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 <clc/clc.h>
24
25#include "math.h"
26#include "tables.h"
27#include "../clcmacro.h"
28
29_CLC_OVERLOAD _CLC_DEF float atan2(float y, float x)
30{
31    const float pi = 0x1.921fb6p+1f;
32    const float piby2 = 0x1.921fb6p+0f;
33    const float piby4 = 0x1.921fb6p-1f;
34    const float threepiby4 = 0x1.2d97c8p+1f;
35
36    float ax = fabs(x);
37    float ay = fabs(y);
38    float v = min(ax, ay);
39    float u = max(ax, ay);
40
41    // Scale since u could be large, as in "regular" divide
42    float s = u > 0x1.0p+96f ? 0x1.0p-32f : 1.0f;
43    float vbyu = s * MATH_DIVIDE(v, s*u);
44
45    float vbyu2 = vbyu * vbyu;
46
47#define USE_2_2_APPROXIMATION
48#if defined USE_2_2_APPROXIMATION
49    float p = mad(vbyu2, mad(vbyu2, -0x1.7e1f78p-9f, -0x1.7d1b98p-3f), -0x1.5554d0p-2f) * vbyu2 * vbyu;
50    float q = mad(vbyu2, mad(vbyu2, 0x1.1a714cp-2f, 0x1.287c56p+0f), 1.0f);
51#else
52    float p = mad(vbyu2, mad(vbyu2, -0x1.55cd22p-5f, -0x1.26cf76p-2f), -0x1.55554ep-2f) * vbyu2 * vbyu;
53    float q = mad(vbyu2, mad(vbyu2, mad(vbyu2, 0x1.9f1304p-5f, 0x1.2656fap-1f), 0x1.76b4b8p+0f), 1.0f);
54#endif
55
56    // Octant 0 result
57    float a = mad(p, MATH_RECIP(q), vbyu);
58
59    // Fix up 3 other octants
60    float at = piby2 - a;
61    a = ay > ax ? at : a;
62    at = pi - a;
63    a = x < 0.0F ? at : a;
64
65    // y == 0 => 0 for x >= 0, pi for x < 0
66    at = as_int(x) < 0 ? pi : 0.0f;
67    a = y == 0.0f ? at : a;
68
69    // if (!FINITE_ONLY()) {
70        // x and y are +- Inf
71        at = x > 0.0f ? piby4 : threepiby4;
72        a = ax == INFINITY & ay == INFINITY ? at : a;
73
74	// x or y is NaN
75	a = isnan(x) | isnan(y) ? as_float(QNANBITPATT_SP32) : a;
76    // }
77
78    // Fixup sign and return
79    return copysign(a, y);
80}
81
82_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan2, float, float);
83
84#ifdef cl_khr_fp64
85
86#pragma OPENCL EXTENSION cl_khr_fp64 : enable
87
88_CLC_OVERLOAD _CLC_DEF double atan2(double y, double x)
89{
90    const double pi = 3.1415926535897932e+00;          /* 0x400921fb54442d18 */
91    const double piby2 = 1.5707963267948966e+00;       /* 0x3ff921fb54442d18 */
92    const double piby4 = 7.8539816339744831e-01;       /* 0x3fe921fb54442d18 */
93    const double three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */
94    const double pi_head = 3.1415926218032836e+00;     /* 0x400921fb50000000 */
95    const double pi_tail = 3.1786509547056392e-08;     /* 0x3e6110b4611a6263 */
96    const double piby2_head = 1.5707963267948965e+00;  /* 0x3ff921fb54442d18 */
97    const double piby2_tail = 6.1232339957367660e-17;  /* 0x3c91a62633145c07 */
98
99    double x2 = x;
100    int xneg = as_int2(x).hi < 0;
101    int xexp = (as_int2(x).hi >> 20) & 0x7ff;
102
103    double y2 = y;
104    int yneg = as_int2(y).hi < 0;
105    int yexp = (as_int2(y).hi >> 20) & 0x7ff;
106
107    int cond2 = (xexp < 1021) & (yexp < 1021);
108    int diffexp = yexp - xexp;
109
110    // Scale up both x and y if they are both below 1/4
111    double x1 = ldexp(x, 1024);
112    int xexp1 = (as_int2(x1).hi >> 20) & 0x7ff;
113    double y1 = ldexp(y, 1024);
114    int yexp1 = (as_int2(y1).hi >> 20) & 0x7ff;
115    int diffexp1 = yexp1 - xexp1;
116
117    diffexp = cond2 ? diffexp1 : diffexp;
118    x = cond2 ? x1 : x;
119    y = cond2 ? y1 : y;
120
121    // General case: take absolute values of arguments
122    double u = fabs(x);
123    double v = fabs(y);
124
125    // Swap u and v if necessary to obtain 0 < v < u. Compute v/u.
