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 __FBSDID("$FreeBSD$");
18
19 #include <float.h>
20
21 #include "math.h"
22 #include "math_private.h"
23
24 static const float
25 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
26 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
27 two25 = 3.355443200e+07, /* 0x4c000000 */
28 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
29 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
30 Lp3 = 2.8571429849e-01, /* 3E924925 */
31 Lp4 = 2.2222198546e-01, /* 3E638E29 */
32 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
33 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
34 Lp7 = 1.4798198640e-01; /* 3E178897 */
35
36 static const float zero = 0.0;
37 static volatile float vzero = 0.0;
38
39 float
log1pf(float x)40 log1pf(float x)
41 {
42 float hfsq,f,c,s,z,R,u;
43 int32_t k,hx,hu,ax;
44
45 GET_FLOAT_WORD(hx,x);
46 ax = hx&0x7fffffff;
47
48 k = 1;
49 if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */
50 if(ax>=0x3f800000) { /* x <= -1.0 */
51 if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */
52 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
53 }
54 if(ax<0x38000000) { /* |x| < 2**-15 */
55 if(two25+x>zero /* raise inexact */
56 &&ax<0x33800000) /* |x| < 2**-24 */
57 return x;
58 else
59 return x - x*x*(float)0.5;
60 }
61 if(hx>0||hx<=((int32_t)0xbe95f619)) {
62 k=0;f=x;hu=1;} /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
63 }
64 if (hx >= 0x7f800000) return x+x;
65 if(k!=0) {
66 if(hx<0x5a000000) {
67 STRICT_ASSIGN(float,u,(float)1.0+x);
68 GET_FLOAT_WORD(hu,u);
69 k = (hu>>23)-127;
70 /* correction term */
71 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
72 c /= u;
73 } else {
74 u = x;
75 GET_FLOAT_WORD(hu,u);
76 k = (hu>>23)-127;
77 c = 0;
78 }
79 hu &= 0x007fffff;
80 /*
81 * The approximation to sqrt(2) used in thresholds is not
82 * critical. However, the ones used above must give less
83 * strict bounds than the one here so that the k==0 case is
84 * never reached from here, since here we have committed to
85 * using the correction term but don't use it if k==0.
86 */
87 if(hu<0x3504f4) { /* u < sqrt(2) */
88 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
89 } else {
90 k += 1;
91 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
92 hu = (0x00800000-hu)>>2;
93 }
94 f = u-(float)1.0;
95 }
96 hfsq=(float)0.5*f*f;
97 if(hu==0) { /* |f| < 2**-20 */
98 if(f==zero) {
99 if(k==0) {
100 return zero;
101 } else {
102 c += k*ln2_lo;
103 return k*ln2_hi+c;
104 }
105 }
106 R = hfsq*((float)1.0-(float)0.66666666666666666*f);
107 if(k==0) return f-R; else
108 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
109 }
110 s = f/((float)2.0+f);
111 z = s*s;
112 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
113 if(k==0) return f-(hfsq-s*(hfsq+R)); else
114 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
115 }
116