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/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
/*
// ALGORITHM DESCRIPTION:
// *
// * Compute cosh(x) as (exp(x)+exp(-x))/2,
// * where exp is calculated as
// * exp(M*ln2 + ln2*(j/2^k) + r) = 2^M * 2^(j/2^k) * exp(r)
// *
// * Special cases:
// *
// * cosh(NaN) = quiet NaN, and raise invalid exception
// * cosh(INF) = that INF
// * cosh(0) = 1
// * cosh(x) overflows for big x and returns MAXLOG+log(2)
//
*/
#include "../imf.h"
#pragma OPENCL FP_CONTRACT OFF
typedef struct {
/*Shared*/
unsigned int _sExp_tbl_PH[32];
unsigned int _sExp_tbl_PL[32];
unsigned int _sExp_tbl_NH[32];
unsigned int _sShifter_UISA;
unsigned int _iIndexMask_UISA;
unsigned int _iDomainRange_UISA;
unsigned int _sPC1_UISA;
unsigned int _sPC2_UISA;
unsigned int _sPC3_UISA;
unsigned int _sInvLn2;
unsigned int _sInvLn2lo;
unsigned int _sLn2hi;
unsigned int _sLn2lo;
unsigned int _sSign;
unsigned int _sOne;
unsigned int _sNOne;
unsigned int _iExpMask;
/* Shared name but with different value */
unsigned int _sShifter;
unsigned int _iIndexMask;
unsigned int _iDomainRange;
unsigned int _sPC1;
unsigned int _sPC2;
unsigned int _sPC3;
unsigned int _sPC4;
// Ints
unsigned int _iHalf;
} __ocl_svml_internal_scosh_ep_data_t;
static __ocl_svml_internal_scosh_ep_data_t __ocl_svml_internal_scosh_ep_data = {
{/* _sExp_tbl_PH 2^(i/32-1), i=0..31 */
0x3f000000u, 0x3f02cd87u, 0x3f05aac3u, 0x3f08980fu, 0x3f0b95c2u,
0x3f0ea43au, 0x3f11c3d3u, 0x3f14f4f0u, 0x3f1837f0u, 0x3f1b8d3au,
0x3f1ef532u, 0x3f227043u, 0x3f25fed7u, 0x3f29a15bu, 0x3f2d583fu,
0x3f3123f6u, 0x3f3504f3u, 0x3f38fbafu, 0x3f3d08a4u, 0x3f412c4du,
0x3f45672au, 0x3f49b9beu, 0x3f4e248cu, 0x3f52a81eu, 0x3f5744fdu,
0x3f5bfbb8u, 0x3f60ccdfu, 0x3f65b907u, 0x3f6ac0c7u, 0x3f6fe4bau,
0x3f75257du, 0x3f7a83b3u},
{/* for i in [|0,...,31|] do printsingle( 2^(i/32-1) -
round(2^(i/32-1),SG,RN)); */
0x00000000u, 0xb2cea7a9u, 0x32cf9891u, 0xb2feda4bu, 0xb1e0aba1u,
0xb2e97465u, 0x32e75624u, 0xb2ae0212u, 0x32a31b71u, 0xb28c5563u,
0x32c12342u, 0x3043125au, 0xb2ac9d5eu, 0xb2962b08u, 0xb1adeaf6u,
0xb2fc5aa8u, 0x324fe77au, 0x328ec5f7u, 0xb2c14fe8u, 0xb256663eu,
0x318aa837u, 0xb2f323a2u, 0x31a8fc24u, 0xb2dc1daau, 0xb254a58au,
0xb2d04a1cu, 0xb19eab59u, 0xb1c41be6u, 0xb1c116deu, 0xb2c8464au,
0x31a92436u, 0xb2123758u},
{/* _sExp_tbl_NH 2^(-i/32-1), i=0..31 */
0x3f000000u, 0x3efa83b3u, 0x3ef5257du, 0x3eefe4bau, 0x3eeac0c7u,
0x3ee5b907u, 0x3ee0ccdfu, 0x3edbfbb8u, 0x3ed744fdu, 0x3ed2a81eu,
0x3ece248cu, 0x3ec9b9beu, 0x3ec5672au, 0x3ec12c4du, 0x3ebd08a4u,
0x3eb8fbafu, 0x3eb504f3u, 0x3eb123f6u, 0x3ead583fu, 0x3ea9a15bu,
0x3ea5fed7u, 0x3ea27043u, 0x3e9ef532u, 0x3e9b8d3au, 0x3e9837f0u,
0x3e94f4f0u, 0x3e91c3d3u, 0x3e8ea43au, 0x3e8b95c2u, 0x3e88980fu,
0x3e85aac3u, 0x3e82cd87u},
0x48c00000u, /* 1.5*2^18 _sShifter_UISA */
0x0000001fu, /* _iIndexMask_UISA */
