1 /* @(#)s_tanh.c 5.1 93/09/24 */
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 #include <sys/cdefs.h>
14 __FBSDID("$FreeBSD$");
15
16 /* Tanh(x)
17 * Return the Hyperbolic Tangent of x
18 *
19 * Method :
20 * x -x
21 * e - e
22 * 0. tanh(x) is defined to be -----------
23 * x -x
24 * e + e
25 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
26 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
27 * -t
28 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
29 * t + 2
30 * 2
31 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
32 * t + 2
33 * 22 <= x <= INF : tanh(x) := 1.
34 *
35 * Special cases:
36 * tanh(NaN) is NaN;
37 * only tanh(0)=0 is exact for finite argument.
38 */
39
40 #include "math.h"
41 #include "math_private.h"
42
43 static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
44
45 double
tanh(double x)46 tanh(double x)
47 {
48 double t,z;
49 int32_t jx,ix;
50
51 GET_HIGH_WORD(jx,x);
52 ix = jx&0x7fffffff;
53
54 /* x is INF or NaN */
55 if(ix>=0x7ff00000) {
56 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
57 else return one/x-one; /* tanh(NaN) = NaN */
58 }
59
60 /* |x| < 22 */
61 if (ix < 0x40360000) { /* |x|<22 */
62 if (ix<0x3e300000) { /* |x|<2**-28 */
63 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
64 }
65 if (ix>=0x3ff00000) { /* |x|>=1 */
66 t = expm1(two*fabs(x));
67 z = one - two/(t+two);
68 } else {
69 t = expm1(-two*fabs(x));
70 z= -t/(t+two);
71 }
72 /* |x| >= 22, return +-1 */
73 } else {
74 z = one - tiny; /* raise inexact flag */
75 }
76 return (jx>=0)? z: -z;
77 }
78