/*
* Copyright (c) 2014,2015 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include <clc/clc.h>
#include "math.h"
#include "ep_log.h"
#include "../clcmacro.h"
_CLC_OVERLOAD _CLC_DEF float asinh(float x) {
uint ux = as_uint(x);
uint ax = ux & EXSIGNBIT_SP32;
uint xsgn = ax ^ ux;
// |x| <= 2
float t = x * x;
float a = mad(t,
mad(t,
mad(t,
mad(t, -1.177198915954942694e-4f, -4.162727710583425360e-2f),
-5.063201055468483248e-1f),
-1.480204186473758321f),
-1.152965835871758072f);
float b = mad(t,
mad(t,
mad(t,
mad(t, 6.284381367285534560e-2f, 1.260024978680227945f),
6.582362487198468066f),
11.99423176003939087f),
6.917795026025976739f);
float q = MATH_DIVIDE(a, b);
float z1 = mad(x*t, q, x);
// |x| > 2
// Arguments greater than 1/sqrt(epsilon) in magnitude are
// approximated by asinh(x) = ln(2) + ln(abs(x)), with sign of x
// Arguments such that 4.0 <= abs(x) <= 1/sqrt(epsilon) are
// approximated by asinhf(x) = ln(abs(x) + sqrt(x*x+1))
// with the sign of x (see Abramowitz and Stegun 4.6.20)
float absx = as_float(ax);
int hi = ax > 0x46000000U;
float y = MATH_SQRT(absx * absx + 1.0f) + absx;
y = hi ? absx : y;
float r = log(y) + (hi ? 0x1.62e430p-1f : 0.0f);
float z2 = as_float(xsgn | as_uint(r));
float z = ax <= 0x40000000 ? z1 : z2;
z = ax < 0x39800000U | ax >= PINFBITPATT_SP32 ? x : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, asinh, float)
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
#define NA0 -0.12845379283524906084997e0
#define NA1 -0.21060688498409799700819e0
#define NA2 -0.10188951822578188309186e0
#define NA3 -0.13891765817243625541799e-1
#define NA4 -0.10324604871728082428024e-3
#define DA0 0.77072275701149440164511e0
#define DA1 0.16104665505597338100747e1
#define DA2 0.11296034614816689554875e1
#define DA3 0.30079351943799465092429e0
#define DA4 0.235224464765951442265117e-1
#define NB0 -0.12186605129448852495563e0
#define NB1 -0.19777978436593069928318e0
#define NB2 -0.94379072395062374824320e-1
#define NB3 -0.12620141363821680162036e-1
#define NB4 -0.903396794842691998748349e-4
#define DB0 0.73119630776696495279434e0
#define DB1 0.15157170446881616648338e1
#define DB2 0.10524909506981282725413e1
#define DB3 0.27663713103600182193817e0
#define DB4 0.21263492900663656707646e-1
#define NC0 -0.81210026327726247622500e-1
#define NC1 -0.12327355080668808750232e0
#define NC2 -0.53704925162784720405664e-1
#define NC3 -0.63106739048128554465450e-2
#define NC4 -0.35326896180771371053534e-4
#define DC0 0.48726015805581794231182e0
#define DC1 0.95890837357081041150936e0
#define DC2 0.62322223426940387752480e0
#define DC3 0.15028684818508081155141e0
#define DC4 0.10302171620320141529445e-1
#define ND0 -0.4638179204422665073e-1
#define ND1 -0.7162729496035415183e-1
#define ND2 -0.3247795155696775148e-1
#define ND3 -0.4225785421291932164e-2
#define ND4 -0.3808984717603160127e-4
#define ND5 0.8023464184964125826e-6
#define DD0 0.2782907534642231184e0
#define DD1 0.5549945896829343308e0
#define DD2 0.3700732511330698879e0
#define DD3 0.9395783438240780722e-1
#define DD4 0.7200057974217143034e-2
#define NE0 -0.121224194072430701e-4
#define NE1 -0.273145455834305218e-3
#define NE2 -0.152866982560895737e-2
#define NE3 -0.292231744584913045e-2
#define NE4 -0.174670900236060220e-2
#define NE5 -0.891754209521081538e-12
#define DE0 0.499426632161317606e-4
#define DE1 0.139591210395547054e-2
#define DE2 0.107665231109108629e-1
#define DE3 0.325809818749873406e-1
#define DE4 0.415222526655158363e-1
#define DE5 0.186315628774716763e-1
#define NF0 -0.195436610112717345e-4
#define NF1 -0.233315515113382977e-3
#define NF2 -0.645380957611087587e-3
#define NF3 -0.478948863920281252e-3
#define NF4 -0.805234112224091742e-12
#define NF5 0.246428598194879283e-13
#define DF0 0.822166621698664729e-4
#define DF1 0.135346265620413852e-2
#define DF2 0.602739242861830658e-2
#define DF3 0.972227795510722956e-2
#define DF4 0.510878800983771167e-2
#define NG0 -0.209689451648100728e-6
#define NG1 -0.219252358028695992e-5
#define NG2 -0.551641756327550939e-5
#define NG3 -0.382300259826830258e-5
