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softfloat.c
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/*
* QEMU float support
*
* The code in this source file is derived from release 2a of the SoftFloat
* IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and
* some later contributions) are provided under that license, as detailed below.
* It has subsequently been modified by contributors to the QEMU Project,
* so some portions are provided under:
* the SoftFloat-2a license
* the BSD license
* GPL-v2-or-later
*
* Any future contributions to this file after December 1st 2014 will be
* taken to be licensed under the Softfloat-2a license unless specifically
* indicated otherwise.
*/
/*
===============================================================================
This C source file is part of the SoftFloat IEC/IEEE Floating-point
Arithmetic Package, Release 2a.
Written by John R. Hauser. This work was made possible in part by the
International Computer Science Institute, located at Suite 600, 1947 Center
Street, Berkeley, California 94704. Funding was partially provided by the
National Science Foundation under grant MIP-9311980. The original version
of this code was written as part of a project to build a fixed-point vector
processor in collaboration with the University of California at Berkeley,
overseen by Profs. Nelson Morgan and John Wawrzynek. More information
is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
arithmetic/SoftFloat.html'.
THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
Derivative works are acceptable, even for commercial purposes, so long as
(1) they include prominent notice that the work is derivative, and (2) they
include prominent notice akin to these four paragraphs for those parts of
this code that are retained.
===============================================================================
*/
/* BSD licensing:
* Copyright (c) 2006, Fabrice Bellard
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its contributors
* may be used to endorse or promote products derived from this software without
* specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
/* Portions of this work are licensed under the terms of the GNU GPL,
* version 2 or later. See the COPYING file in the top-level directory.
*/
/* softfloat (and in particular the code in softfloat-specialize.h) is
* target-dependent and needs the TARGET_* macros.
*/
#include "qemu/osdep.h"
#include "fpu/softfloat.h"
/* We only need stdlib for abort() */
/*----------------------------------------------------------------------------
| Primitive arithmetic functions, including multi-word arithmetic, and
| division and square root approximations. (Can be specialized to target if
| desired.)
*----------------------------------------------------------------------------*/
#include "softfloat-macros.h"
/*----------------------------------------------------------------------------
| Functions and definitions to determine: (1) whether tininess for underflow
| is detected before or after rounding by default, (2) what (if anything)
| happens when exceptions are raised, (3) how signaling NaNs are distinguished
| from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs
| are propagated from function inputs to output. These details are target-
| specific.
*----------------------------------------------------------------------------*/
#include "softfloat-specialize.h"
/*----------------------------------------------------------------------------
| Returns the fraction bits of the half-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline uint32_t extractFloat16Frac(float16 a)
{
return float16_val(a) & 0x3ff;
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the half-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline int extractFloat16Exp(float16 a)
{
return (float16_val(a) >> 10) & 0x1f;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline flag extractFloat16Sign(float16 a)
{
return float16_val(a)>>15;
}
/*----------------------------------------------------------------------------
| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
| and 7, and returns the properly rounded 32-bit integer corresponding to the
| input. If `zSign' is 1, the input is negated before being converted to an
| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input
| is simply rounded to an integer, with the inexact exception raised if the
| input cannot be represented exactly as an integer. However, if the fixed-
| point input is too large, the invalid exception is raised and the largest
| positive or negative integer is returned.
*----------------------------------------------------------------------------*/
static int32_t roundAndPackInt32(flag zSign, uint64_t absZ, float_status *status)
{
int8_t roundingMode;
flag roundNearestEven;
int8_t roundIncrement, roundBits;
int32_t z;
roundingMode = status->float_rounding_mode;
roundNearestEven = ( roundingMode == float_round_nearest_even );
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
roundIncrement = 0x40;
break;
case float_round_to_zero:
roundIncrement = 0;
break;
case float_round_up:
roundIncrement = zSign ? 0 : 0x7f;
break;
case float_round_down:
roundIncrement = zSign ? 0x7f : 0;
break;
default:
abort();
}
roundBits = absZ & 0x7F;
absZ = ( absZ + roundIncrement )>>7;
absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
z = absZ;
if ( zSign ) z = - z;
if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
float_raise(float_flag_invalid, status);
return zSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
}
if (roundBits) {
status->float_exception_flags |= float_flag_inexact;
}
return z;
}
/*----------------------------------------------------------------------------
| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
| `absZ1', with binary point between bits 63 and 64 (between the input words),
| and returns the properly rounded 64-bit integer corresponding to the input.
| If `zSign' is 1, the input is negated before being converted to an integer.
| Ordinarily, the fixed-point input is simply rounded to an integer, with
| the inexact exception raised if the input cannot be represented exactly as
| an integer. However, if the fixed-point input is too large, the invalid
| exception is raised and the largest positive or negative integer is
| returned.
