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/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
/*
// ALGORITHM DESCRIPTION:
// *
// * Compute atanh(x) as 0.5 * log((1 + x)/(1 - x))
// *
// * Special cases:
// *
// * atanh(0) = 0
// * atanh(+1) = +INF
// * atanh(-1) = -INF
// * atanh(x) = NaN if |x| > 1, or if x is a NaN or INF
//
*/
#include "../imf.h"
#pragma OPENCL FP_CONTRACT OFF
typedef struct {
unsigned int Log_HA_table[(1 << 8) + 2];
unsigned int SgnMask;
unsigned int XThreshold;
unsigned int XhMask;
unsigned int ExpMask0;
unsigned int ExpMask2;
unsigned int ha_poly_coeff[2];
unsigned int ExpMask;
unsigned int Two10;
unsigned int MinLog1p;
unsigned int MaxLog1p;
unsigned int HalfMask;
unsigned int L2H;
unsigned int L2L;
unsigned int sOne;
unsigned int sPoly[4];
unsigned int iHiDelta;
unsigned int iLoRange;
unsigned int iBrkValue;
unsigned int iOffExpoMask;
unsigned int sBigThreshold;
unsigned int sC2;
unsigned int sC3;
unsigned int sHalf;
unsigned int sLargestFinite;
unsigned int sLittleThreshold;
unsigned int sSign;
unsigned int sThirtyOne;
unsigned int sTopMask11;
unsigned int sTopMask12;
unsigned int sTopMask8;
unsigned int XScale;
unsigned int TinyRange;
unsigned int sLn2;
/* scalar part follow */
unsigned int sInfs[2];
unsigned int sOnes[2];
unsigned int sZeros[2];
} __ocl_svml_internal_satanh_ep_data_t;
static __ocl_svml_internal_satanh_ep_data_t __ocl_svml_internal_satanh_ep_data =
{
/* Log_HA_table */
{0xc2aeac38u, 0xb93cbf08u, 0xc2aeb034u, 0xb93ce972u, 0xc2aeb424u,
0xb95e1069u, 0xc2aeb814u, 0xb9412b26u, 0xc2aebbfcu, 0xb9272b41u,
0xc2aebfd4u, 0xb950fcd7u, 0xc2aec3acu, 0xb93f86b8u, 0xc2aec77cu,
0xb933aa90u, 0xc2aecb44u, 0xb92e4507u, 0xc2aecf04u, 0xb9302df1u,
0xc2aed2bcu, 0xb93a3869u, 0xc2aed66cu, 0xb94d32f7u, 0xc2aeda1cu,
0xb929e7b5u, 0xc2aeddbcu, 0xb9511c6au, 0xc2aee15cu, 0xb94392acu,
0xc2aee4f4u, 0xb94207fdu, 0xc2aee884u, 0xb94d35eau, 0xc2aeec14u,
0xb925d225u, 0xc2aeef94u, 0xb94c8ea1u, 0xc2aef314u, 0xb94219adu,
0xc2aef68cu, 0xb9471e0bu, 0xc2aef9fcu, 0xb95c430bu, 0xc2aefd6cu,
0xb9422ca0u, 0xc2af00d4u, 0xb9397b7bu, 0xc2af0434u, 0xb942cd1cu,
0xc2af0794u, 0xb91ebbeau, 0xc2af0ae4u, 0xb94ddf49u, 0xc2af0e34u,
0xb950cbabu, 0xc2af1184u, 0xb92812a5u, 0xc2af14c4u, 0xb9544303u,
0xc2af1804u, 0xb955e8d7u, 0xc2af1b44u, 0xb92d8d8du, 0xc2af1e74u,
