1/*
2 * Copyright (c) 2014 Advanced Micro Devices, Inc.
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining a copy
5 * of this software and associated documentation files (the "Software"), to deal
6 * in the Software without restriction, including without limitation the rights
7 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
8 * copies of the Software, and to permit persons to whom the Software is
9 * furnished to do so, subject to the following conditions:
10 *
11 * The above copyright notice and this permission notice shall be included in
12 * all copies or substantial portions of the Software.
13 *
14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
17 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
18 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
19 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
20 * THE SOFTWARE.
21 */
22
23#include "math.h"
24#include "../clcmacro.h"
25
26#include <clc/clc.h>
27
28_CLC_OVERLOAD _CLC_DEF float atan(float x)
29{
30    const float piby2 = 1.5707963267948966f; // 0x3ff921fb54442d18
31
32    uint ux = as_uint(x);
33    uint aux = ux & EXSIGNBIT_SP32;
34    uint sx = ux ^ aux;
35
36    float spiby2 = as_float(sx | as_uint(piby2));
37
38    float v = as_float(aux);
39
40    // Return for NaN
41    float ret = x;
42
43    // 2^26 <= |x| <= Inf => atan(x) is close to piby2
44    ret = aux <= PINFBITPATT_SP32  ? spiby2 : ret;
45
46    // Reduce arguments 2^-19 <= |x| < 2^26
47
48    // 39/16 <= x < 2^26
49    x = -MATH_RECIP(v);
50    float c = 1.57079632679489655800f; // atan(infinity)
51
52    // 19/16 <= x < 39/16
53    int l = aux < 0x401c0000;
54    float xx = MATH_DIVIDE(v - 1.5f, mad(v, 1.5f, 1.0f));
55    x = l ? xx : x;
56    c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)
57
58    // 11/16 <= x < 19/16
59    l = aux < 0x3f980000U;
60    xx =  MATH_DIVIDE(v - 1.0f, 1.0f + v);
61    x = l ? xx : x;
62    c = l ? 7.85398163397448278999e-01f : c; // atan(1)
63
64    // 7/16 <= x < 11/16
65    l = aux < 0x3f300000;
66    xx = MATH_DIVIDE(mad(v, 2.0f, -1.0f), 2.0f + v);
67    x = l ? xx : x;
68    c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)
69
70    // 2^-19 <= x < 7/16
71    l = aux < 0x3ee00000;
72    x = l ? v : x;
73    c = l ? 0.0f : c;
74
75    // Core approximation: Remez(2,2) on [-7/16,7/16]
76
77    float s = x * x;
78    float a = mad(s,
79                  mad(s, 0.470677934286149214138357545549e-2f, 0.192324546402108583211697690500f),
80                  0.296528598819239217902158651186f);
81
82    float b = mad(s,
83                  mad(s, 0.299309699959659728404442796915f, 0.111072499995399550138837673349e1f),
84                  0.889585796862432286486651434570f);
85
86    float q = x * s * MATH_DIVIDE(a, b);
87
88    float z = c - (q - x);
89    float zs = as_float(sx | as_uint(z));
90
91    ret  = aux < 0x4c800000 ?  zs : ret;
92
93    // |x| < 2^-19
94    ret = aux < 0x36000000 ? as_float(ux) : ret;
95    return ret;
96}
97
98_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan, float);
99
100#ifdef cl_khr_fp64
101
102#pragma OPENCL EXTENSION cl_khr_fp64 : enable
103
104
105_CLC_OVERLOAD _CLC_DEF double atan(double x)
106{
107    const double piby2 = 1.5707963267948966e+00; // 0x3ff921fb54442d18
108
109    double v = fabs(x);
110
111    // 2^56 > v > 39/16
112    double a = -1.0;
113    double b = v;
114    // (chi + clo) = arctan(infinity)
115    double chi = 1.57079632679489655800e+00;
116    double clo = 6.12323399573676480327e-17;
117
118    double ta = v - 1.5;
119    double tb = 1.0 + 1.5 * v;
120    int l = v <= 0x1.38p+1; // 39/16 > v > 19/16
121    a = l ? ta : a;
122    b = l ? tb : b;
123    // (chi + clo) = arctan(1.5)
124    chi = l ? 9.82793723247329054082e-01 : chi;
125    clo = l ? 1.39033110312309953701e-17 : clo;
126
127    ta = v - 1.0;
128    tb = 1.0 + v;
129    l = v <= 0x1.3p+0; // 19/16 > v > 11/16
130    a = l ? ta : a;
131    b = l ? tb : b;
132    // (chi + clo) = arctan(1.)
133    chi = l ? 7.85398163397448278999e-01 : chi;
134    clo = l ? 3.06161699786838240164e-17 : clo;
135
136    ta = 2.0 * v - 1.0;
137    tb = 2.0 + v;
138    l = v <= 0x1.6p-1; // 11/16 > v > 7/16
139    a = l ? ta : a;
140    b = l ? tb : b;
141    // (chi + clo) = arctan(0.5)
142    chi = l ? 4.63647609000806093515e-01 : chi;
143    clo = l ? 2.26987774529616809294e-17 : clo;
144
145    l = v <= 0x1.cp-2; // v < 7/16
146    a = l ? v : a;
147    b = l ? 1.0 : b;;
148    chi = l ? 0.0 : chi;
149    clo = l ? 0.0 : clo;
150
151    // Core approximation: Remez(4,4) on [-7/16,7/16]
152    double r = a / b;
153    double s = r * r;
154    double qn = fma(s,
155                    fma(s,
156                        fma(s,
157                            fma(s, 0.142316903342317766e-3,
158                                   0.304455919504853031e-1),
159                            0.220638780716667420e0),
160                        0.447677206805497472e0),
161                    0.268297920532545909e0);
162
163    double qd = fma(s,
164	            fma(s,
165			fma(s,
166			    fma(s, 0.389525873944742195e-1,
167				   0.424602594203847109e0),
168                            0.141254259931958921e1),
169                        0.182596787737507063e1),
170                    0.804893761597637733e0);
171
172    double q = r * s * qn / qd;
173    r = chi - ((q - clo) - r);
174
175    double z = isnan(x) ? x : piby2;
176    z = v <= 0x1.0p+56 ? r : z;
177    z = v < 0x1.0p-26 ? v : z;
178    return x == v ? z : -z;
179}
180
181_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan, double);
182
183#endif // cl_khr_fp64
184