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("$FreeBSD$");
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;
29static volatile float vzero = 0.0;
30
31float
32__ieee754_log2f(float x)
33{
34	float f,hfsq,hi,lo,r,y;
35	int32_t i,k,hx;
36
37	GET_FLOAT_WORD(hx,x);
38
39	k=0;
40	if (hx < 0x00800000) {			/* x < 2**-126  */
41	    if ((hx&0x7fffffff)==0)
42		return -two25/vzero;		/* log(+-0)=-inf */
43	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
44	    k -= 25; x *= two25; /* subnormal number, scale up x */
45	    GET_FLOAT_WORD(hx,x);
46	}
47	if (hx >= 0x7f800000) return x+x;
48	if (hx == 0x3f800000)
49	    return zero;			/* log(1) = +0 */
50	k += (hx>>23)-127;
51	hx &= 0x007fffff;
52	i = (hx+(0x4afb0d))&0x800000;
53	SET_FLOAT_WORD(x,hx|(i^0x3f800000));	/* normalize x or x/2 */
54	k += (i>>23);
55	y = (float)k;
56	f = x - (float)1.0;
57	hfsq = (float)0.5*f*f;
58	r = k_log1pf(f);
59
60	/*
61	 * We no longer need to avoid falling into the multi-precision
62	 * calculations due to compiler bugs breaking Dekker's theorem.
63	 * Keep avoiding this as an optimization.  See e_log2.c for more
64	 * details (some details are here only because the optimization
65	 * is not yet available in double precision).
66	 *
67	 * Another compiler bug turned up.  With gcc on i386,
68	 * (ivln2lo + ivln2hi) would be evaluated in float precision
69	 * despite runtime evaluations using double precision.  So we
70	 * must cast one of its terms to float_t.  This makes the whole
71	 * expression have type float_t, so return is forced to waste
72	 * time clobbering its extra precision.
73	 */
74	if (sizeof(float_t) > sizeof(float))
75		return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y;
76
77	hi = f - hfsq;
78	GET_FLOAT_WORD(hx,hi);
79	SET_FLOAT_WORD(hi,hx&0xfffff000);
80	lo = (f - hi) - hfsq + r;
81	return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y;
82}
83