e_log10.c - vx32 - Local 9vx git repository for patches.
(HTM) git clone git://r-36.net/vx32
(DIR) Log
(DIR) Files
(DIR) Refs
---
e_log10.c (2697B)
---
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[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.10 2003/07/23 04:53:46 peter Exp $";
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 static const double
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 const double zero = 0.0;
60
61 double
62 __ieee754_log10(double x)
63 {
64 double y,z;
65 int32_t i,k,hx;
66 u_int32_t lx;
67
68 EXTRACT_WORDS(hx,lx,x);
69
70 k=0;
71 if (hx < 0x00100000) { /* x < 2**-1022 */
72 if (((hx&0x7fffffff)|lx)==0)
73 return -two54/zero; /* log(+-0)=-inf */
74 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
75 k -= 54; x *= two54; /* subnormal number, scale up x */
76 GET_HIGH_WORD(hx,x);
77 }
78 if (hx >= 0x7ff00000) return x+x;
79 k += (hx>>20)-1023;
80 i = ((u_int32_t)k&0x80000000)>>31;
81 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
82 y = (double)(k+i);
83 SET_HIGH_WORD(x,hx);
84 z = y*log10_2lo + ivln10*__ieee754_log(x);
85 return z+y*log10_2hi;
86 }