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 /* log10(x)
14 * Return the base 10 logarithm of x
15 *
16 * Method :
17 * Let log10_2hi = leading 40 bits of log10(2) and
18 * log10_2lo = log10(2) - log10_2hi,
19 * ivln10 = 1/log(10) rounded.
20 * Then
21 * n = ilogb(x),
22 * if(n<0) n = n+1;
23 * x = scalbn(x,-n);
24 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
25 *
26 * Note 1:
27 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
28 * mode must set to Round-to-Nearest.
29 * Note 2:
30 * [1/log(10)] rounded to 53 bits has error .198 ulps;
31 * log10 is monotonic at all binary break points.
32 *
33 * Special cases:
34 * log10(x) is NaN with signal if x < 0;
35 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
36 * log10(NaN) is that NaN with no signal;
37 * log10(10**N) = N for N=0,1,...,22.
38 *
39 * Constants:
40 * The hexadecimal values are the intended ones for the following constants.
41 * The decimal values may be used, provided that the compiler will convert
42 * from decimal to binary accurately enough to produce the hexadecimal values
43 * shown.
44 */
45
46 #include <float.h>
47 #include <math.h>
48
49 #include "math_private.h"
50
51 static const double
52 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
53 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
54 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
55 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
56
57 static const double zero = 0.0;
58
59 double
log10(double x)60 log10(double x)
61 {
62 double y,z;
63 int32_t i,k,hx;
64 u_int32_t lx;
65
66 EXTRACT_WORDS(hx,lx,x);
67
68 k=0;
69 if (hx < 0x00100000) { /* x < 2**-1022 */
70 if (((hx&0x7fffffff)|lx)==0)
71 return -two54/zero; /* log(+-0)=-inf */
72 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
73 k -= 54; x *= two54; /* subnormal number, scale up x */
74 GET_HIGH_WORD(hx,x);
75 }
76 if (hx >= 0x7ff00000) return x+x;
77 k += (hx>>20)-1023;
78 i = ((u_int32_t)k&0x80000000)>>31;
79 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
80 y = (double)(k+i);
81 SET_HIGH_WORD(x,hx);
82 z = y*log10_2lo + ivln10*log(x);
83 return z+y*log10_2hi;
84 }
85
86 #if LDBL_MANT_DIG == DBL_MANT_DIG
87 __strong_alias(log10l, log10);
88 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
89