0xb95bb7fau, 0xc2af21acu, 0xb920ec71u, 0xc2af24d4u, 0xb93dacccu,
0xc2af27fcu, 0xb9327882u, 0xc2af2b1cu, 0xb93fccb3u, 0xc2af2e3cu,
0xb9262434u, 0xc2af3154u, 0xb925f7a4u, 0xc2af3464u, 0xb93fbd72u,
0xc2af3774u, 0xb933e9f2u, 0xc2af3a7cu, 0xb942ef61u, 0xc2af3d84u,
0xb92d3dfbu, 0xc2af4084u, 0xb93343ffu, 0xc2af437cu, 0xb9556dbfu,
0xc2af4674u, 0xb95425adu, 0xc2af496cu, 0xb92fd461u, 0xc2af4c5cu,
0xb928e0a9u, 0xc2af4f44u, 0xb93faf8eu, 0xc2af522cu, 0xb934a465u,
0xc2af550cu, 0xb94820d2u, 0xc2af57ecu, 0xb93a84d8u, 0xc2af5ac4u,
0xb94c2eddu, 0xc2af5d9cu, 0xb93d7bb5u, 0xc2af606cu, 0xb94ec6aeu,
0xc2af633cu, 0xb9406992u, 0xc2af6604u, 0xb952bcb6u, 0xc2af68ccu,
0xb94616feu, 0xc2af6b8cu, 0xb95acde8u, 0xc2af6e4cu, 0xb951358fu,
0xc2af710cu, 0xb929a0b7u, 0xc2af73c4u, 0xb92460d4u, 0xc2af7674u,
0xb941c60fu, 0xc2af7924u, 0xb9421f4du, 0xc2af7bd4u, 0xb925ba37u,
0xc2af7e7cu, 0xb92ce340u, 0xc2af811cu, 0xb957e5adu, 0xc2af83c4u,
0xb9270b99u, 0xc2af865cu, 0xb95a9dfau, 0xc2af88fcu, 0xb932e4acu,
0xc2af8b94u, 0xb9302671u, 0xc2af8e24u, 0xb952a8fau, 0xc2af90b4u,
0xb95ab0eeu, 0xc2af9344u, 0xb94881e8u, 0xc2af95ccu, 0xb95c5e87u,
0xc2af9854u, 0xb9568869u, 0xc2af9adcu, 0xb9374037u, 0xc2af9d5cu,
0xb93ec5a6u, 0xc2af9fdcu, 0xb92d577du, 0xc2afa254u, 0xb9433399u,
0xc2afa4ccu, 0xb94096f3u, 0xc2afa744u, 0xb925bda3u, 0xc2afa9b4u,
0xb932e2e5u, 0xc2afac24u, 0xb928411du, 0xc2afae8cu, 0xb94611dau,
0xc2afb0f4u, 0xb94c8ddbu, 0xc2afb35cu, 0xb93bed15u, 0xc2afb5bcu,
0xb95466b2u, 0xc2afb81cu, 0xb9563119u, 0xc2afba7cu, 0xb94181f0u,
0xc2afbcd4u, 0xb9568e1eu, 0xc2afbf2cu, 0xb95589d1u, 0xc2afc184u,
0xb93ea881u, 0xc2afc3d4u, 0xb9521cf3u, 0xc2afc624u, 0xb950193bu,
0xc2afc874u, 0xb938cec0u, 0xc2afcabcu, 0xb94c6e3fu, 0xc2afcd04u,
0xb94b27d0u, 0xc2afcf4cu, 0xb9352ae6u, 0xc2afd18cu, 0xb94aa653u,
0xc2afd3ccu, 0xb94bc84cu, 0xc2afd60cu, 0xb938be68u, 0xc2afd844u,
0xb951b5a9u, 0xc2afda7cu, 0xb956da79u, 0xc2afdcb4u, 0xb94858aeu,
0xc2afdeecu, 0xb9265b90u, 0xc2afe11cu, 0xb9310dd5u, 0xc2afe34cu,
0xb92899abu, 0xc2afe574u, 0xb94d28b2u, 0xc2afe7a4u, 0xb91ee407u,
0xc2afe9c4u, 0xb95df440u, 0xc2afebecu, 0xb94a8170u, 0xc2afee14u,
0xb924b32au, 0xc2aff034u, 0xb92cb084u, 0xc2aff254u, 0xb922a015u,
0xc2aff46cu, 0xb946a7fcu, 0xc2aff684u, 0xb958eddfu, 0xc2aff89cu,
0xb95996edu, 0xc2affab4u, 0xb948c7e3u, 0xc2affcccu, 0xb926a508u,
