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 
31 static const double
32 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
33 ivln10hi   =  4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
34 ivln10lo   =  2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
35 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
36 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
37 
38 static const double zero   =  0.0;
39 static volatile double vzero = 0.0;
40 
41 double
__ieee754_log10(double x)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