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#ifndef lint
| 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#ifndef lint
|
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_tanh.c 97413 2002-05-28 18:15:04Z alfred $";
| 14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_tanh.c 160122 2006-07-05 22:59:33Z bde $";
|
15#endif
16
17/* Tanh(x)
18 * Return the Hyperbolic Tangent of x
19 *
20 * Method :
21 * x -x
22 * e - e
23 * 0. tanh(x) is defined to be -----------
24 * x -x
25 * e + e
26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
| 15#endif
16
17/* Tanh(x)
18 * Return the Hyperbolic Tangent of x
19 *
20 * Method :
21 * x -x
22 * e - e
23 * 0. tanh(x) is defined to be -----------
24 * x -x
25 * e + e
26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
27 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
| 27 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0
|
28 * -t
| 28 * -t
|
29 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
| 29 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
|
30 * t + 2
31 * 2
| 30 * t + 2
31 * 2
|
32 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
| 32 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x)
|
33 * t + 2
| 33 * t + 2
|
34 * 22.0 < x <= INF : tanh(x) := 1.
| 34 * 22 <= x <= INF : tanh(x) := 1.
|
35 *
36 * Special cases:
37 * tanh(NaN) is NaN;
38 * only tanh(0)=0 is exact for finite argument.
39 */
40
41#include "math.h"
42#include "math_private.h"
43
| 35 *
36 * Special cases:
37 * tanh(NaN) is NaN;
38 * only tanh(0)=0 is exact for finite argument.
39 */
40
41#include "math.h"
42#include "math_private.h"
43
|
44static const double one=1.0, two=2.0, tiny = 1.0e-300;
| 44static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
|
45
46double
47tanh(double x)
48{
49 double t,z;
50 int32_t jx,ix;
51
| 45
46double
47tanh(double x)
48{
49 double t,z;
50 int32_t jx,ix;
51
|
52 /* High word of |x|. */
| |
53 GET_HIGH_WORD(jx,x);
54 ix = jx&0x7fffffff;
55
56 /* x is INF or NaN */
57 if(ix>=0x7ff00000) {
58 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
59 else return one/x-one; /* tanh(NaN) = NaN */
60 }
61
62 /* |x| < 22 */
63 if (ix < 0x40360000) { /* |x|<22 */
| 52 GET_HIGH_WORD(jx,x);
53 ix = jx&0x7fffffff;
54
55 /* x is INF or NaN */
56 if(ix>=0x7ff00000) {
57 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
58 else return one/x-one; /* tanh(NaN) = NaN */
59 }
60
61 /* |x| < 22 */
62 if (ix < 0x40360000) { /* |x|<22 */
|
64 if (ix<0x3c800000) /* |x|<2**-55 */
65 return x*(one+x); /* tanh(small) = small */
| 63 if (ix<0x3e300000) { /* |x|<2**-28 */
64 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */
65 }
|
66 if (ix>=0x3ff00000) { /* |x|>=1 */
67 t = expm1(two*fabs(x));
68 z = one - two/(t+two);
69 } else {
70 t = expm1(-two*fabs(x));
71 z= -t/(t+two);
72 }
| 66 if (ix>=0x3ff00000) { /* |x|>=1 */
67 t = expm1(two*fabs(x));
68 z = one - two/(t+two);
69 } else {
70 t = expm1(-two*fabs(x));
71 z= -t/(t+two);
72 }
|
73 /* |x| > 22, return +-1 */
| 73 /* |x| >= 22, return +-1 */
|
74 } else {
| 74 } else {
|
75 z = one - tiny; /* raised inexact flag */
| 75 z = one - tiny; /* raise inexact flag */
|
76 }
77 return (jx>=0)? z: -z;
78}
| 76 }
77 return (jx>=0)? z: -z;
78}
|