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/acospi.h | 24 +++++
generic/include/clc/math/acospi.inc | 23 +++++
generic/lib/SOURCES | 1 +
generic/lib/math/acospi.cl | 172 ++++++++++++++++++++++++++++++++++++
5 files changed, 221 insertions(+)
create mode 100644 generic/include/clc/math/acospi.h
create mode 100644 generic/include/clc/math/acospi.inc
create mode 100644 generic/lib/math/acospi.cl
diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
index 269d30d..8ac7fbc 100644
--- a/generic/include/clc/clc.h
+++ b/generic/include/clc/clc.h
@@ -34,6 +34,7 @@
/* 6.11.2 Math Functions */
#include <clc/math/acos.h>
#include <clc/math/acosh.h>
+#include <clc/math/acospi.h>
#include <clc/math/asin.h>
#include <clc/math/atan.h>
#include <clc/math/atan2.h>
diff --git a/generic/include/clc/math/acospi.h b/generic/include/clc/math/acospi.h
new file mode 100644
index 0000000..987657c
--- /dev/null
+++ b/generic/include/clc/math/acospi.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/acospi.inc>
+#include <clc/math/gentype.inc>
diff --git a/generic/include/clc/math/acospi.inc b/generic/include/clc/math/acospi.inc
new file mode 100644
index 0000000..265e6a8
--- /dev/null
+++ b/generic/include/clc/math/acospi.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 acospi(__CLC_GENTYPE x);
diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
index 29c40d8..c6d11e4 100644
--- a/generic/lib/SOURCES
+++ b/generic/lib/SOURCES
@@ -63,6 +63,7 @@ integer/sub_sat_impl.ll
integer/upsample.cl
math/acos.cl
math/acosh.cl
+math/acospi.cl
math/asin.cl
math/atan.cl
math/atan2.cl
diff --git a/generic/lib/math/acospi.cl b/generic/lib/math/acospi.cl
new file mode 100644
index 0000000..c91fc41
--- /dev/null
+++ b/generic/lib/math/acospi.cl
@@ -0,0 +1,172 @@
+/*
+ * 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 "../clcmacro.h"
+
+_CLC_OVERLOAD _CLC_DEF float acospi(float x) {
+ // Computes arccos(x).
+ // The argument is first reduced by noting that arccos(x)
+ // is invalid for abs(x) > 1. For denormal and small
+ // arguments arccos(x) = pi/2 to machine accuracy.
+ // Remaining argument ranges are handled as follows.
+ // For abs(x) <= 0.5 use
+ // arccos(x) = pi/2 - arcsin(x)
+ // = pi/2 - (x + x^3*R(x^2))
+ // where R(x^2) is a rational minimax approximation to
+ // (arcsin(x) - x)/x^3.
+ // For abs(x) > 0.5 exploit the identity:
+ // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
+ // together with the above rational approximation, and
+ // reconstruct the terms carefully.
+
+
+ // Some constants and split constants.
+ const float pi = 3.1415926535897933e+00f;
+ const float piby2_head = 1.5707963267948965580e+00f; /* 0x3ff921fb54442d18 */
+ const float piby2_tail = 6.12323399573676603587e-17f; /* 0x3c91a62633145c07 */
+
+ uint ux = as_uint(x);
+ uint aux = ux & ~SIGNBIT_SP32;
+ int xneg = ux != aux;
+ int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
+
+ float y = as_float(aux);
+
+ // transform if |x| >= 0.5
+ int transform = xexp >= -1;
+
+ float y2 = y * y;
+ float yt = 0.5f * (1.0f - y);
+ float r = transform ? yt : y2;
+
+ // Use a rational approximation for [0.0, 0.5]
+ float a = mad(r, mad(r, mad(r, -0.00396137437848476485201154797087F, -0.0133819288943925804214011424456F),
+ -0.0565298683201845211985026327361F),
+ 0.184161606965100694821398249421F);
git complains about space before tab in indent on the above 2 lines ^^,
and the indentation does look funny
+ float b = mad(r, -0.836411276854206731913362287293F, 1.10496961524520294485512696706F);
+ float u = r * MATH_DIVIDE(a, b);
+
+ float s = MATH_SQRT(r);
+ y = s;
+ float s1 = as_float(as_uint(s) & 0xffff0000);
+ float c = MATH_DIVIDE(r - s1 * s1, s + s1);
+ // float rettn = 1.0f - MATH_DIVIDE(2.0f * (s + (y * u - piby2_tail)), pi);
+ float rettn = 1.0f - MATH_DIVIDE(2.0f * (s + mad(y, u, -piby2_tail)), pi);
+ // float rettp = MATH_DIVIDE(2.0F * s1 + (2.0F * c + 2.0F * y * u), pi);
+ float rettp = MATH_DIVIDE(2.0f*(s1 + mad(y, u, c)), pi);
+ float rett = xneg ? rettn : rettp;
+ // float ret = MATH_DIVIDE(piby2_head - (x - (piby2_tail - x * u)), pi);
+ float ret = MATH_DIVIDE(piby2_head - (x - mad(x, -u, piby2_tail)), pi);
+
+ ret = transform ? rett : ret;
+ ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret;
+ ret = ux == 0x3f800000U ? 0.0f : ret;
+ ret = ux == 0xbf800000U ? 1.0f : ret;
+ ret = xexp < -26 ? 0.5f : ret;
+ return ret;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, acospi, float)
+
+#ifdef cl_khr_fp64
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+_CLC_OVERLOAD _CLC_DEF double acospi(double x) {
+ // Computes arccos(x).
+ // The argument is first reduced by noting that arccos(x)
+ // is invalid for abs(x) > 1. For denormal and small
+ // arguments arccos(x) = pi/2 to machine accuracy.
+ // Remaining argument ranges are handled as follows.
+ // For abs(x) <= 0.5 use
+ // arccos(x) = pi/2 - arcsin(x)
+ // = pi/2 - (x + x^3*R(x^2))
+ // where R(x^2) is a rational minimax approximation to
+ // (arcsin(x) - x)/x^3.
+ // For abs(x) > 0.5 exploit the identity:
+ // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
+ // together with the above rational approximation, and
+ // reconstruct the terms carefully.
+
+ const double pi = 0x1.921fb54442d18p+1;
+ const double piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */
+
+ double y = fabs(x);
+ int xneg = as_int2(x).hi < 0;
+ int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64;
+
+ // abs(x) >= 0.5
+ int transform = xexp >= -1;
+
+ // Transform y into the range [0,0.5)
+ double r1 = 0.5 * (1.0 - y);
+ double s = sqrt(r1);
+ double r = y * y;
+ r = transform ? r1 : r;
+ y = transform ? s : y;
+
+ // Use a rational approximation for [0.0, 0.5]
+ double un = fma(r,
+ fma(r,
+ fma(r,
+ fma(r,
+ fma(r, 0.0000482901920344786991880522822991,
+ 0.00109242697235074662306043804220),
+ -0.0549989809235685841612020091328),
+ 0.275558175256937652532686256258),
+ -0.445017216867635649900123110649),
+ 0.227485835556935010735943483075);
+
+ double ud = fma(r,
+ fma(r,
+ fma(r,
+ fma(r, 0.105869422087204370341222318533,
git complains about trailing whitespace on this line ^^