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("$FreeBSD$");
16
17 /*
18 * Return the base 10 logarithm of x. See e_log.c and k_log.h for most
19 * comments.
20 *
21 * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
22 * in not-quite-routine extra precision.
23 */
24
25 #include <float.h>
26
27 #include "math_private.h"
28 #include "k_log.h"
29
30 static const double
31 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
32 ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
33 ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
34 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
35 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
36
37 static const double zero = 0.0;
38 static volatile double vzero = 0.0;
39
40 double
__ieee754_log10(double x)41 __ieee754_log10(double x)
42 {
43 double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
44 int32_t i,k,hx;
45 u_int32_t lx;
46
47 EXTRACT_WORDS(hx,lx,x);
48
49 k=0;
50 if (hx < 0x00100000) { /* x < 2**-1022 */
51 if (((hx&0x7fffffff)|lx)==0)
52 return -two54/vzero; /* log(+-0)=-inf */
53 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
54 k -= 54; x *= two54; /* subnormal number, scale up x */
55 GET_HIGH_WORD(hx,x);
56 }
57 if (hx >= 0x7ff00000) return x+x;
58 if (hx == 0x3ff00000 && lx == 0)
59 return zero; /* log(1) = +0 */
60 k += (hx>>20)-1023;
61 hx &= 0x000fffff;
62 i = (hx+0x95f64)&0x100000;
63 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
64 k += (i>>20);
65 y = (double)k;
66 f = x - 1.0;
67 hfsq = 0.5*f*f;
68 r = k_log1p(f);
69
70 /* See e_log2.c for most details. */
71 hi = f - hfsq;
72 SET_LOW_WORD(hi,0);
73 lo = (f - hi) - hfsq + r;
74 val_hi = hi*ivln10hi;
75 y2 = y*log10_2hi;
76 val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
77
78 /*
79 * Extra precision in for adding y*log10_2hi is not strictly needed
80 * since there is no very large cancellation near x = sqrt(2) or
81 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
82 * with some parallelism and it reduces the error for many args.
83 */
84 w = y2 + val_hi;
85 val_lo += (y2 - w) + val_hi;
86 val_hi = w;
87
88 return val_lo + val_hi;
89 }
90