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Diffstat (limited to 'src/fpu/softfloat.c')
| -rw-r--r-- | src/fpu/softfloat.c | 7722 |
1 files changed, 7722 insertions, 0 deletions
diff --git a/src/fpu/softfloat.c b/src/fpu/softfloat.c new file mode 100644 index 0000000..f1170fe --- /dev/null +++ b/src/fpu/softfloat.c @@ -0,0 +1,7722 @@ +/* + * 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 "config.h" + +#include "fpu/softfloat.h" + +/* We only need stdlib for abort() */ +#include <stdlib.h> + +/*---------------------------------------------------------------------------- +| 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_fast16_t 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 roundAndPackInt32(flag zSign, uint64_t absZ, float_status *status) +{ + int8 roundingMode; + flag roundNearestEven; + int8 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 roundAndPackInt64(flag zSign, uint64_t absZ0, uint64_t absZ1, + float_status *status) +{ + int8 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 roundAndPackUint64(flag zSign, uint64_t absZ0, + uint64_t absZ1, float_status *status) +{ + int8 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_fast16_t 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_fast16_t *zExpPtr, uint32_t *zSigPtr) +{ + int8 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_fast16_t 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_fast16_t zExp, uint32_t zSig, + float_status *status) +{ + int8 roundingMode; + flag roundNearestEven; + int8 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_fast16_t zExp, uint32_t zSig, + float_status *status) +{ + int8 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_fast16_t 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_fast16_t *zExpPtr, uint64_t *zSigPtr) +{ + int8 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_fast16_t 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_fast16_t zExp, uint64_t zSig, + float_status *status) +{ + int8 roundingMode; + flag roundNearestEven; + int_fast16_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 = 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; + default: + abort(); + } + roundBits = zSig & 0x3FF; + if ( 0x7FD <= (uint16_t) zExp ) { + if ( ( 0x7FD < zExp ) + || ( ( zExp == 0x7FD ) + && ( (int64_t) ( zSig + roundIncrement ) < 0 ) ) + ) { + float_raise(float_flag_overflow | float_flag_inexact, status); + return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 )); + } + 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 (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_fast16_t zExp, uint64_t zSig, + float_status *status) +{ + int8 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 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 *zExpPtr, uint64_t *zSigPtr ) +{ + int8 shiftCount; + + shiftCount = countLeadingZeros64( aSig ); + *zSigPtr = aSig<<shiftCount; + *zExpPtr = 1 - shiftCount; + +} + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an +| extended double-precision floating-point value, returning the result. +*----------------------------------------------------------------------------*/ + +static inline floatx80 packFloatx80( flag zSign, int32 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 roundingPrecision, flag zSign, + int32 zExp, uint64_t zSig0, uint64_t zSig1, + float_status *status) +{ + int8 roundingMode; + flag roundNearestEven, increment, isTiny; + int64 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 roundingPrecision, + flag zSign, int32 zExp, + uint64_t zSig0, uint64_t zSig1, + float_status *status) +{ + int8 shiftCount; + + if ( zSig0 == 0 ) { + zSig0 = zSig1; + zSig1 = 0; + zExp -= 64; + } + shiftCount = countLeadingZeros64( zSig0 ); + shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); + zExp -= shiftCount; + return roundAndPackFloatx80(roundingPrecision, zSign, zExp, + zSig0, zSig1, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the least-significant 64 fraction bits of the quadruple-precision +| floating-point value `a'. +*----------------------------------------------------------------------------*/ + +static inline uint64_t extractFloat128Frac1( float128 a ) +{ + + return a.low; + +} + +/*---------------------------------------------------------------------------- +| Returns the most-significant 48 fraction bits of the quadruple-precision +| floating-point value `a'. +*----------------------------------------------------------------------------*/ + +static inline uint64_t extractFloat128Frac0( float128 a ) +{ + + return a.high & LIT64( 0x0000FFFFFFFFFFFF ); + +} + +/*---------------------------------------------------------------------------- +| Returns the exponent bits of the quadruple-precision floating-point value +| `a'. +*----------------------------------------------------------------------------*/ + +static inline int32 extractFloat128Exp( float128 a ) +{ + + return ( a.high>>48 ) & 0x7FFF; + +} + +/*---------------------------------------------------------------------------- +| Returns the sign bit of the quadruple-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +static inline flag extractFloat128Sign( float128 a ) +{ + + return a.high>>63; + +} + +/*---------------------------------------------------------------------------- +| Normalizes the subnormal quadruple-precision floating-point value +| represented by the denormalized significand formed by the concatenation of +| `aSig0' and `aSig1'. The normalized exponent is stored at the location +| pointed to by `zExpPtr'. The most significant 49 bits of the normalized +| significand are stored at the location pointed to by `zSig0Ptr', and the +| least significant 64 bits of the normalized significand are stored at the +| location pointed to by `zSig1Ptr'. +*----------------------------------------------------------------------------*/ + +static void + normalizeFloat128Subnormal( + uint64_t aSig0, + uint64_t aSig1, + int32 *zExpPtr, + uint64_t *zSig0Ptr, + uint64_t *zSig1Ptr + ) +{ + int8 shiftCount; + + if ( aSig0 == 0 ) { + shiftCount = countLeadingZeros64( aSig1 ) - 15; + if ( shiftCount < 0 ) { + *zSig0Ptr = aSig1>>( - shiftCount ); + *zSig1Ptr = aSig1<<( shiftCount & 63 ); + } + else { + *zSig0Ptr = aSig1<<shiftCount; + *zSig1Ptr = 0; + } + *zExpPtr = - shiftCount - 63; + } + else { + shiftCount = countLeadingZeros64( aSig0 ) - 15; + shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); + *zExpPtr = 1 - shiftCount; + } + +} + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', the exponent `zExp', and the significand formed +| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision +| floating-point value, returning the result. After being shifted into the +| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply +| added together to form the most significant 32 bits of the result. This +| means that any integer portion of `zSig0' 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 `zSig0' and `zSig1' concatenated form a complete, normalized +| significand. +*----------------------------------------------------------------------------*/ + +static inline float128 + packFloat128( flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 ) +{ + float128 z; + + z.low = zSig1; + z.high = ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<48 ) + zSig0; + return z; + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and extended significand formed by the concatenation of `zSig0', `zSig1', +| and `zSig2', and returns the proper quadruple-precision floating-point value +| corresponding to the abstract input. Ordinarily, the abstract value is +| simply rounded and packed into the quadruple-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 quadruple- +| precision floating-point number. +| 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. In the +| usual case that the input significand 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 float128 roundAndPackFloat128(flag zSign, int32 zExp, + uint64_t zSig0, uint64_t zSig1, + uint64_t zSig2, float_status *status) +{ + int8 roundingMode; + flag roundNearestEven, increment, isTiny; + + 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)zSig2 < 0); + break; + case float_round_to_zero: + increment = 0; + break; + case float_round_up: + increment = !zSign && zSig2; + break; + case float_round_down: + increment = zSign && zSig2; + break; + default: + abort(); + } + if ( 0x7FFD <= (uint32_t) zExp ) { + if ( ( 0x7FFD < zExp ) + || ( ( zExp == 0x7FFD ) + && eq128( + LIT64( 0x0001FFFFFFFFFFFF ), + LIT64( 0xFFFFFFFFFFFFFFFF ), + zSig0, + zSig1 + ) + && increment + ) + ) { + 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 + packFloat128( + zSign, + 0x7FFE, + LIT64( 0x0000FFFFFFFFFFFF ), + LIT64( 0xFFFFFFFFFFFFFFFF ) + ); + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( zExp < 0 ) { + if (status->flush_to_zero) { + float_raise(float_flag_output_denormal, status); + return packFloat128(zSign, 0, 0, 0); + } + isTiny = + (status->float_detect_tininess + == float_tininess_before_rounding) + || ( zExp < -1 ) + || ! increment + || lt128( + zSig0, + zSig1, + LIT64( 0x0001FFFFFFFFFFFF ), + LIT64( 0xFFFFFFFFFFFFFFFF ) + ); + shift128ExtraRightJamming( + zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); + zExp = 0; + if (isTiny && zSig2) { + float_raise(float_flag_underflow, status); + } + switch (roundingMode) { + case float_round_nearest_even: + case float_round_ties_away: + increment = ((int64_t)zSig2 < 0); + break; + case float_round_to_zero: + increment = 0; + break; + case float_round_up: + increment = !zSign && zSig2; + break; + case float_round_down: + increment = zSign && zSig2; + break; + default: + abort(); + } + } + } + if (zSig2) { + status->float_exception_flags |= float_flag_inexact; + } + if ( increment ) { + add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); + zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven ); + } + else { + if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; + } + return packFloat128( zSign, zExp, zSig0, zSig1 ); + +} + +/*---------------------------------------------------------------------------- +| 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 quadruple-precision floating-point value corresponding +| to the abstract input. This routine is just like `roundAndPackFloat128' +| except that the input significand has fewer bits and does not have to be +| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating- +| point exponent. +*----------------------------------------------------------------------------*/ + +static float128 normalizeRoundAndPackFloat128(flag zSign, int32 zExp, + uint64_t zSig0, uint64_t zSig1, + float_status *status) +{ + int8 shiftCount; + uint64_t zSig2; + + if ( zSig0 == 0 ) { + zSig0 = zSig1; + zSig1 = 0; + zExp -= 64; + } + shiftCount = countLeadingZeros64( zSig0 ) - 15; + if ( 0 <= shiftCount ) { + zSig2 = 0; + shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); + } + else { + shift128ExtraRightJamming( + zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 ); + } + zExp -= shiftCount; + return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' +| to the single-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 int32_to_float32(int32_t a, float_status *status) +{ + flag zSign; + + if ( a == 0 ) return float32_zero; + if ( a == (int32_t) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); + zSign = ( a < 0 ); + return normalizeRoundAndPackFloat32(zSign, 0x9C, zSign ? -a : a, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' +| to the double-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 int32_to_float64(int32_t a, float_status *status) +{ + flag zSign; + uint32 absA; + int8 shiftCount; + uint64_t zSig; + + if ( a == 0 ) return float64_zero; + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros32( absA ) + 21; + zSig = absA; + return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' +| to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 int32_to_floatx80(int32_t a, float_status *status) +{ + flag zSign; + uint32 absA; + int8 shiftCount; + uint64_t zSig; + + if ( a == 0 ) return packFloatx80( 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros32( absA ) + 32; + zSig = absA; + return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' to +| the quadruple-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 int32_to_float128(int32_t a, float_status *status) +{ + flag zSign; + uint32 absA; + int8 shiftCount; + uint64_t zSig0; + + if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros32( absA ) + 17; + zSig0 = absA; + return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' +| to the single-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 int64_to_float32(int64_t a, float_status *status) +{ + flag zSign; + uint64 absA; + int8 shiftCount; + + if ( a == 0 ) return float32_zero; + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros64( absA ) - 40; + if ( 0 <= shiftCount ) { + return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); + } + else { + shiftCount += 7; + if ( shiftCount < 0 ) { + shift64RightJamming( absA, - shiftCount, &absA ); + } + else { + absA <<= shiftCount; + } + return roundAndPackFloat32(zSign, 0x9C - shiftCount, absA, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' +| to the double-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 int64_to_float64(int64_t a, float_status *status) +{ + flag zSign; + + if ( a == 0 ) return float64_zero; + if ( a == (int64_t) LIT64( 0x8000000000000000 ) ) { + return packFloat64( 1, 0x43E, 0 ); + } + zSign = ( a < 0 ); + return normalizeRoundAndPackFloat64(zSign, 0x43C, zSign ? -a : a, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' +| to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 int64_to_floatx80(int64_t a, float_status *status) +{ + flag zSign; + uint64 absA; + int8 shiftCount; + + if ( a == 0 ) return packFloatx80( 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros64( absA ); + return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' to +| the quadruple-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 int64_to_float128(int64_t a, float_status *status) +{ + flag zSign; + uint64 absA; + int8 shiftCount; + int32 zExp; + uint64_t zSig0, zSig1; + + if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros64( absA ) + 49; + zExp = 0x406E - shiftCount; + if ( 64 <= shiftCount ) { + zSig1 = 0; + zSig0 = absA; + shiftCount -= 64; + } + else { + zSig1 = absA; + zSig0 = 0; + } + shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); + return packFloat128( zSign, zExp, zSig0, zSig1 ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit unsigned integer `a' +| to the single-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 uint64_to_float32(uint64_t a, float_status *status) +{ + int shiftcount; + + if (a == 0) { + return float32_zero; + } + + /* Determine (left) shift needed to put first set bit into bit posn 23 + * (since packFloat32() expects the binary point between bits 23 and 22); + * this is the fast case for smallish numbers. + */ + shiftcount = countLeadingZeros64(a) - 40; + if (shiftcount >= 0) { + return packFloat32(0, 0x95 - shiftcount, a << shiftcount); + } + /* Otherwise we need to do a round-and-pack. roundAndPackFloat32() + * expects the binary point between bits 30 and 29, hence the + 7. + */ + shiftcount += 7; + if (shiftcount < 0) { + shift64RightJamming(a, -shiftcount, &a); + } else { + a <<= shiftcount; + } + + return roundAndPackFloat32(0, 0x9c - shiftcount, a, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit unsigned integer `a' +| to the double-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 uint64_to_float64(uint64_t a, float_status *status) +{ + int exp = 0x43C; + int shiftcount; + + if (a == 0) { + return float64_zero; + } + + shiftcount = countLeadingZeros64(a) - 1; + if (shiftcount < 0) { + shift64RightJamming(a, -shiftcount, &a); + } else { + a <<= shiftcount; + } + return roundAndPackFloat64(0, exp - shiftcount, a, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit unsigned integer `a' +| to the quadruple-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 uint64_to_float128(uint64_t a, float_status *status) +{ + if (a == 0) { + return float128_zero; + } + return normalizeRoundAndPackFloat128(0, 0x406E, a, 0, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 float32_to_int32(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint32_t aSig; + uint64_t aSig64; + + a = float32_squash_input_denormal(a, status); + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( ( aExp == 0xFF ) && aSig ) aSign = 0; + if ( aExp ) aSig |= 0x00800000; + shiftCount = 0xAF - aExp; + aSig64 = aSig; + aSig64 <<= 32; + if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); + return roundAndPackInt32(aSign, aSig64, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int32 float32_to_int32_round_to_zero(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint32_t aSig; + int32_t z; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = aExp - 0x9E; + if ( 0 <= shiftCount ) { + if ( float32_val(a) != 0xCF000000 ) { + float_raise(float_flag_invalid, status); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; + } + return (int32_t) 0x80000000; + } + else if ( aExp <= 0x7E ) { + if (aExp | aSig) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + aSig = ( aSig | 0x00800000 )<<8; + z = aSig>>( - shiftCount ); + if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { + status->float_exception_flags |= float_flag_inexact; + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 16-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int_fast16_t float32_to_int16_round_to_zero(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint32_t aSig; + int32 z; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = aExp - 0x8E; + if ( 0 <= shiftCount ) { + if ( float32_val(a) != 0xC7000000 ) { + float_raise(float_flag_invalid, status); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { + return 0x7FFF; + } + } + return (int32_t) 0xffff8000; + } + else if ( aExp <= 0x7E ) { + if ( aExp | aSig ) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + shiftCount -= 0x10; + aSig = ( aSig | 0x00800000 )<<8; + z = aSig>>( - shiftCount ); + if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { + status->float_exception_flags |= float_flag_inexact; + } + if ( aSign ) { + z = - z; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 float32_to_int64(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint32_t aSig; + uint64_t aSig64, aSigExtra; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = 0xBE - aExp; + if ( shiftCount < 0 ) { + float_raise(float_flag_invalid, status); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + if ( aExp ) aSig |= 0x00800000; + aSig64 = aSig; + aSig64 <<= 40; + shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra ); + return roundAndPackInt64(aSign, aSig64, aSigExtra, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 64-bit unsigned integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| unsigned integer is returned. Otherwise, if the conversion overflows, the +| largest unsigned integer is returned. If the 'a' is negative, the result +| is rounded and zero is returned; values that do not round to zero will +| raise the inexact exception flag. +*----------------------------------------------------------------------------*/ + +uint64 float32_to_uint64(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint32_t aSig; + uint64_t aSig64, aSigExtra; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac(a); + aExp = extractFloat32Exp(a); + aSign = extractFloat32Sign(a); + if ((aSign) && (aExp > 126)) { + float_raise(float_flag_invalid, status); + if (float32_is_any_nan(a)) { + return LIT64(0xFFFFFFFFFFFFFFFF); + } else { + return 0; + } + } + shiftCount = 0xBE - aExp; + if (aExp) { + aSig |= 0x00800000; + } + if (shiftCount < 0) { + float_raise(float_flag_invalid, status); + return LIT64(0xFFFFFFFFFFFFFFFF); + } + + aSig64 = aSig; + aSig64 <<= 40; + shift64ExtraRightJamming(aSig64, 0, shiftCount, &aSig64, &aSigExtra); + return roundAndPackUint64(aSign, aSig64, aSigExtra, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 64-bit unsigned integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. If +| `a' is a NaN, the largest unsigned integer is returned. Otherwise, if the +| conversion overflows, the largest unsigned integer is returned. If the +| 'a' is negative, the result is rounded and zero is returned; values that do +| not round to zero will raise the inexact flag. +*----------------------------------------------------------------------------*/ + +uint64 float32_to_uint64_round_to_zero(float32 a, float_status *status) +{ + signed char current_rounding_mode = status->float_rounding_mode; + set_float_rounding_mode(float_round_to_zero, status); + int64_t v = float32_to_uint64(a, status); + set_float_rounding_mode(current_rounding_mode, status); + return v; +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. If +| `a' is a NaN, the largest positive integer is returned. Otherwise, if the +| conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int64 float32_to_int64_round_to_zero(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint32_t aSig; + uint64_t aSig64; + int64 z; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = aExp - 0xBE; + if ( 0 <= shiftCount ) { + if ( float32_val(a) != 0xDF000000 ) { + float_raise(float_flag_invalid, status); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + else if ( aExp <= 0x7E ) { + if (aExp | aSig) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + aSig64 = aSig | 0x00800000; + aSig64 <<= 40; + z = aSig64>>( - shiftCount ); + if ( (uint64_t) ( aSig64<<( shiftCount & 63 ) ) ) { + status->float_exception_flags |= float_flag_inexact; + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the double-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float32_to_float64(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if (aSig) { + return commonNaNToFloat64(float32ToCommonNaN(a, status), status); + } + return packFloat64( aSign, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + --aExp; + } + return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 float32_to_floatx80(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + + a = float32_squash_input_denormal(a, status); + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if (aSig) { + return commonNaNToFloatx80(float32ToCommonNaN(a, status), status); + } + return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + aSig |= 0x00800000; + return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the double-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float32_to_float128(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + + a = float32_squash_input_denormal(a, status); + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if (aSig) { + return commonNaNToFloat128(float32ToCommonNaN(a, status), status); + } + return packFloat128( aSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + --aExp; + } + return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 ); + +} + +/*---------------------------------------------------------------------------- +| Rounds the single-precision floating-point value `a' to an integer, and +| returns the result as a single-precision floating-point value. The +| operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_round_to_int(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t lastBitMask, roundBitsMask; + uint32_t z; + a = float32_squash_input_denormal(a, status); + + aExp = extractFloat32Exp( a ); + if ( 0x96 <= aExp ) { + if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { + return propagateFloat32NaN(a, a, status); + } + return a; + } + if ( aExp <= 0x7E ) { + if ( (uint32_t) ( float32_val(a)<<1 ) == 0 ) return a; + status->float_exception_flags |= float_flag_inexact; + aSign = extractFloat32Sign( a ); + switch (status->float_rounding_mode) { + case float_round_nearest_even: + if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { + return packFloat32( aSign, 0x7F, 0 ); + } + break; + case float_round_ties_away: + if (aExp == 0x7E) { + return packFloat32(aSign, 0x7F, 0); + } + break; + case float_round_down: + return make_float32(aSign ? 0xBF800000 : 0); + case float_round_up: + return make_float32(aSign ? 0x80000000 : 0x3F800000); + } + return packFloat32( aSign, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x96 - aExp; + roundBitsMask = lastBitMask - 1; + z = float32_val(a); + switch (status->float_rounding_mode) { + case float_round_nearest_even: + z += lastBitMask>>1; + if ((z & roundBitsMask) == 0) { + z &= ~lastBitMask; + } + break; + case float_round_ties_away: + z += lastBitMask >> 1; + break; + case float_round_to_zero: + break; + case float_round_up: + if (!extractFloat32Sign(make_float32(z))) { + z += roundBitsMask; + } + break; + case float_round_down: + if (extractFloat32Sign(make_float32(z))) { + z += roundBitsMask; + } + break; + default: + abort(); + } + z &= ~ roundBitsMask; + if (z != float32_val(a)) { + status->float_exception_flags |= float_flag_inexact; + } + return make_float32(z); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the single-precision +| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated +| before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 addFloat32Sigs(float32 a, float32 b, flag zSign, + float_status *status) +{ + int_fast16_t aExp, bExp, zExp; + uint32_t aSig, bSig, zSig; + int_fast16_t expDiff; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + expDiff = aExp - bExp; + aSig <<= 6; + bSig <<= 6; + if ( 0 < expDiff ) { + if ( aExp == 0xFF ) { + if (aSig) { + return propagateFloat32NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= 0x20000000; + } + shift32RightJamming( bSig, expDiff, &bSig ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0xFF ) { + if (bSig) { + return propagateFloat32NaN(a, b, status); + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= 0x20000000; + } + shift32RightJamming( aSig, - expDiff, &aSig ); + zExp = bExp; + } + else { + if ( aExp == 0xFF ) { + if (aSig | bSig) { + return propagateFloat32NaN(a, b, status); + } + return a; + } + if ( aExp == 0 ) { + if (status->flush_to_zero) { + if (aSig | bSig) { + float_raise(float_flag_output_denormal, status); + } + return packFloat32(zSign, 0, 0); + } + return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); + } + zSig = 0x40000000 + aSig + bSig; + zExp = aExp; + goto roundAndPack; + } + aSig |= 0x20000000; + zSig = ( aSig + bSig )<<1; + --zExp; + if ( (int32_t) zSig < 0 ) { + zSig = aSig + bSig; + ++zExp; + } + roundAndPack: + return roundAndPackFloat32(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the single- +| precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 subFloat32Sigs(float32 a, float32 b, flag zSign, + float_status *status) +{ + int_fast16_t aExp, bExp, zExp; + uint32_t aSig, bSig, zSig; + int_fast16_t expDiff; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + expDiff = aExp - bExp; + aSig <<= 7; + bSig <<= 7; + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0xFF ) { + if (aSig | bSig) { + return propagateFloat32NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + if ( bSig < aSig ) goto aBigger; + if ( aSig < bSig ) goto bBigger; + return packFloat32(status->float_rounding_mode == float_round_down, 0, 0); + bExpBigger: + if ( bExp == 0xFF ) { + if (bSig) { + return propagateFloat32NaN(a, b, status); + } + return packFloat32( zSign ^ 1, 0xFF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= 0x40000000; + } + shift32RightJamming( aSig, - expDiff, &aSig ); + bSig |= 0x40000000; + bBigger: + zSig = bSig - aSig; + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0xFF ) { + if (aSig) { + return propagateFloat32NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= 0x40000000; + } + shift32RightJamming( bSig, expDiff, &bSig ); + aSig |= 0x40000000; + aBigger: + zSig = aSig - bSig; + zExp = aExp; + normalizeRoundAndPack: + --zExp; + return normalizeRoundAndPackFloat32(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the single-precision floating-point values `a' +| and `b'. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_add(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign == bSign ) { + return addFloat32Sigs(a, b, aSign, status); + } + else { + return subFloat32Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the single-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_sub(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign == bSign ) { + return subFloat32Sigs(a, b, aSign, status); + } + else { + return addFloat32Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the single-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_mul(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign, zSign; + int_fast16_t aExp, bExp, zExp; + uint32_t aSig, bSig; + uint64_t zSig64; + uint32_t zSig; + + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + bSign = extractFloat32Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0xFF ) { + if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { + return propagateFloat32NaN(a, b, status); + } + if ( ( bExp | bSig ) == 0 ) { + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( bExp == 0xFF ) { + if (bSig) { + return propagateFloat32NaN(a, b, status); + } + if ( ( aExp | aSig ) == 0 ) { + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); + normalizeFloat32Subnormal( bSig, &bExp, &bSig ); + } + zExp = aExp + bExp - 0x7F; + aSig = ( aSig | 0x00800000 )<<7; + bSig = ( bSig | 0x00800000 )<<8; + shift64RightJamming( ( (uint64_t) aSig ) * bSig, 32, &zSig64 ); + zSig = zSig64; + if ( 0 <= (int32_t) ( zSig<<1 ) ) { + zSig <<= 1; + --zExp; + } + return roundAndPackFloat32(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the single-precision floating-point value `a' +| by the corresponding value `b'. The operation is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_div(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign, zSign; + int_fast16_t aExp, bExp, zExp; + uint32_t aSig, bSig, zSig; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + bSign = extractFloat32Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0xFF ) { + if (aSig) { + return propagateFloat32NaN(a, b, status); + } + if ( bExp == 0xFF ) { + if (bSig) { + return propagateFloat32NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( bExp == 0xFF ) { + if (bSig) { + return propagateFloat32NaN(a, b, status); + } + return packFloat32( zSign, 0, 0 ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + if ( ( aExp | aSig ) == 0 ) { + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + float_raise(float_flag_divbyzero, status); + return packFloat32( zSign, 0xFF, 0 ); + } + normalizeFloat32Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + zExp = aExp - bExp + 0x7D; + aSig = ( aSig | 0x00800000 )<<7; + bSig = ( bSig | 0x00800000 )<<8; + if ( bSig <= ( aSig + aSig ) ) { + aSig >>= 1; + ++zExp; + } + zSig = ( ( (uint64_t) aSig )<<32 ) / bSig; + if ( ( zSig & 0x3F ) == 0 ) { + zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 ); + } + return roundAndPackFloat32(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the single-precision floating-point value `a' +| with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_rem(float32 a, float32 b, float_status *status) +{ + flag aSign, zSign; + int_fast16_t aExp, bExp, expDiff; + uint32_t aSig, bSig; + uint32_t q; + uint64_t aSig64, bSig64, q64; + uint32_t alternateASig; + int32_t sigMean; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + if ( aExp == 0xFF ) { + if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { + return propagateFloat32NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + if ( bExp == 0xFF ) { + if (bSig) { + return propagateFloat32NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + normalizeFloat32Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return a; + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + expDiff = aExp - bExp; + aSig |= 0x00800000; + bSig |= 0x00800000; + if ( expDiff < 32 ) { + aSig <<= 8; + bSig <<= 8; + if ( expDiff < 0 ) { + if ( expDiff < -1 ) return a; + aSig >>= 1; + } + q = ( bSig <= aSig ); + if ( q ) aSig -= bSig; + if ( 0 < expDiff ) { + q = ( ( (uint64_t) aSig )<<32 ) / bSig; + q >>= 32 - expDiff; + bSig >>= 2; + aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; + } + else { + aSig >>= 2; + bSig >>= 2; + } + } + else { + if ( bSig <= aSig ) aSig -= bSig; + aSig64 = ( (uint64_t) aSig )<<40; + bSig64 = ( (uint64_t) bSig )<<40; + expDiff -= 64; + while ( 0 < expDiff ) { + q64 = estimateDiv128To64( aSig64, 0, bSig64 ); + q64 = ( 2 < q64 ) ? q64 - 2 : 0; + aSig64 = - ( ( bSig * q64 )<<38 ); + expDiff -= 62; + } + expDiff += 64; + q64 = estimateDiv128To64( aSig64, 0, bSig64 ); + q64 = ( 2 < q64 ) ? q64 - 2 : 0; + q = q64>>( 64 - expDiff ); + bSig <<= 6; + aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; + } + do { + alternateASig = aSig; + ++q; + aSig -= bSig; + } while ( 0 <= (int32_t) aSig ); + sigMean = aSig + alternateASig; + if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { + aSig = alternateASig; + } + zSign = ( (int32_t) aSig < 0 ); + if ( zSign ) aSig = - aSig; + return normalizeRoundAndPackFloat32(aSign ^ zSign, bExp, aSig, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the single-precision floating-point values +| `a' and `b' then adding 'c', with no intermediate rounding step after the +| multiplication. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic 754-2008. +| The flags argument allows the caller to select negation of the +| addend, the intermediate product, or the final result. (The difference +| between this and having the caller do a separate negation is that negating +| externally will flip the sign bit on NaNs.) +*----------------------------------------------------------------------------*/ + +float32 float32_muladd(float32 a, float32 b, float32 c, int flags, + float_status *status) +{ + flag aSign, bSign, cSign, zSign; + int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; + uint32_t aSig, bSig, cSig; + flag pInf, pZero, pSign; + uint64_t pSig64, cSig64, zSig64; + uint32_t pSig; + int shiftcount; + flag signflip, infzero; + + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + c = float32_squash_input_denormal(c, status); + aSig = extractFloat32Frac(a); + aExp = extractFloat32Exp(a); + aSign = extractFloat32Sign(a); + bSig = extractFloat32Frac(b); + bExp = extractFloat32Exp(b); + bSign = extractFloat32Sign(b); + cSig = extractFloat32Frac(c); + cExp = extractFloat32Exp(c); + cSign = extractFloat32Sign(c); + + infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) || + (aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0)); + + /* It is implementation-defined whether the cases of (0,inf,qnan) + * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN + * they return if they do), so we have to hand this information + * off to the target-specific pick-a-NaN routine. + */ + if (((aExp == 0xff) && aSig) || + ((bExp == 0xff) && bSig) || + ((cExp == 0xff) && cSig)) { + return propagateFloat32MulAddNaN(a, b, c, infzero, status); + } + + if (infzero) { + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + + if (flags & float_muladd_negate_c) { + cSign ^= 1; + } + + signflip = (flags & float_muladd_negate_result) ? 