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 "config.h"
26#include "math.h"
27#include "tables.h"
28#include "../clcmacro.h"
29
30//    Algorithm:
31//
32//    e^x = 2^(x/ln(2)) = 2^(x*(64/ln(2))/64)
33//
34//    x*(64/ln(2)) = n + f, |f| <= 0.5, n is integer
35//    n = 64*m + j,   0 <= j < 64
36//
37//    e^x = 2^((64*m + j + f)/64)
38//        = (2^m) * (2^(j/64)) * 2^(f/64)
39//        = (2^m) * (2^(j/64)) * e^(f*(ln(2)/64))
40//
41//    f = x*(64/ln(2)) - n
42//    r = f*(ln(2)/64) = x - n*(ln(2)/64)
43//
44//    e^x = (2^m) * (2^(j/64)) * e^r
45//
46//    (2^(j/64)) is precomputed
47//
48//    e^r = 1 + r + (r^2)/2! + (r^3)/3! + (r^4)/4! + (r^5)/5!
49//    e^r = 1 + q
50//
51//    q = r + (r^2)/2! + (r^3)/3! + (r^4)/4! + (r^5)/5!
52//
53//    e^x = (2^m) * ( (2^(j/64)) + q*(2^(j/64)) )
54
55_CLC_DEF _CLC_OVERLOAD float __clc_exp10(float x)
56{
57    const float X_MAX =  0x1.344134p+5f; // 128*log2/log10 : 38.53183944498959
58    const float X_MIN = -0x1.66d3e8p+5f; // -149*log2/log10 : -44.8534693539332
59
60    const float R_64_BY_LOG10_2 = 0x1.a934f0p+7f; // 64*log10/log2 : 212.6033980727912
61    const float R_LOG10_2_BY_64_LD = 0x1.340000p-8f; // log2/(64 * log10) lead : 0.004699707
62    const float R_LOG10_2_BY_64_TL = 0x1.04d426p-18f; // log2/(64 * log10) tail : 0.00000388665057
63    const float R_LN10 = 0x1.26bb1cp+1f;
64
65    int return_nan = isnan(x);
66    int return_inf = x > X_MAX;
67    int return_zero = x < X_MIN;
68
69    int n = convert_int(x * R_64_BY_LOG10_2);
70
71    float fn = (float)n;
72    int j = n & 0x3f;
73    int m = n >> 6;
74    int m2 = m << EXPSHIFTBITS_SP32;
75    float r;
76
77    r = R_LN10 * mad(fn, -R_LOG10_2_BY_64_TL, mad(fn, -R_LOG10_2_BY_64_LD, x));
78
79    // Truncated Taylor series for e^r
80    float z2 = mad(mad(mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 0x1.000000p-1f), r*r, r);
81
82    float two_to_jby64 = USE_TABLE(exp_tbl, j);
83    z2 = mad(two_to_jby64, z2, two_to_jby64);
84
85    float z2s = z2 * as_float(0x1 << (m + 149));
86    float z2n = as_float(as_int(z2) + m2);
87    z2 = m <= -126 ? z2s : z2n;
88
89
90    z2 = return_inf ? as_float(PINFBITPATT_SP32) : z2;
91    z2 = return_zero ? 0.0f : z2;
92    z2 = return_nan ? x : z2;
93    return z2;
94}
95_CLC_UNARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_exp10, float)
96
97#ifdef cl_khr_fp64
98_CLC_DEF _CLC_OVERLOAD double __clc_exp10(double x)
99{
100    const double X_MAX = 0x1.34413509f79ffp+8; // 1024*ln(2)/ln(10)
101    const double X_MIN = -0x1.434e6420f4374p+8; // -1074*ln(2)/ln(10)
102
103    const double R_64_BY_LOG10_2 = 0x1.a934f0979a371p+7; // 64*ln(10)/ln(2)
104    const double R_LOG10_2_BY_64_LD = 0x1.3441350000000p-8; // head ln(2)/(64*ln(10))
105    const double R_LOG10_2_BY_64_TL = 0x1.3ef3fde623e25p-37; // tail ln(2)/(64*ln(10))
106    const double R_LN10 = 0x1.26bb1bbb55516p+1; // ln(10)
107
108    int n = convert_int(x * R_64_BY_LOG10_2);
109
110    double dn = (double)n;
111
112    int j = n & 0x3f;
113    int m = n >> 6;
114
115    double r = R_LN10 * fma(-R_LOG10_2_BY_64_TL, dn, fma(-R_LOG10_2_BY_64_LD, dn, x));
116
117    // 6 term tail of Taylor expansion of e^r
118    double z2 = r * fma(r,
119	                fma(r,
120		            fma(r,
121			        fma(r,
122			            fma(r, 0x1.6c16c16c16c17p-10, 0x1.1111111111111p-7),
123			            0x1.5555555555555p-5),
124			        0x1.5555555555555p-3),
125		            0x1.0000000000000p-1),
126		        1.0);
127
128    double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j);
129    z2 = fma(tv.s0 + tv.s1, z2, tv.s1) + tv.s0;
130
131    int small_value = (m < -1022) || ((m == -1022) && (z2 < 1.0));
132
133	int n1 = m >> 2;
134	int n2 = m-n1;
135	double z3= z2 * as_double(((long)n1 + 1023) << 52);
136	z3 *= as_double(((long)n2 + 1023) << 52);
137
138    z2 = ldexp(z2, m);
139    z2 = small_value ? z3: z2;
140
141    z2 = isnan(x) ? x : z2;
142
143    z2 = x > X_MAX ? as_double(PINFBITPATT_DP64) : z2;
144    z2 = x < X_MIN ? 0.0 : z2;
145
146    return z2;
147}
148_CLC_UNARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_exp10, double)
149#endif
150