1*05a0b428SJohn Marino /* @(#)e_log.c 1.3 95/01/18 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunSoft, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino #include <float.h>
14*05a0b428SJohn Marino #include <math.h>
15*05a0b428SJohn Marino
16*05a0b428SJohn Marino #include "math_private.h"
17*05a0b428SJohn Marino
18*05a0b428SJohn Marino static const double
19*05a0b428SJohn Marino ln2 = 0.6931471805599452862268,
20*05a0b428SJohn Marino two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
21*05a0b428SJohn Marino Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
22*05a0b428SJohn Marino Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
23*05a0b428SJohn Marino Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
24*05a0b428SJohn Marino Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
25*05a0b428SJohn Marino Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
26*05a0b428SJohn Marino Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
27*05a0b428SJohn Marino Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
28*05a0b428SJohn Marino
29*05a0b428SJohn Marino static const double zero = 0.0;
30*05a0b428SJohn Marino
31*05a0b428SJohn Marino double
log2(double x)32*05a0b428SJohn Marino log2(double x)
33*05a0b428SJohn Marino {
34*05a0b428SJohn Marino double hfsq,f,s,z,R,w,t1,t2,dk;
35*05a0b428SJohn Marino int32_t k,hx,i,j;
36*05a0b428SJohn Marino u_int32_t lx;
37*05a0b428SJohn Marino
38*05a0b428SJohn Marino EXTRACT_WORDS(hx,lx,x);
39*05a0b428SJohn Marino
40*05a0b428SJohn Marino k=0;
41*05a0b428SJohn Marino if (hx < 0x00100000) { /* x < 2**-1022 */
42*05a0b428SJohn Marino if (((hx&0x7fffffff)|lx)==0)
43*05a0b428SJohn Marino return -two54/zero; /* log(+-0)=-inf */
44*05a0b428SJohn Marino if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
45*05a0b428SJohn Marino k -= 54; x *= two54; /* subnormal number, scale up x */
46*05a0b428SJohn Marino GET_HIGH_WORD(hx,x);
47*05a0b428SJohn Marino }
48*05a0b428SJohn Marino if (hx >= 0x7ff00000) return x+x;
49*05a0b428SJohn Marino k += (hx>>20)-1023;
50*05a0b428SJohn Marino hx &= 0x000fffff;
51*05a0b428SJohn Marino i = (hx+0x95f64)&0x100000;
52*05a0b428SJohn Marino SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
53*05a0b428SJohn Marino k += (i>>20);
54*05a0b428SJohn Marino f = x-1.0;
55*05a0b428SJohn Marino dk = (double)k;
56*05a0b428SJohn Marino if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
57*05a0b428SJohn Marino if (f==zero)
58*05a0b428SJohn Marino return (dk);
59*05a0b428SJohn Marino R = f*f*(0.5-0.33333333333333333*f);
60*05a0b428SJohn Marino return (dk-(R-f)/ln2);
61*05a0b428SJohn Marino }
62*05a0b428SJohn Marino s = f/(2.0+f);
63*05a0b428SJohn Marino z = s*s;
64*05a0b428SJohn Marino i = hx-0x6147a;
65*05a0b428SJohn Marino w = z*z;
66*05a0b428SJohn Marino j = 0x6b851-hx;
67*05a0b428SJohn Marino t1= w*(Lg2+w*(Lg4+w*Lg6));
68*05a0b428SJohn Marino t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
69*05a0b428SJohn Marino i |= j;
70*05a0b428SJohn Marino R = t2+t1;
71*05a0b428SJohn Marino if(i>0) {
72*05a0b428SJohn Marino hfsq=0.5*f*f;
73*05a0b428SJohn Marino return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
74*05a0b428SJohn Marino } else
75*05a0b428SJohn Marino return (dk-((s*(f-R))-f)/ln2);
76*05a0b428SJohn Marino }
77*05a0b428SJohn Marino
78*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
79*05a0b428SJohn Marino __strong_alias(log2l, log2);
80*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
81