1 : 0; + + /* Work out the sign and type of the product */ + pSign = aSign ^ bSign; + if (flags & float_muladd_negate_product) { + pSign ^= 1; + } + pInf = (aExp == 0xff) || (bExp == 0xff); + pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); + + if (cExp == 0xff) { + if (pInf && (pSign ^ cSign)) { + /* addition of opposite-signed infinities => InvalidOperation */ + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + /* Otherwise generate an infinity of the same sign */ + return packFloat32(cSign ^ signflip, 0xff, 0); + } + + if (pInf) { + return packFloat32(pSign ^ signflip, 0xff, 0); + } + + if (pZero) { + if (cExp == 0) { + if (cSig == 0) { + /* Adding two exact zeroes */ + if (pSign == cSign) { + zSign = pSign; + } else if (status->float_rounding_mode == float_round_down) { + zSign = 1; + } else { + zSign = 0; + } + return packFloat32(zSign ^ signflip, 0, 0); + } + /* Exact zero plus a denorm */ + if (status->flush_to_zero) { + float_raise(float_flag_output_denormal, status); + return packFloat32(cSign ^ signflip, 0, 0); + } + } + /* Zero plus something non-zero : just return the something */ + if (flags & float_muladd_halve_result) { + if (cExp == 0) { + normalizeFloat32Subnormal(cSig, &cExp, &cSig); + } + /* Subtract one to halve, and one again because roundAndPackFloat32 + * wants one less than the true exponent. + */ + cExp -= 2; + cSig = (cSig | 0x00800000) << 7; + return roundAndPackFloat32(cSign ^ signflip, cExp, cSig, status); + } + return packFloat32(cSign ^ signflip, cExp, cSig); + } + + if (aExp == 0) { + normalizeFloat32Subnormal(aSig, &aExp, &aSig); + } + if (bExp == 0) { + normalizeFloat32Subnormal(bSig, &bExp, &bSig); + } + + /* Calculate the actual result a * b + c */ + + /* Multiply first; this is easy. */ + /* NB: we subtract 0x7e where float32_mul() subtracts 0x7f + * because we want the true exponent, not the "one-less-than" + * flavour that roundAndPackFloat32() takes. + */ + pExp = aExp + bExp - 0x7e; + aSig = (aSig | 0x00800000) << 7; + bSig = (bSig | 0x00800000) << 8; + pSig64 = (uint64_t)aSig * bSig; + if ((int64_t)(pSig64 << 1) >= 0) { + pSig64 <<= 1; + pExp--; + } + + zSign = pSign ^ signflip; + + /* Now pSig64 is the significand of the multiply, with the explicit bit in + * position 62. + */ + if (cExp == 0) { + if (!cSig) { + /* Throw out the special case of c being an exact zero now */ + shift64RightJamming(pSig64, 32, &pSig64); + pSig = pSig64; + if (flags & float_muladd_halve_result) { + pExp--; + } + return roundAndPackFloat32(zSign, pExp - 1, + pSig, status); + } + normalizeFloat32Subnormal(cSig, &cExp, &cSig); + } + + cSig64 = (uint64_t)cSig << (62 - 23); + cSig64 |= LIT64(0x4000000000000000); + expDiff = pExp - cExp; + + if (pSign == cSign) { + /* Addition */ + if (expDiff > 0) { + /* scale c to match p */ + shift64RightJamming(cSig64, expDiff, &cSig64); + zExp = pExp; + } else if (expDiff < 0) { + /* scale p to match c */ + shift64RightJamming(pSig64, -expDiff, &pSig64); + zExp = cExp; + } else { + /* no scaling needed */ + zExp = cExp; + } + /* Add significands and make sure explicit bit ends up in posn 62 */ + zSig64 = pSig64 + cSig64; + if ((int64_t)zSig64 < 0) { + shift64RightJamming(zSig64, 1, &zSig64); + } else { + zExp--; + } + } else { + /* Subtraction */ + if (expDiff > 0) { + shift64RightJamming(cSig64, expDiff, &cSig64); + zSig64 = pSig64 - cSig64; + zExp = pExp; + } else if (expDiff < 0) { + shift64RightJamming(pSig64, -expDiff, &pSig64); + zSig64 = cSig64 - pSig64; + zExp = cExp; + zSign ^= 1; + } else { + zExp = pExp; + if (cSig64 < pSig64) { + zSig64 = pSig64 - cSig64; + } else if (pSig64 < cSig64) { + zSig64 = cSig64 - pSig64; + zSign ^= 1; + } else { + /* Exact zero */ + zSign = signflip; + if (status->float_rounding_mode == float_round_down) { + zSign ^= 1; + } + return packFloat32(zSign, 0, 0); + } + } + --zExp; + /* Normalize to put the explicit bit back into bit 62. */ + shiftcount = countLeadingZeros64(zSig64) - 1; + zSig64 <<= shiftcount; + zExp -= shiftcount; + } + if (flags & float_muladd_halve_result) { + zExp--; + } + + shift64RightJamming(zSig64, 32, &zSig64); + return roundAndPackFloat32(zSign, zExp, zSig64, status); +} + + +/*---------------------------------------------------------------------------- +| Returns the square root of the single-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_sqrt(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, zExp; + uint32_t aSig, zSig; + uint64_t rem, term; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if (aSig) { + return propagateFloat32NaN(a, float32_zero, status); + } + if ( ! aSign ) return a; + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + if ( aSign ) { + if ( ( aExp | aSig ) == 0 ) return a; + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return float32_zero; + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; + aSig = ( aSig | 0x00800000 )<<8; + zSig = estimateSqrt32( aExp, aSig ) + 2; + if ( ( zSig & 0x7F ) <= 5 ) { + if ( zSig < 2 ) { + zSig = 0x7FFFFFFF; + goto roundAndPack; + } + aSig >>= aExp & 1; + term = ( (uint64_t) zSig ) * zSig; + rem = ( ( (uint64_t) aSig )<<32 ) - term; + while ( (int64_t) rem < 0 ) { + --zSig; + rem += ( ( (uint64_t) zSig )<<1 ) | 1; + } + zSig |= ( rem != 0 ); + } + shift32RightJamming( zSig, 1, &zSig ); + roundAndPack: + return roundAndPackFloat32(0, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the binary exponential of the single-precision floating-point value +| `a'. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +| +| Uses the following identities: +| +| 1. ------------------------------------------------------------------------- +| x x*ln(2) +| 2 = e +| +| 2. ------------------------------------------------------------------------- +| 2 3 4 5 n +| x x x x x x x +| e = 1 + --- + --- + --- + --- + --- + ... + --- + ... +| 1! 2! 3! 4! 5! n! +*----------------------------------------------------------------------------*/ + +static const float64 float32_exp2_coefficients[15] = +{ + const_float64( 0x3ff0000000000000ll ), /* 1 */ + const_float64( 0x3fe0000000000000ll ), /* 2 */ + const_float64( 0x3fc5555555555555ll ), /* 3 */ + const_float64( 0x3fa5555555555555ll ), /* 4 */ + const_float64( 0x3f81111111111111ll ), /* 5 */ + const_float64( 0x3f56c16c16c16c17ll ), /* 6 */ + const_float64( 0x3f2a01a01a01a01all ), /* 7 */ + const_float64( 0x3efa01a01a01a01all ), /* 8 */ + const_float64( 0x3ec71de3a556c734ll ), /* 9 */ + const_float64( 0x3e927e4fb7789f5cll ), /* 10 */ + const_float64( 0x3e5ae64567f544e4ll ), /* 11 */ + const_float64( 0x3e21eed8eff8d898ll ), /* 12 */ + const_float64( 0x3de6124613a86d09ll ), /* 13 */ + const_float64( 0x3da93974a8c07c9dll ), /* 14 */ + const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */ +}; + +float32 float32_exp2(float32 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + float64 r, x, xn; + int i; + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + + if ( aExp == 0xFF) { + if (aSig) { + return propagateFloat32NaN(a, float32_zero, status); + } + return (aSign) ? float32_zero : a; + } + if (aExp == 0) { + if (aSig == 0) return float32_one; + } + + float_raise(float_flag_inexact, status); + + /* ******************************* */ + /* using float64 for approximation */ + /* ******************************* */ + x = float32_to_float64(a, status); + x = float64_mul(x, float64_ln2, status); + + xn = x; + r = float64_one; + for (i = 0 ; i < 15 ; i++) { + float64 f; + + f = float64_mul(xn, float32_exp2_coefficients[i], status); + r = float64_add(r, f, status); + + xn = float64_mul(xn, x, status); + } + + return float64_to_float32(r, status); +} + +/*---------------------------------------------------------------------------- +| Returns the binary log of the single-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ +float32 float32_log2(float32 a, float_status *status) +{ + flag aSign, zSign; + int_fast16_t aExp; + uint32_t aSig, zSig, i; + + a = float32_squash_input_denormal(a, status); + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + if ( aSign ) { + float_raise(float_flag_invalid, status); + return float32_default_nan; + } + if ( aExp == 0xFF ) { + if (aSig) { + return propagateFloat32NaN(a, float32_zero, status); + } + return a; + } + + aExp -= 0x7F; + aSig |= 0x00800000; + zSign = aExp < 0; + zSig = aExp << 23; + + for (i = 1 << 22; i > 0; i >>= 1) { + aSig = ( (uint64_t)aSig * aSig ) >> 23; + if ( aSig & 0x01000000 ) { + aSig >>= 1; + zSig |= i; + } + } + + if ( zSign ) + zSig = -zSig; + + return normalizeRoundAndPackFloat32(zSign, 0x85, zSig, status); +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_eq(float32 a, float32 b, float_status *status) +{ + uint32_t av, bv; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + av = float32_val(a); + bv = float32_val(b); + return ( av == bv ) || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than +| or equal to the corresponding value `b', and 0 otherwise. The invalid +| exception is raised if either operand is a NaN. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_le(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign; + uint32_t av, bv; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + av = float32_val(a); + bv = float32_val(b); + if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); + return ( av == bv ) || ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. The comparison is performed according +| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_lt(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign; + uint32_t av, bv; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + av = float32_val(a); + bv = float32_val(b); + if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); + return ( av != bv ) && ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point values `a' and `b' cannot +| be compared, and 0 otherwise. The invalid exception is raised if either +| operand is a NaN. The comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_unordered(float32 a, float32 b, float_status *status) +{ + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. The comparison is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_eq_quiet(float32 a, float32 b, float_status *status) +{ + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + return ( float32_val(a) == float32_val(b) ) || + ( (uint32_t) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 ); +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than or +| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_le_quiet(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign; + uint32_t av, bv; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + av = float32_val(a); + bv = float32_val(b); + if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); + return ( av == bv ) || ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. Otherwise, the comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_lt_quiet(float32 a, float32 b, float_status *status) +{ + flag aSign, bSign; + uint32_t av, bv; + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + av = float32_val(a); + bv = float32_val(b); + if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); + return ( av != bv ) && ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point values `a' and `b' cannot +| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The +| comparison is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float32_unordered_quiet(float32 a, float32 b, float_status *status) +{ + a = float32_squash_input_denormal(a, status); + b = float32_squash_input_denormal(b, status); + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 float64_to_int32(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint64_t aSig; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; + if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x42C - aExp; + if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); + return roundAndPackInt32(aSign, aSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int32 float64_to_int32_round_to_zero(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint64_t aSig, savedASig; + int32_t z; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( 0x41E < aExp ) { + if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; + goto invalid; + } + else if ( aExp < 0x3FF ) { + if (aExp || aSig) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x433 - aExp; + savedASig = aSig; + aSig >>= shiftCount; + z = aSig; + if ( aSign ) z = - z; + if ( ( z < 0 ) ^ aSign ) { + invalid: + float_raise(float_flag_invalid, status); + return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; + } + if ( ( aSig<<shiftCount ) != savedASig ) { + status->float_exception_flags |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 16-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int_fast16_t float64_to_int16_round_to_zero(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint64_t aSig, savedASig; + int32 z; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( 0x40E < aExp ) { + if ( ( aExp == 0x7FF ) && aSig ) { + aSign = 0; + } + goto invalid; + } + else if ( aExp < 0x3FF ) { + if ( aExp || aSig ) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x433 - aExp; + savedASig = aSig; + aSig >>= shiftCount; + z = aSig; + if ( aSign ) { + z = - z; + } + if ( ( (int16_t)z < 0 ) ^ aSign ) { + invalid: + float_raise(float_flag_invalid, status); + return aSign ? (int32_t) 0xffff8000 : 0x7FFF; + } + if ( ( aSig<<shiftCount ) != savedASig ) { + status->float_exception_flags |= float_flag_inexact; + } + return z; +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 float64_to_int64(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint64_t aSig, aSigExtra; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x433 - aExp; + if ( shiftCount <= 0 ) { + if ( 0x43E < aExp ) { + float_raise(float_flag_invalid, status); + if ( ! aSign + || ( ( aExp == 0x7FF ) + && ( aSig != LIT64( 0x0010000000000000 ) ) ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + aSigExtra = 0; + aSig <<= - shiftCount; + } + else { + shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); + } + return roundAndPackInt64(aSign, aSig, aSigExtra, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int64 float64_to_int64_round_to_zero(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint64_t aSig; + int64 z; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); + shiftCount = aExp - 0x433; + if ( 0 <= shiftCount ) { + if ( 0x43E <= aExp ) { + if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) { + float_raise(float_flag_invalid, status); + if ( ! aSign + || ( ( aExp == 0x7FF ) + && ( aSig != LIT64( 0x0010000000000000 ) ) ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + z = aSig<<shiftCount; + } + else { + if ( aExp < 0x3FE ) { + if (aExp | aSig) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + z = aSig>>( - shiftCount ); + if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { + status->float_exception_flags |= float_flag_inexact; + } + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the single-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float64_to_float32(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint64_t aSig; + uint32_t zSig; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if (aSig) { + return commonNaNToFloat32(float64ToCommonNaN(a, status), status); + } + return packFloat32( aSign, 0xFF, 0 ); + } + shift64RightJamming( aSig, 22, &aSig ); + zSig = aSig; + if ( aExp || zSig ) { + zSig |= 0x40000000; + aExp -= 0x381; + } + return roundAndPackFloat32(aSign, aExp, zSig, status); + +} + + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a +| half-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 float16 packFloat16(flag zSign, int_fast16_t zExp, uint16_t zSig) +{ + return make_float16( + (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig); +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand `zSig', and returns the proper half-precision floating- +| point value corresponding to the abstract input. Ordinarily, the abstract +| value is simply rounded and packed into the half-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 half- +| precision floating-point number. +| The `ieee' flag indicates whether to use IEEE standard half precision, or +| ARM-style "alternative representation", which omits the NaN and Inf +| encodings in order to raise the maximum representable exponent by one. +| The input significand `zSig' has its binary point between bits 22 +| and 23, which is 13 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. +| Note the slightly odd position of the binary point in zSig compared with the +| other roundAndPackFloat functions. This should probably be fixed if we +| need to implement more float16 routines than just conversion. +| The handling of underflow and overflow follows the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 roundAndPackFloat16(flag zSign, int_fast16_t zExp, + uint32_t zSig, flag ieee, + float_status *status) +{ + int maxexp = ieee ? 