0x42AEAC4Eu, /* _iDomainRange_UISA */
0x3F800000u, /* _sPC1_UISA=1 */
0x3f00010fu, /* _sPC2_UISA */
0x3e2aaacdu, /* _sPC3_UISA */
0x3FB8AA3Bu,
/* _sInvLn2 */ // k=0
0x32A57060u, /* _sInvLn2lo*/
0x3F317000u, /* _sLn2hi */
0x3805fdf4u, /* _sLn2lo */
0x80000000u, /* _sSign */
0x3f800000u, /* _sOne */
0xbf800000u, /* _sNOne */
0x7f800000u, /* _iExpMask */
0x4b400000u, /* _sShifter */
0x0000001fu, /* _iIndexMask */
0x42AEAC4Eu, /* _iDomainRange */
0x3f7ffbc9u, /* _sPC1 */
0x3efffb2fu, /* _sPC2 */
0x3e2ccd2eu, /* _sPC3 */
0x3d2ca395u, /* _sPC4 */
// Integer constants
0x3f000000u /* _iHalf*/
}; /*_VAPI_DATA_TYPE*/
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_Shifter = {0x4ac000feu};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_L2E = {0x3FB8AA3Bu};
// log(2) high, low
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_L2H = {0x3f317218u};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_L2L = {0xb102E308u};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_c5 = {0x3c08ba8bu};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_c4 = {0x3d2aec4eu};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_c3 = {0x3e2aaa9cu};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_c2 = {0x3effffe8u};
static __constant union {
unsigned int w;
float f;
int i;
} __scosh_ep_c1 = {0x3f800000u};
__attribute__((always_inline)) inline int
__ocl_svml_internal_scosh_ep(float *a, float *r) {
int nRet = 0;
float x = SPIRV_OCL_BUILTIN(fabs, _f32, )(*a);
union {
unsigned int w;
float f;
int i;
} S, Th, Tlr, Th2, xin, xa, res;
float N, R, poly;
int index_mask;
S.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(x, __scosh_ep_L2E.f,
__scosh_ep_Shifter.f);
N = S.f - __scosh_ep_Shifter.f;
R = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )((-N), __scosh_ep_L2H.f, x);
R = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )((-N), __scosh_ep_L2L.f, R);
// set exponent in place
Th.w = S.w << 22;
// index_mask is based on last bit of S.w
index_mask = 0 - (S.w & 1);
// set Th mantissa
Th.w ^= (index_mask & 0x7504F3u);
// set Tl/Th value
Tlr.w = index_mask & 0x329302AEu;
// polynomial
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(R, __scosh_ep_c5.f,
__scosh_ep_c4.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(R, poly, __scosh_ep_c3.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(R, poly, __scosh_ep_c2.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(R, poly, __scosh_ep_c1.f);
poly = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(R, poly, Tlr.f);
xin.f = x;
xa.w = xin.w & 0x7fffffffu;
// redirect special cases
if (xa.w > 0x42AEAC4Fu)
goto COSHF_SPECIAL;
res.f = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, Th.f, Th.f);
*r = res.f;
return nRet;
COSHF_SPECIAL:
if (xa.w > 0x42b2d4fcu) {
if (xa.w > 0x7f800000u) { // NaN?
