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 /* __ieee754_atanh(x)
13 * Method :
14 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
15 * 2.For x>=0.5
16 * 1 2x x
17 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
18 * 2 1 - x 1 - x
19 *
20 * For x<0.5
21 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
22 *
23 * Special cases:
24 * atanh(x) is NaN if |x| > 1 with signal;
25 * atanh(NaN) is that NaN with no signal;
26 * atanh(+-1) is +-INF with signal.
27 *
28 */
29
30 #include "math.h"
31 #include "math_private.h"
32
33 static const double one = 1.0, huge = 1e300;
34
35 static const double zero = 0.0;
36
__ieee754_atanh(double x)37 double __ieee754_atanh(double x)
38 {
39 double t;
40 int32_t hx,ix;
41 u_int32_t lx;
42 EXTRACT_WORDS(hx,lx,x);
43 ix = hx&0x7fffffff;
44 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
45 return (x-x)/(x-x);
46 if(ix==0x3ff00000)
47 return x/zero;
48 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
49 SET_HIGH_WORD(x,ix);
50 if(ix<0x3fe00000) { /* x < 0.5 */
51 t = x+x;
52 t = 0.5*log1p(t+t*x/(one-x));
53 } else
54 t = 0.5*log1p((x+x)/(one-x));
55 if(hx>=0) return t; else return -t;
56 }
57
58 /*
59 * wrapper atanh(x)
60 */
61 #ifndef _IEEE_LIBM
atanh(double x)62 double atanh(double x)
63 {
64 double z, y;
65 z = __ieee754_atanh(x);
66 if (_LIB_VERSION == _IEEE_ || isnan(x))
67 return z;
68 y = fabs(x);
69 if (y >= 1.0) {
70 if (y > 1.0)
71 return __kernel_standard(x, x, 30); /* atanh(|x|>1) */
72 return __kernel_standard(x, x, 31); /* atanh(|x|==1) */
73 }
74 return z;
75 }
76 #else
77 strong_alias(__ieee754_atanh, atanh)
78 #endif
79 libm_hidden_def(atanh)
80