#define NG4 -0.421182121910667329e-17
#define NG5 0.492236019998237684e-19
#define DG0 0.889178444424237735e-6
#define DG1 0.131152171690011152e-4
#define DG2 0.537955850185616847e-4
#define DG3 0.814966175170941864e-4
#define DG4 0.407786943832260752e-4
#define NH0 -0.178284193496441400e-6
#define NH1 -0.928734186616614974e-6
#define NH2 -0.923318925566302615e-6
#define NH3 -0.776417026702577552e-19
#define NH4 0.290845644810826014e-21
#define DH0 0.786694697277890964e-6
#define DH1 0.685435665630965488e-5
#define DH2 0.153780175436788329e-4
#define DH3 0.984873520613417917e-5
#define NI0 -0.538003743384069117e-10
#define NI1 -0.273698654196756169e-9
#define NI2 -0.268129826956403568e-9
#define NI3 -0.804163374628432850e-29
#define DI0 0.238083376363471960e-9
#define DI1 0.203579344621125934e-8
#define DI2 0.450836980450693209e-8
#define DI3 0.286005148753497156e-8
_CLC_OVERLOAD _CLC_DEF double asinh(double x) {
const double rteps = 0x1.6a09e667f3bcdp-27;
const double recrteps = 0x1.6a09e667f3bcdp+26;
// log2_lead and log2_tail sum to an extra-precise version of log(2)
const double log2_lead = 0x1.62e42ep-1;
const double log2_tail = 0x1.efa39ef35793cp-25;
ulong ux = as_ulong(x);
ulong ax = ux & ~SIGNBIT_DP64;
double absx = as_double(ax);
double t = x * x;
double pn, tn, pd, td;
// XXX we are betting here that we can evaluate 8 pairs of
// polys faster than we can grab 12 coefficients from a table
// This also uses fewer registers
// |x| >= 8
pn = fma(t, fma(t, fma(t, NI3, NI2), NI1), NI0);
pd = fma(t, fma(t, fma(t, DI3, DI2), DI1), DI0);
tn = fma(t, fma(t, fma(t, fma(t, NH4, NH3), NH2), NH1), NH0);
td = fma(t, fma(t, fma(t, DH3, DH2), DH1), DH0);
pn = absx < 8.0 ? tn : pn;
pd = absx < 8.0 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, fma(t, NG5, NG4), NG3), NG2), NG1), NG0);
td = fma(t, fma(t, fma(t, fma(t, DG4, DG3), DG2), DG1), DG0);
pn = absx < 4.0 ? tn : pn;
pd = absx < 4.0 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, fma(t, NF5, NF4), NF3), NF2), NF1), NF0);
td = fma(t, fma(t, fma(t, fma(t, DF4, DF3), DF2), DF1), DF0);
pn = absx < 2.0 ? tn : pn;
pd = absx < 2.0 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, fma(t, NE5, NE4), NE3), NE2), NE1), NE0);
td = fma(t, fma(t, fma(t, fma(t, fma(t, DE5, DE4), DE3), DE2), DE1), DE0);
pn = absx < 1.5 ? tn : pn;
pd = absx < 1.5 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, fma(t, ND5, ND4), ND3), ND2), ND1), ND0);
td = fma(t, fma(t, fma(t, fma(t, DD4, DD3), DD2), DD1), DD0);
pn = absx <= 1.0 ? tn : pn;
pd = absx <= 1.0 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, NC4, NC3), NC2), NC1), NC0);
td = fma(t, fma(t, fma(t, fma(t, DC4, DC3), DC2), DC1), DC0);
pn = absx < 0.75 ? tn : pn;
pd = absx < 0.75 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, NB4, NB3), NB2), NB1), NB0);
td = fma(t, fma(t, fma(t, fma(t, DB4, DB3), DB2), DB1), DB0);
pn = absx < 0.5 ? tn : pn;
pd = absx < 0.5 ? td : pd;
tn = fma(t, fma(t, fma(t, fma(t, NA4, NA3), NA2), NA1), NA0);
td = fma(t, fma(t, fma(t, fma(t, DA4, DA3), DA2), DA1), DA0);
pn = absx < 0.25 ? tn : pn;
pd = absx < 0.25 ? td : pd;
double pq = MATH_DIVIDE(pn, pd);
// |x| <= 1
double result1 = fma(absx*t, pq, absx);
// Other ranges
int xout = absx <= 32.0 | absx > recrteps;
double y = absx + sqrt(fma(absx, absx, 1.0));
y = xout ? absx : y;
double r1, r2;
int xexp;
__clc_ep_log(y, &xexp, &r1, &r2);
double dxexp = (double)(xexp + xout);
r1 = fma(dxexp, log2_lead, r1);
r2 = fma(dxexp, log2_tail, r2);
// 1 < x <= 32
double v2 = (pq + 0.25) / t;
double r = v2 + r1;
double s = ((r1 - r) + v2) + r2;
double v1 = r + s;
v2 = (r - v1) + s;
double result2 = v1 + v2;
// x > 32
double result3 = r1 + r2;
double ret = absx > 1.0 ? result2 : result1;
ret = absx > 32.0 ? result3 : ret;
ret = x < 0.0 ? -ret : ret;
// NaN, +-Inf, or x small enough that asinh(x) = x
ret = ax >= PINFBITPATT_DP64 | absx < rteps ? x : ret;
return ret;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, asinh, double)
#endif
_CLC_DEFINE_UNARY_BUILTIN_FP16(asinh)
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