/*
* The implementations contained in this file are heavily based on the
* implementations found in the Berkeley SoftFloat library. As such, they are
* licensed under the same 3-clause BSD license:
*
* License for Berkeley SoftFloat Release 3e
*
* John R. Hauser
* 2018 January 20
*
* The following applies to the whole of SoftFloat Release 3e as well as to
* each source file individually.
*
* Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Regents of the
* University of California. 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 University 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 REGENTS 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 REGENTS 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.
*/
#version 430
#extension GL_ARB_gpu_shader_int64 : enable
#extension GL_ARB_shader_bit_encoding : enable
#extension GL_EXT_shader_integer_mix : enable
#extension GL_MESA_shader_integer_functions : enable
#pragma warning(off)
/* Software IEEE floating-point rounding mode.
* GLSL spec section "4.7.1 Range and Precision":
* The rounding mode cannot be set and is undefined.
* But here, we are able to define the rounding mode at the compilation time.
*/
#define FLOAT_ROUND_NEAREST_EVEN 0
#define FLOAT_ROUND_TO_ZERO 1
#define FLOAT_ROUND_DOWN 2
#define FLOAT_ROUND_UP 3
#define FLOAT_ROUNDING_MODE FLOAT_ROUND_NEAREST_EVEN
/* Absolute value of a Float64 :
* Clear the sign bit
*/
uint64_t
__fabs64(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
a.y &= 0x7FFFFFFFu;
return packUint2x32(a);
}
/* Returns 1 if the double-precision floating-point value `a' is a NaN;
* otherwise returns 0.
*/
bool
__is_nan(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
return (0xFFE00000u <= (a.y<<1)) &&
((a.x != 0u) || ((a.y & 0x000FFFFFu) != 0u));
}
/* Negate value of a Float64 :
* Toggle the sign bit
*/
uint64_t
__fneg64(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
uint t = a.y;
t ^= (1u << 31);
a.y = mix(t, a.y, __is_nan(__a));
return packUint2x32(a);
}
uint64_t
__fsign64(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
uvec2 retval;
retval.x = 0u;
retval.y = mix((a.y & 0x80000000u) | 0x3FF00000u, 0u, (a.y << 1 | a.x) == 0u);
return packUint2x32(retval);
}
/* Returns the fraction bits of the double-precision floating-point value `a'.*/
uint
__extractFloat64FracLo(uint64_t a)
{
return unpackUint2x32(a).x;
}
uint
__extractFloat64FracHi(uint64_t a)
{
return unpackUint2x32(a).y & 0x000FFFFFu;
}
/* Returns the exponent bits of the double-precision floating-point value `a'.*/
int
__extractFloat64Exp(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
return int((a.y>>20) & 0x7FFu);
}
bool
__feq64_nonnan(uint64_t __a, uint64_t __b)
{
uvec2 a = unpackUint2x32(__a);
uvec2 b = unpackUint2x32(__b);
return (a.x == b.x) &&
((a.y == b.y) || ((a.x == 0u) && (((a.y | b.y)<<1) == 0u)));
}
/* Returns true if the double-precision floating-point value `a' is equal to the
* corresponding value `b', and false otherwise. The comparison is performed
* according to the IEEE Standard for Floating-Point Arithmetic.
*/
bool
__feq64(uint64_t a, uint64_t b)
{
if (__is_nan(a) || __is_nan(b))
return false;
return __feq64_nonnan(a, b);
}
/* Returns true if the double-precision floating-point value `a' is not equal
* to the corresponding value `b', and false otherwise. The comparison is
* performed according to the IEEE Standard for Floating-Point Arithmetic.
*/
bool
__fne64(uint64_t a, uint64_t b)
{
if (__is_nan(a) || __is_nan(b))
return true;
return !__feq64_nonnan(a, b);
}
/* Returns the sign bit of the double-precision floating-point value `a'.*/
uint
__extractFloat64Sign(uint64_t a)
{
return unpackUint2x32(a).y >> 31;
}
/* Returns true if the 64-bit value formed by concatenating `a0' and `a1' is less
* than the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
* returns false.
*/
bool
lt64(uint a0, uint a1, uint b0, uint b1)
{
return (a0 < b0) || ((a0 == b0) && (a1 < b1));
}
bool
__flt64_nonnan(uint64_t __a, uint64_t __b)
{
uvec2 a = unpackUint2x32(__a);
uvec2 b = unpackUint2x32(__b);
uint aSign = __extractFloat64Sign(__a);
uint bSign = __extractFloat64Sign(__b);
if (aSign != bSign)
return (aSign != 0u) && ((((a.y | b.y)<<1) | a.x | b.x) != 0u);
return mix(lt64(a.y, a.x, b.y, b.x), lt64(b.y, b.x, a.y, a.x), aSign != 0u);
}
/* Returns true if the double-precision floating-point value `a' is less than
* the corresponding value `b', and false otherwise. The comparison is performed
* according to the IEEE Standard for Floating-Point Arithmetic.
*/
bool
__flt64(uint64_t a, uint64_t b)
{
if (__is_nan(a) || __is_nan(b))
return false;
return __flt64_nonnan(a, b);
}
/* Returns true if the double-precision floating-point value `a' is greater
* than or equal to * the corresponding value `b', and false otherwise. The
* comparison is performed * according to the IEEE Standard for Floating-Point
* Arithmetic.
*/
bool
__fge64(uint64_t a, uint64_t b)
{
if (__is_nan(a) || __is_nan(b))
return false;
return !__flt64_nonnan(a, b);
}
/* Adds the 64-bit value formed by concatenating `a0' and `a1' to the 64-bit
* value formed by concatenating `b0' and `b1'. Addition is modulo 2^64, so
* any carry out is lost. The result is broken into two 32-bit pieces which
* are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
*/
void
__add64(uint a0, uint a1, uint b0, uint b1,
out uint z0Ptr,
out uint z1Ptr)
{
uint z1 = a1 + b1;
z1Ptr = z1;
z0Ptr = a0 + b0 + uint(z1 < a1);
}
/* Subtracts the 64-bit value formed by concatenating `b0' and `b1' from the
* 64-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
* 2^64, so any borrow out (carry out) is lost. The result is broken into two
* 32-bit pieces which are stored at the locations pointed to by `z0Ptr' and
* `z1Ptr'.
*/
void
__sub64(uint a0, uint a1, uint b0, uint b1,
out uint z0Ptr,
out uint z1Ptr)
{
z1Ptr = a1 - b1;
z0Ptr = a0 - b0 - uint(a1 < b1);
}
/* Shifts the 64-bit value formed by concatenating `a0' and `a1' right by the
* number of bits given in `count'. If any nonzero bits are shifted off, they
* are "jammed" into the least significant bit of the result by setting the
* least significant bit to 1. The value of `count' can be arbitrarily large;
* in particular, if `count' is greater than 64, the result will be either 0
* or 1, depending on whether the concatenation of `a0' and `a1' is zero or
* nonzero. The result is broken into two 32-bit pieces which are stored at
* the locations pointed to by `z0Ptr' and `z1Ptr'.
