forked from OSchip/llvm-project
184 lines
5.3 KiB
Common Lisp
184 lines
5.3 KiB
Common Lisp
/*
|
|
* 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
|