0xc2affedcu, 0xb9335235u, 0xc2b000ecu, 0xb92ef2d4u, 0xc2b002f4u,
0xb959a9e1u, 0xc2b00504u, 0xb93399eeu, 0xc2b0070cu, 0xb93ce522u,
0xc2b00914u, 0xb935ad3du, 0xc2b00b14u, 0xb95e1399u, 0xc2b00d1cu,
0xb936392bu, 0xc2b00f1cu, 0xb93e3e84u}
/*== SgnMask ==*/
,
0x7fffffffu
/*== XThreshold ==*/
,
0x39800000u
/*== XhMask ==*/
,
0xffffff00u
/*== ExpMask0 ==*/
,
0x7f800000u
/*== ExpMask2 ==*/
,
0x7b000000u
/*== ha_poly_coeff[2] ==*/
,
{
// VHEX_BROADCAST( S, 3fE35103 ) /* coeff3 */
0x3eAAAB39u /* coeff2 */
,
0xbf000036u /* coeff1 */
}
/*== ExpMask ==*/
,
0x007fffffu
/*== Two10 ==*/
,
0x3b800000u
/*== MinLog1p ==*/
,
0xbf7fffffu
/*== MaxLog1p ==*/
,
0x7a800000u
/*== HalfMask ==*/
,
0xffffff00u
/*== L2H ==*/
,
0x3f317200u
/*== L2L ==*/
,
0x35bfbe00u
/*== sOne = SP 1.0 ==*/
,
0x3f800000u
/*== sPoly[] = SP polynomial ==*/
,
{
0xbf000000u /* -5.0000000000000000000000000e-01 P0 */
,
0x3eaa7160u /* 3.3289623260498046875000000e-01 P1 */
,
0xbe88e8feu /* -2.6740258932113647460937500e-01 P2 */
,
0x3e612933u /* 2.1988372504711151123046875e-01 P3 */
}
/*== iHiDelta = SP 80000000-7f000000 ==*/
,
0x01000000u
/*== iLoRange = SP 00800000+iHiDelta ==*/
,
0x01800000u
/*== iBrkValue = SP 2/3 ==*/
,
0x3f2aaaabu
/*== iOffExpoMask = SP significand mask ==*/
,
0x007fffffu
/*== sBigThreshold ==*/
,
0x4E800000u
/*== sC2 ==*/
,
0x3EC00000u
/*== sC3 ==*/
,
0x3EA00000u
/*== sHalf ==*/
,
0x3F000000u
/*== sLargestFinite ==*/
,
0x7F7FFFFFu
/*== sLittleThreshold ==*/
,
0x3D800000u
/*== sSign ==*/
,
0x80000000u
/*== sThirtyOne ==*/
,
0x41F80000u
/*== sTopMask11 ==*/
,
0xFFFFE000u
/*== sTopMask12 ==*/
,
0xFFFFF000u
/*== sTopMask8 ==*/
,
0xFFFF0000u
/*== XScale ==*/
,
0x30800000u
/*== TinyRange ==*/
,
0x0C000000u
/*== sLn2 = SP ln(2) ==*/
,
0x3f317218u
/* scalar part follow */
/*== sInfs = SP infinity, +/- ==*/
,
{0x7f800000u, 0xff800000u}
/*== sOnes = SP one, +/- ==*/
,
{0x3f800000u, 0xbf800000u}
/*== sZeros = SP zero +/- ==*/
,
{0x00000000u, 0x80000000u}}; /*sLn_Table*/
static __constant _iml_v2_sp_union_t __satanh_ep__imlsAtanhTab[3] = {
/* Other simple constants */
0x3F800000, /* ONE = 1.0 */
0x00000000, /* ZERO = 0.0 */
0x7F800000 /* INF = 0x7f800000 */
};
#pragma float_control(push)
#pragma float_control(precise, on)
// This is called for all inputs x with |x| >= 1, and for infinity and NaN.
