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.h"
28#include "math_private.h"
29#include "k_log.h"
30
31static const double
32two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
33ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
34ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
35log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
36log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
37
38static const double zero   =  0.0;
39static volatile double vzero = 0.0;
40
41double
42__ieee754_log10(double x)
43{
44	double f,hfsq,hi,lo,r,val_hi,val_lo,w,y,y2;
45	int32_t i,k,hx;
46	u_int32_t lx;
47
48	EXTRACT_WORDS(hx,lx,x);
49
50	k=0;
51	if (hx < 0x00100000) {			/* x < 2**-1022  */
52	    if (((hx&0x7fffffff)|lx)==0)
53		return -two54/vzero;		/* log(+-0)=-inf */
54	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
55	    k -= 54; x *= two54; /* subnormal number, scale up x */
56	    GET_HIGH_WORD(hx,x);
57	}
58	if (hx >= 0x7ff00000) return x+x;
59	if (hx == 0x3ff00000 && lx == 0)
60	    return zero;			/* log(1) = +0 */
61	k += (hx>>20)-1023;
62	hx &= 0x000fffff;
63	i = (hx+0x95f64)&0x100000;
64	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
65	k += (i>>20);
66	y = (double)k;
67	f = x - 1.0;
68	hfsq = 0.5*f*f;
69	r = k_log1p(f);
70
71	/* See e_log2.c for most details. */
72	hi = f - hfsq;
73	SET_LOW_WORD(hi,0);
74	lo = (f - hi) - hfsq + r;
75	val_hi = hi*ivln10hi;
76	y2 = y*log10_2hi;
77	val_lo = y*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
78
79	/*
80	 * Extra precision in for adding y*log10_2hi is not strictly needed
81	 * since there is no very large cancellation near x = sqrt(2) or
82	 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
83	 * with some parallelism and it reduces the error for many args.
84	 */
85	w = y2 + val_hi;
86	val_lo += (y2 - w) + val_hi;
87	val_hi = w;
88
89	return val_lo + val_hi;
90}
91
92#if (LDBL_MANT_DIG == 53)
93__weak_reference(log10, log10l);
94#endif
95