[Libclc-dev] [PATCH 4/9] Implement asinh builtin
Tom Stellard
thomas.stellard at amd.com
Thu Mar 12 13:11:41 PDT 2015
This implementation was ported from the AMD builtin library
and has been tested with piglit, OpenCV, and the ocl conformance tests.
---
generic/include/clc/clc.h | 1 +
generic/include/clc/math/asinh.h | 24 +++
generic/include/clc/math/asinh.inc | 23 +++
generic/lib/SOURCES | 1 +
generic/lib/math/asinh.cl | 293 +++++++++++++++++++++++++++++++++++++
5 files changed, 342 insertions(+)
create mode 100644 generic/include/clc/math/asinh.h
create mode 100644 generic/include/clc/math/asinh.inc
create mode 100644 generic/lib/math/asinh.cl
diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
index 8ac7fbc..44abf12 100644
--- a/generic/include/clc/clc.h
+++ b/generic/include/clc/clc.h
@@ -36,6 +36,7 @@
#include <clc/math/acosh.h>
#include <clc/math/acospi.h>
#include <clc/math/asin.h>
+#include <clc/math/asinh.h>
#include <clc/math/atan.h>
#include <clc/math/atan2.h>
#include <clc/math/copysign.h>
diff --git a/generic/include/clc/math/asinh.h b/generic/include/clc/math/asinh.h
new file mode 100644
index 0000000..64417b8
--- /dev/null
+++ b/generic/include/clc/math/asinh.h
@@ -0,0 +1,24 @@
+/*
+ * 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.
+ */
+
+#define __CLC_BODY <clc/math/asinh.inc>
+#include <clc/math/gentype.inc>
diff --git a/generic/include/clc/math/asinh.inc b/generic/include/clc/math/asinh.inc
new file mode 100644
index 0000000..a544008
--- /dev/null
+++ b/generic/include/clc/math/asinh.inc
@@ -0,0 +1,23 @@
+/*
+ * 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.
+ */
+
+_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE asinh(__CLC_GENTYPE x);
diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
index c6d11e4..48f459b 100644
--- a/generic/lib/SOURCES
+++ b/generic/lib/SOURCES
@@ -65,6 +65,7 @@ math/acos.cl
math/acosh.cl
math/acospi.cl
math/asin.cl
+math/asinh.cl
math/atan.cl
math/atan2.cl
math/copysign.cl
diff --git a/generic/lib/math/asinh.cl b/generic/lib/math/asinh.cl
new file mode 100644
index 0000000..cfddb31
--- /dev/null
+++ b/generic/lib/math/asinh.cl
@@ -0,0 +1,293 @@
+/*
+ * 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
--
2.0.4
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