1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
|
/*
* 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.
*/
#ifdef cl_khr_fp64
#include <clc/clc.h>
#include "ep_log.h"
#include "math.h"
#include "tables.h"
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
#define LN0 8.33333333333317923934e-02
#define LN1 1.25000000037717509602e-02
#define LN2 2.23213998791944806202e-03
#define LN3 4.34887777707614552256e-04
#define LF0 8.33333333333333593622e-02
#define LF1 1.24999999978138668903e-02
#define LF2 2.23219810758559851206e-03
_CLC_DEF void __clc_ep_log(double x, int *xexp, double *r1, double *r2)
{
// Computes natural log(x). Algorithm based on:
// Ping-Tak Peter Tang
// "Table-driven implementation of the logarithm function in IEEE
// floating-point arithmetic"
// ACM Transactions on Mathematical Software (TOMS)
// Volume 16, Issue 4 (December 1990)
int near_one = x >= 0x1.e0faap-1 & x <= 0x1.1082cp+0;
ulong ux = as_ulong(x);
ulong uxs = as_ulong(as_double(0x03d0000000000000UL | ux) - 0x1.0p-962);
int c = ux < IMPBIT_DP64;
ux = c ? uxs : ux;
int expadjust = c ? 60 : 0;
// Store the exponent of x in xexp and put f into the range [0.5,1)
int xexp1 = ((as_int2(ux).hi >> 20) & 0x7ff) - EXPBIAS_DP64 - expadjust;
double f = as_double(HALFEXPBITS_DP64 | (ux & MANTBITS_DP64));
*xexp = near_one ? 0 : xexp1;
double r = x - 1.0;
double u1 = MATH_DIVIDE(r, 2.0 + r);
double ru1 = -r * u1;
u1 = u1 + u1;
int index = as_int2(ux).hi >> 13;
index = ((0x80 | (index & 0x7e)) >> 1) + (index & 0x1);
double f1 = index * 0x1.0p-7;
double f2 = f - f1;
double u2 = MATH_DIVIDE(f2, fma(0.5, f2, f1));
double2 tv = USE_TABLE(ln_tbl, (index - 64));
double z1 = tv.s0;
double q = tv.s1;
z1 = near_one ? r : z1;
q = near_one ? 0.0 : q;
double u = near_one ? u1 : u2;
double v = u*u;
double cc = near_one ? ru1 : u2;
double z21 = fma(v, fma(v, fma(v, LN3, LN2), LN1), LN0);
double z22 = fma(v, fma(v, LF2, LF1), LF0);
double z2 = near_one ? z21 : z22;
z2 = fma(u*v, z2, cc) + q;
*r1 = z1;
*r2 = z2;
}
#endif
|