*----------------------------------------------------------------------------*/
static int64_t roundAndPackInt64(flag zSign, uint64_t absZ0, uint64_t absZ1,
float_status *status)
{
int8_t roundingMode;
flag roundNearestEven, increment;
int64_t z;
roundingMode = status->float_rounding_mode;
roundNearestEven = ( roundingMode == float_round_nearest_even );
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
increment = ((int64_t) absZ1 < 0);
break;
case float_round_to_zero:
increment = 0;
break;
case float_round_up:
increment = !zSign && absZ1;
break;
case float_round_down:
increment = zSign && absZ1;
break;
default:
abort();
}
if ( increment ) {
++absZ0;
if ( absZ0 == 0 ) goto overflow;
absZ0 &= ~ ( ( (uint64_t) ( absZ1<<1 ) == 0 ) & roundNearestEven );
}
z = absZ0;
if ( zSign ) z = - z;
if ( z && ( ( z < 0 ) ^ zSign ) ) {
overflow:
float_raise(float_flag_invalid, status);
return
zSign ? (int64_t) LIT64( 0x8000000000000000 )
: LIT64( 0x7FFFFFFFFFFFFFFF );
}
if (absZ1) {
status->float_exception_flags |= float_flag_inexact;
}
return z;
}
/*----------------------------------------------------------------------------
| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
| `absZ1', with binary point between bits 63 and 64 (between the input words),
| and returns the properly rounded 64-bit unsigned integer corresponding to the
| input. Ordinarily, the fixed-point input is simply rounded to an integer,
| with the inexact exception raised if the input cannot be represented exactly
| as an integer. However, if the fixed-point input is too large, the invalid
| exception is raised and the largest unsigned integer is returned.
*----------------------------------------------------------------------------*/
static int64_t roundAndPackUint64(flag zSign, uint64_t absZ0,
uint64_t absZ1, float_status *status)
{
int8_t roundingMode;
flag roundNearestEven, increment;
roundingMode = status->float_rounding_mode;
roundNearestEven = (roundingMode == float_round_nearest_even);
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
increment = ((int64_t)absZ1 < 0);
break;
case float_round_to_zero:
increment = 0;
break;
case float_round_up:
increment = !zSign && absZ1;
break;
case float_round_down:
increment = zSign && absZ1;
break;
default:
abort();
}
if (increment) {
++absZ0;
if (absZ0 == 0) {
float_raise(float_flag_invalid, status);
return LIT64(0xFFFFFFFFFFFFFFFF);
}
absZ0 &= ~(((uint64_t)(absZ1<<1) == 0) & roundNearestEven);
}
if (zSign && absZ0) {
float_raise(float_flag_invalid, status);
return 0;
}
if (absZ1) {
status->float_exception_flags |= float_flag_inexact;
}
return absZ0;
}
/*----------------------------------------------------------------------------
| Returns the fraction bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline uint32_t extractFloat32Frac( float32 a )
{
return float32_val(a) & 0x007FFFFF;
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline int extractFloat32Exp(float32 a)
{
return ( float32_val(a)>>23 ) & 0xFF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline flag extractFloat32Sign( float32 a )
{
return float32_val(a)>>31;
}
/*----------------------------------------------------------------------------
| If `a' is denormal and we are in flush-to-zero mode then set the
| input-denormal exception and return zero. Otherwise just return the value.
