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
27static const double
28two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
29ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
30ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
31log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
32log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
33
34static const double zero   =  0.0;
35static volatile double vzero = 0.0;
36
37double
38log10(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