29 : 30; + uint32_t mask; + uint32_t increment; + bool rounding_bumps_exp; + bool is_tiny = false; + + /* Calculate the mask of bits of the mantissa which are not + * representable in half-precision and will be lost. + */ + if (zExp < 1) { + /* Will be denormal in halfprec */ + mask = 0x00ffffff; + if (zExp >= -11) { + mask >>= 11 + zExp; + } + } else { + /* Normal number in halfprec */ + mask = 0x00001fff; + } + + switch (status->float_rounding_mode) { + case float_round_nearest_even: + increment = (mask + 1) >> 1; + if ((zSig & mask) == increment) { + increment = zSig & (increment << 1); + } + break; + case float_round_ties_away: + increment = (mask + 1) >> 1; + break; + case float_round_up: + increment = zSign ? 0 : mask; + break; + case float_round_down: + increment = zSign ? mask : 0; + break; + default: /* round_to_zero */ + increment = 0; + break; + } + + rounding_bumps_exp = (zSig + increment >= 0x01000000); + + if (zExp > maxexp || (zExp == maxexp && rounding_bumps_exp)) { + if (ieee) { + float_raise(float_flag_overflow | float_flag_inexact, status); + return packFloat16(zSign, 0x1f, 0); + } else { + float_raise(float_flag_invalid, status); + return packFloat16(zSign, 0x1f, 0x3ff); + } + } + + if (zExp < 0) { + /* Note that flush-to-zero does not affect half-precision results */ + is_tiny = + (status->float_detect_tininess == float_tininess_before_rounding) + || (zExp < -1) + || (!rounding_bumps_exp); + } + if (zSig & mask) { + float_raise(float_flag_inexact, status); + if (is_tiny) { + float_raise(float_flag_underflow, status); + } + } + + zSig += increment; + if (rounding_bumps_exp) { + zSig >>= 1; + zExp++; + } + + if (zExp < -10) { + return packFloat16(zSign, 0, 0); + } + if (zExp < 0) { + zSig >>= -zExp; + zExp = 0; + } + return packFloat16(zSign, zExp, zSig >> 13); +} + +static void normalizeFloat16Subnormal(uint32_t aSig, int_fast16_t *zExpPtr, + uint32_t *zSigPtr) +{ + int8_t shiftCount = countLeadingZeros32(aSig) - 21; + *zSigPtr = aSig << shiftCount; + *zExpPtr = 1 - shiftCount; +} + +/* Half precision floats come in two formats: standard IEEE and "ARM" format. + The latter gains extra exponent range by omitting the NaN/Inf encodings. */ + +float32 float16_to_float32(float16 a, flag ieee, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + + aSign = extractFloat16Sign(a); + aExp = extractFloat16Exp(a); + aSig = extractFloat16Frac(a); + + if (aExp == 0x1f && ieee) { + if (aSig) { + return commonNaNToFloat32(float16ToCommonNaN(a, status), status); + } + return packFloat32(aSign, 0xff, 0); + } + if (aExp == 0) { + if (aSig == 0) { + return packFloat32(aSign, 0, 0); + } + + normalizeFloat16Subnormal(aSig, &aExp, &aSig); + aExp--; + } + return packFloat32( aSign, aExp + 0x70, aSig << 13); +} + +float16 float32_to_float16(float32 a, flag ieee, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + + a = float32_squash_input_denormal(a, status); + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if (aSig) { + /* Input is a NaN */ + if (!ieee) { + float_raise(float_flag_invalid, status); + return packFloat16(aSign, 0, 0); + } + return commonNaNToFloat16( + float32ToCommonNaN(a, status), status); + } + /* Infinity */ + if (!ieee) { + float_raise(float_flag_invalid, status); + return packFloat16(aSign, 0x1f, 0x3ff); + } + return packFloat16(aSign, 0x1f, 0); + } + if (aExp == 0 && aSig == 0) { + return packFloat16(aSign, 0, 0); + } + /* Decimal point between bits 22 and 23. Note that we add the 1 bit + * even if the input is denormal; however this is harmless because + * the largest possible single-precision denormal is still smaller + * than the smallest representable half-precision denormal, and so we + * will end up ignoring aSig and returning via the "always return zero" + * codepath. + */ + aSig |= 0x00800000; + aExp -= 0x71; + + return roundAndPackFloat16(aSign, aExp, aSig, ieee, status); +} + +float64 float16_to_float64(float16 a, flag ieee, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint32_t aSig; + + aSign = extractFloat16Sign(a); + aExp = extractFloat16Exp(a); + aSig = extractFloat16Frac(a); + + if (aExp == 0x1f && ieee) { + if (aSig) { + return commonNaNToFloat64( + float16ToCommonNaN(a, status), status); + } + return packFloat64(aSign, 0x7ff, 0); + } + if (aExp == 0) { + if (aSig == 0) { + return packFloat64(aSign, 0, 0); + } + + normalizeFloat16Subnormal(aSig, &aExp, &aSig); + aExp--; + } + return packFloat64(aSign, aExp + 0x3f0, ((uint64_t)aSig) << 42); +} + +float16 float64_to_float16(float64 a, flag ieee, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint64_t aSig; + uint32_t zSig; + + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac(a); + aExp = extractFloat64Exp(a); + aSign = extractFloat64Sign(a); + if (aExp == 0x7FF) { + if (aSig) { + /* Input is a NaN */ + if (!ieee) { + float_raise(float_flag_invalid, status); + return packFloat16(aSign, 0, 0); + } + return commonNaNToFloat16( + float64ToCommonNaN(a, status), status); + } + /* Infinity */ + if (!ieee) { + float_raise(float_flag_invalid, status); + return packFloat16(aSign, 0x1f, 0x3ff); + } + return packFloat16(aSign, 0x1f, 0); + } + shift64RightJamming(aSig, 29, &aSig); + zSig = aSig; + if (aExp == 0 && zSig == 0) { + return packFloat16(aSign, 0, 0); + } + /* Decimal point between bits 22 and 23. Note that we add the 1 bit + * even if the input is denormal; however this is harmless because + * the largest possible single-precision denormal is still smaller + * than the smallest representable half-precision denormal, and so we + * will end up ignoring aSig and returning via the "always return zero" + * codepath. + */ + zSig |= 0x00800000; + aExp -= 0x3F1; + + return roundAndPackFloat16(aSign, aExp, zSig, ieee, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 float64_to_floatx80(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint64_t aSig; + + a = float64_squash_input_denormal(a, status); + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if (aSig) { + return commonNaNToFloatx80(float64ToCommonNaN(a, status), status); + } + return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + return + packFloatx80( + aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the quadruple-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float64_to_float128(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint64_t aSig, zSig0, zSig1; + + a = float64_squash_input_denormal(a, status); + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if (aSig) { + return commonNaNToFloat128(float64ToCommonNaN(a, status), status); + } + return packFloat128( aSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + --aExp; + } + shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); + return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); + +} + +/*---------------------------------------------------------------------------- +| Rounds the double-precision floating-point value `a' to an integer, and +| returns the result as a double-precision floating-point value. The +| operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_round_to_int(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint64_t lastBitMask, roundBitsMask; + uint64_t z; + a = float64_squash_input_denormal(a, status); + + aExp = extractFloat64Exp( a ); + if ( 0x433 <= aExp ) { + if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { + return propagateFloat64NaN(a, a, status); + } + return a; + } + if ( aExp < 0x3FF ) { + if ( (uint64_t) ( float64_val(a)<<1 ) == 0 ) return a; + status->float_exception_flags |= float_flag_inexact; + aSign = extractFloat64Sign( a ); + switch (status->float_rounding_mode) { + case float_round_nearest_even: + if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { + return packFloat64( aSign, 0x3FF, 0 ); + } + break; + case float_round_ties_away: + if (aExp == 0x3FE) { + return packFloat64(aSign, 0x3ff, 0); + } + break; + case float_round_down: + return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0); + case float_round_up: + return make_float64( + aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 )); + } + return packFloat64( aSign, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x433 - aExp; + roundBitsMask = lastBitMask - 1; + z = float64_val(a); + switch (status->float_rounding_mode) { + case float_round_nearest_even: + z += lastBitMask >> 1; + if ((z & roundBitsMask) == 0) { + z &= ~lastBitMask; + } + break; + case float_round_ties_away: + z += lastBitMask >> 1; + break; + case float_round_to_zero: + break; + case float_round_up: + if (!extractFloat64Sign(make_float64(z))) { + z += roundBitsMask; + } + break; + case float_round_down: + if (extractFloat64Sign(make_float64(z))) { + z += roundBitsMask; + } + break; + default: + abort(); + } + z &= ~ roundBitsMask; + if (z != float64_val(a)) { + status->float_exception_flags |= float_flag_inexact; + } + return make_float64(z); + +} + +float64 float64_trunc_to_int(float64 a, float_status *status) +{ + int oldmode; + float64 res; + oldmode = status->float_rounding_mode; + status->float_rounding_mode = float_round_to_zero; + res = float64_round_to_int(a, status); + status->float_rounding_mode = oldmode; + return res; +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the double-precision +| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated +| before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float64 addFloat64Sigs(float64 a, float64 b, flag zSign, + float_status *status) +{ + int_fast16_t aExp, bExp, zExp; + uint64_t aSig, bSig, zSig; + int_fast16_t expDiff; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + expDiff = aExp - bExp; + aSig <<= 9; + bSig <<= 9; + if ( 0 < expDiff ) { + if ( aExp == 0x7FF ) { + if (aSig) { + return propagateFloat64NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= LIT64( 0x2000000000000000 ); + } + shift64RightJamming( bSig, expDiff, &bSig ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0x7FF ) { + if (bSig) { + return propagateFloat64NaN(a, b, status); + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= LIT64( 0x2000000000000000 ); + } + shift64RightJamming( aSig, - expDiff, &aSig ); + zExp = bExp; + } + else { + if ( aExp == 0x7FF ) { + if (aSig | bSig) { + return propagateFloat64NaN(a, b, status); + } + return a; + } + if ( aExp == 0 ) { + if (status->flush_to_zero) { + if (aSig | bSig) { + float_raise(float_flag_output_denormal, status); + } + return packFloat64(zSign, 0, 0); + } + return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); + } + zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; + zExp = aExp; + goto roundAndPack; + } + aSig |= LIT64( 0x2000000000000000 ); + zSig = ( aSig + bSig )<<1; + --zExp; + if ( (int64_t) zSig < 0 ) { + zSig = aSig + bSig; + ++zExp; + } + roundAndPack: + return roundAndPackFloat64(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the double- +| precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float64 subFloat64Sigs(float64 a, float64 b, flag zSign, + float_status *status) +{ + int_fast16_t aExp, bExp, zExp; + uint64_t aSig, bSig, zSig; + int_fast16_t expDiff; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + expDiff = aExp - bExp; + aSig <<= 10; + bSig <<= 10; + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0x7FF ) { + if (aSig | bSig) { + return propagateFloat64NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + if ( bSig < aSig ) goto aBigger; + if ( aSig < bSig ) goto bBigger; + return packFloat64(status->float_rounding_mode == float_round_down, 0, 0); + bExpBigger: + if ( bExp == 0x7FF ) { + if (bSig) { + return propagateFloat64NaN(a, b, status); + } + return packFloat64( zSign ^ 1, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= LIT64( 0x4000000000000000 ); + } + shift64RightJamming( aSig, - expDiff, &aSig ); + bSig |= LIT64( 0x4000000000000000 ); + bBigger: + zSig = bSig - aSig; + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0x7FF ) { + if (aSig) { + return propagateFloat64NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= LIT64( 0x4000000000000000 ); + } + shift64RightJamming( bSig, expDiff, &bSig ); + aSig |= LIT64( 0x4000000000000000 ); + aBigger: + zSig = aSig - bSig; + zExp = aExp; + normalizeRoundAndPack: + --zExp; + return normalizeRoundAndPackFloat64(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the double-precision floating-point values `a' +| and `b'. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_add(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign == bSign ) { + return addFloat64Sigs(a, b, aSign, status); + } + else { + return subFloat64Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the double-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_sub(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign == bSign ) { + return subFloat64Sigs(a, b, aSign, status); + } + else { + return addFloat64Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the double-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_mul(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign, zSign; + int_fast16_t aExp, bExp, zExp; + uint64_t aSig, bSig, zSig0, zSig1; + + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + bSign = extractFloat64Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FF ) { + if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { + return propagateFloat64NaN(a, b, status); + } + if ( ( bExp | bSig ) == 0 ) { + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( bExp == 0x7FF ) { + if (bSig) { + return propagateFloat64NaN(a, b, status); + } + if ( ( aExp | aSig ) == 0 ) { + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); + normalizeFloat64Subnormal( bSig, &bExp, &bSig ); + } + zExp = aExp + bExp - 0x3FF; + aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; + bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; + mul64To128( aSig, bSig, &zSig0, &zSig1 ); + zSig0 |= ( zSig1 != 0 ); + if ( 0 <= (int64_t) ( zSig0<<1 ) ) { + zSig0 <<= 1; + --zExp; + } + return roundAndPackFloat64(zSign, zExp, zSig0, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the double-precision floating-point value `a' +| by the corresponding value `b'. The operation is performed according to +| the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_div(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign, zSign; + int_fast16_t aExp, bExp, zExp; + uint64_t aSig, bSig, zSig; + uint64_t rem0, rem1; + uint64_t term0, term1; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + bSign = extractFloat64Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FF ) { + if (aSig) { + return propagateFloat64NaN(a, b, status); + } + if ( bExp == 0x7FF ) { + if (bSig) { + return propagateFloat64NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( bExp == 0x7FF ) { + if (bSig) { + return propagateFloat64NaN(a, b, status); + } + return packFloat64( zSign, 0, 0 ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + if ( ( aExp | aSig ) == 0 ) { + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + float_raise(float_flag_divbyzero, status); + return packFloat64( zSign, 0x7FF, 0 ); + } + normalizeFloat64Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + zExp = aExp - bExp + 0x3FD; + aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; + bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; + if ( bSig <= ( aSig + aSig ) ) { + aSig >>= 1; + ++zExp; + } + zSig = estimateDiv128To64( aSig, 0, bSig ); + if ( ( zSig & 0x1FF ) <= 2 ) { + mul64To128( bSig, zSig, &term0, &term1 ); + sub128( aSig, 0, term0, term1, &rem0, &rem1 ); + while ( (int64_t) rem0 < 0 ) { + --zSig; + add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); + } + zSig |= ( rem1 != 0 ); + } + return roundAndPackFloat64(zSign, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the double-precision floating-point value `a' +| with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_rem(float64 a, float64 b, float_status *status) +{ + flag aSign, zSign; + int_fast16_t aExp, bExp, expDiff; + uint64_t aSig, bSig; + uint64_t q, alternateASig; + int64_t sigMean; + + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + if ( aExp == 0x7FF ) { + if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { + return propagateFloat64NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + if ( bExp == 0x7FF ) { + if (bSig) { + return propagateFloat64NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + normalizeFloat64Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return a; + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + expDiff = aExp - bExp; + aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; + bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; + if ( expDiff < 0 ) { + if ( expDiff < -1 ) return a; + aSig >>= 1; + } + q = ( bSig <= aSig ); + if ( q ) aSig -= bSig; + expDiff -= 64; + while ( 0 < expDiff ) { + q = estimateDiv128To64( aSig, 0, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + aSig = - ( ( bSig>>2 ) * q ); + expDiff -= 62; + } + expDiff += 64; + if ( 0 < expDiff ) { + q = estimateDiv128To64( aSig, 0, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + q >>= 64 - expDiff; + bSig >>= 2; + aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; + } + else { + aSig >>= 2; + bSig >>= 2; + } + do { + alternateASig = aSig; + ++q; + aSig -= bSig; + } while ( 0 <= (int64_t) aSig ); + sigMean = aSig + alternateASig; + if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { + aSig = alternateASig; + } + zSign = ( (int64_t) aSig < 0 ); + if ( zSign ) aSig = - aSig; + return normalizeRoundAndPackFloat64(aSign ^ zSign, bExp, aSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the double-precision floating-point values +| `a' and `b' then adding 'c', with no intermediate rounding step after the +| multiplication. