} |
7036 |
if (aExp != 0) { |
7037 |
aSig |= 0x00800000;
|
7038 |
} else if (aSig == 0) { |
7039 |
return a;
|
7040 |
} else {
|
7041 |
aExp++; |
7042 |
} |
7043 |
|
7044 |
if (n > 0x200) { |
7045 |
n = 0x200;
|
7046 |
} else if (n < -0x200) { |
7047 |
n = -0x200;
|
7048 |
} |
7049 |
|
7050 |
aExp += n - 1;
|
7051 |
aSig <<= 7;
|
7052 |
return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
|
7053 |
} |
7054 |
|
7055 |
float64 float64_scalbn( float64 a, int n STATUS_PARAM )
|
7056 |
{ |
7057 |
flag aSign; |
7058 |
int16_t aExp; |
7059 |
uint64_t aSig; |
7060 |
|
7061 |
a = float64_squash_input_denormal(a STATUS_VAR); |
7062 |
aSig = extractFloat64Frac( a ); |
7063 |
aExp = extractFloat64Exp( a ); |
7064 |
aSign = extractFloat64Sign( a ); |
7065 |
|
7066 |
if ( aExp == 0x7FF ) { |
7067 |
if ( aSig ) {
|
7068 |
return propagateFloat64NaN( a, a STATUS_VAR );
|
7069 |
} |
7070 |
return a;
|
7071 |
} |
7072 |
if (aExp != 0) { |
7073 |
aSig |= LIT64( 0x0010000000000000 );
|
7074 |
} else if (aSig == 0) { |
7075 |
return a;
|
7076 |
} else {
|
7077 |
aExp++; |
7078 |
} |
7079 |
|
7080 |
if (n > 0x1000) { |
7081 |
n = 0x1000;
|
7082 |
} else if (n < -0x1000) { |
7083 |
n = -0x1000;
|
7084 |
} |
7085 |
|
7086 |
aExp += n - 1;
|
7087 |
aSig <<= 10;
|
7088 |
return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR );
|
7089 |
} |
7090 |
|
7091 |
floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM )
|
7092 |
{ |
7093 |
flag aSign; |
7094 |
int32_t aExp; |
7095 |
uint64_t aSig; |
7096 |
|
7097 |
aSig = extractFloatx80Frac( a ); |
7098 |
aExp = extractFloatx80Exp( a ); |
7099 |
aSign = extractFloatx80Sign( a ); |
7100 |
|
7101 |
if ( aExp == 0x7FFF ) { |
7102 |
if ( aSig<<1 ) { |
7103 |
return propagateFloatx80NaN( a, a STATUS_VAR );
|
7104 |
} |
7105 |
return a;
|
7106 |
} |
7107 |
|
7108 |
if (aExp == 0) { |
7109 |
if (aSig == 0) { |
7110 |
return a;
|
7111 |
} |
7112 |
aExp++; |
7113 |
} |
7114 |
|
7115 |
if (n > 0x10000) { |
7116 |
n = 0x10000;
|
7117 |
} else if (n < -0x10000) { |
7118 |
n = -0x10000;
|
7119 |
} |
7120 |
|
7121 |
aExp += n; |
7122 |
return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision),
|
7123 |
aSign, aExp, aSig, 0 STATUS_VAR );
|
7124 |
} |
7125 |
|
7126 |
float128 float128_scalbn( float128 a, int n STATUS_PARAM )
|
7127 |
{ |
7128 |
flag aSign; |
7129 |
int32_t aExp; |
7130 |
uint64_t aSig0, aSig1; |
7131 |
|
7132 |
aSig1 = extractFloat128Frac1( a ); |
7133 |
aSig0 = extractFloat128Frac0( a ); |
7134 |
aExp = extractFloat128Exp( a ); |
7135 |
aSign = extractFloat128Sign( a ); |
7136 |
if ( aExp == 0x7FFF ) { |
7137 |
if ( aSig0 | aSig1 ) {
|
7138 |
return propagateFloat128NaN( a, a STATUS_VAR );
|
7139 |
} |
7140 |
return a;
|
7141 |
} |
7142 |
if (aExp != 0) { |
7143 |
aSig0 |= LIT64( 0x0001000000000000 );
|
7144 |
} else if (aSig0 == 0 && aSig1 == 0) { |
7145 |
return a;
|
7146 |
} else {
|
7147 |
aExp++; |
7148 |
} |
7149 |
|
7150 |
if (n > 0x10000) { |
7151 |
n = 0x10000;
|
7152 |
} else if (n < -0x10000) { |
7153 |
n = -0x10000;
|
7154 |
} |
7155 |
|
7156 |
aExp += n - 1;
|
7157 |
return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
|
7158 |
STATUS_VAR ); |
7159 |
|
7160 |
} |