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 /* Tanh(x)
13 * Return the Hyperbolic Tangent of x
14 *
15 * Method :
16 * x -x
17 * e - e
18 * 0. tanh(x) is defined to be -----------
19 * x -x
20 * e + e
21 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
22 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
23 * -t
24 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
25 * t + 2
26 * 2
27 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
28 * t + 2
29 * 22 <= x <= INF : tanh(x) := 1.
30 *
31 * Special cases:
32 * tanh(NaN) is NaN;
33 * only tanh(0)=0 is exact for finite argument.
34 */
35
36 #include <float.h>
37
38 #include "math.h"
39 #include "math_private.h"
40
41 static const volatile double tiny = 1.0e-300;
42 static const double one = 1.0, two = 2.0, huge = 1.0e300;
43
44 double
tanh(double x)45 tanh(double x)
46 {
47 double t,z;
48 int32_t jx,ix;
49
50 GET_HIGH_WORD(jx,x);
51 ix = jx&0x7fffffff;
52
53 /* x is INF or NaN */
54 if(ix>=0x7ff00000) {
55 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
56 else return one/x-one; /* tanh(NaN) = NaN */
57 }
58
59 /* |x| < 22 */
60 if (ix < 0x40360000) { /* |x|<22 */
61 if (ix<0x3e300000) { /* |x|<2**-28 */
62 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
63 }
64 if (ix>=0x3ff00000) { /* |x|>=1 */
65 t = expm1(two*fabs(x));
66 z = one - two/(t+two);
67 } else {
68 t = expm1(-two*fabs(x));
69 z= -t/(t+two);
70 }
71 /* |x| >= 22, return +-1 */
72 } else {
73 z = one - tiny; /* raise inexact flag */
74 }
75 return (jx>=0)? z: -z;
76 }
77
78 #if (LDBL_MANT_DIG == 53)
79 __weak_reference(tanh, tanhl);
80 #endif
81