1
2 /* @(#)e_atanh.c 1.3 95/01/18 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15 #include <sys/cdefs.h>
16 __FBSDID("$FreeBSD$");
17
18 /* __ieee754_atanh(x)
19 * Method :
20 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
21 * 2.For x>=0.5
22 * 1 2x x
23 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
24 * 2 1 - x 1 - x
25 *
26 * For x<0.5
27 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
28 *
29 * Special cases:
30 * atanh(x) is NaN if |x| > 1 with signal;
31 * atanh(NaN) is that NaN with no signal;
32 * atanh(+-1) is +-INF with signal.
33 *
34 */
35
36 #include <float.h>
37
38 #include "math.h"
39 #include "math_private.h"
40
41 static const double one = 1.0, huge = 1e300;
42 static const double zero = 0.0;
43
44 double
__ieee754_atanh(double x)45 __ieee754_atanh(double x)
46 {
47 double t;
48 int32_t hx,ix;
49 u_int32_t lx;
50 EXTRACT_WORDS(hx,lx,x);
51 ix = hx&0x7fffffff;
52 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
53 return (x-x)/(x-x);
54 if(ix==0x3ff00000)
55 return x/zero;
56 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
57 SET_HIGH_WORD(x,ix);
58 if(ix<0x3fe00000) { /* x < 0.5 */
59 t = x+x;
60 t = 0.5*log1p(t+t*x/(one-x));
61 } else
62 t = 0.5*log1p((x+x)/(one-x));
63 if(hx>=0) return t; else return -t;
64 }
65
66 #if LDBL_MANT_DIG == 53
67 __weak_reference(atanh, atanhl);
68 #endif
69