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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;
} __dexp_ha_p_L2E = {0x3ff71547652B82FEuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_Shifter = {0x43280000000007feuL};
// -log(2)_high
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_NL2H = {0xbfe62e42fefa39efuL};
// -log(2)_low
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_NL2L = {0xbc7abc9e3b39803fuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c0 = {0x3fdffffffffffe76uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c1 = {0x3fc5555555555462uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c2 = {0x3fa55555556228ceuL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c3 = {0x3f811111111ac486uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c4 = {0x3f56c16b8144bd5buL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c5 = {0x3f2a019f7560fba3uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c6 = {0x3efa072e44b58159uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_c7 = {0x3ec722bccc270959uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_p_one = {0x3ff0000000000000uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_thres = {0x4086232A00000000uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_min_norm = {0x0010000000000000uL};
static __constant union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} __dexp_ha_Inf = {0x7ff0000000000000uL};
__attribute__((always_inline)) inline int
__ocl_svml_internal_dexp_ha(double *a, double *r) {
int nRet = 0;
double x = *a;
union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} xi, zero, res_special, scale;
union {
unsigned long w;
unsigned int w32[2];
int s32[2];
double f;
} idx, T, Tlr;
double N, R, R0, poly, res;
int expon32, mask32, mask_h;
unsigned int xa32, sgn_x, expon_corr;
// x*log2(e) + Shifter
idx.f = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(x, __dexp_ha_p_L2E.f,
__dexp_ha_p_Shifter.f);
// x*log2(e), rounded to 1 fractional bit
N = idx.f - __dexp_ha_p_Shifter.f;
// bit mask to select "table" value
mask32 = idx.w32[0] << 31;
// prepare exponent
expon32 = idx.w32[0] << (20 + 31 - 32);
// initial reduced argument
R0 = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(__dexp_ha_p_NL2H.f, N, x);
// reduced argument
R = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(__dexp_ha_p_NL2L.f, N, R0);
// start polynomial computation
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(__dexp_ha_p_c7.f, R,
__dexp_ha_p_c6.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_c5.f);
// bit mask to select "table" value
mask32 = mask32 >> 31;
// polynomial
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_c4.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_c3.f);
// "table" correction
// mask.w &= 0x000EA09E667F3BCDuL;
mask_h = mask32 & 0x000EA09E;
// polynomial
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_c2.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_c1.f);
// combine exponent, "table" value
T.w32[1] = expon32 ^ mask_h;
T.w32[0] = mask32 & 0x667F3BCD;
Tlr.w32[1] = 0x3C6E51C5 ^ (mask32 & (0xBC8FD36E ^ 0x3C6E51C5)); // 0xBC93B3EF;
Tlr.w32[0] = 0;
// polynomial
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_c0.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, __dexp_ha_p_one.f);
poly = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(poly, R, Tlr.f);
// if (xa32 > 0x4086232Au)
if (SPIRV_OCL_BUILTIN(fabs, _f64, )(x) >= __dexp_ha_thres.f)
goto EXP_SPECIAL_PATH;
// result
res = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, poly, T.f);
*r = res;
return nRet;
EXP_SPECIAL_PATH:
xi.f = x;
xa32 = xi.w32[1] & 0x7fffffffu;
// sign of x
sgn_x = xa32 ^ xi.w32[1];
if (xa32 < 0x40879127u) {
expon_corr = sgn_x ? 0x08000000u : 0xF8000000u;
scale.w = sgn_x ? 0x37f0000000000000uL : 0x47f0000000000000uL;
// apply correction (+/-128) to exponent embedded in T
T.w32[1] += expon_corr;
// result
res = SPIRV_OCL_BUILTIN(fma, _f64_f64_f64, )(T.f, poly, T.f);
// final scaling
res *= scale.f;
} else {
// underflow or overflow?
res_special.w = sgn_x ? 0x0000000000000000uL : 0x7ff0000000000000uL;
// check for NaNs
xi.w32[1] = xa32;
res_special.f = (xi.w <= 0x7ff0000000000000uL) ? res_special.f : x;
// quietize NaNs
zero.w = 0;
res = res_special.f + zero.f;
}
nRet = (res < __dexp_ha_min_norm.f) ? 4 : nRet;
nRet = (res == __dexp_ha_Inf.f) ? 3 : nRet;
*r = res;
return nRet;
}
double __ocl_svml_exp_ha(double x) {
double r;
__ocl_svml_internal_dexp_ha(&x, &r);
return r;
}
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