[PATCH] libclc/math: Add cospi
Aaron Watry
awatry at gmail.com
Wed Dec 17 16:35:48 PST 2014
Ported from the libclc/amd-builtins branch
v2: Rename sincos_f_piby4 to __libclc__sincosf_piby4
Add cospi(double) implementation instead of using llvm.cos
Notes:
The sincosD_piby4.h file is mostly the same as the builtin implementation
released by AMD. The inline attribute declaration is changed, and M_PI is
used instead of a constant double. Otherwise, the only difference is that
the header explicitly enables the fp64 pragma.
Piglit lacks the built-in capability to test double-precision CL builtins
at the moment. I hacked the cospi(float) tests to use cospi(double) to
verify that the implementation runs and produces reasonable results, but
I have NOT added new test cases to piglit which exercise the additional
precision of the double-precision data type for cospi.
Signed-off-by: Aaron Watry <awatry at gmail.com>
CC: Tom Stellard <tom at stellard.net>
CC: Jeroen Ketema <j.ketema at imperial.ac.uk>
CC: Matt Arsenault <Matthew.Arsenault at amd.com>
---
generic/include/clc/clc.h | 1 +
generic/include/clc/math/cospi.h | 3 +
generic/include/clc/math/cospi.inc | 1 +
generic/lib/SOURCES | 1 +
generic/lib/math/cospi.cl | 136 +++++++++++++++++++++++++++++++++++++
generic/lib/math/sincosD_piby4.h | 78 +++++++++++++++++++++
generic/lib/math/sincospiF_piby4.h | 56 +++++++++++++++
7 files changed, 276 insertions(+)
create mode 100644 generic/include/clc/math/cospi.h
create mode 100644 generic/include/clc/math/cospi.inc
create mode 100644 generic/lib/math/cospi.cl
create mode 100644 generic/lib/math/sincosD_piby4.h
create mode 100644 generic/lib/math/sincospiF_piby4.h
diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
index bd92fdb..bff6ddd 100644
--- a/generic/include/clc/clc.h
+++ b/generic/include/clc/clc.h
@@ -38,6 +38,7 @@
#include <clc/math/atan2.h>
#include <clc/math/copysign.h>
#include <clc/math/cos.h>
+#include <clc/math/cospi.h>
#include <clc/math/ceil.h>
#include <clc/math/exp.h>
#include <clc/math/exp10.h>
diff --git a/generic/include/clc/math/cospi.h b/generic/include/clc/math/cospi.h
new file mode 100644
index 0000000..427733b
--- /dev/null
+++ b/generic/include/clc/math/cospi.h
@@ -0,0 +1,3 @@
+#define __CLC_BODY <clc/math/cospi.inc>
+#include <clc/math/gentype.inc>
+#undef __CLC_BODY
diff --git a/generic/include/clc/math/cospi.inc b/generic/include/clc/math/cospi.inc
new file mode 100644
index 0000000..1e786cf
--- /dev/null
+++ b/generic/include/clc/math/cospi.inc
@@ -0,0 +1 @@
+_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE cospi(__CLC_GENTYPE a);
diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
index b76fec9..2b9426e 100644
--- a/generic/lib/SOURCES
+++ b/generic/lib/SOURCES
@@ -57,6 +57,7 @@ math/atan.cl
math/atan2.cl
math/copysign.cl
math/cos.cl
+math/cospi.cl
math/exp.cl
math/exp10.cl
math/fmax.cl
diff --git a/generic/lib/math/cospi.cl b/generic/lib/math/cospi.cl
new file mode 100644
index 0000000..108b637
--- /dev/null
+++ b/generic/lib/math/cospi.cl
@@ -0,0 +1,136 @@
+/*
+ * Copyright (c) 2014 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 "sincos_helpers.h"