*r = x + x;
return nRet;
}
// overflow
res.w = 0x7f800000;
*r = res.f;
nRet = 3;
return nRet;
}
S.w += 0xfe;
Th2.w = (S.w >> 2) & 0xff;
S.w -= (Th2.w << 1);
Th2.w <<= 23; // second exponent scale
Th.w = S.w << 22;
// set Th mantissa
Th.w ^= (index_mask & 0x7504F3u);
res.f = 0.5f * SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(poly, Th.f, Th.f);
res.f *= Th2.f;
*r = res.f;
return nRet;
}
float __ocl_svml_coshf_ep(float x) {
float r;
unsigned int vm;
float va1;
float vr1;
va1 = x;
{
float sN;
float sM;
float sR;
float sR2;
float sSinh_r;
float sOut;
float sG1;
float sG2;
float sXSign;
float sAbsX;
unsigned int iM;
unsigned int iAbsX;
unsigned int iRangeMask;
float sInvLn2;
float sShifter;
float sPC[6];
unsigned int iHalf;
unsigned int iDomainRange;
sInvLn2 = as_float(__ocl_svml_internal_scosh_ep_data._sInvLn2);
sShifter = as_float(__ocl_svml_internal_scosh_ep_data._sShifter);
sPC[0] = as_float(__ocl_svml_internal_scosh_ep_data._sPC1); // x^1
sPC[1] = as_float(__ocl_svml_internal_scosh_ep_data._sPC2); // x^2
sPC[2] = as_float(__ocl_svml_internal_scosh_ep_data._sPC3); //...
sPC[3] = as_float(__ocl_svml_internal_scosh_ep_data._sPC4);
sXSign = as_float(__ocl_svml_internal_scosh_ep_data._sSign);
iHalf = (__ocl_svml_internal_scosh_ep_data._iHalf);
iDomainRange = (__ocl_svml_internal_scosh_ep_data._iDomainRange);
/* -------------------- Implementation ------------------- */
/* ............... Abs argument ............................ */
sAbsX = as_float((~(as_uint(sXSign)) & as_uint(va1)));
/* ............... Load argument ............................ */
// dM = x/log(2) + RShifter
sM = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sAbsX, sInvLn2, sShifter);
/* ...............Check for overflow\underflow ............. */
// iAbsX = bitimage(abs(x))
iAbsX = as_uint(sAbsX);
iRangeMask = ((unsigned int)(-(signed int)((signed int)iAbsX >=
(signed int)iDomainRange)));
vm = 0;
vm = iRangeMask;
/* R computation: */
// sN = sM - RShifter
sN = (sM - sShifter);
sOut = as_float(__ocl_svml_internal_scosh_ep_data._sLn2hi);
// sR = sX - sN*Log2_hi
sR = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(-(sOut), sN, sAbsX);
sOut = as_float(__ocl_svml_internal_scosh_ep_data._sLn2lo);
// sR = (sX - sN*Log2_hi) - sN*Log2_lo
sR = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(-(sOut), sN, sR);
/* G1,G2 2^N,2^(-N) computation: */
iM = as_uint(sM);
// iM now is an EXP(2^N)
iM = ((unsigned int)(iM) << (23));
// sR2 = sR^2,shaffled
sR2 = (sR * sR);
iAbsX = (iHalf + iM);
// sG1=2^(N-1)
sG1 = as_float(iAbsX);
iAbsX = (iHalf - iM);
// sG2=2^(-N-1)
sG2 = as_float(iAbsX);
sM = sG1;
// sG1 = 2^(N-1)-2^(-N-1)
sG1 = (sG1 - sG2);
// sG2 = 2^(N-1)+2^(-N-1)
sG2 = (sM + sG2);
/*....sinh(r) = r*(a1+r^2*a3) ....*/
sSinh_r = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(
sPC[2], sR2, sPC[0]); // sSinh_r = (a1+r^2*a3) --mul r later
/*....sinh(X) = sG2 + r*(sG1*sSinh_r + sG2*r*(a2+r2*a4)) */
sOut = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sPC[3], sR2,
sPC[1]); // sOut = (a2+a4*dR2)
sSinh_r = (sSinh_r * sG1); // sG1*sSinh_r
sOut = (sOut * sG2); // sOut = sG2*(a2+r2*a4)
sOut = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(
sOut, sR, sSinh_r); // sOut = sG1*sSinh_r + sG2*r*(a2+r2*a4)
vr1 = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(
sR, sOut, sG2); // sOut = sG2 + r*(sG1*sSinh_r + sG2*r*(a2+r2*a4))
/* ................... Ret H ...................... */
}
if (__builtin_expect((vm) != 0, 0)) {
float __cout_a1;
float __cout_r1;
((float *)&__cout_a1)[0] = va1;
((float *)&__cout_r1)[0] = vr1;
__ocl_svml_internal_scosh_ep(&__cout_a1, &__cout_r1);
vr1 = ((float *)&__cout_r1)[0];
}
r = vr1;
return r;
}
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