*/
void
__shift64RightJamming(uint a0,
uint a1,
int count,
out uint z0Ptr,
out uint z1Ptr)
{
uint z0;
uint z1;
int negCount = (-count) & 31;
z0 = mix(0u, a0, count == 0);
z0 = mix(z0, (a0 >> count), count < 32);
z1 = uint((a0 | a1) != 0u); /* count >= 64 */
uint z1_lt64 = (a0>>(count & 31)) | uint(((a0<<negCount) | a1) != 0u);
z1 = mix(z1, z1_lt64, count < 64);
z1 = mix(z1, (a0 | uint(a1 != 0u)), count == 32);
uint z1_lt32 = (a0<<negCount) | (a1>>count) | uint ((a1<<negCount) != 0u);
z1 = mix(z1, z1_lt32, count < 32);
z1 = mix(z1, a1, count == 0);
z1Ptr = z1;
z0Ptr = z0;
}
/* Shifts the 96-bit value formed by concatenating `a0', `a1', and `a2' right
* by 32 _plus_ the number of bits given in `count'. The shifted result is
* at most 64 nonzero bits; these are broken into two 32-bit pieces which are
* stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
* off form a third 32-bit result as follows: The _last_ bit shifted off is
* the most-significant bit of the extra result, and the other 31 bits of the
* extra result are all zero if and only if _all_but_the_last_ bits shifted off
* were all zero. This extra result is stored in the location pointed to by
* `z2Ptr'. The value of `count' can be arbitrarily large.
* (This routine makes more sense if `a0', `a1', and `a2' are considered
* to form a fixed-point value with binary point between `a1' and `a2'. This
* fixed-point value is shifted right by the number of bits given in `count',
* and the integer part of the result is returned at the locations pointed to
* by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
* corrupted as described above, and is returned at the location pointed to by
* `z2Ptr'.)
*/
void
__shift64ExtraRightJamming(uint a0, uint a1, uint a2,
int count,
out uint z0Ptr,
out uint z1Ptr,
out uint z2Ptr)
{
uint z0 = 0u;
uint z1;
uint z2;
int negCount = (-count) & 31;
z2 = mix(uint(a0 != 0u), a0, count == 64);
z2 = mix(z2, a0 << negCount, count < 64);
z2 = mix(z2, a1 << negCount, count < 32);
z1 = mix(0u, (a0 >> (count & 31)), count < 64);
z1 = mix(z1, (a0<<negCount) | (a1>>count), count < 32);
a2 = mix(a2 | a1, a2, count < 32);
z0 = mix(z0, a0 >> count, count < 32);
z2 |= uint(a2 != 0u);
z0 = mix(z0, 0u, (count == 32));
z1 = mix(z1, a0, (count == 32));
z2 = mix(z2, a1, (count == 32));
z0 = mix(z0, a0, (count == 0));
z1 = mix(z1, a1, (count == 0));
z2 = mix(z2, a2, (count == 0));
z2Ptr = z2;
z1Ptr = z1;
z0Ptr = z0;
}
/* Shifts the 64-bit value formed by concatenating `a0' and `a1' left by the
* number of bits given in `count'. Any bits shifted off are lost. The value
* of `count' must be less than 32. The result is broken into two 32-bit
* pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
*/
void
__shortShift64Left(uint a0, uint a1,
int count,
out uint z0Ptr,
out uint z1Ptr)
{
z1Ptr = a1<<count;
z0Ptr = mix((a0 << count | (a1 >> ((-count) & 31))), a0, count == 0);
}
/* Packs the sign `zSign', the exponent `zExp', and the significand formed by
* the concatenation of `zFrac0' and `zFrac1' into a double-precision floating-
* point value, returning the result. After being shifted into the proper
* positions, the three fields `zSign', `zExp', and `zFrac0' are simply added
* together to form the most significant 32 bits of the result. This means
* that any integer portion of `zFrac0' 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
* `zFrac0' and `zFrac1' concatenated form a complete, normalized significand.
*/
uint64_t
__packFloat64(uint zSign, int zExp, uint zFrac0, uint zFrac1)
{
uvec2 z;
z.y = (zSign << 31) + (uint(zExp) << 20) + zFrac0;
z.x = zFrac1;
return packUint2x32(z);
}
/* Takes an abstract floating-point value having sign `zSign', exponent `zExp',
* and extended significand formed by the concatenation of `zFrac0', `zFrac1',
* and `zFrac2', 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 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 IEEE Standard for Floating-Point Arithmetic.
*/
uint64_t
__roundAndPackFloat64(uint zSign,
int zExp,
uint zFrac0,
uint zFrac1,
uint zFrac2)
{
bool roundNearestEven;
bool increment;
roundNearestEven = FLOAT_ROUNDING_MODE == FLOAT_ROUND_NEAREST_EVEN;
increment = int(zFrac2) < 0;
if (!roundNearestEven) {
if (FLOAT_ROUNDING_MODE == FLOAT_ROUND_TO_ZERO) {
increment = false;
} else {
if (zSign != 0u) {
increment = (FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN) &&
(zFrac2 != 0u);
} else {
increment = (FLOAT_ROUNDING_MODE == FLOAT_ROUND_UP) &&
(zFrac2 != 0u);
}
}
}
if (0x7FD <= zExp) {
if ((0x7FD < zExp) ||
((zExp == 0x7FD) &&
(0x001FFFFFu == zFrac0 && 0xFFFFFFFFu == zFrac1) &&
increment)) {
if ((FLOAT_ROUNDING_MODE == FLOAT_ROUND_TO_ZERO) ||
((zSign != 0u) && (FLOAT_ROUNDING_MODE == FLOAT_ROUND_UP)) ||
((zSign == 0u) && (FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN))) {
return __packFloat64(zSign, 0x7FE, 0x000FFFFFu, 0xFFFFFFFFu);
}
return __packFloat64(zSign, 0x7FF, 0u, 0u);
}
if (zExp < 0) {
__shift64ExtraRightJamming(
zFrac0, zFrac1, zFrac2, -zExp, zFrac0, zFrac1, zFrac2);
zExp = 0;
if (roundNearestEven) {
increment = zFrac2 < 0u;
} else {
if (zSign != 0u) {
increment = (FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN) &&
(zFrac2 != 0u);
} else {
increment = (FLOAT_ROUNDING_MODE == FLOAT_ROUND_UP) &&
(zFrac2 != 0u);
}
}
}
}
if (increment) {
__add64(zFrac0, zFrac1, 0u, 1u, zFrac0, zFrac1);
zFrac1 &= ~((zFrac2 + uint(zFrac2 == 0u)) & uint(roundNearestEven));
} else {
zExp = mix(zExp, 0, (zFrac0 | zFrac1) == 0u);
}
return __packFloat64(zSign, zExp, zFrac0, zFrac1);
}
uint64_t
__roundAndPackUInt64(uint zSign, uint zFrac0, uint zFrac1, uint zFrac2)
{
bool roundNearestEven;
bool increment;
uint64_t default_nan = 0xFFFFFFFFFFFFFFFFUL;
roundNearestEven = FLOAT_ROUNDING_MODE == FLOAT_ROUND_NEAREST_EVEN;
if (zFrac2 >= 0x80000000u)
increment = false;
if (!roundNearestEven) {
if (zSign != 0u) {
if ((FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN) && (zFrac2 != 0u)) {
increment = false;
}
} else {
increment = (FLOAT_ROUNDING_MODE == FLOAT_ROUND_UP) &&
(zFrac2 != 0u);
}
}
if (increment) {
__add64(zFrac0, zFrac1, 0u, 1u, zFrac0, zFrac1);
if ((zFrac0 | zFrac1) != 0u)
zFrac1 &= ~(1u) + uint(zFrac2 == 0u) & uint(roundNearestEven);
}
return mix(packUint2x32(uvec2(zFrac1, zFrac0)), default_nan,
(zSign !=0u && (zFrac0 | zFrac1) != 0u));
}
int64_t
__roundAndPackInt64(uint zSign, uint zFrac0, uint zFrac1, uint zFrac2)
{
bool roundNearestEven;
bool increment;
int64_t default_NegNaN = -0x7FFFFFFFFFFFFFFEL;
int64_t default_PosNaN = 0xFFFFFFFFFFFFFFFFL;
roundNearestEven = FLOAT_ROUNDING_MODE == FLOAT_ROUND_NEAREST_EVEN;
if (zFrac2 >= 0x80000000u)
increment = false;
if (!roundNearestEven) {
if (zSign != 0u) {
increment = ((FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN) &&
(zFrac2 != 0u));
} else {
increment = (FLOAT_ROUNDING_MODE == FLOAT_ROUND_UP) &&
(zFrac2 != 0u);
}
}
if (increment) {
__add64(zFrac0, zFrac1, 0u, 1u, zFrac0, zFrac1);
if ((zFrac0 | zFrac1) != 0u)
zFrac1 &= ~(1u) + uint(zFrac2 == 0u) & uint(roundNearestEven);
}
int64_t absZ = mix(int64_t(packUint2x32(uvec2(zFrac1, zFrac0))),
-int64_t(packUint2x32(uvec2(zFrac1, zFrac0))),
(zSign != 0u));
int64_t nan = mix(default_PosNaN, default_NegNaN, bool(zSign));
return mix(absZ, nan, bool(zSign ^ uint(absZ < 0)) && bool(absZ));
}
/* Returns the number of leading 0 bits before the most-significant 1 bit of
* `a'. If `a' is zero, 32 is returned.
