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 <float.h>
41
42 #include "math.h"
43 #include "math_private.h"
44
45 static const volatile double tiny = 1.0e-300;
46 static const double one = 1.0, two = 2.0, huge = 1.0e300;
47
48 double
tanh(double x)49 tanh(double x)
50 {
51 double t,z;
52 int32_t jx,ix;
53
54 GET_HIGH_WORD(jx,x);
55 ix = jx&0x7fffffff;
56
57 /* x is INF or NaN */
58 if(ix>=0x7ff00000) {
59 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
60 else return one/x-one; /* tanh(NaN) = NaN */
61 }
62
63 /* |x| < 22 */
64 if (ix < 0x40360000) { /* |x|<22 */
65 if (ix<0x3e300000) { /* |x|<2**-28 */
66 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
67 }
68 if (ix>=0x3ff00000) { /* |x|>=1 */
69 t = expm1(two*fabs(x));
70 z = one - two/(t+two);
71 } else {
72 t = expm1(-two*fabs(x));
73 z= -t/(t+two);
74 }
75 /* |x| >= 22, return +-1 */
76 } else {
77 z = one - tiny; /* raise inexact flag */
78 }
79 return (jx>=0)? z: -z;
80 }
81
82 #if (LDBL_MANT_DIG == 53)
83 __weak_reference(tanh, tanhl);
84 #endif
85