1
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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 /*
14 * Return the base 10 logarithm of x. See e_log.c and k_log.h for most
15 * comments.
16 *
17 * log10(x) = (f - 0.5*f*f + k_log1p(f)) / ln10 + k * log10(2)
18 * in not-quite-routine extra precision.
19 */
20
21 #include <float.h>
22
23 #include "math.h"
24 #include "math_private.h"
25 #include "k_log.h"
26
27 static const double
28 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
29 ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
30 ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
31 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
32 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
33
34 static const double zero = 0.0;
35 static volatile double vzero = 0.0;
36
37 double
log10(double x)38 log10(double x)
39 {
40 double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
41 int32_t i,k,hx;
42 u_int32_t lx;
43
44 EXTRACT_WORDS(hx,lx,x);
45
46 k=0;
47 if (hx < 0x00100000) { /* x < 2**-1022 */
48 if (((hx&0x7fffffff)|lx)==0)
49 return -two54/vzero; /* log(+-0)=-inf */
50 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
51 k -= 54; x *= two54; /* subnormal number, scale up x */
52 GET_HIGH_WORD(hx,x);
53 }
54 if (hx >= 0x7ff00000) return x+x;
55 if (hx == 0x3ff00000 && lx == 0)
56 return zero; /* log(1) = +0 */
57 k += (hx>>20)-1023;
58 hx &= 0x000fffff;
59 i = (hx+0x95f64)&0x100000;
60 SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
61 k += (i>>20);
62 y = (double)k;
63 f = x - 1.0;
64 hfsq = 0.5*f*f;
65 r = k_log1p(f);
66
67 /* See e_log2.c for most details. */
68 hi = f - hfsq;
69 SET_LOW_WORD(hi,0);
70 lo = (f - hi) - hfsq + r;
71 val_hi = hi*ivln10hi;
72 y2 = y*log10_2hi;
73 val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
74
75 /*
76 * Extra precision in for adding y*log10_2hi is not strictly needed
77 * since there is no very large cancellation near x = sqrt(2) or
78 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
79 * with some parallelism and it reduces the error for many args.
80 */
81 w = y2 + val_hi;
82 val_lo += (y2 - w) + val_hi;
83 val_hi = w;
84
85 return val_lo + val_hi;
86 }
87
88 #if (LDBL_MANT_DIG == 53)
89 __weak_reference(log10, log10l);
90 #endif
91