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/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
#include "../imf.h"
#pragma OPENCL FP_CONTRACT OFF
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c7 = {0x37d2d82du};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c6 = {0x3952d831u};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c5 = {0x3ab606ceu};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c4 = {0x3c08852cu};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c3 = {0x3d2aaab0u};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c2 = {0x3e2aaab0u};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c1 = {0xb07ec280u};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_c0 = {0xb09f34cfu};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_fL2E = {0x3FB8AA3Bu};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_fShifter = {0x4b40007fu};
// log(2) high, low
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_NL2H = {0xbf317218u};
static __constant union {
unsigned int w;
float f;
int i;
} __sexpm1_ha_NL2L = {0x3102E308u};
__attribute__((always_inline)) inline int
__ocl_svml_internal_sexpm1_ha(float *a, float *pres) {
int nRet = 0;
float xin = *a;
// float expm1f(float xin)
union {
unsigned int w;
float f;
int i;
} xf, fN, xL2E, fS, xa;
union {
unsigned int w;
float f;
int i;
} T, sc, res;
float R, Rh, Rl, A, B, Bh, Th, Tl;
float H, poly, Rhh, Rhl, ThRh, ThRh_l;
float H1, H2, Rhh2, Rhl2, poly0;
xf.f = xin;
xL2E.f =
SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(xf.f, __sexpm1_ha_fL2E.f, 0.0f);
fN.f = SPIRV_OCL_BUILTIN(trunc, _f32, )(xL2E.f);
fS.f = __sexpm1_ha_fShifter.f + fN.f;
// reduced argument
Rh = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fN.f, __sexpm1_ha_NL2H.f, xf.f);
Rl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(fN.f, __sexpm1_ha_NL2L.f, 0.0f);
R = Rh + Rl;
// 2^N
T.w = fS.w << 23;
// e^R - 1
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(__sexpm1_ha_c7.f, R,
__sexpm1_ha_c6.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __sexpm1_ha_c5.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __sexpm1_ha_c4.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __sexpm1_ha_c3.f);
poly0 = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __sexpm1_ha_c2.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly0, R, __sexpm1_ha_c1.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __sexpm1_ha_c0.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, Rl);
// maxabs(T,-1), minabs(T,-1)
A = (xin >= 0.0f) ? T.f : -1.0f;
B = (xin >= 0.0f) ? -1.0f : T.f;
Th = T.f - 1.0f;
Bh = Th - A;
Tl = B - Bh;
// T*Rh
ThRh = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(T.f, Rh, 0.0f);
ThRh_l = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(T.f, Rh, -ThRh);
// Th + Th*Rh
H = ThRh + Th;
// 2*H
H1 = H + H;
// (Th*Rh)_high
Rhh = H - Th;
// (Th*Rh)_low
Rhl = ThRh - Rhh;
Tl = Tl + Rhl + ThRh_l;
// H+H+Rh*Rh
H2 = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(ThRh, Rh, H1);
// Rh^2_high
Rhh2 = H2 - H1;
// Rh^2_low
Rhl2 = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(ThRh, Rh, -Rhh2);
// Tl += 0.5*Rhl2 + Rh*Rl
Tl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(ThRh, Rl, Tl);
Tl = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(Rhl2, 0.5f, Tl);
// 2^N*poly + Tl
res.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(T.f, poly, Tl);
res.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(H2, 0.5f, res.f);
// ensure expm1(-0)=-0
xa.f = SPIRV_OCL_BUILTIN(fabs, _f32, )(xf.f);
res.w |= (xf.w ^ xa.w);
if (SPIRV_OCL_BUILTIN(fabs, _f32, )(xf.f) <= 87.0f) {
*pres = res.f;
return nRet;
}
// special case and overflow path
if (xf.f < 0) {
*pres = -1.0f;
return nRet;
}
if (!(xf.f < 128.0f)) {
// +Inf or NaN?
xa.w = xf.w & 0x7fffffff;
if (xa.w > 0x7f800000) {
*pres = xf.f + res.f;
return nRet;
}
// overflow
res.w = 0x7f800000 - 1;
res.f = res.f * res.f; // to set OF flag
//
nRet = 3;
{
*pres = res.f;
return nRet;
}
}
// at or near overflow
// 2^(N-64), N=(int)dN
T.w = (fS.w - 64) << 23;
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly0, R, 0.5f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, __sexpm1_ha_c1.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, R, Rl);
poly += Rh;
res.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(T.f, poly, T.f);
// final scaling
sc.w = 0x5f800000u;
res.f *= sc.f;
// determine if overflow
if (res.w == 0x7f800000)
nRet = 3;
*pres = res.f;
return nRet;
}
float __ocl_svml_expm1f_ha(float x) {
float r;
__ocl_svml_internal_sexpm1_ha(&x, &r);
return r;
}
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