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 #ifndef lint
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_logf.c,v 1.8 2005/11/12 18:20:09 bde Exp $";
18 #endif
19
20 #include "math.h"
21 #include "math_private.h"
22
23 static const float
24 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
25 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
26 two25 = 3.355443200e+07, /* 0x4c000000 */
27 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
28 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
29 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
30 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
31 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
32
33 static const float zero = 0.0;
34
35 float
__ieee754_logf(float x)36 __ieee754_logf(float x)
37 {
38 float hfsq,f,s,z,R,w,t1,t2,dk;
39 int32_t k,ix,i,j;
40
41 GET_FLOAT_WORD(ix,x);
42
43 k=0;
44 if (ix < 0x00800000) { /* x < 2**-126 */
45 if ((ix&0x7fffffff)==0)
46 return -two25/zero; /* log(+-0)=-inf */
47 if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
48 k -= 25; x *= two25; /* subnormal number, scale up x */
49 GET_FLOAT_WORD(ix,x);
50 }
51 if (ix >= 0x7f800000) return x+x;
52 k += (ix>>23)-127;
53 ix &= 0x007fffff;
54 i = (ix+(0x95f64<<3))&0x800000;
55 SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
56 k += (i>>23);
57 f = x-(float)1.0;
58 if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
59 if(f==zero) if(k==0) return zero; else {dk=(float)k;
60 return dk*ln2_hi+dk*ln2_lo;}
61 R = f*f*((float)0.5-(float)0.33333333333333333*f);
62 if(k==0) return f-R; else {dk=(float)k;
63 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
64 }
65 s = f/((float)2.0+f);
66 dk = (float)k;
67 z = s*s;
68 i = ix-(0x6147a<<3);
69 w = z*z;
70 j = (0x6b851<<3)-ix;
71 t1= w*(Lg2+w*Lg4);
72 t2= z*(Lg1+w*Lg3);
73 i |= j;
74 R = t2+t1;
75 if(i>0) {
76 hfsq=(float)0.5*f*f;
77 if(k==0) return f-(hfsq-s*(hfsq+R)); else
78 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
79 } else {
80 if(k==0) return f-s*(f-R); else
81 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
82 }
83 }
84