*/
int
__countLeadingZeros32(uint a)
{
int shiftCount;
shiftCount = mix(31 - findMSB(a), 32, a == 0u);
return shiftCount;
}
/* 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 double-precision floating-point value corresponding
* to the abstract input. This routine is just like `__roundAndPackFloat64'
* 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.
*/
uint64_t
__normalizeRoundAndPackFloat64(uint zSign,
int zExp,
uint zFrac0,
uint zFrac1)
{
int shiftCount;
uint zFrac2;
if (zFrac0 == 0u) {
zExp -= 32;
zFrac0 = zFrac1;
zFrac1 = 0u;
}
shiftCount = __countLeadingZeros32(zFrac0) - 11;
if (0 <= shiftCount) {
zFrac2 = 0u;
__shortShift64Left(zFrac0, zFrac1, shiftCount, zFrac0, zFrac1);
} else {
__shift64ExtraRightJamming(
zFrac0, zFrac1, 0u, -shiftCount, zFrac0, zFrac1, zFrac2);
}
zExp -= shiftCount;
return __roundAndPackFloat64(zSign, zExp, zFrac0, zFrac1, zFrac2);
}
/* Takes two double-precision floating-point values `a' and `b', one of which
* is a NaN, and returns the appropriate NaN result.
*/
uint64_t
__propagateFloat64NaN(uint64_t __a, uint64_t __b)
{
bool aIsNaN = __is_nan(__a);
bool bIsNaN = __is_nan(__b);
uvec2 a = unpackUint2x32(__a);
uvec2 b = unpackUint2x32(__b);
a.y |= 0x00080000u;
b.y |= 0x00080000u;
return packUint2x32(mix(b, mix(a, b, bvec2(bIsNaN, bIsNaN)), bvec2(aIsNaN, aIsNaN)));
}
/* Returns the result of adding the double-precision floating-point values
* `a' and `b'. The operation is performed according to the IEEE Standard for
* Floating-Point Arithmetic.
*/
uint64_t
__fadd64(uint64_t a, uint64_t b)
{
uint aSign = __extractFloat64Sign(a);
uint bSign = __extractFloat64Sign(b);
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
uint bFracLo = __extractFloat64FracLo(b);
uint bFracHi = __extractFloat64FracHi(b);
int aExp = __extractFloat64Exp(a);
int bExp = __extractFloat64Exp(b);
uint zFrac0 = 0u;
uint zFrac1 = 0u;
int expDiff = aExp - bExp;
if (aSign == bSign) {
uint zFrac2 = 0u;
int zExp;
bool orig_exp_diff_is_zero = (expDiff == 0);
if (orig_exp_diff_is_zero) {
if (aExp == 0x7FF) {
bool propagate = (aFracHi | aFracLo | bFracHi | bFracLo) != 0u;
return mix(a, __propagateFloat64NaN(a, b), propagate);
}
__add64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
if (aExp == 0)
return __packFloat64(aSign, 0, zFrac0, zFrac1);
zFrac2 = 0u;
zFrac0 |= 0x00200000u;
zExp = aExp;
__shift64ExtraRightJamming(
zFrac0, zFrac1, zFrac2, 1, zFrac0, zFrac1, zFrac2);
} else if (0 < expDiff) {
if (aExp == 0x7FF) {
bool propagate = (aFracHi | aFracLo) != 0u;
return mix(a, __propagateFloat64NaN(a, b), propagate);
}
expDiff = mix(expDiff, expDiff - 1, bExp == 0);
bFracHi = mix(bFracHi | 0x00100000u, bFracHi, bExp == 0);
__shift64ExtraRightJamming(
bFracHi, bFracLo, 0u, expDiff, bFracHi, bFracLo, zFrac2);
zExp = aExp;
} else if (expDiff < 0) {
if (bExp == 0x7FF) {
bool propagate = (bFracHi | bFracLo) != 0u;
return mix(__packFloat64(aSign, 0x7ff, 0u, 0u), __propagateFloat64NaN(a, b), propagate);
}
expDiff = mix(expDiff, expDiff + 1, aExp == 0);
aFracHi = mix(aFracHi | 0x00100000u, aFracHi, aExp == 0);
__shift64ExtraRightJamming(
aFracHi, aFracLo, 0u, - expDiff, aFracHi, aFracLo, zFrac2);
zExp = bExp;
}
if (!orig_exp_diff_is_zero) {
aFracHi |= 0x00100000u;
__add64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
--zExp;
if (!(zFrac0 < 0x00200000u)) {
__shift64ExtraRightJamming(zFrac0, zFrac1, zFrac2, 1, zFrac0, zFrac1, zFrac2);
++zExp;
}
}
return __roundAndPackFloat64(aSign, zExp, zFrac0, zFrac1, zFrac2);
} else {
int zExp;
__shortShift64Left(aFracHi, aFracLo, 10, aFracHi, aFracLo);
__shortShift64Left(bFracHi, bFracLo, 10, bFracHi, bFracLo);
if (0 < expDiff) {
if (aExp == 0x7FF) {
bool propagate = (aFracHi | aFracLo) != 0u;
return mix(a, __propagateFloat64NaN(a, b), propagate);
}
expDiff = mix(expDiff, expDiff - 1, bExp == 0);
bFracHi = mix(bFracHi | 0x40000000u, bFracHi, bExp == 0);
__shift64RightJamming(bFracHi, bFracLo, expDiff, bFracHi, bFracLo);
aFracHi |= 0x40000000u;
__sub64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
zExp = aExp;
--zExp;
return __normalizeRoundAndPackFloat64(aSign, zExp - 10, zFrac0, zFrac1);
}
if (expDiff < 0) {
if (bExp == 0x7FF) {
bool propagate = (bFracHi | bFracLo) != 0u;
return mix(__packFloat64(aSign ^ 1u, 0x7ff, 0u, 0u), __propagateFloat64NaN(a, b), propagate);
}
expDiff = mix(expDiff, expDiff + 1, aExp == 0);
aFracHi = mix(aFracHi | 0x40000000u, aFracHi, aExp == 0);
__shift64RightJamming(aFracHi, aFracLo, - expDiff, aFracHi, aFracLo);
bFracHi |= 0x40000000u;
__sub64(bFracHi, bFracLo, aFracHi, aFracLo, zFrac0, zFrac1);
zExp = bExp;
aSign ^= 1u;
--zExp;
return __normalizeRoundAndPackFloat64(aSign, zExp - 10, zFrac0, zFrac1);
}
if (aExp == 0x7FF) {
bool propagate = (aFracHi | aFracLo | bFracHi | bFracLo) != 0u;
return mix(0xFFFFFFFFFFFFFFFFUL, __propagateFloat64NaN(a, b), propagate);
}
bExp = mix(bExp, 1, aExp == 0);
aExp = mix(aExp, 1, aExp == 0);
bool zexp_normal = false;
bool blta = true;
if (bFracHi < aFracHi) {
__sub64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
zexp_normal = true;
}
else if (aFracHi < bFracHi) {
__sub64(bFracHi, bFracLo, aFracHi, aFracLo, zFrac0, zFrac1);
blta = false;
zexp_normal = true;
}
else if (bFracLo < aFracLo) {
__sub64(aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1);
zexp_normal = true;
}
else if (aFracLo < bFracLo) {
__sub64(bFracHi, bFracLo, aFracHi, aFracLo, zFrac0, zFrac1);
blta = false;
zexp_normal = true;
}
zExp = mix(bExp, aExp, blta);
aSign = mix(aSign ^ 1u, aSign, blta);
uint64_t retval_0 = __packFloat64(uint(FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN), 0, 0u, 0u);
uint64_t retval_1 = __normalizeRoundAndPackFloat64(aSign, zExp - 11, zFrac0, zFrac1);
return mix(retval_0, retval_1, zexp_normal);
}
}
/* Multiplies `a' by `b' to obtain a 64-bit product. The product is broken
* into two 32-bit pieces which are stored at the locations pointed to by
* `z0Ptr' and `z1Ptr'.
