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/*
* 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 "math.h"
#include "../clcmacro.h"
#include <clc/clc.h>
_CLC_OVERLOAD _CLC_DEF float atan(float x)
{
const float piby2 = 1.5707963267948966f; // 0x3ff921fb54442d18
uint ux = as_uint(x);
uint aux = ux & EXSIGNBIT_SP32;
uint sx = ux ^ aux;
float spiby2 = as_float(sx | as_uint(piby2));
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 ? spiby2 : 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);
float zs = as_float(sx | as_uint(z));
ret = aux < 0x4c800000 ? zs : ret;
// |x| < 2^-19
ret = aux < 0x36000000 ? as_float(ux) : ret;
return ret;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan, float);
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double atan(double x)
{
const double piby2 = 1.5707963267948966e+00; // 0x3ff921fb54442d18
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);
double z = isnan(x) ? x : piby2;
z = v <= 0x1.0p+56 ? r : z;
z = v < 0x1.0p-26 ? v : z;
return x == v ? z : -z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan, double);
#endif // cl_khr_fp64
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