generic/lib/math/atanpi.cl

/*
 * 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 atanpi(float x) {
    const float pi = 3.1415926535897932f;

    uint ux = as_uint(x);
    uint aux = ux & EXSIGNBIT_SP32;
    uint sx = ux ^ aux;

    float xbypi = MATH_DIVIDE(x, pi);
    float shalf = as_float(sx | as_uint(0.5f));

    float v = as_float(aux);

    // Return for NaN
    float ret = x;

    // 2^26 <= |x| <= Inf => atan(x) is close to piby2
    ret = aux <= PINFBITPATT_SP32  ? shalf : ret;

    // Reduce arguments 2^-19 <= |x| < 2^26

    // 39/16 <= x < 2^26
    x = -MATH_RECIP(v);
    float c = 1.57079632679489655800f; // atan(infinity)

    // 19/16 <= x < 39/16
    int l = aux < 0x401c0000;
    float xx = MATH_DIVIDE(v - 1.5f, mad(v, 1.5f, 1.0f));
    x = l ? xx : x;
    c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)

    // 11/16 <= x < 19/16
    l = aux < 0x3f980000U;
    xx =  MATH_DIVIDE(v - 1.0f, 1.0f + v);
    x = l ? xx : x;
    c = l ? 7.85398163397448278999e-01f : c; // atan(1)

    // 7/16 <= x < 11/16
    l = aux < 0x3f300000;
    xx = MATH_DIVIDE(mad(v, 2.0f, -1.0f), 2.0f + v);
    x = l ? xx : x;
    c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)

    // 2^-19 <= x < 7/16
    l = aux < 0x3ee00000;
    x = l ? v : x;
    c = l ? 0.0f : c;

    // Core approximation: Remez(2,2) on [-7/16,7/16]

    float s = x * x;
    float a = mad(s,
                  mad(s, 0.470677934286149214138357545549e-2f, 0.192324546402108583211697690500f),
                  0.296528598819239217902158651186f);

    float b = mad(s,
                  mad(s, 0.299309699959659728404442796915f, 0.111072499995399550138837673349e1f),
                  0.889585796862432286486651434570f);

    float q = x * s * MATH_DIVIDE(a, b);

    float z = c - (q - x);
    z = MATH_DIVIDE(z, pi);
    float zs = as_float(sx | as_uint(z));

    ret  = aux < 0x4c800000 ?  zs : ret;

    // |x| < 2^-19
    ret = aux < 0x36000000 ? xbypi : ret;
    return ret;
}

_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atanpi, float)

#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable

_CLC_OVERLOAD _CLC_DEF double atanpi(double x) {
    const double pi = 0x1.921fb54442d18p+1;

    double v = fabs(x);

    // 2^56 > v > 39/16
    double a = -1.0;
    double b = v;
    // (chi + clo) = arctan(infinity)
    double chi = 1.57079632679489655800e+00;
    double clo = 6.12323399573676480327e-17;

    double ta = v - 1.5;
    double tb = 1.0 + 1.5 * v;
    int l = v <= 0x1.38p+1; // 39/16 > v > 19/16
    a = l ? ta : a;
    b = l ? tb : b;
    // (chi + clo) = arctan(1.5)
    chi = l ? 9.82793723247329054082e-01 : chi;
    clo = l ? 1.39033110312309953701e-17 : clo;

    ta = v - 1.0;
    tb = 1.0 + v;
    l = v <= 0x1.3p+0; // 19/16 > v > 11/16
    a = l ? ta : a;
    b = l ? tb : b;
    // (chi + clo) = arctan(1.)
    chi = l ? 7.85398163397448278999e-01 : chi;
    clo = l ? 3.06161699786838240164e-17 : clo;

    ta = 2.0 * v - 1.0;
    tb = 2.0 + v;
    l = v <= 0x1.6p-1; // 11/16 > v > 7/16
    a = l ? ta : a;
    b = l ? tb : b;
    // (chi + clo) = arctan(0.5)
    chi = l ? 4.63647609000806093515e-01 : chi;
    clo = l ? 2.26987774529616809294e-17 : clo;

    l = v <= 0x1.cp-2; // v < 7/16
    a = l ? v : a;
    b = l ? 1.0 : b;;
    chi = l ? 0.0 : chi;
    clo = l ? 0.0 : clo;

    // Core approximation: Remez(4,4) on [-7/16,7/16]
    double r = a / b;
    double s = r * r;
    double qn = fma(s,
                    fma(s,
                        fma(s,
                            fma(s, 0.142316903342317766e-3,
                                   0.304455919504853031e-1),
                            0.220638780716667420e0),
                        0.447677206805497472e0),
                    0.268297920532545909e0);

    double qd = fma(s,
	            fma(s,
			fma(s,
			    fma(s, 0.389525873944742195e-1,
				   0.424602594203847109e0),
                            0.141254259931958921e1),
                        0.182596787737507063e1),
                    0.804893761597637733e0);

    double q = r * s * qn / qd;
    r = (chi - ((q - clo) - r)) / pi;
    double vp = v / pi;

    double z = isnan(x) ? x : 0.5;
    z = v <= 0x1.0p+56 ? r : z;
    z = v < 0x1.0p-26 ? vp : z;
    return x == v ? z : -z;
}

_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atanpi, double)

#endif