*/
void
__mul32To64(uint a, uint b, out uint z0Ptr, out uint z1Ptr)
{
uint aLow = a & 0x0000FFFFu;
uint aHigh = a>>16;
uint bLow = b & 0x0000FFFFu;
uint bHigh = b>>16;
uint z1 = aLow * bLow;
uint zMiddleA = aLow * bHigh;
uint zMiddleB = aHigh * bLow;
uint z0 = aHigh * bHigh;
zMiddleA += zMiddleB;
z0 += ((uint(zMiddleA < zMiddleB)) << 16) + (zMiddleA >> 16);
zMiddleA <<= 16;
z1 += zMiddleA;
z0 += uint(z1 < zMiddleA);
z1Ptr = z1;
z0Ptr = z0;
}
/* Multiplies the 64-bit value formed by concatenating `a0' and `a1' to the
* 64-bit value formed by concatenating `b0' and `b1' to obtain a 128-bit
* product. The product is broken into four 32-bit pieces which are stored at
* the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
*/
void
__mul64To128(uint a0, uint a1, uint b0, uint b1,
out uint z0Ptr,
out uint z1Ptr,
out uint z2Ptr,
out uint z3Ptr)
{
uint z0 = 0u;
uint z1 = 0u;
uint z2 = 0u;
uint z3 = 0u;
uint more1 = 0u;
uint more2 = 0u;
__mul32To64(a1, b1, z2, z3);
__mul32To64(a1, b0, z1, more2);
__add64(z1, more2, 0u, z2, z1, z2);
__mul32To64(a0, b0, z0, more1);
__add64(z0, more1, 0u, z1, z0, z1);
__mul32To64(a0, b1, more1, more2);
__add64(more1, more2, 0u, z2, more1, z2);
__add64(z0, z1, 0u, more1, z0, z1);
z3Ptr = z3;
z2Ptr = z2;
z1Ptr = z1;
z0Ptr = z0;
}
/* Normalizes the subnormal double-precision floating-point value represented
* by the denormalized significand formed by the concatenation of `aFrac0' and
* `aFrac1'. The normalized exponent is stored at the location pointed to by
* `zExpPtr'. The most significant 21 bits of the normalized significand are
* stored at the location pointed to by `zFrac0Ptr', and the least significant
* 32 bits of the normalized significand are stored at the location pointed to
* by `zFrac1Ptr'.
*/
void
__normalizeFloat64Subnormal(uint aFrac0, uint aFrac1,
out int zExpPtr,
out uint zFrac0Ptr,
out uint zFrac1Ptr)
{
int shiftCount;
uint temp_zfrac0, temp_zfrac1;
shiftCount = __countLeadingZeros32(mix(aFrac0, aFrac1, aFrac0 == 0u)) - 11;
zExpPtr = mix(1 - shiftCount, -shiftCount - 31, aFrac0 == 0u);
temp_zfrac0 = mix(aFrac1<<shiftCount, aFrac1>>(-shiftCount), shiftCount < 0);
temp_zfrac1 = mix(0u, aFrac1<<(shiftCount & 31), shiftCount < 0);
__shortShift64Left(aFrac0, aFrac1, shiftCount, zFrac0Ptr, zFrac1Ptr);
zFrac0Ptr = mix(zFrac0Ptr, temp_zfrac0, aFrac0 == 0);
zFrac1Ptr = mix(zFrac1Ptr, temp_zfrac1, aFrac0 == 0);
}
/* Returns the result of multiplying the double-precision floating-point values
* `a' and `b'. The operation is performed according to the IEEE Standard for
* Floating-Point Arithmetic.
