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1 
2 /* @(#)e_log10.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 /* __ieee754_log10(x)
15  * Return the base 10 logarithm of x
16  *
17  * Method :
18  *	Let log10_2hi = leading 40 bits of ieee_log10(2) and
19  *	    log10_2lo = ieee_log10(2) - log10_2hi,
20  *	    ivln10   = 1/ieee_log(10) rounded.
21  *	Then
22  *		n = ieee_ilogb(x),
23  *		if(n<0)  n = n+1;
24  *		x = ieee_scalbn(x,-n);
25  *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*ieee_log(x))
26  *
27  * Note 1:
28  *	To guarantee ieee_log10(10**n)=n, where 10**n is normal, the rounding
29  *	mode must set to Round-to-Nearest.
30  * Note 2:
31  *	[1/ieee_log(10)] rounded to 53 bits has error  .198   ulps;
32  *	log10 is monotonic at all binary break points.
33  *
34  * Special cases:
35  *	log10(x) is NaN with signal if x < 0;
36  *	log10(+INF) is +INF with no signal; ieee_log10(0) is -INF with signal;
37  *	log10(NaN) is that NaN with no signal;
38  *	log10(10**N) = N  for N=0,1,...,22.
39  *
40  * Constants:
41  * The hexadecimal values are the intended ones for the following constants.
42  * The decimal values may be used, provided that the compiler will convert
43  * from decimal to binary accurately enough to produce the hexadecimal values
44  * shown.
45  */
46 
47 #include "fdlibm.h"
48 
49 #ifdef __STDC__
50 static const double
51 #else
52 static double
53 #endif
54 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
55 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
56 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
57 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
58 
59 static double zero   =  0.0;
60 
61 #ifdef __STDC__
__ieee754_log10(double x)62 	double __ieee754_log10(double x)
63 #else
64 	double __ieee754_log10(x)
65 	double x;
66 #endif
67 {
68 	double y,z;
69 	int i,k,hx;
70 	unsigned lx;
71 
72 	hx = __HI(x);	/* high word of x */
73 	lx = __LO(x);	/* low word of x */
74 
75         k=0;
76         if (hx < 0x00100000) {                  /* x < 2**-1022  */
77             if (((hx&0x7fffffff)|lx)==0)
78                 return -two54/zero;             /* ieee_log(+-0)=-inf */
79             if (hx<0) return (x-x)/zero;        /* ieee_log(-#) = NaN */
80             k -= 54; x *= two54; /* subnormal number, scale up x */
81             hx = __HI(x);                /* high word of x */
82         }
83 	if (hx >= 0x7ff00000) return x+x;
84 	k += (hx>>20)-1023;
85 	i  = ((unsigned)k&0x80000000)>>31;
86         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
87         y  = (double)(k+i);
88         __HI(x) = hx;
89 	z  = y*log10_2lo + ivln10*__ieee754_log(x);
90 	return  z+y*log10_2hi;
91 }
92