1 /* e_logf.c -- float version of e_log.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 "math.h"
17 #include "math_private.h"
18
19 static const float
20 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
21 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
22 two25 = 3.355443200e+07, /* 0x4c000000 */
23 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
24 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
25 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
26 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
27 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
28
29 static const float zero = 0.0;
30 static volatile float vzero = 0.0;
31
32 float
logf(float x)33 logf(float x)
34 {
35 float hfsq,f,s,z,R,w,t1,t2,dk;
36 int32_t k,ix,i,j;
37
38 GET_FLOAT_WORD(ix,x);
39
40 k=0;
41 if (ix < 0x00800000) { /* x < 2**-126 */
42 if ((ix&0x7fffffff)==0)
43 return -two25/vzero; /* log(+-0)=-inf */
44 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
45 k -= 25; x *= two25; /* subnormal number, scale up x */
46 GET_FLOAT_WORD(ix,x);
47 }
48 if (ix >= 0x7f800000) return x+x;
49 k += (ix>>23)-127;
50 ix &= 0x007fffff;
51 i = (ix+(0x95f64<<3))&0x800000;
52 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
53 k += (i>>23);
54 f = x-(float)1.0;
55 if((0x007fffff&(0x8000+ix))<0xc000) { /* -2**-9 <= f < 2**-9 */
56 if(f==zero) {
57 if(k==0) {
58 return zero;
59 } else {
60 dk=(float)k;
61 return dk*ln2_hi+dk*ln2_lo;
62 }
63 }
64 R = f*f*((float)0.5-(float)0.33333333333333333*f);
65 if(k==0) return f-R; else {dk=(float)k;
66 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
67 }
68 s = f/((float)2.0+f);
69 dk = (float)k;
70 z = s*s;
71 i = ix-(0x6147a<<3);
72 w = z*z;
73 j = (0x6b851<<3)-ix;
74 t1= w*(Lg2+w*Lg4);
75 t2= z*(Lg1+w*Lg3);
76 i |= j;
77 R = t2+t1;
78 if(i>0) {
79 hfsq=(float)0.5*f*f;
80 if(k==0) return f-(hfsq-s*(hfsq+R)); else
81 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
82 } else {
83 if(k==0) return f-s*(f-R); else
84 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
85 }
86 }
87