1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12 /*
13 * See comments in log10.c.
14 */
15
16 #include <math.h>
17 #include <stdint.h>
18
19 static const float
20 ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */
21 ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */
22 log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
23 log10_2lo = 7.9034151668e-07, /* 0x355427db */
24 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
25 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
26 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
27 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
28 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
29
_mylog10f(float x)30 float _mylog10f(float x)
31 {
32 union {float f; uint32_t i;} u = {x};
33 float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo;
34 uint32_t ix;
35 int k;
36
37 ix = u.i;
38 k = 0;
39 if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
40 if (ix<<1 == 0)
41 return -1/(x*x); /* log(+-0)=-inf */
42 if (ix>>31)
43 return (x-x)/0.0f; /* log(-#) = NaN */
44 /* subnormal number, scale up x */
45 k -= 25;
46 x *= 0x1p25f;
47 u.f = x;
48 ix = u.i;
49 } else if (ix >= 0x7f800000) {
50 return x;
51 } else if (ix == 0x3f800000)
52 return 0;
53
54 /* reduce x into [sqrt(2)/2, sqrt(2)] */
55 ix += 0x3f800000 - 0x3f3504f3;
56 k += (int)(ix>>23) - 0x7f;
57 ix = (ix&0x007fffff) + 0x3f3504f3;
58 u.i = ix;
59 x = u.f;
60
61 f = x - 1.0f;
62 s = f/(2.0f + f);
63 z = s*s;
64 w = z*z;
65 t1= w*(Lg2+w*Lg4);
66 t2= z*(Lg1+w*Lg3);
67 R = t2 + t1;
68 hfsq = 0.5f*f*f;
69
70 hi = f - hfsq;
71 u.f = hi;
72 u.i &= 0xfffff000;
73 hi = u.f;
74 lo = f - hi - hfsq + s*(hfsq+R);
75 dk = k;
76 return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*log10_2hi;
77 }
78