*----------------------------------------------------------------------------*/
float32 float32_squash_input_denormal(float32 a, float_status *status)
{
if (status->flush_inputs_to_zero) {
if (extractFloat32Exp(a) == 0 && extractFloat32Frac(a) != 0) {
float_raise(float_flag_input_denormal, status);
return make_float32(float32_val(a) & 0x80000000);
}
}
return a;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal single-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
| significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
static void
normalizeFloat32Subnormal(uint32_t aSig, int *zExpPtr, uint32_t *zSigPtr)
{
int8_t shiftCount;
shiftCount = countLeadingZeros32( aSig ) - 8;
*zSigPtr = aSig<<shiftCount;
*zExpPtr = 1 - shiftCount;
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| single-precision floating-point value, returning the result. After being
| shifted into the proper positions, the three fields are simply added
| together to form the result. This means that any integer portion of `zSig'
| will be added into the exponent. Since a properly normalized significand
| will have an integer portion equal to 1, the `zExp' input should be 1 less
| than the desired result exponent whenever `zSig' is a complete, normalized
| significand.
*----------------------------------------------------------------------------*/
static inline float32 packFloat32(flag zSign, int zExp, uint32_t zSig)
{
return make_float32(
( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) zExp )<<23 ) + zSig);
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input. Ordinarily, the abstract
| value is simply rounded and packed into the single-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal single-
| precision floating-point number.
| The input significand `zSig' has its binary point between bits 30
| and 29, which is 7 bits to the left of the usual location. This shifted
| significand must be normalized or smaller. If `zSig' is not normalized,
| `zExp' must be 0; in that case, the result returned is a subnormal number,
| and it must not require rounding. In the usual case that `zSig' is
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
| The handling of underflow and overflow follows the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static float32 roundAndPackFloat32(flag zSign, int zExp, uint32_t zSig,
float_status *status)
{
int8_t roundingMode;
flag roundNearestEven;
int8_t roundIncrement, roundBits;
flag isTiny;
roundingMode = status->float_rounding_mode;
roundNearestEven = ( roundingMode == float_round_nearest_even );
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
roundIncrement = 0x40;
break;
case float_round_to_zero:
roundIncrement = 0;
break;
case float_round_up:
roundIncrement = zSign ? 0 : 0x7f;
break;
case float_round_down:
roundIncrement = zSign ? 0x7f : 0;
break;
default:
abort();
break;
}
roundBits = zSig & 0x7F;
if ( 0xFD <= (uint16_t) zExp ) {
if ( ( 0xFD < zExp )
|| ( ( zExp == 0xFD )
&& ( (int32_t) ( zSig + roundIncrement ) < 0 ) )
) {
float_raise(float_flag_overflow | float_flag_inexact, status);
return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 ));
}
if ( zExp < 0 ) {
if (status->flush_to_zero) {
float_raise(float_flag_output_denormal, status);
return packFloat32(zSign, 0, 0);
}
isTiny =
(status->float_detect_tininess
== float_tininess_before_rounding)
|| ( zExp < -1 )
|| ( zSig + roundIncrement < 0x80000000 );
shift32RightJamming( zSig, - zExp, &zSig );
zExp = 0;
roundBits = zSig & 0x7F;
if (isTiny && roundBits) {
float_raise(float_flag_underflow, status);
}
}
}
if (roundBits) {
status->float_exception_flags |= float_flag_inexact;
}
zSig = ( zSig + roundIncrement )>>7;
zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
if ( zSig == 0 ) zExp = 0;
return packFloat32( zSign, zExp, zSig );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input. This routine is just like
| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/
static float32
normalizeRoundAndPackFloat32(flag zSign, int zExp, uint32_t zSig,
float_status *status)
{
int8_t shiftCount;
shiftCount = countLeadingZeros32( zSig ) - 1;
return roundAndPackFloat32(zSign, zExp - shiftCount, zSig<<shiftCount,
status);
}
/*----------------------------------------------------------------------------
| Returns the fraction bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline uint64_t extractFloat64Frac( float64 a )
{
return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF );
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline int extractFloat64Exp(float64 a)
{
return ( float64_val(a)>>52 ) & 0x7FF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/
static inline flag extractFloat64Sign( float64 a )
{
return float64_val(a)>>63;
}
/*----------------------------------------------------------------------------
| If `a' is denormal and we are in flush-to-zero mode then set the
| input-denormal exception and return zero. Otherwise just return the value.