+#include "sincospiF_piby4.h"
+#include "../clcmacro.h"
+#ifdef cl_khr_fp64
+#include "sincosD_piby4.h"
+#endif
+
+_CLC_OVERLOAD _CLC_DEF float cospi(float x)
+{
+ int ix = as_int(x) & 0x7fffffff;
+ float ax = as_float(ix);
+ int iax = (int)ax;
+ float r = ax - iax;
+ int xodd = iax & 0x1 ? 0x80000000 : 0;
+
+ // Initialize with return for +-Inf and NaN
+ int ir = 0x7fc00000;
+
+ // 2^24 <= |x| < Inf, the result is always even integer
+ ir = ix < 0x7f800000 ? 0x3f800000 : ir;
+
+ // 2^23 <= |x| < 2^24, the result is always integer
+ ir = ix < 0x4b800000 ? xodd | 0x3f800000 : ir;
+
+ // 0x1.0p-7 <= |x| < 2^23, result depends on which 0.25 interval
+
+ // r < 1.0
+ float a = 1.0f - r;
+ int e = 1;
+ int s = xodd ^ 0x80000000;
+
+ // r <= 0.75
+ int c = r <= 0.75f;
+ a = c ? r - 0.5f : a;
+ e = c ? 0 : e;
+
+ // r < 0.5
+ c = r < 0.5f;
+ a = c ? 0.5f - r : a;
+ s = c ? xodd : s;
+
+ // r <= 0.25
+ c = r <= 0.25f;
+ a = c ? r : a;
+ e = c ? 1 : e;
+
+ float2 t = __libclc__sincosf_piby4(a * M_PI_F);
+ int jr = s ^ as_int(e ? t.hi : t.lo);
+
+ ir = ix < 0x4b000000 ? jr : ir;
+
+ return as_float(ir);
+}
+
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cospi, float);
+
+#ifdef cl_khr_fp64
+
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+_CLC_OVERLOAD _CLC_DEF double cospi(double x) {
+
+ long ix = as_long(x) & 0x7fffffffffffffffL;
+ double ax = as_double(ix);
+ long iax = (long)ax;
+ double r = ax - (double)iax;
+ long xodd = iax & 0x1L ? 0x8000000000000000L : 0L;
+
+ // Initialize with return for +-Inf and NaN
+ long ir = 0x7ff8000000000000L;
+
+ // 2^53 <= |x| < Inf, the result is always even integer
+ ir = ix < 0x7ff0000000000000 ? 0x3ff0000000000000L : ir;
+
+ // 2^52 <= |x| < 2^53, the result is always integer
+ ir = ax < 0x1.0p+53 ? xodd | 0x3ff0000000000000L : ir;
+
+ // 0x1.0p-7 <= |x| < 2^52, result depends on which 0.25 interval
+
+ // r < 1.0
+ double a = 1.0 - r;
+ int e = 1;
+ long s = xodd ^ 0x8000000000000000L;
+
+ // r <= 0.75
+ int c = r <= 0.75;
+ double t = r - 0.5;
+ a = c ? t : a;
+ e = c ? 0 : e;
+
+ // r < 0.5
+ c = r < 0.5;
+ t = 0.5 - r;
+ a = c ? t : a;
+ s = c ? xodd : s;
+
+ // r <= 0.25
+ c = r <= 0.25;
+ a = c ? r : a;
+ e = c ? 1 : e;
+
+ double2 sc = __libclc__sincos_piby4(a * M_PI, 0.0);
+ long jr = s ^ as_long(e ? sc.hi : sc.lo);
+
+ ir = ax < 0x1.0p+52 ? jr : ir;
+
+ return as_double(ir);
+}
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cospi, double);
+#endif
diff --git a/generic/lib/math/sincosD_piby4.h b/generic/lib/math/sincosD_piby4.h
new file mode 100644
index 0000000..a00db85
--- /dev/null
+++ b/generic/lib/math/sincosD_piby4.h
@@ -0,0 +1,78 @@
+/*
+ * Copyright (c) 2014 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.
+ */
+
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+_CLC_INLINE double2
+__libclc__sincos_piby4(double x, double xx)
+{
+ // Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
+ // = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
+ // = x * f(w)
+ // where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
+ // We use a minimax approximation of (f(w) - 1) / w
+ // because this produces an expansion in even powers of x.