//
// For +/- 1 return correspondingly signed infinity
// For larger arguments or infinity, return NaN
// For NaN, just return the same NaN
__attribute__((always_inline)) inline int
__ocl_svml_internal_satanh_ep(float *a, float *r) {
int nRet = 0;
float absx;
float fRes;
float sp_a = (*a);
/* Get absolute value of argument */
absx = sp_a;
(((_iml_v2_sp_union_t *)&absx)->hex[0] =
(((_iml_v2_sp_union_t *)&absx)->hex[0] & 0x7FFFFFFF) |
((_iml_uint32_t)(0) << 31));
// First consider finite inputs
if ((((((_iml_v2_sp_union_t *)&*a)->hex[0] >> 23) & 0xFF) !=
0xFF)) { // If x is +/- 1, return corresponding infinity.
if (((((_iml_v2_sp_union_t *)&(absx))->hex[0] ==
((__constant _iml_v2_sp_union_t *)&(
((__constant float *)__satanh_ep__imlsAtanhTab)[0]))
->hex[0])
? 1
: 0)) {
(*r) = (*a) / ((__constant float *)__satanh_ep__imlsAtanhTab)[1];
nRet = 2;
return nRet;
}
// Otherwise return NaN and raise invalid
{
(*r) = (float)(((__constant float *)__satanh_ep__imlsAtanhTab)[2] *
((__constant float *)__satanh_ep__imlsAtanhTab)[1]);
nRet = 1;
return nRet;
}
} else { // If x is infinite, return NaN and raise invalid
if (((((_iml_v2_sp_union_t *)&(absx))->hex[0] ==
((__constant _iml_v2_sp_union_t *)&(
((__constant float *)__satanh_ep__imlsAtanhTab)[2]))
->hex[0])
? 1
: 0)) {
(*r) = (float)(sp_a * ((__constant float *)__satanh_ep__imlsAtanhTab)[1]);
nRet = 1;
return nRet;
}
// Otherwise reflect input NaN
{
(*r) = (float)((*a) * (*a));
return nRet;
}
}
}
#pragma float_control(pop)
float __ocl_svml_atanhf_ep(float x) {
float r;
unsigned int vm;
float va1;
float vr1;
va1 = x;
{
float SgnMask;
unsigned int iSpecialMask;
float sSpecialMask;
float sTinyMask;
float sD;
float sE;
float sH;
float sHalf;
float sInput;
float sL;
float sQHi;
float sQLo;
float sR;
float sResult;
float sSign;
float sTmp1;
float sTmp2;
float sTmp3;
float sTmp4;
float sTopMask12;
float sU;
float sUHi;
float suLo;
float sUTmp;
float sV;
float sVHi;
float sVLo;
float sZ;
float sTinyRes;
float sTinyRange;
unsigned int iBrkValue;
unsigned int iOffExpoMask;
float One;
unsigned int iOne;
float sExp;
float X;
float Xl;
float A;
float B;
float Rl;
float Rh;
float Rlh;
float sR2;
float Kh;
float sLn2;
float sPoly[4];
unsigned int iX;
float sN;
unsigned int iN;
unsigned int iR;
float sP;
unsigned int iExp;
// Load constants including One = 1
One = as_float(__ocl_svml_internal_satanh_ep_data.sOne);
SgnMask = as_float(__ocl_svml_internal_satanh_ep_data.SgnMask);
// Strip off the sign, so treat X as positive until right at the end
sInput = as_float((as_uint(va1) & as_uint(SgnMask)));
// Check whether |X| < 1, in which case we use the main function.
sSpecialMask = as_float(((unsigned int)(-(signed int)(!(sInput < One)))));
iSpecialMask = as_uint(sSpecialMask);
vm = 0;
vm = iSpecialMask;
sTinyRange = as_float(__ocl_svml_internal_satanh_ep_data.TinyRange);
sTinyMask = as_float(((unsigned int)(-(signed int)(sInput < sTinyRange))));
sTinyRes = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(va1, va1, va1);
// Record the sign for eventual reincorporation.
sSign = as_float(__ocl_svml_internal_satanh_ep_data.sSign);
sSign = as_float((as_uint(va1) & as_uint(sSign)));
// Or the sign bit in with the tiny result to handle atanh(-0) correctly
sTinyRes = as_float((as_uint(sTinyRes) | as_uint(sSign)));
// Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
// the upper part UHi being <= 12 bits long. Then we have
// atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + uLo)).
