986
|
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 log10(2) and
|
|
19 |
* log10_2lo = log10(2) - log10_2hi,
|
|
20 |
* ivln10 = 1/log(10) rounded.
|
|
21 |
* Then
|
|
22 |
* n = ilogb(x),
|
|
23 |
* if(n<0) n = n+1;
|
|
24 |
* x = scalbn(x,-n);
|
|
25 |
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
|
|
26 |
*
|
|
27 |
* Note 1:
|
|
28 |
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
|
|
29 |
* mode must set to Round-to-Nearest.
|
|
30 |
* Note 2:
|
|
31 |
* [1/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; 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__
|
|
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; /* log(+-0)=-inf */
|
|
79 |
if (hx<0) return (x-x)/zero; /* 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 |
}
|