xref: /freebsd/lib/msun/src/e_log2f.c (revision 55141f2c8991b2a6adbf30bb0fe3e6cbc303f06d)
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 /*
14  * Float version of e_log2.c.  See the latter for most comments.
15  */
16 
17 #include "math.h"
18 #include "math_private.h"
19 #include "k_logf.h"
20 
21 static const float
22 two25      =  3.3554432000e+07, /* 0x4c000000 */
23 ivln2hi    =  1.4428710938e+00, /* 0x3fb8b000 */
24 ivln2lo    = -1.7605285393e-04; /* 0xb9389ad4 */
25 
26 static const float zero   =  0.0;
27 static volatile float vzero = 0.0;
28 
29 float
30 log2f(float x)
31 {
32 	float f,hfsq,hi,lo,r,y;
33 	int32_t i,k,hx;
34 
35 	GET_FLOAT_WORD(hx,x);
36 
37 	k=0;
38 	if (hx < 0x00800000) {			/* x < 2**-126  */
39 	    if ((hx&0x7fffffff)==0)
40 		return -two25/vzero;		/* log(+-0)=-inf */
41 	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
42 	    k -= 25; x *= two25; /* subnormal number, scale up x */
43 	    GET_FLOAT_WORD(hx,x);
44 	}
45 	if (hx >= 0x7f800000) return x+x;
46 	if (hx == 0x3f800000)
47 	    return zero;			/* log(1) = +0 */
48 	k += (hx>>23)-127;
49 	hx &= 0x007fffff;
50 	i = (hx+(0x4afb0d))&0x800000;
51 	SET_FLOAT_WORD(x,hx|(i^0x3f800000));	/* normalize x or x/2 */
52 	k += (i>>23);
53 	y = (float)k;
54 	f = x - (float)1.0;
55 	hfsq = (float)0.5*f*f;
56 	r = k_log1pf(f);
57 
58 	/*
59 	 * We no longer need to avoid falling into the multi-precision
60 	 * calculations due to compiler bugs breaking Dekker's theorem.
61 	 * Keep avoiding this as an optimization.  See e_log2.c for more
62 	 * details (some details are here only because the optimization
63 	 * is not yet available in double precision).
64 	 *
65 	 * Another compiler bug turned up.  With gcc on i386,
66 	 * (ivln2lo + ivln2hi) would be evaluated in float precision
67 	 * despite runtime evaluations using double precision.  So we
68 	 * must cast one of its terms to float_t.  This makes the whole
69 	 * expression have type float_t, so return is forced to waste
70 	 * time clobbering its extra precision.
71 	 */
72 	if (sizeof(float_t) > sizeof(float))
73 		return (r - hfsq + f) * ((float_t)ivln2lo + ivln2hi) + y;
74 
75 	hi = f - hfsq;
76 	GET_FLOAT_WORD(hx,hi);
77 	SET_FLOAT_WORD(hi,hx&0xfffff000);
78 	lo = (f - hi) - hfsq + r;
79 	return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + y;
80 }
81