126    int swap_vu = u < v;
127    double uu = u;
128    u = swap_vu ? v : u;
129    v = swap_vu ? uu : v;
130
131    double vbyu = v / u;
132    double q1, q2;
133
134    // General values of v/u. Use a look-up table and series expansion.
135
136    {
137        double val = vbyu > 0.0625 ? vbyu : 0.063;
138        int index = convert_int(fma(256.0, val, 0.5));
139	double2 tv = USE_TABLE(atan_jby256_tbl, index - 16);
140	q1 = tv.s0;
141	q2 = tv.s1;
142        double c = (double)index * 0x1.0p-8;
143
144        // We're going to scale u and v by 2^(-u_exponent) to bring them close to 1
145        // u_exponent could be EMAX so we have to do it in 2 steps
146        int m = -((int)(as_ulong(u) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64);
147	//double um = __amdil_ldexp_f64(u, m);
148	//double vm = __amdil_ldexp_f64(v, m);
149	double um = ldexp(u, m);
150	double vm = ldexp(v, m);
151
152        // 26 leading bits of u
153        double u1 = as_double(as_ulong(um) & 0xfffffffff8000000UL);
154        double u2 = um - u1;
155
156        double r = MATH_DIVIDE(fma(-c, u2, fma(-c, u1, vm)), fma(c, vm, um));
157
158        // Polynomial approximation to atan(r)
159        double s = r * r;
160        q2 = q2 + fma((s * fma(-s, 0.19999918038989143496, 0.33333333333224095522)), -r, r);
161    }
162
163
164    double q3, q4;
165    {
166        q3 = 0.0;
167        q4 = vbyu;
168    }
169
170    double q5, q6;
171    {
172        double u1 = as_double(as_ulong(u) & 0xffffffff00000000UL);
173        double u2 = u - u1;
174        double vu1 = as_double(as_ulong(vbyu) & 0xffffffff00000000UL);
175        double vu2 = vbyu - vu1;
176
177        q5 = 0.0;
178        double s = vbyu * vbyu;
179        q6 = vbyu + fma(-vbyu * s,
180                        fma(-s,
181                            fma(-s,
182                                fma(-s,
183                                    fma(-s, 0.90029810285449784439E-01,
184                                        0.11110736283514525407),
185                                    0.14285713561807169030),
186                                0.19999999999393223405),
187                            0.33333333333333170500),
188			 MATH_DIVIDE(fma(-u, vu2, fma(-u2, vu1, fma(-u1, vu1, v))), u));
189    }
190
191
192    q3 = vbyu < 0x1.d12ed0af1a27fp-27 ? q3 : q5;
193    q4 = vbyu < 0x1.d12ed0af1a27fp-27 ? q4 : q6;
194
195    q1 = vbyu > 0.0625 ? q1 : q3;
196    q2 = vbyu > 0.0625 ? q2 : q4;
197
198    // Tidy-up according to which quadrant the arguments lie in
199    double res1, res2, res3, res4;
200    q1 = swap_vu ? piby2_head - q1 : q1;
201    q2 = swap_vu ? piby2_tail - q2 : q2;
202    q1 = xneg ? pi_head - q1 : q1;
203    q2 = xneg ? pi_tail - q2 : q2;
204    q1 = q1 + q2;
205    res4 = yneg ? -q1 : q1;
206
207    res1 = yneg ? -three_piby4 : three_piby4;
208    res2 = yneg ? -piby4 : piby4;
209    res3 = xneg ? res1 : res2;
210
211    res3 = isinf(x2) & isinf(y2) ? res3 : res4;
212    res1 = yneg ? -pi : pi;
213
214    // abs(x)/abs(y) > 2^56 and x < 0
215    res3 = (diffexp < -56 && xneg) ? res1 : res3;
216
217    res4 = MATH_DIVIDE(y, x);
218    // x positive and dominant over y by a factor of 2^28
219    res3 = diffexp < -28 & xneg == 0 ? res4 : res3;
220
221    // abs(y)/abs(x) > 2^56
222    res4 = yneg ? -piby2 : piby2;       // atan(y/x) is insignificant compared to piby2
223    res3 = diffexp > 56 ? res4 : res3;
224
225    res3 = x2 == 0.0 ? res4 : res3;   // Zero x gives +- pi/2 depending on sign of y
226    res4 = xneg ? res1 : y2;
227
228    res3 = y2 == 0.0 ? res4 : res3;   // Zero y gives +-0 for positive x and +-pi for negative x
229    res3 = isnan(y2) ? y2 : res3;
230    res3 = isnan(x2) ? x2 : res3;
231
232    return res3;
233}
234
235_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan2, double, double);
236
237#endif
238