| /* |
| * 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 |