+ // If xx (the tail of x) is non-zero, we add a correction
+ // term g(x,xx) = (1-x*x/2)*xx to the result, where g(x,xx)
+ // is an approximation to cos(x)*sin(xx) valid because
+ // xx is tiny relative to x.
+
+ // Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
+ // = f(w)
+ // where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
+ // We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
+ // because this produces an expansion in even powers of x.
+ // If xx (the tail of x) is non-zero, we subtract a correction
+ // term g(x,xx) = x*xx to the result, where g(x,xx)
+ // is an approximation to sin(x)*sin(xx) valid because
+ // xx is tiny relative to x.
+
+ const double sc1 = -0.166666666666666646259241729;
+ const double sc2 = 0.833333333333095043065222816e-2;
+ const double sc3 = -0.19841269836761125688538679e-3;
+ const double sc4 = 0.275573161037288022676895908448e-5;
+ const double sc5 = -0.25051132068021699772257377197e-7;
+ const double sc6 = 0.159181443044859136852668200e-9;
+
+ const double cc1 = 0.41666666666666665390037e-1;
+ const double cc2 = -0.13888888888887398280412e-2;
+ const double cc3 = 0.248015872987670414957399e-4;
+ const double cc4 = -0.275573172723441909470836e-6;
+ const double cc5 = 0.208761463822329611076335e-8;
+ const double cc6 = -0.113826398067944859590880e-10;
+
+ double x2 = x * x;
+ double x3 = x2 * x;
+ double r = 0.5 * x2;
+ double t = 1.0 - r;
+
+ double sp = fma(fma(fma(fma(sc6, x2, sc5), x2, sc4), x2, sc3), x2, sc2);
+
+ double cp = t + fma(fma(fma(fma(fma(fma(cc6, x2, cc5), x2, cc4), x2, cc3), x2, cc2), x2, cc1),
+ x2*x2, fma(x, xx, (1.0 - t) - r));
+
+ double2 ret;
+ ret.lo = x - fma(-x3, sc1, fma(fma(-x3, sp, 0.5*xx), x2, -xx));
+ ret.hi = cp;
+
+ return ret;
+}
diff --git a/generic/lib/math/sincospiF_piby4.h b/generic/lib/math/sincospiF_piby4.h
new file mode 100644
index 0000000..90ecb1d
--- /dev/null
+++ b/generic/lib/math/sincospiF_piby4.h
@@ -0,0 +1,56 @@
+/*
+ * Copyright (c) 2014 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.
+ */
+
+// Evaluate single precisions in and cos of value in interval [-pi/4, pi/4]
+_CLC_INLINE float2
+__libclc__sincosf_piby4(float x)
+{
+ // Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
+ // = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
+ // = x * f(w)
+ // where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
+ // We use a minimax approximation of (f(w) - 1) / w
+ // because this produces an expansion in even powers of x.
+
+ // Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
+ // = f(w)
+ // where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
+ // We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
+ // because this produces an expansion in even powers of x.
+
+ const float sc1 = -0.166666666638608441788607926e0F;
+ const float sc2 = 0.833333187633086262120839299e-2F;
+ const float sc3 = -0.198400874359527693921333720e-3F;
+ const float sc4 = 0.272500015145584081596826911e-5F;
+
+ const float cc1 = 0.41666666664325175238031e-1F;
+ const float cc2 = -0.13888887673175665567647e-2F;
+ const float cc3 = 0.24800600878112441958053e-4F;
+ const float cc4 = -0.27301013343179832472841e-6F;
+
+ float x2 = x * x;
+
+ float2 ret;
+ ret.x = mad(x*x2, mad(x2, mad(x2, mad(x2, sc4, sc3), sc2), sc1), x);
+ ret.y = mad(x2*x2, mad(x2, mad(x2, mad(x2, cc4, cc3), cc2), cc1), mad(x2, -0.5f, 1.0f));
+ return ret;
+}
--
2.1.0
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