*/
uint64_t
__fmul64(uint64_t a, uint64_t b)
{
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint zFrac2 = 0u;
uint zFrac3 = 0u;
int zExp;
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
uint bFracLo = __extractFloat64FracLo(b);
uint bFracHi = __extractFloat64FracHi(b);
int aExp = __extractFloat64Exp(a);
uint aSign = __extractFloat64Sign(a);
int bExp = __extractFloat64Exp(b);
uint bSign = __extractFloat64Sign(b);
uint zSign = aSign ^ bSign;
if (aExp == 0x7FF) {
if (((aFracHi | aFracLo) != 0u) ||
((bExp == 0x7FF) && ((bFracHi | bFracLo) != 0u))) {
return __propagateFloat64NaN(a, b);
}
if ((uint(bExp) | bFracHi | bFracLo) == 0u)
return 0xFFFFFFFFFFFFFFFFUL;
return __packFloat64(zSign, 0x7FF, 0u, 0u);
}
if (bExp == 0x7FF) {
if ((bFracHi | bFracLo) != 0u)
return __propagateFloat64NaN(a, b);
if ((uint(aExp) | aFracHi | aFracLo) == 0u)
return 0xFFFFFFFFFFFFFFFFUL;
return __packFloat64(zSign, 0x7FF, 0u, 0u);
}
if (aExp == 0) {
if ((aFracHi | aFracLo) == 0u)
return __packFloat64(zSign, 0, 0u, 0u);
__normalizeFloat64Subnormal(aFracHi, aFracLo, aExp, aFracHi, aFracLo);
}
if (bExp == 0) {
if ((bFracHi | bFracLo) == 0u)
return __packFloat64(zSign, 0, 0u, 0u);
__normalizeFloat64Subnormal(bFracHi, bFracLo, bExp, bFracHi, bFracLo);
}
zExp = aExp + bExp - 0x400;
aFracHi |= 0x00100000u;
__shortShift64Left(bFracHi, bFracLo, 12, bFracHi, bFracLo);
__mul64To128(
aFracHi, aFracLo, bFracHi, bFracLo, zFrac0, zFrac1, zFrac2, zFrac3);
__add64(zFrac0, zFrac1, aFracHi, aFracLo, zFrac0, zFrac1);
zFrac2 |= uint(zFrac3 != 0u);
if (0x00200000u <= zFrac0) {
__shift64ExtraRightJamming(
zFrac0, zFrac1, zFrac2, 1, zFrac0, zFrac1, zFrac2);
++zExp;
}
return __roundAndPackFloat64(zSign, zExp, zFrac0, zFrac1, zFrac2);
}
uint64_t
__ffma64(uint64_t a, uint64_t b, uint64_t c)
{
return __fadd64(__fmul64(a, b), c);
}
/* Shifts the 64-bit value formed by concatenating `a0' and `a1' right by the
* number of bits given in `count'. Any bits shifted off are lost. The value
* of `count' can be arbitrarily large; in particular, if `count' is greater
* than 64, the result will be 0. The result is broken into two 32-bit pieces
* which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
*/
void
__shift64Right(uint a0, uint a1,
int count,
out uint z0Ptr,
out uint z1Ptr)
{
uint z0;
uint z1;
int negCount = (-count) & 31;
z0 = 0u;
z0 = mix(z0, (a0 >> count), count < 32);
z0 = mix(z0, a0, count == 0);
z1 = mix(0u, (a0 >> (count & 31)), count < 64);
z1 = mix(z1, (a0<<negCount) | (a1>>count), count < 32);
z1 = mix(z1, a0, count == 0);
z1Ptr = z1;
z0Ptr = z0;
}
/* Returns the result of converting the double-precision floating-point value
* `a' to the unsigned integer format. The conversion is performed according
* to the IEEE Standard for Floating-Point Arithmetic.
*/
uint
__fp64_to_uint(uint64_t a)
{
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
int aExp = __extractFloat64Exp(a);
uint aSign = __extractFloat64Sign(a);
if ((aExp == 0x7FF) && ((aFracHi | aFracLo) != 0u))
return 0xFFFFFFFFu;
aFracHi |= mix(0u, 0x00100000u, aExp != 0);
int shiftDist = 0x427 - aExp;
if (0 < shiftDist)
__shift64RightJamming(aFracHi, aFracLo, shiftDist, aFracHi, aFracLo);
if ((aFracHi & 0xFFFFF000u) != 0u)
return mix(~0u, 0u, (aSign != 0u));
uint z = 0u;
uint zero = 0u;
__shift64Right(aFracHi, aFracLo, 12, zero, z);
uint expt = mix(~0u, 0u, (aSign != 0u));
return mix(z, expt, (aSign != 0u) && (z != 0u));
}
uint64_t
__uint_to_fp64(uint a)
{
if (a == 0u)
return 0ul;
int shiftDist = __countLeadingZeros32(a) + 21;
uint aHigh = 0u;
uint aLow = 0u;
int negCount = (- shiftDist) & 31;
aHigh = mix(0u, a<< shiftDist - 32, shiftDist < 64);
aLow = 0u;
aHigh = mix(aHigh, 0u, shiftDist == 0);
aLow = mix(aLow, a, shiftDist ==0);
aHigh = mix(aHigh, a >> negCount, shiftDist < 32);
aLow = mix(aLow, a << shiftDist, shiftDist < 32);
return __packFloat64(0u, 0x432 - shiftDist, aHigh, aLow);
}
uint64_t
__uint64_to_fp64(uint64_t a)
{
if (a == 0u)
return 0ul;
uvec2 aFrac = unpackUint2x32(a);
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
if ((aFracHi & 0x80000000u) != 0u) {
__shift64RightJamming(aFracHi, aFracLo, 1, aFracHi, aFracLo);
return __roundAndPackFloat64(0, 0x433, aFracHi, aFracLo, 0u);
} else {
return __normalizeRoundAndPackFloat64(0, 0x432, aFrac.y, aFrac.x);
}
}
uint64_t
__fp64_to_uint64(uint64_t a)
{
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
int aExp = __extractFloat64Exp(a);
uint aSign = __extractFloat64Sign(a);
uint zFrac2 = 0u;
uint64_t default_nan = 0xFFFFFFFFFFFFFFFFUL;
aFracHi = mix(aFracHi, aFracHi | 0x00100000u, aExp != 0);
int shiftCount = 0x433 - aExp;
if ( shiftCount <= 0 ) {
if (shiftCount < -11 && aExp == 0x7FF) {
if ((aFracHi | aFracLo) != 0u)
return __propagateFloat64NaN(a, a);
return mix(default_nan, a, aSign == 0u);
}
__shortShift64Left(aFracHi, aFracLo, -shiftCount, aFracHi, aFracLo);
} else {
__shift64ExtraRightJamming(aFracHi, aFracLo, zFrac2, shiftCount,
aFracHi, aFracLo, zFrac2);
}
return __roundAndPackUInt64(aSign, aFracHi, aFracLo, zFrac2);
}
int64_t
__fp64_to_int64(uint64_t a)
{
uint zFrac2 = 0u;
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
int aExp = __extractFloat64Exp(a);
uint aSign = __extractFloat64Sign(a);
int64_t default_NegNaN = -0x7FFFFFFFFFFFFFFEL;
int64_t default_PosNaN = 0xFFFFFFFFFFFFFFFFL;
aFracHi = mix(aFracHi, aFracHi | 0x00100000u, aExp != 0);
int shiftCount = 0x433 - aExp;
if (shiftCount <= 0) {
if (shiftCount < -11 && aExp == 0x7FF) {
if ((aFracHi | aFracLo) != 0u)
return default_NegNaN;
return mix(default_NegNaN, default_PosNaN, aSign == 0u);
}
__shortShift64Left(aFracHi, aFracLo, -shiftCount, aFracHi, aFracLo);
} else {
__shift64ExtraRightJamming(aFracHi, aFracLo, zFrac2, shiftCount,
aFracHi, aFracLo, zFrac2);
}
return __roundAndPackInt64(aSign, aFracHi, aFracLo, zFrac2);
}
uint64_t
__fp32_to_uint64(float f)
{
uint a = floatBitsToUint(f);
uint aFrac = a & 0x007FFFFFu;
int aExp = int((a>>23) & 0xFFu);
uint aSign = a>>31;
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint zFrac2 = 0u;
uint64_t default_nan = 0xFFFFFFFFFFFFFFFFUL;
int shiftCount = 0xBE - aExp;
if (shiftCount <0) {
if (aExp == 0xFF)
return default_nan;
}
aFrac = mix(aFrac, aFrac | 0x00800000u, aExp != 0);
__shortShift64Left(aFrac, 0, 40, zFrac0, zFrac1);
if (shiftCount != 0) {
__shift64ExtraRightJamming(zFrac0, zFrac1, zFrac2, shiftCount,
zFrac0, zFrac1, zFrac2);
}
return __roundAndPackUInt64(aSign, zFrac0, zFrac1, zFrac2);
}
int64_t
__fp32_to_int64(float f)
{
uint a = floatBitsToUint(f);
uint aFrac = a & 0x007FFFFFu;
int aExp = int((a>>23) & 0xFFu);
uint aSign = a>>31;
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint zFrac2 = 0u;
int64_t default_NegNaN = -0x7FFFFFFFFFFFFFFEL;
int64_t default_PosNaN = 0xFFFFFFFFFFFFFFFFL;
int shiftCount = 0xBE - aExp;
if (shiftCount <0) {
if (aExp == 0xFF && aFrac != 0u)
return default_NegNaN;
return mix(default_NegNaN, default_PosNaN, aSign == 0u);
}
aFrac = mix(aFrac, aFrac | 0x00800000u, aExp != 0);
__shortShift64Left(aFrac, 0, 40, zFrac0, zFrac1);
if (shiftCount != 0) {
__shift64ExtraRightJamming(zFrac0, zFrac1, zFrac2, shiftCount,
zFrac0, zFrac1, zFrac2);
}
return __roundAndPackInt64(aSign, zFrac0, zFrac1, zFrac2);
}
uint64_t
__int64_to_fp64(int64_t a)
{
if (a==0)
return 0ul;
uint64_t absA = mix(uint64_t(a), uint64_t(-a), a < 0);
uint aFracHi = __extractFloat64FracHi(absA);
uvec2 aFrac = unpackUint2x32(absA);
uint zSign = uint(a < 0);
if ((aFracHi & 0x80000000u) != 0u) {
return mix(0ul, __packFloat64(1, 0x434, 0u, 0u), a < 0);
}
return __normalizeRoundAndPackFloat64(zSign, 0x432, aFrac.y, aFrac.x);
}
/* 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 IEEE Standard for 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.