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic 754-2008. +| The flags argument allows the caller to select negation of the +| addend, the intermediate product, or the final result. (The difference +| between this and having the caller do a separate negation is that negating +| externally will flip the sign bit on NaNs.) +*----------------------------------------------------------------------------*/ + +float64 float64_muladd(float64 a, float64 b, float64 c, int flags, + float_status *status) +{ + flag aSign, bSign, cSign, zSign; + int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; + uint64_t aSig, bSig, cSig; + flag pInf, pZero, pSign; + uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1; + int shiftcount; + flag signflip, infzero; + + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + c = float64_squash_input_denormal(c, status); + aSig = extractFloat64Frac(a); + aExp = extractFloat64Exp(a); + aSign = extractFloat64Sign(a); + bSig = extractFloat64Frac(b); + bExp = extractFloat64Exp(b); + bSign = extractFloat64Sign(b); + cSig = extractFloat64Frac(c); + cExp = extractFloat64Exp(c); + cSign = extractFloat64Sign(c); + + infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) || + (aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0)); + + /* It is implementation-defined whether the cases of (0,inf,qnan) + * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN + * they return if they do), so we have to hand this information + * off to the target-specific pick-a-NaN routine. + */ + if (((aExp == 0x7ff) && aSig) || + ((bExp == 0x7ff) && bSig) || + ((cExp == 0x7ff) && cSig)) { + return propagateFloat64MulAddNaN(a, b, c, infzero, status); + } + + if (infzero) { + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + + if (flags & float_muladd_negate_c) { + cSign ^= 1; + } + + signflip = (flags & float_muladd_negate_result) ? 1 : 0; + + /* Work out the sign and type of the product */ + pSign = aSign ^ bSign; + if (flags & float_muladd_negate_product) { + pSign ^= 1; + } + pInf = (aExp == 0x7ff) || (bExp == 0x7ff); + pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); + + if (cExp == 0x7ff) { + if (pInf && (pSign ^ cSign)) { + /* addition of opposite-signed infinities => InvalidOperation */ + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + /* Otherwise generate an infinity of the same sign */ + return packFloat64(cSign ^ signflip, 0x7ff, 0); + } + + if (pInf) { + return packFloat64(pSign ^ signflip, 0x7ff, 0); + } + + if (pZero) { + if (cExp == 0) { + if (cSig == 0) { + /* Adding two exact zeroes */ + if (pSign == cSign) { + zSign = pSign; + } else if (status->float_rounding_mode == float_round_down) { + zSign = 1; + } else { + zSign = 0; + } + return packFloat64(zSign ^ signflip, 0, 0); + } + /* Exact zero plus a denorm */ + if (status->flush_to_zero) { + float_raise(float_flag_output_denormal, status); + return packFloat64(cSign ^ signflip, 0, 0); + } + } + /* Zero plus something non-zero : just return the something */ + if (flags & float_muladd_halve_result) { + if (cExp == 0) { + normalizeFloat64Subnormal(cSig, &cExp, &cSig); + } + /* Subtract one to halve, and one again because roundAndPackFloat64 + * wants one less than the true exponent. + */ + cExp -= 2; + cSig = (cSig | 0x0010000000000000ULL) << 10; + return roundAndPackFloat64(cSign ^ signflip, cExp, cSig, status); + } + return packFloat64(cSign ^ signflip, cExp, cSig); + } + + if (aExp == 0) { + normalizeFloat64Subnormal(aSig, &aExp, &aSig); + } + if (bExp == 0) { + normalizeFloat64Subnormal(bSig, &bExp, &bSig); + } + + /* Calculate the actual result a * b + c */ + + /* Multiply first; this is easy. */ + /* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff + * because we want the true exponent, not the "one-less-than" + * flavour that roundAndPackFloat64() takes. + */ + pExp = aExp + bExp - 0x3fe; + aSig = (aSig | LIT64(0x0010000000000000))<<10; + bSig = (bSig | LIT64(0x0010000000000000))<<11; + mul64To128(aSig, bSig, &pSig0, &pSig1); + if ((int64_t)(pSig0 << 1) >= 0) { + shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1); + pExp--; + } + + zSign = pSign ^ signflip; + + /* Now [pSig0:pSig1] is the significand of the multiply, with the explicit + * bit in position 126. + */ + if (cExp == 0) { + if (!cSig) { + /* Throw out the special case of c being an exact zero now */ + shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1); + if (flags & float_muladd_halve_result) { + pExp--; + } + return roundAndPackFloat64(zSign, pExp - 1, + pSig1, status); + } + normalizeFloat64Subnormal(cSig, &cExp, &cSig); + } + + /* Shift cSig and add the explicit bit so [cSig0:cSig1] is the + * significand of the addend, with the explicit bit in position 126. + */ + cSig0 = cSig << (126 - 64 - 52); + cSig1 = 0; + cSig0 |= LIT64(0x4000000000000000); + expDiff = pExp - cExp; + + if (pSign == cSign) { + /* Addition */ + if (expDiff > 0) { + /* scale c to match p */ + shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); + zExp = pExp; + } else if (expDiff < 0) { + /* scale p to match c */ + shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); + zExp = cExp; + } else { + /* no scaling needed */ + zExp = cExp; + } + /* Add significands and make sure explicit bit ends up in posn 126 */ + add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); + if ((int64_t)zSig0 < 0) { + shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1); + } else { + zExp--; + } + shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1); + if (flags & float_muladd_halve_result) { + zExp--; + } + return roundAndPackFloat64(zSign, zExp, zSig1, status); + } else { + /* Subtraction */ + if (expDiff > 0) { + shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); + sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); + zExp = pExp; + } else if (expDiff < 0) { + shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); + sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); + zExp = cExp; + zSign ^= 1; + } else { + zExp = pExp; + if (lt128(cSig0, cSig1, pSig0, pSig1)) { + sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); + } else if (lt128(pSig0, pSig1, cSig0, cSig1)) { + sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); + zSign ^= 1; + } else { + /* Exact zero */ + zSign = signflip; + if (status->float_rounding_mode == float_round_down) { + zSign ^= 1; + } + return packFloat64(zSign, 0, 0); + } + } + --zExp; + /* Do the equivalent of normalizeRoundAndPackFloat64() but + * starting with the significand in a pair of uint64_t. + */ + if (zSig0) { + shiftcount = countLeadingZeros64(zSig0) - 1; + shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1); + if (zSig1) { + zSig0 |= 1; + } + zExp -= shiftcount; + } else { + shiftcount = countLeadingZeros64(zSig1); + if (shiftcount == 0) { + zSig0 = (zSig1 >> 1) | (zSig1 & 1); + zExp -= 63; + } else { + shiftcount--; + zSig0 = zSig1 << shiftcount; + zExp -= (shiftcount + 64); + } + } + if (flags & float_muladd_halve_result) { + zExp--; + } + return roundAndPackFloat64(zSign, zExp, zSig0, status); + } +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the double-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_sqrt(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, zExp; + uint64_t aSig, zSig, doubleZSig; + uint64_t rem0, rem1, term0, term1; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if (aSig) { + return propagateFloat64NaN(a, a, status); + } + if ( ! aSign ) return a; + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + if ( aSign ) { + if ( ( aExp | aSig ) == 0 ) return a; + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return float64_zero; + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; + aSig |= LIT64( 0x0010000000000000 ); + zSig = estimateSqrt32( aExp, aSig>>21 ); + aSig <<= 9 - ( aExp & 1 ); + zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); + if ( ( zSig & 0x1FF ) <= 5 ) { + doubleZSig = zSig<<1; + mul64To128( zSig, zSig, &term0, &term1 ); + sub128( aSig, 0, term0, term1, &rem0, &rem1 ); + while ( (int64_t) rem0 < 0 ) { + --zSig; + doubleZSig -= 2; + add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); + } + zSig |= ( ( rem0 | rem1 ) != 0 ); + } + return roundAndPackFloat64(0, zExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the binary log of the double-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ +float64 float64_log2(float64 a, float_status *status) +{ + flag aSign, zSign; + int_fast16_t aExp; + uint64_t aSig, aSig0, aSig1, zSig, i; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + if ( aSign ) { + float_raise(float_flag_invalid, status); + return float64_default_nan; + } + if ( aExp == 0x7FF ) { + if (aSig) { + return propagateFloat64NaN(a, float64_zero, status); + } + return a; + } + + aExp -= 0x3FF; + aSig |= LIT64( 0x0010000000000000 ); + zSign = aExp < 0; + zSig = (uint64_t)aExp << 52; + for (i = 1LL << 51; i > 0; i >>= 1) { + mul64To128( aSig, aSig, &aSig0, &aSig1 ); + aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 ); + if ( aSig & LIT64( 0x0020000000000000 ) ) { + aSig >>= 1; + zSig |= i; + } + } + + if ( zSign ) + zSig = -zSig; + return normalizeRoundAndPackFloat64(zSign, 0x408, zSig, status); +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is equal to the +| corresponding value `b', and 0 otherwise. The invalid exception is raised +| if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_eq(float64 a, float64 b, float_status *status) +{ + uint64_t av, bv; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + av = float64_val(a); + bv = float64_val(b); + return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than or +| equal to the corresponding value `b', and 0 otherwise. The invalid +| exception is raised if either operand is a NaN. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_le(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign; + uint64_t av, bv; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + av = float64_val(a); + bv = float64_val(b); + if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); + return ( av == bv ) || ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. The comparison is performed according +| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_lt(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign; + uint64_t av, bv; + + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + av = float64_val(a); + bv = float64_val(b); + if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); + return ( av != bv ) && ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point values `a' and `b' cannot +| be compared, and 0 otherwise. The invalid exception is raised if either +| operand is a NaN. The comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_unordered(float64 a, float64 b, float_status *status) +{ + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise(float_flag_invalid, status); + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is equal to the +| corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception.The comparison is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_eq_quiet(float64 a, float64 b, float_status *status) +{ + uint64_t av, bv; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + av = float64_val(a); + bv = float64_val(b); + return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than or +| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_le_quiet(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign; + uint64_t av, bv; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + av = float64_val(a); + bv = float64_val(b); + if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); + return ( av == bv ) || ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. Otherwise, the comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_lt_quiet(float64 a, float64 b, float_status *status) +{ + flag aSign, bSign; + uint64_t av, bv; + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + av = float64_val(a); + bv = float64_val(b); + if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); + return ( av != bv ) && ( aSign ^ ( av < bv ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point values `a' and `b' cannot +| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The +| comparison is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float64_unordered_quiet(float64 a, float64 b, float_status *status) +{ + a = float64_squash_input_denormal(a, status); + b = float64_squash_input_denormal(b, status); + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 32-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic---which means in particular that the conversion +| is rounded according to the current rounding mode. If `a' is a NaN, the +| largest positive integer is returned. Otherwise, if the conversion +| overflows, the largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 floatx80_to_int32(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; + shiftCount = 0x4037 - aExp; + if ( shiftCount <= 0 ) shiftCount = 1; + shift64RightJamming( aSig, shiftCount, &aSig ); + return roundAndPackInt32(aSign, aSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 32-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic, except that the conversion is always rounded +| toward zero. If `a' is a NaN, the largest positive integer is returned. +| Otherwise, if the conversion overflows, the largest integer with the same +| sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 floatx80_to_int32_round_to_zero(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig, savedASig; + int32_t z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( 0x401E < aExp ) { + if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; + goto invalid; + } + else if ( aExp < 0x3FFF ) { + if (aExp || aSig) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + shiftCount = 0x403E - aExp; + savedASig = aSig; + aSig >>= shiftCount; + z = aSig; + if ( aSign ) z = - z; + if ( ( z < 0 ) ^ aSign ) { + invalid: + float_raise(float_flag_invalid, status); + return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; + } + if ( ( aSig<<shiftCount ) != savedASig ) { + status->float_exception_flags |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 64-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic---which means in particular that the conversion +| is rounded according to the current rounding mode. If `a' is a NaN, +| the largest positive integer is returned. Otherwise, if the conversion +| overflows, the largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 floatx80_to_int64(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig, aSigExtra; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + shiftCount = 0x403E - aExp; + if ( shiftCount <= 0 ) { + if ( shiftCount ) { + float_raise(float_flag_invalid, status); + if ( ! aSign + || ( ( aExp == 0x7FFF ) + && ( aSig != LIT64( 0x8000000000000000 ) ) ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + aSigExtra = 0; + } + else { + shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); + } + return roundAndPackInt64(aSign, aSig, aSigExtra, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 64-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic, except that the conversion is always rounded +| toward zero. If `a' is a NaN, the largest positive integer is returned. +| Otherwise, if the conversion overflows, the largest integer with the same +| sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 floatx80_to_int64_round_to_zero(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig; + int64 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + shiftCount = aExp - 0x403E; + if ( 0 <= shiftCount ) { + aSig &= LIT64( 0x7FFFFFFFFFFFFFFF ); + if ( ( a.high != 0xC03E ) || aSig ) { + float_raise(float_flag_invalid, status); + if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + else if ( aExp < 0x3FFF ) { + if (aExp | aSig) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + z = aSig>>( - shiftCount ); + if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { + status->float_exception_flags |= float_flag_inexact; + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the single-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 floatx80_to_float32(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t aSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( aExp == 0x7FFF ) { + if ( (uint64_t) ( aSig<<1 ) ) { + return commonNaNToFloat32(floatx80ToCommonNaN(a, status), status); + } + return packFloat32( aSign, 0xFF, 0 ); + } + shift64RightJamming( aSig, 33, &aSig ); + if ( aExp || aSig ) aExp -= 0x3F81; + return roundAndPackFloat32(aSign, aExp, aSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the double-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 floatx80_to_float64(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t aSig, zSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( aExp == 0x7FFF ) { + if ( (uint64_t) ( aSig<<1 ) ) { + return commonNaNToFloat64(floatx80ToCommonNaN(a, status), status); + } + return packFloat64( aSign, 0x7FF, 0 ); + } + shift64RightJamming( aSig, 1, &zSig ); + if ( aExp || aSig ) aExp -= 0x3C01; + return roundAndPackFloat64(aSign, aExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the quadruple-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 floatx80_to_float128(floatx80 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp; + uint64_t aSig, zSig0, zSig1; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) { + return commonNaNToFloat128(floatx80ToCommonNaN(a, status), status); + } + shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); + return packFloat128( aSign, aExp, zSig0, zSig1 ); + +} + +/*---------------------------------------------------------------------------- +| Rounds the extended double-precision floating-point value `a' to an integer, +| and returns the result as an extended quadruple-precision floating-point +| value. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_round_to_int(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t lastBitMask, roundBitsMask; + floatx80 z; + + aExp = extractFloatx80Exp( a ); + if ( 0x403E <= aExp ) { + if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) { + return propagateFloatx80NaN(a, a, status); + } + return a; + } + if ( aExp < 0x3FFF ) { + if ( ( aExp == 0 ) + && ( (uint64_t) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { + return a; + } + status->float_exception_flags |= float_flag_inexact; + aSign = extractFloatx80Sign( a ); + switch (status->float_rounding_mode) { + case float_round_nearest_even: + if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) + ) { + return + packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); + } + break; + case float_round_ties_away: + if (aExp == 0x3FFE) { + return packFloatx80(aSign, 0x3FFF, LIT64(0x8000000000000000)); + } + break; + case float_round_down: + return + aSign ? + packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) + : packFloatx80( 0, 0, 0 ); + case float_round_up: + return + aSign ? packFloatx80( 1, 0, 0 ) + : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); + } + return packFloatx80( aSign, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x403E - aExp; + roundBitsMask = lastBitMask - 1; + z = a; + switch (status->float_rounding_mode) { + case float_round_nearest_even: + z.low += lastBitMask>>1; + if ((z.low & roundBitsMask) == 0) { + z.low &= ~lastBitMask; + } + break; + case float_round_ties_away: + z.low += lastBitMask >> 1; + break; + case float_round_to_zero: + break; + case float_round_up: + if (!extractFloatx80Sign(z)) { + z.low += roundBitsMask; + } + break; + case float_round_down: + if (extractFloatx80Sign(z)) { + z.low += roundBitsMask; + } + break; + default: + abort(); + } + z.low &= ~ roundBitsMask; + if ( z.low == 0 ) { + ++z.high; + z.low = LIT64( 0x8000000000000000 ); + } + if (z.low != a.low) { + status->float_exception_flags |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the extended double- +| precision floating-point values `a' and `b'. If `zSign' is 1, the sum is +| negated before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static floatx80 addFloatx80Sigs(floatx80 a, floatx80 b, flag zSign, + float_status *status) +{ + int32 aExp, bExp, zExp; + uint64_t aSig, bSig, zSig0, zSig1; + int32 expDiff; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + expDiff = aExp - bExp; + if ( 0 < expDiff ) { + if ( aExp == 0x7FFF ) { + if ((uint64_t)(aSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) --expDiff; + shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0x7FFF ) { + if ((uint64_t)(bSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) ++expDiff; + shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); + zExp = bExp; + } + else { + if ( aExp == 0x7FFF ) { + if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { + return propagateFloatx80NaN(a, b, status); + } + return a; + } + zSig1 = 0; + zSig0 = aSig + bSig; + if ( aExp == 0 ) { + normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); + goto roundAndPack; + } + zExp = aExp; + goto shiftRight1; + } + zSig0 = aSig + bSig; + if ( (int64_t) zSig0 < 0 ) goto roundAndPack; + shiftRight1: + shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); + zSig0 |= LIT64( 0x8000000000000000 ); + ++zExp; + roundAndPack: + return roundAndPackFloatx80(status->floatx80_rounding_precision, + zSign, zExp, zSig0, zSig1, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the extended +| double-precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static floatx80 subFloatx80Sigs(floatx80 a, floatx80 b, flag zSign, + float_status *status) +{ + int32 aExp, bExp, zExp; + uint64_t aSig, bSig, zSig0, zSig1; + int32 expDiff; + floatx80 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + expDiff = aExp - bExp; + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0x7FFF ) { + if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { + return propagateFloatx80NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + zSig1 = 0; + if ( bSig < aSig ) goto aBigger; + if ( aSig < bSig ) goto bBigger; + return packFloatx80(status->float_rounding_mode == float_round_down, 0, 0); + bExpBigger: + if ( bExp == 0x7FFF ) { + if ((uint64_t)(bSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) ++expDiff; + shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); + bBigger: + sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0x7FFF ) { + if ((uint64_t)(aSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) --expDiff; + shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); + aBigger: + sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); + zExp = aExp; + normalizeRoundAndPack: + return normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision, + zSign, zExp, zSig0, zSig1, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the extended double-precision floating-point +| values `a' and `b'. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_add(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign; + + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign == bSign ) { + return addFloatx80Sigs(a, b, aSign, status); + } + else { + return subFloatx80Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the extended double-precision floating- +| point values `a' and `b'. The operation is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_sub(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign; + + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign == bSign ) { + return subFloatx80Sigs(a, b, aSign, status); + } + else { + return addFloatx80Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the extended double-precision floating- +| point values `a' and `b'. The operation is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_mul(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + uint64_t aSig, bSig, zSig0, zSig1; + floatx80 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + bSign = extractFloatx80Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ( (uint64_t) ( aSig<<1 ) + || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { + return propagateFloatx80NaN(a, b, status); + } + if ( ( bExp | bSig ) == 0 ) goto invalid; + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( bExp == 0x7FFF ) { + if ((uint64_t)(bSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + if ( ( aExp | aSig ) == 0 ) { + invalid: + float_raise(float_flag_invalid, status); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); + normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); + normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); + } + zExp = aExp + bExp - 0x3FFE; + mul64To128( aSig, bSig, &zSig0, &zSig1 ); + if ( 0 < (int64_t) zSig0 ) { + shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); + --zExp; + } + return roundAndPackFloatx80(status->floatx80_rounding_precision, + zSign, zExp, zSig0, zSig1, status); +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the extended double-precision floating-point +| value `a' by the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + uint64_t aSig, bSig, zSig0, zSig1; + uint64_t rem0, rem1, rem2, term0, term1, term2; + floatx80 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + bSign = extractFloatx80Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ((uint64_t)(aSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + if ( bExp == 0x7FFF ) { + if ((uint64_t)(bSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + goto invalid; + } + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( bExp == 0x7FFF ) { + if ((uint64_t)(bSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + return packFloatx80( zSign, 0, 0 ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + if ( ( aExp | aSig ) == 0 ) { + invalid: + float_raise(float_flag_invalid, status); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + float_raise(float_flag_divbyzero, status); + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); + normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); + } + zExp = aExp - bExp + 0x3FFE; + rem1 = 0; + if ( bSig <= aSig ) { + shift128Right( aSig, 0, 1, &aSig, &rem1 ); + ++zExp; + } + zSig0 = estimateDiv128To64( aSig, rem1, bSig ); + mul64To128( bSig, zSig0, &term0, &term1 ); + sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); + while ( (int64_t) rem0 < 0 ) { + --zSig0; + add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); + } + zSig1 = estimateDiv128To64( rem1, 0, bSig ); + if ( (uint64_t) ( zSig1<<1 ) <= 8 ) { + mul64To128( bSig, zSig1, &term1, &term2 ); + sub128( rem1, 0, term1, term2, &rem1, &rem2 ); + while ( (int64_t) rem1 < 0 ) { + --zSig1; + add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); + } + zSig1 |= ( ( rem1 | rem2 ) != 0 ); + } + return roundAndPackFloatx80(status->floatx80_rounding_precision, + zSign, zExp, zSig0, zSig1, status); +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the extended double-precision floating-point value +| `a' with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_rem(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, zSign; + int32 aExp, bExp, expDiff; + uint64_t aSig0, aSig1, bSig; + uint64_t q, term0, term1, alternateASig0, alternateASig1; + floatx80 z; + + aSig0 = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + if ( aExp == 0x7FFF ) { + if ( (uint64_t) ( aSig0<<1 ) + || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { + return propagateFloatx80NaN(a, b, status); + } + goto invalid; + } + if ( bExp == 0x7FFF ) { + if ((uint64_t)(bSig << 1)) { + return propagateFloatx80NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + invalid: + float_raise(float_flag_invalid, status); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a; + normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); + } + bSig |= LIT64( 0x8000000000000000 ); + zSign = aSign; + expDiff = aExp - bExp; + aSig1 = 0; + if ( expDiff < 0 ) { + if ( expDiff < -1 ) return a; + shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); + expDiff = 0; + } + q = ( bSig <= aSig0 ); + if ( q ) aSig0 -= bSig; + expDiff -= 64; + while ( 0 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + mul64To128( bSig, q, &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); + shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); + expDiff -= 62; + } + expDiff += 64; + if ( 0 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + q >>= 64 - expDiff; + mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); + shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); + while ( le128( term0, term1, aSig0, aSig1 ) ) { + ++q; + sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); + } + } + else { + term1 = 0; + term0 = bSig; + } + sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); + if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) + || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) + && ( q & 1 ) ) + ) { + aSig0 = alternateASig0; + aSig1 = alternateASig1; + zSign = ! zSign; + } + return + normalizeRoundAndPackFloatx80( + 80, zSign, bExp + expDiff, aSig0, aSig1, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the extended double-precision floating-point +| value `a'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_sqrt(floatx80 a, float_status *status) +{ + flag aSign; + int32 aExp, zExp; + uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0; + uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; + floatx80 z; + + aSig0 = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( aExp == 0x7FFF ) { + if ((uint64_t)(aSig0 << 1)) { + return propagateFloatx80NaN(a, a, status); + } + if ( ! aSign ) return a; + goto invalid; + } + if ( aSign ) { + if ( ( aExp | aSig0 ) == 0 ) return a; + invalid: + float_raise(float_flag_invalid, status); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + if ( aExp == 0 ) { + if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); + normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); + } + zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; + zSig0 = estimateSqrt32( aExp, aSig0>>32 ); + shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); + zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); + doubleZSig0 = zSig0<<1; + mul64To128( zSig0, zSig0, &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); + while ( (int64_t) rem0 < 0 ) { + --zSig0; + doubleZSig0 -= 2; + add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); + } + zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); + if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { + if ( zSig1 == 0 ) zSig1 = 1; + mul64To128( doubleZSig0, zSig1, &term1, &term2 ); + sub128( rem1, 0, term1, term2, &rem1, &rem2 ); + mul64To128( zSig1, zSig1, &term2, &term3 ); + sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); + while ( (int64_t) rem1 < 0 ) { + --zSig1; + shortShift128Left( 0, zSig1, 1, &term2, &term3 ); + term3 |= 1; + term2 |= doubleZSig0; + add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); + } + zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); + } + shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); + zSig0 |= doubleZSig0; + return roundAndPackFloatx80(status->floatx80_rounding_precision, + 0, zExp, zSig0, zSig1, status); +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is equal +| to the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int floatx80_eq(floatx80 a, floatx80 b, float_status *status) +{ + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is +| less than or equal to the corresponding value `b', and 0 otherwise. The +| invalid exception is raised if either operand is a NaN. The comparison is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +int floatx80_le(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is +| less than the corresponding value `b', and 0 otherwise. The invalid +| exception is raised if either operand is a NaN. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int floatx80_lt(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point values `a' and `b' +| cannot be compared, and 0 otherwise. The invalid exception is raised if +| either operand is a NaN. The comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ +int floatx80_unordered(floatx80 a, floatx80 b, float_status *status) +{ + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise(float_flag_invalid, status); + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is +| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. The comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int floatx80_eq_quiet(floatx80 a, floatx80 b, float_status *status) +{ + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is less +| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs +| do not cause an exception. Otherwise, the comparison is performed according +| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int floatx80_le_quiet(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is less +| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause +| an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point values `a' and `b' +| cannot be compared, and 0 otherwise. Quiet NaNs do not cause an exception. +| The comparison is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ +int floatx80_unordered_quiet(floatx80 a, floatx80 b, float_status *status) +{ + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 32-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 float128_to_int32(float128 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; + if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); + aSig0 |= ( aSig1 != 0 ); + shiftCount = 0x4028 - aExp; + if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); + return roundAndPackInt32(aSign, aSig0, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 32-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. If +| `a' is a NaN, the largest positive integer is returned. Otherwise, if the +| conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int32 float128_to_int32_round_to_zero(float128 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig0, aSig1, savedASig; + int32_t z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + aSig0 |= ( aSig1 != 0 ); + if ( 0x401E < aExp ) { + if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; + goto invalid; + } + else if ( aExp < 0x3FFF ) { + if (aExp || aSig0) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + aSig0 |= LIT64( 0x0001000000000000 ); + shiftCount = 0x402F - aExp; + savedASig = aSig0; + aSig0 >>= shiftCount; + z = aSig0; + if ( aSign ) z = - z; + if ( ( z < 0 ) ^ aSign ) { + invalid: + float_raise(float_flag_invalid, status); + return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; + } + if ( ( aSig0<<shiftCount ) != savedASig ) { + status->float_exception_flags |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 64-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 float128_to_int64(float128 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); + shiftCount = 0x402F - aExp; + if ( shiftCount <= 0 ) { + if ( 0x403E < aExp ) { + float_raise(float_flag_invalid, status); + if ( ! aSign + || ( ( aExp == 0x7FFF ) + && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) + ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); + } + else { + shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); + } + return roundAndPackInt64(aSign, aSig0, aSig1, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 64-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int64 float128_to_int64_round_to_zero(float128 a, float_status *status) +{ + flag aSign; + int32 aExp, shiftCount; + uint64_t aSig0, aSig1; + int64 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); + shiftCount = aExp - 0x402F; + if ( 0 < shiftCount ) { + if ( 0x403E <= aExp ) { + aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); + if ( ( a.high == LIT64( 0xC03E000000000000 ) ) + && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { + if (aSig1) { + status->float_exception_flags |= float_flag_inexact; + } + } + else { + float_raise(float_flag_invalid, status); + if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (int64_t) LIT64( 0x8000000000000000 ); + } + z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); + if ( (uint64_t) ( aSig1<<shiftCount ) ) { + status->float_exception_flags |= float_flag_inexact; + } + } + else { + if ( aExp < 0x3FFF ) { + if ( aExp | aSig0 | aSig1 ) { + status->float_exception_flags |= float_flag_inexact; + } + return 0; + } + z = aSig0>>( - shiftCount ); + if ( aSig1 + || ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) { + status->float_exception_flags |= float_flag_inexact; + } + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the single-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float128_to_float32(float128 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t aSig0, aSig1; + uint32_t zSig; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return commonNaNToFloat32(float128ToCommonNaN(a, status), status); + } + return packFloat32( aSign, 0xFF, 0 ); + } + aSig0 |= ( aSig1 != 0 ); + shift64RightJamming( aSig0, 18, &aSig0 ); + zSig = aSig0; + if ( aExp || zSig ) { + zSig |= 0x40000000; + aExp -= 0x3F81; + } + return roundAndPackFloat32(aSign, aExp, zSig, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float128_to_float64(float128 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return commonNaNToFloat64(float128ToCommonNaN(a, status), status); + } + return packFloat64( aSign, 0x7FF, 0 ); + } + shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); + aSig0 |= ( aSig1 != 0 ); + if ( aExp || aSig0 ) { + aSig0 |= LIT64( 0x4000000000000000 ); + aExp -= 0x3C01; + } + return roundAndPackFloat64(aSign, aExp, aSig0, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the extended double-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 float128_to_floatx80(float128 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return commonNaNToFloatx80(float128ToCommonNaN(a, status), status); + } + return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + else { + aSig0 |= LIT64( 0x0001000000000000 ); + } + shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); + return roundAndPackFloatx80(80, aSign, aExp, aSig0, aSig1, status); + +} + +/*---------------------------------------------------------------------------- +| Rounds the quadruple-precision floating-point value `a' to an integer, and +| returns the result as a quadruple-precision floating-point value. The +| operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_round_to_int(float128 a, float_status *status) +{ + flag aSign; + int32 aExp; + uint64_t lastBitMask, roundBitsMask; + float128 z; + + aExp = extractFloat128Exp( a ); + if ( 0x402F <= aExp ) { + if ( 0x406F <= aExp ) { + if ( ( aExp == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) + ) { + return propagateFloat128NaN(a, a, status); + } + return a; + } + lastBitMask = 1; + lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; + roundBitsMask = lastBitMask - 1; + z = a; + switch (status->float_rounding_mode) { + case float_round_nearest_even: + if ( lastBitMask ) { + add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); + if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; + } + else { + if ( (int64_t) z.low < 0 ) { + ++z.high; + if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1; + } + } + break; + case float_round_ties_away: + if (lastBitMask) { + add128(z.high, z.low, 0, lastBitMask >> 1, &z.high, &z.low); + } else { + if ((int64_t) z.low < 0) { + ++z.high; + } + } + break; + case float_round_to_zero: + break; + case float_round_up: + if (!extractFloat128Sign(z)) { + add128(z.high, z.low, 0, roundBitsMask, &z.high, &z.low); + } + break; + case float_round_down: + if (extractFloat128Sign(z)) { + add128(z.high, z.low, 0, roundBitsMask, &z.high, &z.low); + } + break; + default: + abort(); + } + z.low &= ~ roundBitsMask; + } + else { + if ( aExp < 0x3FFF ) { + if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a; + status->float_exception_flags |= float_flag_inexact; + aSign = extractFloat128Sign( a ); + switch (status->float_rounding_mode) { + case float_round_nearest_even: + if ( ( aExp == 0x3FFE ) + && ( extractFloat128Frac0( a ) + | extractFloat128Frac1( a ) ) + ) { + return packFloat128( aSign, 0x3FFF, 0, 0 ); + } + break; + case float_round_ties_away: + if (aExp == 0x3FFE) { + return packFloat128(aSign, 0x3FFF, 0, 0); + } + break; + case float_round_down: + return + aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) + : packFloat128( 0, 0, 0, 0 ); + case float_round_up: + return + aSign ? packFloat128( 1, 0, 0, 0 ) + : packFloat128( 0, 0x3FFF, 0, 0 ); + } + return packFloat128( aSign, 0, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x402F - aExp; + roundBitsMask = lastBitMask - 1; + z.low = 0; + z.high = a.high; + switch (status->float_rounding_mode) { + case float_round_nearest_even: + z.high += lastBitMask>>1; + if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { + z.high &= ~ lastBitMask; + } + break; + case float_round_ties_away: + z.high += lastBitMask>>1; + break; + case float_round_to_zero: + break; + case float_round_up: + if (!extractFloat128Sign(z)) { + z.high |= ( a.low != 0 ); + z.high += roundBitsMask; + } + break; + case float_round_down: + if (extractFloat128Sign(z)) { + z.high |= (a.low != 0); + z.high += roundBitsMask; + } + break; + default: + abort(); + } + z.high &= ~ roundBitsMask; + } + if ( ( z.low != a.low ) || ( z.high != a.high ) ) { + status->float_exception_flags |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the quadruple-precision +| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated +| before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float128 addFloat128Sigs(float128 a, float128 b, flag zSign, + float_status *status) +{ + int32 aExp, bExp, zExp; + uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; + int32 expDiff; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + expDiff = aExp - bExp; + if ( 0 < expDiff ) { + if ( aExp == 0x7FFF ) { + if (aSig0 | aSig1) { + return propagateFloat128NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig0 |= LIT64( 0x0001000000000000 ); + } + shift128ExtraRightJamming( + bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0x7FFF ) { + if (bSig0 | bSig1) { + return propagateFloat128NaN(a, b, status); + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig0 |= LIT64( 0x0001000000000000 ); + } + shift128ExtraRightJamming( + aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); + zExp = bExp; + } + else { + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 | bSig0 | bSig1 ) { + return propagateFloat128NaN(a, b, status); + } + return a; + } + add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); + if ( aExp == 0 ) { + if (status->flush_to_zero) { + if (zSig0 | zSig1) { + float_raise(float_flag_output_denormal, status); + } + return packFloat128(zSign, 0, 0, 0); + } + return packFloat128( zSign, 0, zSig0, zSig1 ); + } + zSig2 = 0; + zSig0 |= LIT64( 0x0002000000000000 ); + zExp = aExp; + goto shiftRight1; + } + aSig0 |= LIT64( 0x0001000000000000 ); + add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); + --zExp; + if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; + ++zExp; + shiftRight1: + shift128ExtraRightJamming( + zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); + roundAndPack: + return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the quadruple- +| precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float128 subFloat128Sigs(float128 a, float128 b, flag zSign, + float_status *status) +{ + int32 aExp, bExp, zExp; + uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; + int32 expDiff; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + expDiff = aExp - bExp; + shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); + shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 | bSig0 | bSig1 ) { + return propagateFloat128NaN(a, b, status); + } + float_raise(float_flag_invalid, status); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + if ( bSig0 < aSig0 ) goto aBigger; + if ( aSig0 < bSig0 ) goto bBigger; + if ( bSig1 < aSig1 ) goto aBigger; + if ( aSig1 < bSig1 ) goto bBigger; + return packFloat128(status->float_rounding_mode == float_round_down, + 0, 0, 0); + bExpBigger: + if ( bExp == 0x7FFF ) { + if (bSig0 | bSig1) { + return propagateFloat128NaN(a, b, status); + } + return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig0 |= LIT64( 0x4000000000000000 ); + } + shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); + bSig0 |= LIT64( 0x4000000000000000 ); + bBigger: + sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0x7FFF ) { + if (aSig0 | aSig1) { + return propagateFloat128NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig0 |= LIT64( 0x4000000000000000 ); + } + shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); + aSig0 |= LIT64( 0x4000000000000000 ); + aBigger: + sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); + zExp = aExp; + normalizeRoundAndPack: + --zExp; + return normalizeRoundAndPackFloat128(zSign, zExp - 14, zSig0, zSig1, + status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the quadruple-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_add(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign; + + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign == bSign ) { + return addFloat128Sigs(a, b, aSign, status); + } + else { + return subFloat128Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the quadruple-precision floating-point +| values `a' and `b'. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_sub(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign; + + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign == bSign ) { + return subFloat128Sigs(a, b, aSign, status); + } + else { + return addFloat128Sigs(a, b, aSign, status); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the quadruple-precision floating-point +| values `a' and `b'. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_mul(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + bSign = extractFloat128Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ( ( aSig0 | aSig1 ) + || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { + return propagateFloat128NaN(a, b, status); + } + if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( bExp == 0x7FFF ) { + if (bSig0 | bSig1) { + return propagateFloat128NaN(a, b, status); + } + if ( ( aExp | aSig0 | aSig1 ) == 0 ) { + invalid: + float_raise(float_flag_invalid, status); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + if ( bExp == 0 ) { + if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); + normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); + } + zExp = aExp + bExp - 0x4000; + aSig0 |= LIT64( 0x0001000000000000 ); + shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); + mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); + add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); + zSig2 |= ( zSig3 != 0 ); + if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { + shift128ExtraRightJamming( + zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); + ++zExp; + } + return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the quadruple-precision floating-point value +| `a' by the corresponding value `b'. The operation is performed according to +| the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_div(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; + uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + bSign = extractFloat128Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if (aSig0 | aSig1) { + return propagateFloat128NaN(a, b, status); + } + if ( bExp == 0x7FFF ) { + if (bSig0 | bSig1) { + return propagateFloat128NaN(a, b, status); + } + goto invalid; + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( bExp == 0x7FFF ) { + if (bSig0 | bSig1) { + return propagateFloat128NaN(a, b, status); + } + return packFloat128( zSign, 0, 0, 0 ); + } + if ( bExp == 0 ) { + if ( ( bSig0 | bSig1 ) == 0 ) { + if ( ( aExp | aSig0 | aSig1 ) == 0 ) { + invalid: + float_raise(float_flag_invalid, status); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + float_raise(float_flag_divbyzero, status); + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + zExp = aExp - bExp + 0x3FFD; + shortShift128Left( + aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); + shortShift128Left( + bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); + if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { + shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); + ++zExp; + } + zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); + mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); + sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); + while ( (int64_t) rem0 < 0 ) { + --zSig0; + add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); + } + zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); + if ( ( zSig1 & 0x3FFF ) <= 4 ) { + mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); + sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); + while ( (int64_t) rem1 < 0 ) { + --zSig1; + add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); + } + zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); + } + shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); + return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the quadruple-precision floating-point value `a' +| with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_rem(float128 a, float128 b, float_status *status) +{ + flag aSign, zSign; + int32 aExp, bExp, expDiff; + uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; + uint64_t allZero, alternateASig0, alternateASig1, sigMean1; + int64_t sigMean0; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + if ( aExp == 0x7FFF ) { + if ( ( aSig0 | aSig1 ) + || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { + return propagateFloat128NaN(a, b, status); + } + goto invalid; + } + if ( bExp == 0x7FFF ) { + if (bSig0 | bSig1) { + return propagateFloat128NaN(a, b, status); + } + return a; + } + if ( bExp == 0 ) { + if ( ( bSig0 | bSig1 ) == 0 ) { + invalid: + float_raise(float_flag_invalid, status); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return a; + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + expDiff = aExp - bExp; + if ( expDiff < -1 ) return a; + shortShift128Left( + aSig0 | LIT64( 0x0001000000000000 ), + aSig1, + 15 - ( expDiff < 0 ), + &aSig0, + &aSig1 + ); + shortShift128Left( + bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); + q = le128( bSig0, bSig1, aSig0, aSig1 ); + if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); + expDiff -= 64; + while ( 0 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig0 ); + q = ( 4 < q ) ? q - 4 : 0; + mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); + shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); + shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); + sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); + expDiff -= 61; + } + if ( -64 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig0 ); + q = ( 4 < q ) ? q - 4 : 0; + q >>= - expDiff; + shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); + expDiff += 52; + if ( expDiff < 0 ) { + shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); + } + else { + shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); + } + mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); + sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); + } + else { + shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); + shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); + } + do { + alternateASig0 = aSig0; + alternateASig1 = aSig1; + ++q; + sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); + } while ( 0 <= (int64_t) aSig0 ); + add128( + aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 ); + if ( ( sigMean0 < 0 ) + || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { + aSig0 = alternateASig0; + aSig1 = alternateASig1; + } + zSign = ( (int64_t) aSig0 < 0 ); + if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); + return normalizeRoundAndPackFloat128(aSign ^ zSign, bExp - 4, aSig0, aSig1, + status); +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the quadruple-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_sqrt(float128 a, float_status *status) +{ + flag aSign; + int32 aExp, zExp; + uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; + uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if (aSig0 | aSig1) { + return propagateFloat128NaN(a, a, status); + } + if ( ! aSign ) return a; + goto invalid; + } + if ( aSign ) { + if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; + invalid: + float_raise(float_flag_invalid, status); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; + aSig0 |= LIT64( 0x0001000000000000 ); + zSig0 = estimateSqrt32( aExp, aSig0>>17 ); + shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); + zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); + doubleZSig0 = zSig0<<1; + mul64To128( zSig0, zSig0, &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); + while ( (int64_t) rem0 < 0 ) { + --zSig0; + doubleZSig0 -= 2; + add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); + } + zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); + if ( ( zSig1 & 0x1FFF ) <= 5 ) { + if ( zSig1 == 0 ) zSig1 = 1; + mul64To128( doubleZSig0, zSig1, &term1, &term2 ); + sub128( rem1, 0, term1, term2, &rem1, &rem2 ); + mul64To128( zSig1, zSig1, &term2, &term3 ); + sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); + while ( (int64_t) rem1 < 0 ) { + --zSig1; + shortShift128Left( 0, zSig1, 1, &term2, &term3 ); + term3 |= 1; + term2 |= doubleZSig0; + add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); + } + zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); + } + shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); + return roundAndPackFloat128(0, zExp, zSig0, zSig1, zSig2, status); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_eq(float128 a, float128 b, float_status *status) +{ + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| or equal to the corresponding value `b', and 0 otherwise. The invalid +| exception is raised if either operand is a NaN. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_le(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. The comparison is performed according +| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_lt(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise(float_flag_invalid, status); + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot +| be compared, and 0 otherwise. The invalid exception is raised if either +| operand is a NaN. The comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_unordered(float128 a, float128 b, float_status *status) +{ + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise(float_flag_invalid, status); + return 1; + } + return 0; +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. The comparison is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_eq_quiet(float128 a, float128 b, float_status *status) +{ + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_le_quiet(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. Otherwise, the comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_lt_quiet(float128 a, float128 b, float_status *status) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot +| be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The +| comparison is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +int float128_unordered_quiet(float128 a, float128 b, float_status *status) +{ + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return 1; + } + return 0; +} + +/* misc functions */ +float32 uint32_to_float32(uint32_t a, float_status *status) +{ + return int64_to_float32(a, status); +} + +float64 uint32_to_float64(uint32_t a, float_status *status) +{ + return int64_to_float64(a, status); +} + +uint32 float32_to_uint32(float32 a, float_status *status) +{ + int64_t v; + uint32 res; + int old_exc_flags = get_float_exception_flags(status); + + v = float32_to_int64(a, status); + if (v < 0) { + res = 0; + } else if (v > 0xffffffff) { + res = 0xffffffff; + } else { + return v; + } + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint32 float32_to_uint32_round_to_zero(float32 a, float_status *status) +{ + int64_t v; + uint32 res; + int old_exc_flags = get_float_exception_flags(status); + + v = float32_to_int64_round_to_zero(a, status); + if (v < 0) { + res = 0; + } else if (v > 0xffffffff) { + res = 0xffffffff; + } else { + return v; + } + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +int_fast16_t float32_to_int16(float32 a, float_status *status) +{ + int32_t v; + int_fast16_t res; + int old_exc_flags = get_float_exception_flags(status); + + v = float32_to_int32(a, status); + if (v < -0x8000) { + res = -0x8000; + } else if (v > 0x7fff) { + res = 0x7fff; + } else { + return v; + } + + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint_fast16_t float32_to_uint16(float32 a, float_status *status) +{ + int32_t v; + uint_fast16_t res; + int old_exc_flags = get_float_exception_flags(status); + + v = float32_to_int32(a, status); + if (v < 0) { + res = 0; + } else if (v > 0xffff) { + res = 0xffff; + } else { + return v; + } + + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint_fast16_t float32_to_uint16_round_to_zero(float32 a, float_status *status) +{ + int64_t v; + uint_fast16_t res; + int old_exc_flags = get_float_exception_flags(status); + + v = float32_to_int64_round_to_zero(a, status); + if (v < 0) { + res = 0; + } else if (v > 0xffff) { + res = 0xffff; + } else { + return v; + } + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint32 float64_to_uint32(float64 a, float_status *status) +{ + uint64_t v; + uint32 res; + int old_exc_flags = get_float_exception_flags(status); + + v = float64_to_uint64(a, status); + if (v > 0xffffffff) { + res = 0xffffffff; + } else { + return v; + } + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint32 float64_to_uint32_round_to_zero(float64 a, float_status *status) +{ + uint64_t v; + uint32 res; + int old_exc_flags = get_float_exception_flags(status); + + v = float64_to_uint64_round_to_zero(a, status); + if (v > 0xffffffff) { + res = 0xffffffff; + } else { + return v; + } + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +int_fast16_t float64_to_int16(float64 a, float_status *status) +{ + int64_t v; + int_fast16_t res; + int old_exc_flags = get_float_exception_flags(status); + + v = float64_to_int32(a, status); + if (v < -0x8000) { + res = -0x8000; + } else if (v > 0x7fff) { + res = 0x7fff; + } else { + return v; + } + + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint_fast16_t float64_to_uint16(float64 a, float_status *status) +{ + int64_t v; + uint_fast16_t res; + int old_exc_flags = get_float_exception_flags(status); + + v = float64_to_int32(a, status); + if (v < 0) { + res = 0; + } else if (v > 0xffff) { + res = 0xffff; + } else { + return v; + } + + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +uint_fast16_t float64_to_uint16_round_to_zero(float64 a, float_status *status) +{ + int64_t v; + uint_fast16_t res; + int old_exc_flags = get_float_exception_flags(status); + + v = float64_to_int64_round_to_zero(a, status); + if (v < 0) { + res = 0; + } else if (v > 0xffff) { + res = 0xffff; + } else { + return v; + } + set_float_exception_flags(old_exc_flags, status); + float_raise(float_flag_invalid, status); + return res; +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 64-bit unsigned integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. If the conversion overflows, the +| largest unsigned integer is returned. If 'a' is negative, the value is +| rounded and zero is returned; negative values that do not round to zero +| will raise the inexact exception. +*----------------------------------------------------------------------------*/ + +uint64_t float64_to_uint64(float64 a, float_status *status) +{ + flag aSign; + int_fast16_t aExp, shiftCount; + uint64_t aSig, aSigExtra; + a = float64_squash_input_denormal(a, status); + + aSig = extractFloat64Frac(a); + aExp = extractFloat64Exp(a); + aSign = extractFloat64Sign(a); + if (aSign && (aExp > 1022)) { + float_raise(float_flag_invalid, status); + if (float64_is_any_nan(a)) { + return LIT64(0xFFFFFFFFFFFFFFFF); + } else { + return 0; + } + } + if (aExp) { + aSig |= LIT64(0x0010000000000000); + } + shiftCount = 0x433 - aExp; + if (shiftCount <= 0) { + if (0x43E < aExp) { + float_raise(float_flag_invalid, status); + return LIT64(0xFFFFFFFFFFFFFFFF); + } + aSigExtra = 0; + aSig <<= -shiftCount; + } else { + shift64ExtraRightJamming(aSig, 0, shiftCount, &aSig, &aSigExtra); + } + return roundAndPackUint64(aSign, aSig, aSigExtra, status); +} + +uint64_t float64_to_uint64_round_to_zero(float64 a, float_status *status) +{ + signed char current_rounding_mode = status->float_rounding_mode; + set_float_rounding_mode(float_round_to_zero, status); + int64_t v = float64_to_uint64(a, status); + set_float_rounding_mode(current_rounding_mode, status); + return v; +} + +#define COMPARE(s, nan_exp) \ +static inline int float ## s ## _compare_internal(float ## s a, float ## s b,\ + int is_quiet, float_status *status) \ +{ \ + flag aSign, bSign; \ + uint ## s ## _t av, bv; \ + a = float ## s ## _squash_input_denormal(a, status); \ + b = float ## s ## _squash_input_denormal(b, status); \ + \ + if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ + extractFloat ## s ## Frac( a ) ) || \ + ( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ + extractFloat ## s ## Frac( b ) )) { \ + if (!is_quiet || \ + float ## s ## _is_signaling_nan( a ) || \ + float ## s ## _is_signaling_nan( b ) ) { \ + float_raise(float_flag_invalid, status); \ + } \ + return float_relation_unordered; \ + } \ + aSign = extractFloat ## s ## Sign( a ); \ + bSign = extractFloat ## s ## Sign( b ); \ + av = float ## s ## _val(a); \ + bv = float ## s ## _val(b); \ + if ( aSign != bSign ) { \ + if ( (uint ## s ## _t) ( ( av | bv )<<1 ) == 0 ) { \ + /* zero case */ \ + return float_relation_equal; \ + } else { \ + return 1 - (2 * aSign); \ + } \ + } else { \ + if (av == bv) { \ + return float_relation_equal; \ + } else { \ + return 1 - 2 * (aSign ^ ( av < bv )); \ + } \ + } \ +} \ + \ +int float ## s ## _compare(float ## s a, float ## s b, float_status *status) \ +{ \ + return float ## s ## _compare_internal(a, b, 0, status); \ +} \ + \ +int float ## s ## _compare_quiet(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _compare_internal(a, b, 1, status); \ +} + +COMPARE(32, 0xff) +COMPARE(64, 0x7ff) + +static inline int floatx80_compare_internal(floatx80 a, floatx80 b, + int is_quiet, float_status *status) +{ + flag aSign, bSign; + + if (( ( extractFloatx80Exp( a ) == 0x7fff ) && + ( extractFloatx80Frac( a )<<1 ) ) || + ( ( extractFloatx80Exp( b ) == 0x7fff ) && + ( extractFloatx80Frac( b )<<1 ) )) { + if (!is_quiet || + floatx80_is_signaling_nan( a ) || + floatx80_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return float_relation_unordered; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + + if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) && + ( ( a.low | b.low ) == 0 ) ) { + /* zero case */ + return float_relation_equal; + } else { + return 1 - (2 * aSign); + } + } else { + if (a.low == b.low && a.high == b.high) { + return float_relation_equal; + } else { + return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); + } + } +} + +int floatx80_compare(floatx80 a, floatx80 b, float_status *status) +{ + return floatx80_compare_internal(a, b, 0, status); +} + +int floatx80_compare_quiet(floatx80 a, floatx80 b, float_status *status) +{ + return floatx80_compare_internal(a, b, 1, status); +} + +static inline int float128_compare_internal(float128 a, float128 b, + int is_quiet, float_status *status) +{ + flag aSign, bSign; + + if (( ( extractFloat128Exp( a ) == 0x7fff ) && + ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) || + ( ( extractFloat128Exp( b ) == 0x7fff ) && + ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) { + if (!is_quiet || + float128_is_signaling_nan( a ) || + float128_is_signaling_nan( b ) ) { + float_raise(float_flag_invalid, status); + } + return float_relation_unordered; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) { + /* zero case */ + return float_relation_equal; + } else { + return 1 - (2 * aSign); + } + } else { + if (a.low == b.low && a.high == b.high) { + return float_relation_equal; + } else { + return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); + } + } +} + +int float128_compare(float128 a, float128 b, float_status *status) +{ + return float128_compare_internal(a, b, 0, status); +} + +int float128_compare_quiet(float128 a, float128 b, float_status *status) +{ + return float128_compare_internal(a, b, 1, status); +} + +/* min() and max() functions. These can't be implemented as + * 'compare and pick one input' because that would mishandle + * NaNs and +0 vs -0. + * + * minnum() and maxnum() functions. These are similar to the min() + * and max() functions but if one of the arguments is a QNaN and + * the other is numerical then the numerical argument is returned. + * minnum() and maxnum correspond to the IEEE 754-2008 minNum() + * and maxNum() operations. min() and max() are the typical min/max + * semantics provided by many CPUs which predate that specification. + * + * minnummag() and maxnummag() functions correspond to minNumMag() + * and minNumMag() from the IEEE-754 2008. + */ +#define MINMAX(s) \ +static inline float ## s float ## s ## _minmax(float ## s a, float ## s b, \ + int ismin, int isieee, \ + int ismag, \ + float_status *status) \ +{ \ + flag aSign, bSign; \ + uint ## s ## _t av, bv, aav, abv; \ + a = float ## s ## _squash_input_denormal(a, status); \ + b = float ## s ## _squash_input_denormal(b, status); \ + if (float ## s ## _is_any_nan(a) || \ + float ## s ## _is_any_nan(b)) { \ + if (isieee) { \ + if (float ## s ## _is_quiet_nan(a) && \ + !float ## s ##_is_any_nan(b)) { \ + return b; \ + } else if (float ## s ## _is_quiet_nan(b) && \ + !float ## s ## _is_any_nan(a)) { \ + return a; \ + } \ + } \ + return propagateFloat ## s ## NaN(a, b, status); \ + } \ + aSign = extractFloat ## s ## Sign(a); \ + bSign = extractFloat ## s ## Sign(b); \ + av = float ## s ## _val(a); \ + bv = float ## s ## _val(b); \ + if (ismag) { \ + aav = float ## s ## _abs(av); \ + abv = float ## s ## _abs(bv); \ + if (aav != abv) { \ + if (ismin) { \ + return (aav < abv) ? a : b; \ + } else { \ + return (aav < abv) ? b : a; \ + } \ + } \ + } \ + if (aSign != bSign) { \ + if (ismin) { \ + return aSign ? a : b; \ + } else { \ + return aSign ? b : a; \ + } \ + } else { \ + if (ismin) { \ + return (aSign ^ (av < bv)) ? a : b; \ + } else { \ + return (aSign ^ (av < bv)) ? b : a; \ + } \ + } \ +} \ + \ +float ## s float ## s ## _min(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _minmax(a, b, 1, 0, 0, status); \ +} \ + \ +float ## s float ## s ## _max(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _minmax(a, b, 0, 0, 0, status); \ +} \ + \ +float ## s float ## s ## _minnum(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _minmax(a, b, 1, 1, 0, status); \ +} \ + \ +float ## s float ## s ## _maxnum(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _minmax(a, b, 0, 1, 0, status); \ +} \ + \ +float ## s float ## s ## _minnummag(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _minmax(a, b, 1, 1, 1, status); \ +} \ + \ +float ## s float ## s ## _maxnummag(float ## s a, float ## s b, \ + float_status *status) \ +{ \ + return float ## s ## _minmax(a, b, 0, 1, 1, status); \ +} + +MINMAX(32) +MINMAX(64) + + +/* Multiply A by 2 raised to the power N. */ +float32 float32_scalbn(float32 a, int n, float_status *status) +{ + flag aSign; + int16_t aExp; + uint32_t aSig; + + a = float32_squash_input_denormal(a, status); + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + + if ( aExp == 0xFF ) { + if ( aSig ) { + return propagateFloat32NaN(a, a, status); + } + return a; + } + if (aExp != 0) { + aSig |= 0x00800000; + } else if (aSig == 0) { + return a; + } else { + aExp++; + } + + if (n > 0x200) { + n = 0x200; + } else if (n < -0x200) { + n = -0x200; + } + + aExp += n - 1; + aSig <<= 7; + return normalizeRoundAndPackFloat32(aSign, aExp, aSig, status); +} + +float64 float64_scalbn(float64 a, int n, float_status *status) +{ + flag aSign; + int16_t aExp; + uint64_t aSig; + + a = float64_squash_input_denormal(a, status); + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + + if ( aExp == 0x7FF ) { + if ( aSig ) { + return propagateFloat64NaN(a, a, status); + } + return a; + } + if (aExp != 0) { + aSig |= LIT64( 0x0010000000000000 ); + } else if (aSig == 0) { + return a; + } else { + aExp++; + } + + if (n > 0x1000) { + n = 0x1000; + } else if (n < -0x1000) { + n = -0x1000; + } + + aExp += n - 1; + aSig <<= 10; + return normalizeRoundAndPackFloat64(aSign, aExp, aSig, status); +} + +floatx80 floatx80_scalbn(floatx80 a, int n, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + + if ( aExp == 0x7FFF ) { + if ( aSig<<1 ) { + return propagateFloatx80NaN(a, a, status); + } + return a; + } + + if (aExp == 0) { + if (aSig == 0) { + return a; + } + aExp++; + } + + if (n > 0x10000) { + n = 0x10000; + } else if (n < -0x10000) { + n = -0x10000; + } + + aExp += n; + return normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision, + aSign, aExp, aSig, 0, status); +} + +float128 float128_scalbn(float128 a, int n, float_status *status) +{ + flag aSign; + int32_t aExp; + uint64_t aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return propagateFloat128NaN(a, a, status); + } + return a; + } + if (aExp != 0) { + aSig0 |= LIT64( 0x0001000000000000 ); + } else if (aSig0 == 0 && aSig1 == 0) { + return a; + } else { + aExp++; + } + + if (n > 0x10000) { + n = 0x10000; + } else if (n < -0x10000) { + n = -0x10000; + } + + aExp += n - 1; + return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1 + , status); + +} |