*----------------------------------------------------------------------------*/
float64 float64_squash_input_denormal(float64 a, float_status *status)
{
if (status->flush_inputs_to_zero) {
if (extractFloat64Exp(a) == 0 && extractFloat64Frac(a) != 0) {
float_raise(float_flag_input_denormal, status);
return make_float64(float64_val(a) & (1ULL << 63));
}
}
return a;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal double-precision floating-point value represented
| by the denormalized significand `aSig'. The normalized exponent and
| significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
static void
normalizeFloat64Subnormal(uint64_t aSig, int *zExpPtr, uint64_t *zSigPtr)
{
int8_t shiftCount;
shiftCount = countLeadingZeros64( aSig ) - 11;
*zSigPtr = aSig<<shiftCount;
*zExpPtr = 1 - shiftCount;
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| double-precision floating-point value, returning the result. After being
| shifted into the proper positions, the three fields are simply added
| together to form the result. This means that any integer portion of `zSig'
| will be added into the exponent. Since a properly normalized significand
| will have an integer portion equal to 1, the `zExp' input should be 1 less
| than the desired result exponent whenever `zSig' is a complete, normalized
| significand.
*----------------------------------------------------------------------------*/
static inline float64 packFloat64(flag zSign, int zExp, uint64_t zSig)
{
return make_float64(
( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig);
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper double-precision floating-
| point value corresponding to the abstract input. Ordinarily, the abstract
| value is simply rounded and packed into the double-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal double-
| precision floating-point number.
| The input significand `zSig' has its binary point between bits 62
| and 61, which is 10 bits to the left of the usual location. This shifted
| significand must be normalized or smaller. If `zSig' is not normalized,
| `zExp' must be 0; in that case, the result returned is a subnormal number,
| and it must not require rounding. In the usual case that `zSig' is
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
| The handling of underflow and overflow follows the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static float64 roundAndPackFloat64(flag zSign, int zExp, uint64_t zSig,
float_status *status)
{
int8_t roundingMode;
flag roundNearestEven;
int roundIncrement, roundBits;
flag isTiny;
roundingMode = status->float_rounding_mode;
roundNearestEven = ( roundingMode == float_round_nearest_even );
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
roundIncrement = 0x200;
break;
case float_round_to_zero:
roundIncrement = 0;
break;
case float_round_up:
roundIncrement = zSign ? 0 : 0x3ff;
break;
case float_round_down:
roundIncrement = zSign ? 0x3ff : 0;
break;
case float_round_to_odd:
roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
break;
default:
abort();
}
roundBits = zSig & 0x3FF;
if ( 0x7FD <= (uint16_t) zExp ) {
if ( ( 0x7FD < zExp )
|| ( ( zExp == 0x7FD )
&& ( (int64_t) ( zSig + roundIncrement ) < 0 ) )
) {
bool overflow_to_inf = roundingMode != float_round_to_odd &&
roundIncrement != 0;
float_raise(float_flag_overflow | float_flag_inexact, status);
return packFloat64(zSign, 0x7FF, -(!overflow_to_inf));
}
if ( zExp < 0 ) {
if (status->flush_to_zero) {
float_raise(float_flag_output_denormal, status);
return packFloat64(zSign, 0, 0);
}
isTiny =
(status->float_detect_tininess
== float_tininess_before_rounding)
|| ( zExp < -1 )
|| ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
shift64RightJamming( zSig, - zExp, &zSig );
zExp = 0;
roundBits = zSig & 0x3FF;
if (isTiny && roundBits) {
float_raise(float_flag_underflow, status);
}
if (roundingMode == float_round_to_odd) {
/*
* For round-to-odd case, the roundIncrement depends on
* zSig which just changed.
*/
roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
}
}
}
if (roundBits) {
status->float_exception_flags |= float_flag_inexact;
}
zSig = ( zSig + roundIncrement )>>10;
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
if ( zSig == 0 ) zExp = 0;
return packFloat64( zSign, zExp, zSig );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper double-precision floating-
| point value corresponding to the abstract input. This routine is just like
| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/
static float64
normalizeRoundAndPackFloat64(flag zSign, int zExp, uint64_t zSig,
float_status *status)
{
int8_t shiftCount;
shiftCount = countLeadingZeros64( zSig ) - 1;
return roundAndPackFloat64(zSign, zExp - shiftCount, zSig<<shiftCount,
status);
}
/*----------------------------------------------------------------------------
| Returns the fraction bits of the extended double-precision floating-point
| value `a'.
