xref: /freebsd/lib/msun/src/e_log10.c (revision 380a989b3223d455375b4fae70fd0b9bdd43bafb)
1 /* @(#)e_log10.c 5.1 93/09/24 */
2 /*
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  *
6  * Developed at SunPro, a Sun Microsystems, Inc. business.
7  * Permission to use, copy, modify, and distribute this
8  * software is freely granted, provided that this notice
9  * is preserved.
10  * ====================================================
11  */
12 
13 #ifndef lint
14 static char rcsid[] = "$Id$";
15 #endif
16 
17 /* __ieee754_log10(x)
18  * Return the base 10 logarithm of x
19  *
20  * Method :
21  *	Let log10_2hi = leading 40 bits of log10(2) and
22  *	    log10_2lo = log10(2) - log10_2hi,
23  *	    ivln10   = 1/log(10) rounded.
24  *	Then
25  *		n = ilogb(x),
26  *		if(n<0)  n = n+1;
27  *		x = scalbn(x,-n);
28  *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
29  *
30  * Note 1:
31  *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
32  *	mode must set to Round-to-Nearest.
33  * Note 2:
34  *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
35  *	log10 is monotonic at all binary break points.
36  *
37  * Special cases:
38  *	log10(x) is NaN with signal if x < 0;
39  *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
40  *	log10(NaN) is that NaN with no signal;
41  *	log10(10**N) = N  for N=0,1,...,22.
42  *
43  * Constants:
44  * The hexadecimal values are the intended ones for the following constants.
45  * The decimal values may be used, provided that the compiler will convert
46  * from decimal to binary accurately enough to produce the hexadecimal values
47  * shown.
48  */
49 
50 #include "math.h"
51 #include "math_private.h"
52 
53 #ifdef __STDC__
54 static const double
55 #else
56 static double
57 #endif
58 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
59 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
60 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
61 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
62 
63 #ifdef __STDC__
64 static const double zero   =  0.0;
65 #else
66 static double zero   =  0.0;
67 #endif
68 
69 #ifdef __STDC__
70 	double __generic___ieee754_log10(double x)
71 #else
72 	double __generic___ieee754_log10(x)
73 	double x;
74 #endif
75 {
76 	double y,z;
77 	int32_t i,k,hx;
78 	u_int32_t lx;
79 
80 	EXTRACT_WORDS(hx,lx,x);
81 
82         k=0;
83         if (hx < 0x00100000) {                  /* x < 2**-1022  */
84             if (((hx&0x7fffffff)|lx)==0)
85                 return -two54/zero;             /* log(+-0)=-inf */
86             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
87             k -= 54; x *= two54; /* subnormal number, scale up x */
88 	    GET_HIGH_WORD(hx,x);
89         }
90 	if (hx >= 0x7ff00000) return x+x;
91 	k += (hx>>20)-1023;
92 	i  = ((u_int32_t)k&0x80000000)>>31;
93         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
94         y  = (double)(k+i);
95 	SET_HIGH_WORD(x,hx);
96 	z  = y*log10_2lo + ivln10*__ieee754_log(x);
97 	return  z+y*log10_2hi;
98 }
99