*/
int
__fp64_to_int(uint64_t a)
{
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
int aExp = __extractFloat64Exp(a);
uint aSign = __extractFloat64Sign(a);
uint absZ = 0u;
uint aFracExtra = 0u;
int shiftCount = aExp - 0x413;
if (0 <= shiftCount) {
if (0x41E < aExp) {
if ((aExp == 0x7FF) && bool(aFracHi | aFracLo))
aSign = 0u;
return mix(0x7FFFFFFF, 0x80000000, bool(aSign));
}
__shortShift64Left(aFracHi | 0x00100000u, aFracLo, shiftCount, absZ, aFracExtra);
} else {
if (aExp < 0x3FF)
return 0;
aFracHi |= 0x00100000u;
aFracExtra = ( aFracHi << (shiftCount & 31)) | aFracLo;
absZ = aFracHi >> (- shiftCount);
}
int z = mix(int(absZ), -int(absZ), (aSign != 0u));
int nan = mix(0x7FFFFFFF, 0x80000000, bool(aSign));
return mix(z, nan, bool(aSign ^ uint(z < 0)) && bool(z));
}
/* 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 IEEE Standard for Floating-Point Arithmetic.
*/
uint64_t
__int_to_fp64(int a)
{
uint zFrac0 = 0u;
uint zFrac1 = 0u;
if (a==0)
return __packFloat64(0u, 0, 0u, 0u);
uint zSign = uint(a < 0);
uint absA = mix(uint(a), uint(-a), a < 0);
int shiftCount = __countLeadingZeros32(absA) - 11;
if (0 <= shiftCount) {
zFrac0 = absA << shiftCount;
zFrac1 = 0u;
} else {
__shift64Right(absA, 0u, -shiftCount, zFrac0, zFrac1);
}
return __packFloat64(zSign, 0x412 - shiftCount, zFrac0, zFrac1);
}
bool
__fp64_to_bool(uint64_t a)
{
return !__feq64_nonnan(__fabs64(a), 0ul);
}
uint64_t
__bool_to_fp64(bool a)
{
return __int_to_fp64(int(a));
}
/* Packs the sign `zSign', exponent `zExp', and significand `zFrac' 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 `zFrac' is a complete, normalized
* significand.
*/
float
__packFloat32(uint zSign, int zExp, uint zFrac)
{
return uintBitsToFloat((zSign<<31) + (uint(zExp)<<23) + zFrac);
}
/* Takes an abstract floating-point value having sign `zSign', exponent `zExp',
* and significand `zFrac', 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 `zFrac' 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 `zFrac' 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 `zFrac' is
* normalized, `zExp' must be 1 less than the "true" floating-point exponent.
* The handling of underflow and overflow follows the IEEE Standard for
* Floating-Point Arithmetic.
*/
float
__roundAndPackFloat32(uint zSign, int zExp, uint zFrac)
{
bool roundNearestEven;
int roundIncrement;
int roundBits;
roundNearestEven = FLOAT_ROUNDING_MODE == FLOAT_ROUND_NEAREST_EVEN;
roundIncrement = 0x40;
if (!roundNearestEven) {
if (FLOAT_ROUNDING_MODE == FLOAT_ROUND_TO_ZERO) {
roundIncrement = 0;
} else {
roundIncrement = 0x7F;
if (zSign != 0u) {
if (FLOAT_ROUNDING_MODE == FLOAT_ROUND_UP)
roundIncrement = 0;
} else {
if (FLOAT_ROUNDING_MODE == FLOAT_ROUND_DOWN)
roundIncrement = 0;
}
}
}
roundBits = int(zFrac & 0x7Fu);
if (0xFDu <= uint(zExp)) {
if ((0xFD < zExp) || ((zExp == 0xFD) && (int(zFrac) + roundIncrement) < 0))
return __packFloat32(zSign, 0xFF, 0u) - float(roundIncrement == 0);
int count = -zExp;
bool zexp_lt0 = zExp < 0;
uint zFrac_lt0 = mix(uint(zFrac != 0u), (zFrac>>count) | uint((zFrac<<((-count) & 31)) != 0u), (-zExp) < 32);
zFrac = mix(zFrac, zFrac_lt0, zexp_lt0);
roundBits = mix(roundBits, int(zFrac) & 0x7f, zexp_lt0);
zExp = mix(zExp, 0, zexp_lt0);
}
zFrac = (zFrac + uint(roundIncrement))>>7;
zFrac &= ~uint(((roundBits ^ 0x40) == 0) && roundNearestEven);
return __packFloat32(zSign, mix(zExp, 0, zFrac == 0u), zFrac);
}
/* 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 IEEE Standard for Floating-Point Arithmetic.
