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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 long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_Tbl_exp[] = {
{0x0000000000000000uL}, {0x0000000000000000uL}, {0x0001b5586cf9890fuL},
{0x3c979aa65d837b6duL}, {0x000372b83c7d517buL}, {0xbc801b15eaa59348uL},
{0x0001387a6e756238uL}, {0x3c968efde3a8a894uL}, {0x000706fe0a31b715uL},
{0x3c834d754db0abb6uL}, {0x0006dea64c123422uL}, {0x3c859f48a72a4c6duL},
{0x0002bfdad5362a27uL}, {0x3c7690cebb7aafb0uL}, {0x0002ab07dd485429uL},
{0x3c9063e1e21c5409uL}, {0x000ea09e667f3bcduL}, {0xbc93b3efbf5e2229uL},
{0x000ea11473eb0187uL}, {0xbc7b32dcb94da51duL}, {0x0002ace5422aa0dbuL},
{0x3c8db72fc1f0eab5uL}, {0x0002c49182a3f090uL}, {0x3c71affc2b91ce27uL},
{0x0006e89f995ad3aduL}, {0x3c8c1a7792cb3386uL}, {0x0001199bdd85529cuL},
{0x3c736eae30af0cb3uL}, {0x00035818dcfba487uL}, {0x3c74a385a63d07a8uL},
{0x0001a4afa2a490dauL}, {0xbc8ff7128fd391f0uL},
};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc7 = {0x3efa01f8f4be0535uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc6 = {0x3f2a01f8f4b129ccuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc5 = {0x3f56c16c16304601uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc4 = {0x3f81111110a65711uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc3 = {0x3fa555555555560auL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc2 = {0x3fc55555555555f9uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc1 = {0x3fe0000000000000uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_dc0 = {0xbc13b588106b310fuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_Shifter = {0x4338000000003ff0uL};
//__STATIC __CONST INT_DOUBLE_TYPE _VSTATIC(L2E) = { 0x3ff71547652B82FEuL };
static __constant union {
unsigned int w;
float f;
int i;
} __dexpm1_ha_fL2E = {0x41B8AA3Bu};
static __constant union {
unsigned int w;
float f;
int i;
} __dexpm1_ha_fShifter = {0x4b403ff0u};
// -log(2)_high/16
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_p_NL2H = {0xbfa62e42fefa39f0uL};
// -log(2)_low/16
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ha_p_NL2L = {0x3c5950d871319ff0uL};
__attribute__((always_inline)) inline int
__ocl_svml_internal_dexpm1_ha(double *pxin, double *pres) {
int nRet = 0;
double xin = *pxin;
// double expm1(double xin)
union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} x, T, Tlr, sc, xa, res;
double dN, Rh, Rl, R, poly, A, B, Bh, Th, Tl;
double H, Rhh, Rhl, ThRh, ThRh_l;
int index;
union {
unsigned int w;
float f;
int i;
} xf, fN, xL2E, fS;
x.f = xin;
xf.f = (float)xin;
xL2E.f =
SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(xf.f, __dexpm1_ha_fL2E.f, 0.0f);
fN.f = SPIRV_OCL_BUILTIN(trunc, _f32, )(xL2E.f);
fS.f = __dexpm1_ha_fShifter.f + fN.f;
dN = (double)fN.f;
index = (fS.w & 0xf) << 1;
// reduced argument
Rh = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(dN, __dexpm1_ha_p_NL2H.f, x.f);
Rl = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(dN, __dexpm1_ha_p_NL2L.f, 0.0);
R = Rh + Rl;
// 2^N, N=(int)dN
T.w32[1] = (fS.w << (20 - 4)) ^ __dexpm1_ha_Tbl_exp[index].w32[1];
T.w32[0] = __dexpm1_ha_Tbl_exp[index].w32[0];
Tlr.w32[1] = __dexpm1_ha_Tbl_exp[index + 1].w32[1];
Tlr.w32[0] = 0;
// Tlr.f = _VSTATIC(Tbl_exp)[index + 1].f + Rl;
Tlr.f += Rl;
// e^R - 1
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(__dexpm1_ha_dc7.f, R,
__dexpm1_ha_dc6.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ha_dc5.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ha_dc4.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ha_dc3.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ha_dc2.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ha_dc1.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ha_dc0.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, Tlr.f);
// maxabs(T,-1), minabs(T,-1)
A = (xin >= 0.0) ? T.f : -1.0;
B = (xin >= 0.0) ? -1.0 : T.f;
Th = T.f - 1.0;
Bh = Th - A;
Tl = B - Bh;
// T*Rh
ThRh = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, Rh, 0.0);
ThRh_l = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, Rh, -ThRh);
// Th + Th*Rh
H = ThRh + Th;
// (Th*Rh)_high
Rhh = H - Th;
// (Th*Rh)_low
Rhl = ThRh - Rhh;
Tl = Tl + Rhl + ThRh_l;
// 2^N*poly + Tl
res.f = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, poly, Tl);
res.f = res.f + H;
if (SPIRV_OCL_BUILTIN(fabs, _f32, )(xf.f) <= 708.0f) {
*pres = res.f;
return nRet;
}
// special case and overflow path
if (xf.f < 0) {
*pres = -1.0;
return nRet;
}
if (!(xf.f < 1024.0)) {
// +Inf or NaN?
xa.w = x.w & 0x7fffffffffffffffuL;
if (xa.w > 0x7ff0000000000000uL) {
*pres = x.f + res.f;
return nRet;
}
// overflow
res.w = 0x7ff0000000000000uL - 1;
res.f = res.f * res.f; // to set OF flag
nRet = 3;
{
*pres = res.f;
return nRet;
}
}
// at or near overflow
// 2^(N-512), N=(int)dN
T.w32[1] =
((fS.w - 512 * 16) << (20 - 4)) ^ __dexpm1_ha_Tbl_exp[index].w32[1];
T.w32[0] = __dexpm1_ha_Tbl_exp[index].w32[0];
// T.w = ((S.w - 512 * 16) << (52 - 4)) ^ _VSTATIC(Tbl_exp)[index].w;
poly += Rh;
res.f = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, poly, T.f);
// final scaling
sc.w = 0x5ff0000000000000uL;
res.f *= sc.f;
// determine if overflow
if (res.w == 0x7ff0000000000000uL)
nRet = 3;
*pres = res.f;
return nRet;
}
double __ocl_svml_expm1_ha(double x) {
double r;
__ocl_svml_internal_dexpm1_ha(&x, &r);
return r;
}
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