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
95
96
97
98
99
100
101
102
103
104
105
106
|
/* s_log1pf.c -- float version of s_log1p.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
two25 = 3.355443200e+07, /* 0x4c000000 */
Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
Lp3 = 2.8571429849e-01, /* 3E924925 */
Lp4 = 2.2222198546e-01, /* 3E638E29 */
Lp5 = 1.8183572590e-01, /* 3E3A3325 */
Lp6 = 1.5313838422e-01, /* 3E1CD04F */
Lp7 = 1.4798198640e-01; /* 3E178897 */
static const float zero = 0.0;
float
__log1pf(float x)
{
float hfsq,f,c,s,z,R,u;
int32_t k,hx,hu,ax;
GET_FLOAT_WORD(hx,x);
ax = hx&0x7fffffff;
k = 1;
if (hx < 0x3ed413d7) { /* x < 0.41422 */
if(ax>=0x3f800000) { /* x <= -1.0 */
if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=-inf */
else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
}
if(ax<0x31000000) { /* |x| < 2**-29 */
math_force_eval(two25+x); /* raise inexact */
if (ax<0x24800000) /* |x| < 2**-54 */
{
if (fabsf (x) < FLT_MIN)
{
float force_underflow = x * x;
math_force_eval (force_underflow);
}
return x;
}
else
return x - x*x*(float)0.5;
}
if(hx>0||hx<=((int32_t)0xbe95f61f)) {
k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
}
if (hx >= 0x7f800000) return x+x;
if(k!=0) {
if(hx<0x5a000000) {
u = (float)1.0+x;
GET_FLOAT_WORD(hu,u);
k = (hu>>23)-127;
/* correction term */
c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
c /= u;
} else {
u = x;
GET_FLOAT_WORD(hu,u);
k = (hu>>23)-127;
c = 0;
}
hu &= 0x007fffff;
if(hu<0x3504f7) {
SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
} else {
k += 1;
SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
hu = (0x00800000-hu)>>2;
}
f = u-(float)1.0;
}
hfsq=(float)0.5*f*f;
if(hu==0) { /* |f| < 2**-20 */
if(f==zero) {
if(k==0) return zero;
else {c += k*ln2_lo; return k*ln2_hi+c;}
}
R = hfsq*((float)1.0-(float)0.66666666666666666*f);
if(k==0) return f-R; else
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
}
s = f/((float)2.0+f);
z = s*s;
R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}
|
