1 | /* s_log1pf.c -- float version of s_log1p.c. |
2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
3 | */ |
4 | |
5 | /* |
6 | * ==================================================== |
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
8 | * |
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
10 | * Permission to use, copy, modify, and distribute this |
11 | * software is freely granted, provided that this notice |
12 | * is preserved. |
13 | * ==================================================== |
14 | */ |
15 | |
16 | #include <float.h> |
17 | #include <math.h> |
18 | #include <math_private.h> |
19 | |
20 | static const float |
21 | ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ |
22 | ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ |
23 | two25 = 3.355443200e+07, /* 0x4c000000 */ |
24 | Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ |
25 | Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ |
26 | Lp3 = 2.8571429849e-01, /* 3E924925 */ |
27 | Lp4 = 2.2222198546e-01, /* 3E638E29 */ |
28 | Lp5 = 1.8183572590e-01, /* 3E3A3325 */ |
29 | Lp6 = 1.5313838422e-01, /* 3E1CD04F */ |
30 | Lp7 = 1.4798198640e-01; /* 3E178897 */ |
31 | |
32 | static const float zero = 0.0; |
33 | |
34 | float |
35 | __log1pf(float x) |
36 | { |
37 | float hfsq,f,c,s,z,R,u; |
38 | int32_t k,hx,hu,ax; |
39 | |
40 | GET_FLOAT_WORD(hx,x); |
41 | ax = hx&0x7fffffff; |
42 | |
43 | k = 1; |
44 | if (hx < 0x3ed413d7) { /* x < 0.41422 */ |
45 | if(ax>=0x3f800000) { /* x <= -1.0 */ |
46 | if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=-inf */ |
47 | else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ |
48 | } |
49 | if(ax<0x31000000) { /* |x| < 2**-29 */ |
50 | math_force_eval(two25+x); /* raise inexact */ |
51 | if (ax<0x24800000) /* |x| < 2**-54 */ |
52 | { |
53 | math_check_force_underflow (x); |
54 | return x; |
55 | } |
56 | else |
57 | return x - x*x*(float)0.5; |
58 | } |
59 | if(hx>0||hx<=((int32_t)0xbe95f61f)) { |
60 | k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ |
61 | } |
62 | if (hx >= 0x7f800000) return x+x; |
63 | if(k!=0) { |
64 | if(hx<0x5a000000) { |
65 | u = (float)1.0+x; |
66 | GET_FLOAT_WORD(hu,u); |
67 | k = (hu>>23)-127; |
68 | /* correction term */ |
69 | c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); |
70 | c /= u; |
71 | } else { |
72 | u = x; |
73 | GET_FLOAT_WORD(hu,u); |
74 | k = (hu>>23)-127; |
75 | c = 0; |
76 | } |
77 | hu &= 0x007fffff; |
78 | if(hu<0x3504f7) { |
79 | SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ |
80 | } else { |
81 | k += 1; |
82 | SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ |
83 | hu = (0x00800000-hu)>>2; |
84 | } |
85 | f = u-(float)1.0; |
86 | } |
87 | hfsq=(float)0.5*f*f; |
88 | if(hu==0) { /* |f| < 2**-20 */ |
89 | if(f==zero) { |
90 | if(k==0) return zero; |
91 | else {c += k*ln2_lo; return k*ln2_hi+c;} |
92 | } |
93 | R = hfsq*((float)1.0-(float)0.66666666666666666*f); |
94 | if(k==0) return f-R; else |
95 | return k*ln2_hi-((R-(k*ln2_lo+c))-f); |
96 | } |
97 | s = f/((float)2.0+f); |
98 | z = s*s; |
99 | R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); |
100 | if(k==0) return f-(hfsq-s*(hfsq+R)); else |
101 | return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); |
102 | } |
103 | |