libclc: Use amd builtin for asin implementation

[awatry]

Summary

Fixes a wimpy-mode CTS failure for asin(float).

Passes non-wimpy for both float/double on RX580.

[jvesely]

reviewd on libclc ML

libclc/generic/lib/math/asin.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.
+ */
+
+// TODO: Enable half precision when atan2 is implemented
 #include <clc/clc.h>
 
-#define __CLC_BODY <asin.inc>
-#include <clc/math/gentype.inc>
+#include "math.h"
+#include "../clcmacro.h"
+
+_CLC_OVERLOAD _CLC_DEF float asin(float x) {
+    // Computes arcsin(x).
+    // The argument is first reduced by noting that arcsin(x)
+    // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
+    // For denormal and small arguments arcsin(x) = x to machine
+    // accuracy. Remaining argument ranges are handled as follows.
+    // For abs(x) <= 0.5 use
+    // arcsin(x) = 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:
+    // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
+    // together with the above rational approximation, and
+    // reconstruct the terms carefully.
+
+    const float piby2_tail = 7.5497894159e-08F;   /* 0x33a22168 */
+    const float hpiby2_head = 7.8539812565e-01F;  /* 0x3f490fda */
+    const float piby2 = 1.5707963705e+00F;        /* 0x3fc90fdb */
+
+    uint ux = as_uint(x);
+    uint aux = ux & EXSIGNBIT_SP32;
+    uint xs = ux ^ aux;
+    float spiby2 = as_float(xs | as_uint(piby2));
+    int xexp = (int)(aux >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
+    float y = as_float(aux);
+
+    // abs(x) >= 0.5
+    int transform = xexp >= -1;
+
+    float y2 = y * y;
+    float rt = 0.5f * (1.0f - y);
+    float r = transform ? rt : 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);
+    float s1 = as_float(as_uint(s) & 0xffff0000);
+    float c = MATH_DIVIDE(mad(-s1, s1, r), s + s1);
+    float p = mad(2.0f*s, u, -mad(c, -2.0f, piby2_tail));
+    float q = mad(s1, -2.0f, hpiby2_head);
+    float vt = hpiby2_head - (p - q);
+    float v = mad(y, u, y);
+    v = transform ? vt : v;
+
+    float ret = as_float(xs | as_uint(v));
+    ret = aux > 0x3f800000U ? as_float(QNANBITPATT_SP32) : ret;
+    ret = aux == 0x3f800000U ? spiby2 : ret;
+    ret = xexp < -14 ? x : ret;
+
+    return ret;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, asin, float);
+
+#ifdef cl_khr_fp64
+
+#pragma OPENCL EXTENSION cl_khr_fp64 : enable
+
+_CLC_OVERLOAD _CLC_DEF double asin(double x) {
+    // Computes arcsin(x).
+    // The argument is first reduced by noting that arcsin(x)
+    // is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x).
+    // For denormal and small arguments arcsin(x) = x to machine
+    // accuracy. Remaining argument ranges are handled as follows.
+    // For abs(x) <= 0.5 use
+    // arcsin(x) = 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:
+    // arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2)
+    // together with the above rational approximation, and
+    // reconstruct the terms carefully.
+
+    const double piby2_tail = 6.1232339957367660e-17;  /* 0x3c91a62633145c07 */
+    const double hpiby2_head = 7.8539816339744831e-01; /* 0x3fe921fb54442d18 */
+    const double piby2 = 1.5707963267948965e+00;       /* 0x3ff921fb54442d18 */
+
+    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 asin carefully in transformed region
+    double s = sqrt(r);
+    double sh = as_double(as_ulong(s) & 0xffffffff00000000UL);
+    double c = MATH_DIVIDE(fma(-sh, sh, r), s + sh);
+    double p = fma(2.0*s, u, -fma(-2.0, c, piby2_tail));
+    double q = fma(-2.0, sh, hpiby2_head);
+    double vt = hpiby2_head - (p - q);
+    double v = fma(y, u, y);
+    v = transform ? vt : v;
+
+    v = xexp < -28 ? y : v;
+    v = xexp >= 0 ? as_double(QNANBITPATT_DP64) : v;
+    v = y == 1.0 ? piby2 : v;
+
+    return xneg ? -v : v;
+}
+
+_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, asin, double);
+
+#endif // cl_khr_fp64

libclc/generic/lib/math/asin.inc

-// 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 asin(__CLC_GENTYPE x) {
-  return atan2(x, sqrt( (__CLC_GENTYPE)__CLC_CONST(1.0) - (x*x) ));
-}
-
-#undef __CLC_CONST
-
-#endif