*/
float
__fp64_to_fp32(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
uint zFrac = 0u;
uint allZero = 0u;
uint aFracLo = __extractFloat64FracLo(__a);
uint aFracHi = __extractFloat64FracHi(__a);
int aExp = __extractFloat64Exp(__a);
uint aSign = __extractFloat64Sign(__a);
if (aExp == 0x7FF) {
__shortShift64Left(a.y, a.x, 12, a.y, a.x);
float rval = uintBitsToFloat((aSign<<31) | 0x7FC00000u | (a.y>>9));
rval = mix(__packFloat32(aSign, 0xFF, 0u), rval, (aFracHi | aFracLo) != 0u);
return rval;
}
__shift64RightJamming(aFracHi, aFracLo, 22, allZero, zFrac);
zFrac = mix(zFrac, zFrac | 0x40000000u, aExp != 0);
return __roundAndPackFloat32(aSign, aExp - 0x381, zFrac);
}
float
__uint64_to_fp32(uint64_t __a)
{
uint zFrac = 0u;
uvec2 aFrac = unpackUint2x32(__a);
int shiftCount = __countLeadingZeros32(mix(aFrac.y, aFrac.x, aFrac.y == 0u));
shiftCount -= mix(40, 8, aFrac.y == 0u);
if (0 <= shiftCount) {
__shortShift64Left(aFrac.y, aFrac.x, shiftCount, aFrac.y, aFrac.x);
bool is_zero = (aFrac.y | aFrac.x) == 0u;
return mix(__packFloat32(0u, 0x95 - shiftCount, aFrac.x), 0, is_zero);
}
shiftCount += 7;
__shift64RightJamming(aFrac.y, aFrac.x, -shiftCount, aFrac.y, aFrac.x);
zFrac = mix(aFrac.x<<shiftCount, aFrac.x, shiftCount < 0);
return __roundAndPackFloat32(0u, 0x9C - shiftCount, zFrac);
}
float
__int64_to_fp32(int64_t __a)
{
uint zFrac = 0u;
uint aSign = uint(__a < 0);
uint64_t absA = mix(uint64_t(__a), uint64_t(-__a), __a < 0);
uvec2 aFrac = unpackUint2x32(absA);
int shiftCount = __countLeadingZeros32(mix(aFrac.y, aFrac.x, aFrac.y == 0u));
shiftCount -= mix(40, 8, aFrac.y == 0u);
if (0 <= shiftCount) {
__shortShift64Left(aFrac.y, aFrac.x, shiftCount, aFrac.y, aFrac.x);
bool is_zero = (aFrac.y | aFrac.x) == 0u;
return mix(__packFloat32(aSign, 0x95 - shiftCount, aFrac.x), 0, absA == 0u);
}
shiftCount += 7;
__shift64RightJamming(aFrac.y, aFrac.x, -shiftCount, aFrac.y, aFrac.x);
zFrac = mix(aFrac.x<<shiftCount, aFrac.x, shiftCount < 0);
return __roundAndPackFloat32(aSign, 0x9C - shiftCount, zFrac);
}
/* Returns the result of converting the single-precision floating-point value
* `a' to the double-precision floating-point format.
*/
uint64_t
__fp32_to_fp64(float f)
{
uint a = floatBitsToUint(f);
uint aFrac = a & 0x007FFFFFu;
int aExp = int((a>>23) & 0xFFu);
uint aSign = a>>31;
uint zFrac0 = 0u;
uint zFrac1 = 0u;
if (aExp == 0xFF) {
if (aFrac != 0u) {
uint nanLo = 0u;
uint nanHi = a<<9;
__shift64Right(nanHi, nanLo, 12, nanHi, nanLo);
nanHi |= ((aSign<<31) | 0x7FF80000u);
return packUint2x32(uvec2(nanLo, nanHi));
}
return __packFloat64(aSign, 0x7FF, 0u, 0u);
}
if (aExp == 0) {
if (aFrac == 0u)
return __packFloat64(aSign, 0, 0u, 0u);
/* Normalize subnormal */
int shiftCount = __countLeadingZeros32(aFrac) - 8;
aFrac <<= shiftCount;
aExp = 1 - shiftCount;
--aExp;
}
__shift64Right(aFrac, 0u, 3, zFrac0, zFrac1);
return __packFloat64(aSign, aExp + 0x380, zFrac0, zFrac1);
}
/* Adds the 96-bit value formed by concatenating `a0', `a1', and `a2' to the
* 96-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
* modulo 2^96, so any carry out is lost. The result is broken into three
* 32-bit pieces which are stored at the locations pointed to by `z0Ptr',
* `z1Ptr', and `z2Ptr'.
*/
void
__add96(uint a0, uint a1, uint a2,
uint b0, uint b1, uint b2,
out uint z0Ptr,
out uint z1Ptr,
out uint z2Ptr)
{
uint z2 = a2 + b2;
uint carry1 = uint(z2 < a2);
uint z1 = a1 + b1;
uint carry0 = uint(z1 < a1);
uint z0 = a0 + b0;
z1 += carry1;
z0 += uint(z1 < carry1);
z0 += carry0;
z2Ptr = z2;
z1Ptr = z1;
z0Ptr = z0;
}
/* Subtracts the 96-bit value formed by concatenating `b0', `b1', and `b2' from
* the 96-bit value formed by concatenating `a0', `a1', and `a2'. Subtraction
* is modulo 2^96, so any borrow out (carry out) is lost. The result is broken
* into three 32-bit pieces which are stored at the locations pointed to by
* `z0Ptr', `z1Ptr', and `z2Ptr'.
*/
void
__sub96(uint a0, uint a1, uint a2,
uint b0, uint b1, uint b2,
out uint z0Ptr,
out uint z1Ptr,
out uint z2Ptr)
{
uint z2 = a2 - b2;
uint borrow1 = uint(a2 < b2);
uint z1 = a1 - b1;
uint borrow0 = uint(a1 < b1);
uint z0 = a0 - b0;
z0 -= uint(z1 < borrow1);
z1 -= borrow1;
z0 -= borrow0;
z2Ptr = z2;
z1Ptr = z1;
z0Ptr = z0;
}
/* Returns an approximation to the 32-bit integer quotient obtained by dividing
* `b' into the 64-bit value formed by concatenating `a0' and `a1'. The
* divisor `b' must be at least 2^31. If q is the exact quotient truncated
* toward zero, the approximation returned lies between q and q + 2 inclusive.
* If the exact quotient q is larger than 32 bits, the maximum positive 32-bit
* unsigned integer is returned.
*/
uint
__estimateDiv64To32(uint a0, uint a1, uint b)
{
uint b0;
uint b1;
uint rem0 = 0u;
uint rem1 = 0u;
uint term0 = 0u;
uint term1 = 0u;
uint z;
if (b <= a0)
return 0xFFFFFFFFu;
b0 = b>>16;
z = (b0<<16 <= a0) ? 0xFFFF0000u : (a0 / b0)<<16;
__mul32To64(b, z, term0, term1);
__sub64(a0, a1, term0, term1, rem0, rem1);
while (int(rem0) < 0) {
z -= 0x10000u;
b1 = b<<16;
__add64(rem0, rem1, b0, b1, rem0, rem1);
}
rem0 = (rem0<<16) | (rem1>>16);
z |= (b0<<16 <= rem0) ? 0xFFFFu : rem0 / b0;
return z;
}
uint
__sqrtOddAdjustments(int index)
{
uint res = 0u;
if (index == 0)
res = 0x0004u;
if (index == 1)
res = 0x0022u;
if (index == 2)
res = 0x005Du;
if (index == 3)
res = 0x00B1u;
if (index == 4)
res = 0x011Du;
if (index == 5)
res = 0x019Fu;
if (index == 6)
res = 0x0236u;
if (index == 7)
res = 0x02E0u;
if (index == 8)
res = 0x039Cu;
if (index == 9)
res = 0x0468u;
if (index == 10)
res = 0x0545u;
if (index == 11)
res = 0x631u;
if (index == 12)
res = 0x072Bu;
if (index == 13)
res = 0x0832u;
if (index == 14)
res = 0x0946u;
if (index == 15)
res = 0x0A67u;
return res;
}
uint
__sqrtEvenAdjustments(int index)
{
uint res = 0u;
if (index == 0)
res = 0x0A2Du;
if (index == 1)
res = 0x08AFu;
if (index == 2)
res = 0x075Au;
if (index == 3)
res = 0x0629u;
if (index == 4)
res = 0x051Au;
if (index == 5)
res = 0x0429u;
if (index == 6)
res = 0x0356u;
if (index == 7)
res = 0x029Eu;
if (index == 8)
res = 0x0200u;
if (index == 9)
res = 0x0179u;
if (index == 10)
res = 0x0109u;
if (index == 11)
res = 0x00AFu;
if (index == 12)
res = 0x0068u;
if (index == 13)
res = 0x0034u;
if (index == 14)
res = 0x0012u;
if (index == 15)
res = 0x0002u;
return res;
}
/* Returns an approximation to the square root of the 32-bit significand given
* by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
* `aExp' (the least significant bit) is 1, the integer returned approximates
* 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
* is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
* case, the approximation returned lies strictly within +/-2 of the exact
* value.
