libclc: Use acos implementation from amd_builtins

[jvesely]

Summary

Fixes acos CTS (1 thread, scalar) on AMD Turks.

[jvesely]

similar to @awatry 's asin patch. Improves accuracy and fixes issues with r600.

[jvesely]

ping

[tstellar]

LGTM.

libclc/generic/lib/math/acos.cl

+/*
+ * 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>
 
-#define __CLC_BODY <acos.inc>
-#include <clc/math/gentype.inc>
+#include "math.h"
+#include "../clcmacro.h"
+
+_CLC_OVERLOAD _CLC_DEF float acos(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 piby2 = 1.5707963705e+00F;
+    const float pi = 3.1415926535897933e+00F;
+    const float piby2_head = 1.5707963267948965580e+00F;
+    const float piby2_tail = 6.12323399573676603587e-17F;
+
+    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);
+
+    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(mad(s1, -s1, r), s + s1);
+    float rettn = mad(s + mad(y, u, -piby2_tail), -2.0f, pi);
+    float rettp = 2.0F * (s1 + mad(y, u, c));
+    float rett = xneg ? rettn : rettp;
+    float ret = piby2_head - (x - mad(x, -u, piby2_tail));
+
+    ret = transform ? rett : ret;
+    ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret;
+    ret = ux == 0x3f800000U ? 0.0f : ret;
+    ret = ux == 0xbf800000U ? pi : ret;
+    ret = xexp < -26 ? piby2 : ret;
+    return ret;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, acos, float);
+
+#ifdef cl_khr_fp64
+
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+_CLC_OVERLOAD _CLC_DEF double acos(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 = 3.1415926535897933e+00;             /* 0x400921fb54442d18 */
+    const double piby2 = 1.5707963267948965580e+00;       /* 0x3ff921fb54442d18 */
+    const double piby2_head = 1.5707963267948965580e+00;  /* 0x3ff921fb54442d18 */
+    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;
+
+    double rt = 0.5 * (1.0 - y);
+    double y2 = y * y;
+    double r = transform ? rt : y2;
+
+    // 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,
+                                   -0.943639137032492685763471240072),
+                            2.76568859157270989520376345954),
+                        -3.28431505720958658909889444194),
+                    1.36491501334161032038194214209);
+
+    double u = r * MATH_DIVIDE(un, ud);
+
+    // Reconstruct acos carefully in transformed region
+    double s = sqrt(r);
+    double ztn =  fma(-2.0, (s + fma(s, u, -piby2_tail)), pi);
+
+    double s1 = as_double(as_ulong(s) & 0xffffffff00000000UL);
+    double c = MATH_DIVIDE(fma(-s1, s1, r), s + s1);
+    double ztp = 2.0 * (s1 + fma(s, u, c));
+    double zt =  xneg ? ztn : ztp;
+    double z = piby2_head - (x - fma(-x, u, piby2_tail));
+
+    z =  transform ? zt : z;
+
+    z = xexp < -56 ? piby2 : z;
+    z = isnan(x) ? as_double((as_ulong(x) | QNANBITPATT_DP64)) : z;
+    z = x == 1.0 ? 0.0 : z;
+    z = x == -1.0 ? pi : z;
+
+    return z;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, acos, double);
+
+#endif // cl_khr_fp64

libclc/generic/lib/math/acos.inc

-/*
- * There are multiple formulas for calculating arccosine of x:
- * 1) acos(x) = (1/2*pi) + i * ln(i*x + sqrt(1-x^2)) (notice the 'i'...)
- * 2) acos(x) = pi/2 + asin(-x) (asin isn't implemented yet)
- * 3) acos(x) = pi/2 - asin(x) (ditto)
- * 4) acos(x) = 2*atan2(sqrt(1-x), sqrt(1+x))
- * 5) acos(x) = pi/2 - atan2(x, ( sqrt(1-x^2) ) )
- *
- * Options 1-3 are not currently usable, #5 generates more concise radeonsi
- * bitcode and assembly than #4 (134 vs 132 instructions on radeonsi), but
- * precision of #4 may be better.
- */
-
-// TODO: Enable half precision when atan2 is implemented
-#if __CLC_FPSIZE > 16
-
-#if __CLC_FPSIZE == 64
-#define __CLC_CONST(x) x
-#elif __CLC_FPSIZE == 32
-#define __CLC_CONST(x) x ## f
-#elif __CLC_FPSIZE == 16
-#define __CLC_CONST(x) x ## h
-#endif
-
-_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE acos(__CLC_GENTYPE x) {
-  return (
-    (__CLC_GENTYPE) __CLC_CONST(2.0) * atan2(
-      sqrt((__CLC_GENTYPE) __CLC_CONST(1.0) - x),
-      sqrt((__CLC_GENTYPE) __CLC_CONST(1.0) + x)
-    )
-  );
-}
-
-#undef __CLC_CONST
-
-#endif