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
23 static const float
24 two25 = 3.3554432000e+07, /* 0x4c000000 */
25 ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */
26 ivln2lo = -1.7605285393e-04; /* 0xb9389ad4 */
27
28 static const float zero = 0.0;
29 static volatile float vzero = 0.0;
30
31 float
__ieee754_log2f(float x)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