1df930be7Sderaadt /* @(#)e_log10.c 5.1 93/09/24 */
2df930be7Sderaadt /*
3df930be7Sderaadt * ====================================================
4df930be7Sderaadt * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5df930be7Sderaadt *
6df930be7Sderaadt * Developed at SunPro, a Sun Microsystems, Inc. business.
7df930be7Sderaadt * Permission to use, copy, modify, and distribute this
8df930be7Sderaadt * software is freely granted, provided that this notice
9df930be7Sderaadt * is preserved.
10df930be7Sderaadt * ====================================================
11df930be7Sderaadt */
12df930be7Sderaadt
137b36286aSmartynas /* log10(x)
14df930be7Sderaadt * Return the base 10 logarithm of x
15df930be7Sderaadt *
16df930be7Sderaadt * Method :
17df930be7Sderaadt * Let log10_2hi = leading 40 bits of log10(2) and
18df930be7Sderaadt * log10_2lo = log10(2) - log10_2hi,
19df930be7Sderaadt * ivln10 = 1/log(10) rounded.
20df930be7Sderaadt * Then
21df930be7Sderaadt * n = ilogb(x),
22df930be7Sderaadt * if(n<0) n = n+1;
23df930be7Sderaadt * x = scalbn(x,-n);
24df930be7Sderaadt * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
25df930be7Sderaadt *
26df930be7Sderaadt * Note 1:
27df930be7Sderaadt * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
28df930be7Sderaadt * mode must set to Round-to-Nearest.
29df930be7Sderaadt * Note 2:
30df930be7Sderaadt * [1/log(10)] rounded to 53 bits has error .198 ulps;
31df930be7Sderaadt * log10 is monotonic at all binary break points.
32df930be7Sderaadt *
33df930be7Sderaadt * Special cases:
34df930be7Sderaadt * log10(x) is NaN with signal if x < 0;
35df930be7Sderaadt * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
36df930be7Sderaadt * log10(NaN) is that NaN with no signal;
37df930be7Sderaadt * log10(10**N) = N for N=0,1,...,22.
38df930be7Sderaadt *
39df930be7Sderaadt * Constants:
40df930be7Sderaadt * The hexadecimal values are the intended ones for the following constants.
41df930be7Sderaadt * The decimal values may be used, provided that the compiler will convert
42df930be7Sderaadt * from decimal to binary accurately enough to produce the hexadecimal values
43df930be7Sderaadt * shown.
44df930be7Sderaadt */
45df930be7Sderaadt
4649393c00Smartynas #include <float.h>
4749393c00Smartynas #include <math.h>
4849393c00Smartynas
49df930be7Sderaadt #include "math_private.h"
50df930be7Sderaadt
51df930be7Sderaadt static const double
52df930be7Sderaadt two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
53df930be7Sderaadt ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
54df930be7Sderaadt log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
55df930be7Sderaadt log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
56df930be7Sderaadt
57df930be7Sderaadt static const double zero = 0.0;
58df930be7Sderaadt
59e7beb4a7Smillert double
log10(double x)607b36286aSmartynas log10(double x)
61df930be7Sderaadt {
62df930be7Sderaadt double y,z;
63df930be7Sderaadt int32_t i,k,hx;
64df930be7Sderaadt u_int32_t lx;
65df930be7Sderaadt
66df930be7Sderaadt EXTRACT_WORDS(hx,lx,x);
67df930be7Sderaadt
68df930be7Sderaadt k=0;
69df930be7Sderaadt if (hx < 0x00100000) { /* x < 2**-1022 */
70df930be7Sderaadt if (((hx&0x7fffffff)|lx)==0)
71df930be7Sderaadt return -two54/zero; /* log(+-0)=-inf */
72df930be7Sderaadt if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
73df930be7Sderaadt k -= 54; x *= two54; /* subnormal number, scale up x */
74df930be7Sderaadt GET_HIGH_WORD(hx,x);
75df930be7Sderaadt }
76df930be7Sderaadt if (hx >= 0x7ff00000) return x+x;
77df930be7Sderaadt k += (hx>>20)-1023;
78df930be7Sderaadt i = ((u_int32_t)k&0x80000000)>>31;
79df930be7Sderaadt hx = (hx&0x000fffff)|((0x3ff-i)<<20);
80df930be7Sderaadt y = (double)(k+i);
81df930be7Sderaadt SET_HIGH_WORD(x,hx);
827b36286aSmartynas z = y*log10_2lo + ivln10*log(x);
83df930be7Sderaadt return z+y*log10_2hi;
84df930be7Sderaadt }
85*2f2c0062Sguenther DEF_STD(log10);
86*2f2c0062Sguenther LDBL_MAYBE_UNUSED_CLONE(log10);
87