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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_ep_dc7 = {0x3efa5b0597ae2842uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc6 = {0x3f2a5b062ac4ca1auL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc5 = {0x3f56c0d9c1d50009uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc4 = {0x3f8110a57824968buL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc3 = {0x3fa555560b7d4cbeuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc2 = {0x3fc55555faec57afuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc1 = {0x3fdfffffff013d80uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_dc0 = {0xbe13e699df82e534uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_Shifter = {0x43380000000003ffuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_L2E = {0x3ff71547652B82FEuL};
static __constant union {
unsigned int w;
float f;
int i;
} __dexpm1_ep_fL2E = {0x3FB8AA3Bu};
static __constant union {
unsigned int w;
float f;
int i;
} __dexpm1_ep_fShifter = {0x4b4003ffu};
// -log(2)_high
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_p_NL2H = {0xbfe62e42fefa39efuL};
// -log(2)_low
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexpm1_ep_p_NL2L = {0xbc7abc9e3b39803fuL};
__attribute__((always_inline)) inline int
__ocl_svml_internal_dexpm1_ep(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, sc, xa, res;
double dN, R, poly, Th;
union {
unsigned int w;
float f;
int i;
} x0f, fS, fN;
x0f.f = (float)xin;
// 2^52*1.5 + x*log2(e)
fS.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(x0f.f, __dexpm1_ep_fL2E.f,
__dexpm1_ep_fShifter.f);
// dN = rint(x*log2(e))
fN.f = fS.f - __dexpm1_ep_fShifter.f;
// reduced argument
dN = (double)fN.f;
// reduced argument
R = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(dN, __dexpm1_ep_p_NL2H.f, xin);
// R = DP_FMA(dN, _VSTATIC(p_NL2L).f, R);
// 2^N, N=(int)dN
T.w32[1] = fS.w << 20;
T.w32[0] = 0;
// e^R - 1
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(__dexpm1_ep_dc7.f, R,
__dexpm1_ep_dc6.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ep_dc5.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ep_dc4.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ep_dc3.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ep_dc2.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ep_dc1.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexpm1_ep_dc0.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, R);
// maxabs(T,-1), minabs(T,-1)
Th = T.f - 1.0;
// 2^N*poly + Tl
res.f = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, poly, Th);
if (SPIRV_OCL_BUILTIN(fabs, _f32, )(x0f.f) <= 708.0f) {
*pres = res.f;
return nRet;
}
// special path
if (x0f.f < 0) {
*pres = -1.0;
return nRet;
}
if (!(x0f.f < 1024.0f)) {
// +Inf or NaN?
x.f = xin;
xa.w = x.w & 0x7fffffffffffffffuL;
if (xa.w > 0x7ff0000000000000uL) {
*pres = x.f + res.f;
return nRet;
}
// overflow
res.w = (res.w & 0x0007ffffffffffffuL) | 0x7fd0000000000000uL;
res.f = res.f * xin; // 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) << 20;
T.w32[0] = 0;
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_ep(double x) {
double r;
__ocl_svml_internal_dexpm1_ep(&x, &r);
return r;
}
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