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#include <sys/cdefs.h>
| 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#include <sys/cdefs.h>
|
15__FBSDID("$FreeBSD: head/lib/msun/src/e_log10.c 176451 2008-02-22 02:30:36Z das $");
| 15__FBSDID("$FreeBSD: head/lib/msun/src/e_log2.c 216211 2010-12-05 22:11:22Z das $");
|
16
| 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.
| 17/* log2(x)
18 * Return the base 2 logarithm of x.
|
48 */
49
50#include "math.h"
51#include "math_private.h"
| 19 */
20
21#include "math.h"
22#include "math_private.h"
|
| 23#include "k_log.h"
|
52
53static const double
54two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
| 24
25static const double
26two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
55ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
56log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
57log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
| 27ivln2hi = 0x1.71547652000p+0,
28ivln2lo = 0x1.705fc2eefa2p-33;
|
58
59static const double zero = 0.0;
60
61double
| 29
30static const double zero = 0.0;
31
32double
|
62__ieee754_log10(double x)
| 33__ieee754_log2(double x)
|
63{
| 34{
|
64 double y,z;
| 35 double f,hi,lo;
|
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;
| 36 int32_t i,k,hx;
37 u_int32_t lx;
38
39 EXTRACT_WORDS(hx,lx,x);
40
41 k=0;
42 if (hx < 0x00100000) { /* x < 2**-1022 */
43 if (((hx&0x7fffffff)|lx)==0)
44 return -two54/zero; /* log(+-0)=-inf */
45 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
46 k -= 54; x *= two54; /* subnormal number, scale up x */
47 GET_HIGH_WORD(hx,x);
48 }
49 if (hx >= 0x7ff00000) return x+x;
50 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;
| 51 hx &= 0x000fffff;
52 i = (hx+0x95f64)&0x100000;
53 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
54 k += (i>>20);
55 f = __kernel_log(x);
56 hi = x = x - 1;
57 SET_LOW_WORD(hi,0);
58 lo = x - hi;
59 return (x+f)*ivln2lo + (lo+f)*ivln2hi + hi*ivln2hi + k;
|
86}
| 60}
|