*----------------------------------------------------------------------------*/
static inline uint64_t extractFloatx80Frac( floatx80 a )
{
return a.low;
}
/*----------------------------------------------------------------------------
| Returns the exponent bits of the extended double-precision floating-point
| value `a'.
*----------------------------------------------------------------------------*/
static inline int32_t extractFloatx80Exp( floatx80 a )
{
return a.high & 0x7FFF;
}
/*----------------------------------------------------------------------------
| Returns the sign bit of the extended double-precision floating-point value
| `a'.
*----------------------------------------------------------------------------*/
static inline flag extractFloatx80Sign( floatx80 a )
{
return a.high>>15;
}
/*----------------------------------------------------------------------------
| Normalizes the subnormal extended double-precision floating-point value
| represented by the denormalized significand `aSig'. The normalized exponent
| and significand are stored at the locations pointed to by `zExpPtr' and
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
static void
normalizeFloatx80Subnormal( uint64_t aSig, int32_t *zExpPtr, uint64_t *zSigPtr )
{
int8_t shiftCount;
shiftCount = countLeadingZeros64( aSig );
*zSigPtr = aSig<<shiftCount;
*zExpPtr = 1 - shiftCount;
}
/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
| extended double-precision floating-point value, returning the result.
*----------------------------------------------------------------------------*/
static inline floatx80 packFloatx80( flag zSign, int32_t zExp, uint64_t zSig )
{
floatx80 z;
z.low = zSig;
z.high = ( ( (uint16_t) zSign )<<15 ) + zExp;
return z;
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and extended significand formed by the concatenation of `zSig0' and `zSig1',
| and returns the proper extended double-precision floating-point value
| corresponding to the abstract input. Ordinarily, the abstract value is
| rounded and packed into the extended double-precision format, with the
| inexact exception raised if the abstract input cannot be represented
| exactly. However, if the abstract value is too large, the overflow and
| inexact exceptions are raised and an infinity or maximal finite value is
| returned. If the abstract value is too small, the input value is rounded to
| a subnormal number, and the underflow and inexact exceptions are raised if
| the abstract input cannot be represented exactly as a subnormal extended
| double-precision floating-point number.
| If `roundingPrecision' is 32 or 64, the result is rounded to the same
| number of bits as single or double precision, respectively. Otherwise, the
| result is rounded to the full precision of the extended double-precision
| format.
| The input significand must be normalized or smaller. If the input
| significand is not normalized, `zExp' must be 0; in that case, the result
| returned is a subnormal number, and it must not require rounding. The
| handling of underflow and overflow follows the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
static floatx80 roundAndPackFloatx80(int8_t roundingPrecision, flag zSign,
int32_t zExp, uint64_t zSig0, uint64_t zSig1,
float_status *status)
{
int8_t roundingMode;
flag roundNearestEven, increment, isTiny;
int64_t roundIncrement, roundMask, roundBits;
roundingMode = status->float_rounding_mode;
roundNearestEven = ( roundingMode == float_round_nearest_even );
if ( roundingPrecision == 80 ) goto precision80;
if ( roundingPrecision == 64 ) {
roundIncrement = LIT64( 0x0000000000000400 );
roundMask = LIT64( 0x00000000000007FF );
}
else if ( roundingPrecision == 32 ) {
roundIncrement = LIT64( 0x0000008000000000 );
roundMask = LIT64( 0x000000FFFFFFFFFF );
}
else {
goto precision80;
}
zSig0 |= ( zSig1 != 0 );
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
break;
case float_round_to_zero:
roundIncrement = 0;
break;
case float_round_up:
roundIncrement = zSign ? 0 : roundMask;
break;
case float_round_down:
