e_log2f.c revision 226376 
1/*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12#include <sys/cdefs.h>
13__FBSDID("$FreeBSD: head/lib/msun/src/e_log2f.c 226376 2011-10-15 05:23:28Z das $");
14
15/*
16 * Float version of e_log2.c.  See the latter for most comments.
17 */
18
19#include "math.h"
20#include "math_private.h"
21#include "k_logf.h"
22
23static const float
24two25      =  3.3554432000e+07, /* 0x4c000000 */
25ivln2hi    =  1.4428710938e+00, /* 0x3fb8b000 */
26ivln2lo    = -1.7605285393e-04; /* 0xb9389ad4 */
27
28static const float zero   =  0.0;
29
30float
31__ieee754_log2f(float x)
32{
33	float f,hfsq,hi,lo,r,y;
34	int32_t i,k,hx;
35
36	GET_FLOAT_WORD(hx,x);
37
38	k=0;
39	if (hx < 0x00800000) {			/* x < 2**-126  */
40	    if ((hx&0x7fffffff)==0)
41		return -two25/zero;		/* log(+-0)=-inf */
42	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
43	    k -= 25; x *= two25; /* subnormal number, scale up x */
44	    GET_FLOAT_WORD(hx,x);
45	}
46	if (hx >= 0x7f800000) return x+x;
47	if (hx == 0x3f800000)
48	    return zero;			/* log(1) = +0 */
49	k += (hx>>23)-127;
50	hx &= 0x007fffff;
51	i = (hx+(0x4afb0d))&0x800000;
52	SET_FLOAT_WORD(x,hx|(i^0x3f800000));	/* normalize x or x/2 */
53	k += (i>>23);
54	y = (float)k;
55	f = x - (float)1.0;
56	hfsq = (float)0.5*f*f;
57	r = k_log1pf(f);
58
59	/*
60	 * We no longer need to avoid falling into the multi-precision
61	 * calculations due to compiler bugs breaking Dekker's theorem.
62	 * Keep avoiding this as an optimization.  See e_log2.c for more
63	 * details (some details are here only because the optimization
64	 * is not yet available in double precision).
65	 *
66	 * Another compiler bug turned up.  With gcc on i386,
67	 * (ivln2lo + ivln2hi) would be evaluated in float precision
68	 * despite runtime evaluations using double precision.  So we
69	 * must cast one of its terms to float_t.  This makes the whole
70	 * expression have type float_t, so return is forced to waste
71	 * time clobbering its extra precision.
72	 */
73	if (sizeof(float_t) > sizeof(float))
74		return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y;
75
76	hi = f - hfsq;
77	GET_FLOAT_WORD(hx,hi);
78	SET_FLOAT_WORD(hi,hx&0xfffff000);
79	lo = (f - hi) - hfsq + r;
80	return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y;
81}
82