1/*
2 * Copyright (c) 2014,2015 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 "../clcmacro.h"
27
28_CLC_OVERLOAD _CLC_DEF float exp(float x) {
29
30    // Reduce x
31    const float ln2HI = 0x1.62e300p-1f;
32    const float ln2LO = 0x1.2fefa2p-17f;
33    const float invln2 = 0x1.715476p+0f;
34
35    float fhalF = x < 0.0f ? -0.5f : 0.5f;
36    int p  = mad(x, invln2, fhalF);
37    float fp = (float)p;
38    float hi = mad(fp, -ln2HI, x); // t*ln2HI is exact here
39    float lo = -fp*ln2LO;
40
41    // Evaluate poly
42    float t = hi + lo;
43    float tt  = t*t;
44    float v = mad(tt,
45                  -mad(tt,
46                       mad(tt,
47                           mad(tt,
48                               mad(tt, 0x1.637698p-25f, -0x1.bbd41cp-20f),
49                               0x1.1566aap-14f),
50                           -0x1.6c16c2p-9f),
51                       0x1.555556p-3f),
52                  t);
53
54    float y = 1.0f - (((-lo) - MATH_DIVIDE(t * v, 2.0f - v)) - hi);
55
56    // Scale by 2^p
57    float r =  as_float(as_int(y) + (p << 23));
58
59    const float ulim =  0x1.62e430p+6f; // ln(largest_normal) = 88.72283905206835305366
60    const float llim = -0x1.5d589ep+6f; // ln(smallest_normal) = -87.33654475055310898657
61
62    r = x < llim ? 0.0f : r;
63    r = x < ulim ? r : as_float(0x7f800000);
64    return isnan(x) ? x : r;
65}
66
67_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, exp, float)
68
69#ifdef cl_khr_fp64
70
71#include "exp_helper.h"
72
73#pragma OPENCL EXTENSION cl_khr_fp64 : enable
74
75_CLC_OVERLOAD _CLC_DEF double exp(double x) {
76
77    const double X_MIN = -0x1.74910d52d3051p+9; // -1075*ln(2)
78    const double X_MAX = 0x1.62e42fefa39efp+9; // 1024*ln(2)
79    const double R_64_BY_LOG2 = 0x1.71547652b82fep+6; // 64/ln(2)
80    const double R_LOG2_BY_64_LD = 0x1.62e42fefa0000p-7; // head ln(2)/64
81    const double R_LOG2_BY_64_TL = 0x1.cf79abc9e3b39p-46; // tail ln(2)/64
82
83    int n = convert_int(x * R_64_BY_LOG2);
84    double r = fma(-R_LOG2_BY_64_TL, (double)n, fma(-R_LOG2_BY_64_LD, (double)n, x));
85    return __clc_exp_helper(x, X_MIN, X_MAX, r, n);
86}
87
88_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, exp, double)
89
90#endif
91