roundIncrement = zSign ? roundMask : 0;
break;
default:
abort();
}
roundBits = zSig0 & roundMask;
if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) {
if ( ( 0x7FFE < zExp )
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
) {
goto overflow;
}
if ( zExp <= 0 ) {
if (status->flush_to_zero) {
float_raise(float_flag_output_denormal, status);
return packFloatx80(zSign, 0, 0);
}
isTiny =
(status->float_detect_tininess
== float_tininess_before_rounding)
|| ( zExp < 0 )
|| ( zSig0 <= zSig0 + roundIncrement );
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
zExp = 0;
roundBits = zSig0 & roundMask;
if (isTiny && roundBits) {
float_raise(float_flag_underflow, status);
}
if (roundBits) {
status->float_exception_flags |= float_flag_inexact;
}
zSig0 += roundIncrement;
if ( (int64_t) zSig0 < 0 ) zExp = 1;
roundIncrement = roundMask + 1;
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
roundMask |= roundIncrement;
}
zSig0 &= ~ roundMask;
return packFloatx80( zSign, zExp, zSig0 );
}
}
if (roundBits) {
status->float_exception_flags |= float_flag_inexact;
}
zSig0 += roundIncrement;
if ( zSig0 < roundIncrement ) {
++zExp;
zSig0 = LIT64( 0x8000000000000000 );
}
roundIncrement = roundMask + 1;
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
roundMask |= roundIncrement;
}
zSig0 &= ~ roundMask;
if ( zSig0 == 0 ) zExp = 0;
return packFloatx80( zSign, zExp, zSig0 );
precision80:
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
increment = ((int64_t)zSig1 < 0);
break;
case float_round_to_zero:
increment = 0;
break;
case float_round_up:
increment = !zSign && zSig1;
break;
case float_round_down:
increment = zSign && zSig1;
break;
default:
abort();
}
if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) {
if ( ( 0x7FFE < zExp )
|| ( ( zExp == 0x7FFE )
&& ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
&& increment
)
) {
roundMask = 0;
overflow:
float_raise(float_flag_overflow | float_flag_inexact, status);
if ( ( roundingMode == float_round_to_zero )
|| ( zSign && ( roundingMode == float_round_up ) )
|| ( ! zSign && ( roundingMode == float_round_down ) )
) {
return packFloatx80( zSign, 0x7FFE, ~ roundMask );
}
return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
}
if ( zExp <= 0 ) {
isTiny =
(status->float_detect_tininess
== float_tininess_before_rounding)
|| ( zExp < 0 )
|| ! increment
|| ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
zExp = 0;
if (isTiny && zSig1) {
float_raise(float_flag_underflow, status);
}
if (zSig1) {
status->float_exception_flags |= float_flag_inexact;
}
switch (roundingMode) {
case float_round_nearest_even:
case float_round_ties_away:
increment = ((int64_t)zSig1 < 0);
break;
case float_round_to_zero:
increment = 0;
break;
case float_round_up:
increment = !zSign && zSig1;
break;
case float_round_down:
increment = zSign && zSig1;
break;
default:
abort();
}
if ( increment ) {
++zSig0;
zSig0 &=
~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven );
if ( (int64_t) zSig0 < 0 ) zExp = 1;
}
return packFloatx80( zSign, zExp, zSig0 );
}
}
if (zSig1) {
status->float_exception_flags |= float_flag_inexact;
}
if ( increment ) {
++zSig0;
if ( zSig0 == 0 ) {
++zExp;
zSig0 = LIT64( 0x8000000000000000 );
}
else {
zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven );
}
}
else {
if ( zSig0 == 0 ) zExp = 0;
}
return packFloatx80( zSign, zExp, zSig0 );
}
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent
| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
| and returns the proper extended double-precision floating-point value
| corresponding to the abstract input. This routine is just like
| `roundAndPackFloatx80' except that the input significand does not have to be
| normalized.
*----------------------------------------------------------------------------*/
static floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
flag zSign, int32_t zExp,
uint64_t zSig0, uint64_t zSig1,
float_status *status)
{
int8_t shiftCount;
if ( zSig0 == 0 ) {
zSig0 = zSig1;
zSig1 = 0;
zExp -= 64;
}
shiftCount = countLeadingZeros64( zSig0 );