*/
uint
__estimateSqrt32(int aExp, uint a)
{
uint z;
int index = int(a>>27 & 15u);
if ((aExp & 1) != 0) {
z = 0x4000u + (a>>17) - __sqrtOddAdjustments(index);
z = ((a / z)<<14) + (z<<15);
a >>= 1;
} else {
z = 0x8000u + (a>>17) - __sqrtEvenAdjustments(index);
z = a / z + z;
z = (0x20000u <= z) ? 0xFFFF8000u : (z<<15);
if (z <= a)
return uint(int(a)>>1);
}
return ((__estimateDiv64To32(a, 0u, z))>>1) + (z>>1);
}
/* Returns the square root of the double-precision floating-point value `a'.
* The operation is performed according to the IEEE Standard for Floating-Point
* Arithmetic.
*/
uint64_t
__fsqrt64(uint64_t a)
{
uint zFrac0 = 0u;
uint zFrac1 = 0u;
uint zFrac2 = 0u;
uint doubleZFrac0 = 0u;
uint rem0 = 0u;
uint rem1 = 0u;
uint rem2 = 0u;
uint rem3 = 0u;
uint term0 = 0u;
uint term1 = 0u;
uint term2 = 0u;
uint term3 = 0u;
uint64_t default_nan = 0xFFFFFFFFFFFFFFFFUL;
uint aFracLo = __extractFloat64FracLo(a);
uint aFracHi = __extractFloat64FracHi(a);
int aExp = __extractFloat64Exp(a);
uint aSign = __extractFloat64Sign(a);
if (aExp == 0x7FF) {
if ((aFracHi | aFracLo) != 0u)
return __propagateFloat64NaN(a, a);
if (aSign == 0u)
return a;
return default_nan;
}
if (aSign != 0u) {
if ((uint(aExp) | aFracHi | aFracLo) == 0u)
return a;
return default_nan;
}
if (aExp == 0) {
if ((aFracHi | aFracLo) == 0u)
return __packFloat64(0u, 0, 0u, 0u);
__normalizeFloat64Subnormal(aFracHi, aFracLo, aExp, aFracHi, aFracLo);
}
int zExp = ((aExp - 0x3FF)>>1) + 0x3FE;
aFracHi |= 0x00100000u;
__shortShift64Left(aFracHi, aFracLo, 11, term0, term1);
zFrac0 = (__estimateSqrt32(aExp, term0)>>1) + 1u;
if (zFrac0 == 0u)
zFrac0 = 0x7FFFFFFFu;
doubleZFrac0 = zFrac0 + zFrac0;
__shortShift64Left(aFracHi, aFracLo, 9 - (aExp & 1), aFracHi, aFracLo);
__mul32To64(zFrac0, zFrac0, term0, term1);
__sub64(aFracHi, aFracLo, term0, term1, rem0, rem1);
while (int(rem0) < 0) {
--zFrac0;
doubleZFrac0 -= 2u;
__add64(rem0, rem1, 0u, doubleZFrac0 | 1u, rem0, rem1);
}
zFrac1 = __estimateDiv64To32(rem1, 0u, doubleZFrac0);
if ((zFrac1 & 0x1FFu) <= 5u) {
if (zFrac1 == 0u)
zFrac1 = 1u;
__mul32To64(doubleZFrac0, zFrac1, term1, term2);
__sub64(rem1, 0u, term1, term2, rem1, rem2);
__mul32To64(zFrac1, zFrac1, term2, term3);
__sub96(rem1, rem2, 0u, 0u, term2, term3, rem1, rem2, rem3);
while (int(rem1) < 0) {
--zFrac1;
__shortShift64Left(0u, zFrac1, 1, term2, term3);
term3 |= 1u;
term2 |= doubleZFrac0;
__add96(rem1, rem2, rem3, 0u, term2, term3, rem1, rem2, rem3);
}
zFrac1 |= uint((rem1 | rem2 | rem3) != 0u);
}
__shift64ExtraRightJamming(zFrac0, zFrac1, 0u, 10, zFrac0, zFrac1, zFrac2);
return __roundAndPackFloat64(0u, zExp, zFrac0, zFrac1, zFrac2);
}
uint64_t
__ftrunc64(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
int aExp = __extractFloat64Exp(__a);
uint zLo;
uint zHi;
int unbiasedExp = aExp - 1023;
int fracBits = 52 - unbiasedExp;
uint maskLo = mix(~0u << fracBits, 0u, fracBits >= 32);
uint maskHi = mix(~0u << (fracBits - 32), ~0u, fracBits < 33);
zLo = maskLo & a.x;
zHi = maskHi & a.y;
zLo = mix(zLo, 0u, unbiasedExp < 0);
zHi = mix(zHi, 0u, unbiasedExp < 0);
zLo = mix(zLo, a.x, unbiasedExp > 52);
zHi = mix(zHi, a.y, unbiasedExp > 52);
return packUint2x32(uvec2(zLo, zHi));
}
uint64_t
__ffloor64(uint64_t a)
{
bool is_positive = __fge64(a, 0ul);
uint64_t tr = __ftrunc64(a);
if (is_positive || __feq64(tr, a)) {
return tr;
} else {
return __fadd64(tr, 0xbff0000000000000ul /* -1.0 */);
}
}
uint64_t
__fround64(uint64_t __a)
{
uvec2 a = unpackUint2x32(__a);
int unbiasedExp = __extractFloat64Exp(__a) - 1023;
uint aHi = a.y;
uint aLo = a.x;
if (unbiasedExp < 20) {
if (unbiasedExp < 0) {
if ((aHi & 0x80000000u) != 0u && aLo == 0u) {
return 0;
}
aHi &= 0x80000000u;
if ((a.y & 0x000FFFFFu) == 0u && a.x == 0u) {
aLo = 0u;
return packUint2x32(uvec2(aLo, aHi));
}
aHi = mix(aHi, (aHi | 0x3FF00000u), unbiasedExp == -1);
aLo = 0u;
} else {
uint maskExp = 0x000FFFFFu >> unbiasedExp;
uint lastBit = maskExp + 1;
aHi += 0x00080000u >> unbiasedExp;
if ((aHi & maskExp) == 0u)
aHi &= ~lastBit;
aHi &= ~maskExp;
aLo = 0u;
}
} else if (unbiasedExp > 51 || unbiasedExp == 1024) {
return __a;
} else {
uint maskExp = 0xFFFFFFFFu >> (unbiasedExp - 20);
if ((aLo & maskExp) == 0u)
return __a;
uint tmp = aLo + (1u << (51 - unbiasedExp));
if(tmp < aLo)
aHi += 1u;
aLo = tmp;
aLo &= ~maskExp;
}
return packUint2x32(uvec2(aLo, aHi));
}
uint64_t
__fmin64(uint64_t a, uint64_t b)
{
if (__is_nan(a)) return b;
if (__is_nan(b)) return a;
if (__flt64_nonnan(a, b)) return a;
return b;
}
uint64_t
__fmax64(uint64_t a, uint64_t b)
{
if (__is_nan(a)) return b;
if (__is_nan(b)) return a;
if (__flt64_nonnan(a, b)) return b;
return a;
}
uint64_t
__ffract64(uint64_t a)
{
return __fadd64(a, __fneg64(__ffloor64(a)));
}