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