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 <sys/cdefs.h>
17 #if defined(LIBM_SCCS) && !defined(lint)
18 __RCSID("$NetBSD: s_log1pf.c,v 1.9 2024/07/16 14:52:50 riastradh Exp $");
19 #endif
20
21 #include "namespace.h"
22
23 #include "math.h"
24 #include "math_private.h"
25
26 static const float
27 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
28 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
29 two25 = 3.355443200e+07, /* 0x4c000000 */
30 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
31 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
32 Lp3 = 2.8571429849e-01, /* 3E924925 */
33 Lp4 = 2.2222198546e-01, /* 3E638E29 */
34 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
35 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
36 Lp7 = 1.4798198640e-01; /* 3E178897 */
37
38 static const float zero = 0.0;
39
__weak_alias(log1pf,_log1pf)40 __weak_alias(log1pf, _log1pf)
41 float
42 log1pf(float x)
43 {
44 float hfsq,f,c,s,z,R,u;
45 int32_t k,hx,hu,ax;
46
47 f = c = 0;
48 hu = 0;
49 GET_FLOAT_WORD(hx,x);
50 ax = hx&0x7fffffff;
51
52 k = 1;
53 if (hx < 0x3ed413d7) { /* x < 0.41422 */
54 if(ax>=0x3f800000) { /* x <= -1.0 */
55 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
56 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
57 }
58 if(ax<0x31000000) { /* |x| < 2**-29 */
59 if(two25+x>zero /* raise inexact */
60 &&ax<0x24800000) /* |x| < 2**-54 */
61 return x;
62 else
63 return x - x*x*(float)0.5;
64 }
65 if(hx>0||hx<=((int32_t)0xbe95f61f)) {
66 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
67 }
68 if (hx >= 0x7f800000) return x+x;
69 if(k!=0) {
70 if(hx<0x5a000000) {
71 u = (float)1.0+x;
72 GET_FLOAT_WORD(hu,u);
73 k = (hu>>23)-127;
74 /* correction term */
75 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
76 c /= u;
77 } else {
78 u = x;
79 GET_FLOAT_WORD(hu,u);
80 k = (hu>>23)-127;
81 c = 0;
82 }
83 hu &= 0x007fffff;
84 if(hu<0x3504f7) {
85 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
86 } else {
87 k += 1;
88 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
89 hu = (0x00800000-hu)>>2;
90 }
91 f = u-(float)1.0;
92 }
93 hfsq=(float)0.5*f*f;
94 if(hu==0) { /* |f| < 2**-20 */
95 if(f==zero) { if(k==0) return zero;
96 else {c += k*ln2_lo; return k*ln2_hi+c;}
97 }
98 R = hfsq*((float)1.0-(float)0.66666666666666666*f);
99 if(k==0) return f-R; else
100 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
101 }
102 s = f/((float)2.0+f);
103 z = s*s;
104 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
105 if(k==0) return f-(hfsq-s*(hfsq+R)); else
106 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
107 }
108