sV = (sInput + sInput);
sU = (One - sInput);
sUTmp = (One - sU);
sUTmp = (sUTmp - sInput);
sTopMask12 = as_float(__ocl_svml_internal_satanh_ep_data.sTopMask12);
sZ = (1.0f / (sU));
sR = as_float((as_uint(sZ) & as_uint(sTopMask12)));
// No need to split sU when FMA is available
sE = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(-(sR), sU, One);
sE = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(-(sR), sUTmp, sE);
// Split V as well into upper 12 bits and lower part, so that we can get
// a preliminary quotient estimate without rounding error.
sVHi = as_float((as_uint(sV) & as_uint(sTopMask12)));
sVLo = (sV - sVHi);
// Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo
sQHi = (sR * sVHi);
sQLo = (sR * sVLo);
// Compute D = E + E^2
sD = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sE, sE, sE);
// Compute R * (VHi + VLo) * (1 + E + E^2)
// = R * (VHi + VLo) * (1 + D)
// = QHi + (QHi * D + QLo + QLo * D)
sTmp1 = (sD * sQHi);
sTmp2 = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sD, sQLo, sQLo);
sTmp3 = (sTmp1 + sTmp2);
// Now finally accumulate the high and low parts of the
// argument to log1p, H + L, with a final compensated summation.
sH = (sQHi + sTmp3);
sTmp4 = (sQHi - sH);
sL = (sTmp4 + sTmp3);
// Now we feed into the log1p code, using H in place of _VARG1 and
// later incorporating L into the reduced argument.
// compute 1+x as high, low parts
A = ((One > sH) ? One : sH);
B = ((One < sH) ? One : sH);
X = (A + B);
Xl = (A - X);
Xl = (Xl + B);
Xl = (Xl + sL);
iX = as_uint(X);
/* reduction: compute r,n */
iBrkValue = (__ocl_svml_internal_satanh_ep_data.iBrkValue);
iOffExpoMask = (__ocl_svml_internal_satanh_ep_data.iOffExpoMask);
iX = (iX - iBrkValue);
iR = (iX & iOffExpoMask);
iN = ((signed int)iX >> (23));
iR = (iR + iBrkValue);
sN = ((float)((int)(iN)));
sR = as_float(iR);
iExp = ((unsigned int)(iN) << (23));
iOne = as_uint(One);
iExp = (iOne - iExp);
sExp = as_float(iExp);
Rl = (Xl * sExp);
/* polynomial evaluation */
Rh = (sR - One);
sR = (Rh + Rl);
sPoly[3] = as_float(__ocl_svml_internal_satanh_ep_data.sPoly[3]);
sPoly[2] = as_float(__ocl_svml_internal_satanh_ep_data.sPoly[2]);
sP = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sPoly[3], sR, sPoly[2]);
sPoly[1] = as_float(__ocl_svml_internal_satanh_ep_data.sPoly[1]);
sP = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sP, sR, sPoly[1]);
sPoly[0] = as_float(__ocl_svml_internal_satanh_ep_data.sPoly[0]);
sP = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sP, sR, sPoly[0]);
sP = (sP * sR);
sP = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sP, sR, sR);
/* final reconstruction */
sLn2 = as_float(__ocl_svml_internal_satanh_ep_data.sLn2);
// Result = N*Log(2) + P
sResult = SPIRV_OCL_BUILTIN(fma, _f32_f32_f32, )(sN, sLn2, sP);
// Finally, halve the result and reincorporate the sign:
sHalf = as_float(__ocl_svml_internal_satanh_ep_data.sHalf);
// Half = Half^Sign
sHalf = as_float((as_uint(sHalf) ^ as_uint(sSign)));
// Result = Half*Result
vr1 = (sHalf * sResult);
// Blend main path result and tiny arguments path result
vr1 = as_float((((~as_uint(sTinyMask)) & as_uint(vr1)) |
(as_uint(sTinyMask) & as_uint(sTinyRes))));
}
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_satanh_ep(&__cout_a1, &__cout_r1);
vr1 = ((float *)&__cout_r1)[0];
}
r = vr1;
return r;
}
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