1*05a0b428SJohn Marino /* e_logf.c -- float version of e_log.c.
2*05a0b428SJohn Marino * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3*05a0b428SJohn Marino */
4*05a0b428SJohn Marino
5*05a0b428SJohn Marino /*
6*05a0b428SJohn Marino * ====================================================
7*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
10*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
11*05a0b428SJohn Marino * software is freely granted, provided that this notice
12*05a0b428SJohn Marino * is preserved.
13*05a0b428SJohn Marino * ====================================================
14*05a0b428SJohn Marino */
15*05a0b428SJohn Marino
16*05a0b428SJohn Marino #include "math.h"
17*05a0b428SJohn Marino #include "math_private.h"
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino static const float
20*05a0b428SJohn Marino ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
21*05a0b428SJohn Marino ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
22*05a0b428SJohn Marino two25 = 3.355443200e+07, /* 0x4c000000 */
23*05a0b428SJohn Marino Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
24*05a0b428SJohn Marino Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
25*05a0b428SJohn Marino Lg3 = 2.8571429849e-01, /* 3E924925 */
26*05a0b428SJohn Marino Lg4 = 2.2222198546e-01, /* 3E638E29 */
27*05a0b428SJohn Marino Lg5 = 1.8183572590e-01, /* 3E3A3325 */
28*05a0b428SJohn Marino Lg6 = 1.5313838422e-01, /* 3E1CD04F */
29*05a0b428SJohn Marino Lg7 = 1.4798198640e-01; /* 3E178897 */
30*05a0b428SJohn Marino
31*05a0b428SJohn Marino static const float zero = 0.0;
32*05a0b428SJohn Marino
33*05a0b428SJohn Marino float
logf(float x)34*05a0b428SJohn Marino logf(float x)
35*05a0b428SJohn Marino {
36*05a0b428SJohn Marino float hfsq,f,s,z,R,w,t1,t2,dk;
37*05a0b428SJohn Marino int32_t k,ix,i,j;
38*05a0b428SJohn Marino
39*05a0b428SJohn Marino GET_FLOAT_WORD(ix,x);
40*05a0b428SJohn Marino
41*05a0b428SJohn Marino k=0;
42*05a0b428SJohn Marino if (ix < 0x00800000) { /* x < 2**-126 */
43*05a0b428SJohn Marino if ((ix&0x7fffffff)==0)
44*05a0b428SJohn Marino return -two25/zero; /* log(+-0)=-inf */
45*05a0b428SJohn Marino if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
46*05a0b428SJohn Marino k -= 25; x *= two25; /* subnormal number, scale up x */
47*05a0b428SJohn Marino GET_FLOAT_WORD(ix,x);
48*05a0b428SJohn Marino }
49*05a0b428SJohn Marino if (ix >= 0x7f800000) return x+x;
50*05a0b428SJohn Marino k += (ix>>23)-127;
51*05a0b428SJohn Marino ix &= 0x007fffff;
52*05a0b428SJohn Marino i = (ix+(0x95f64<<3))&0x800000;
53*05a0b428SJohn Marino SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
54*05a0b428SJohn Marino k += (i>>23);
55*05a0b428SJohn Marino f = x-(float)1.0;
56*05a0b428SJohn Marino if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
57*05a0b428SJohn Marino if(f==zero) {if(k==0) return zero; else {dk=(float)k;
58*05a0b428SJohn Marino return dk*ln2_hi+dk*ln2_lo;}}
59*05a0b428SJohn Marino R = f*f*((float)0.5-(float)0.33333333333333333*f);
60*05a0b428SJohn Marino if(k==0) return f-R; else {dk=(float)k;
61*05a0b428SJohn Marino return dk*ln2_hi-((R-dk*ln2_lo)-f);}
62*05a0b428SJohn Marino }
63*05a0b428SJohn Marino s = f/((float)2.0+f);
64*05a0b428SJohn Marino dk = (float)k;
65*05a0b428SJohn Marino z = s*s;
66*05a0b428SJohn Marino i = ix-(0x6147a<<3);
67*05a0b428SJohn Marino w = z*z;
68*05a0b428SJohn Marino j = (0x6b851<<3)-ix;
69*05a0b428SJohn Marino t1= w*(Lg2+w*(Lg4+w*Lg6));
70*05a0b428SJohn Marino t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
71*05a0b428SJohn Marino i |= j;
72*05a0b428SJohn Marino R = t2+t1;
73*05a0b428SJohn Marino if(i>0) {
74*05a0b428SJohn Marino hfsq=(float)0.5*f*f;
75*05a0b428SJohn Marino if(k==0) return f-(hfsq-s*(hfsq+R)); else
76*05a0b428SJohn Marino return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
77*05a0b428SJohn Marino } else {
78*05a0b428SJohn Marino if(k==0) return f-s*(f-R); else
79*05a0b428SJohn Marino return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
80*05a0b428SJohn Marino }
81*05a0b428SJohn Marino }
82