1 /* $NetBSD: n_tanh.c,v 1.7 2014/03/06 10:59:00 martin Exp $ */
2 /*
3 * Copyright (c) 1985, 1993
4 * The Regents of the University of California. All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 * may be used to endorse or promote products derived from this software
16 * without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 */
30
31 #ifndef lint
32 #if 0
33 static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93";
34 #endif
35 #endif /* not lint */
36
37 /* TANH(X)
38 * RETURN THE HYPERBOLIC TANGENT OF X
39 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
40 * CODED IN C BY K.C. NG, 1/8/85;
41 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
42 *
43 * Required system supported functions :
44 * copysign(x,y)
45 * finite(x)
46 *
47 * Required kernel function:
48 * expm1(x) ...exp(x)-1
49 *
50 * Method :
51 * 1. reduce x to non-negative by tanh(-x) = - tanh(x).
52 * 2.
53 * 0 < x <= 1.e-10 : tanh(x) := x
54 * -expm1(-2x)
55 * 1.e-10 < x <= 1 : tanh(x) := --------------
56 * expm1(-2x) + 2
57 * 2
58 * 1 <= x <= 22.0 : tanh(x) := 1 - ---------------
59 * expm1(2x) + 2
60 * 22.0 < x <= INF : tanh(x) := 1.
61 *
62 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
63 *
64 * Special cases:
65 * tanh(NaN) is NaN;
66 * only tanh(0)=0 is exact for finite argument.
67 *
68 * Accuracy:
69 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
70 * In a test run with 1,024,000 random arguments on a VAX, the maximum
71 * observed error was 2.22 ulps (units in the last place).
72 */
73
74 #include "mathimpl.h"
75
76 double
tanh(double x)77 tanh(double x)
78 {
79 static const double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
80 double t, sign;
81
82 #if !defined(__vax__)&&!defined(tahoe)
83 if(x!=x) return(x); /* x is NaN */
84 #endif /* !defined(__vax__)&&!defined(tahoe) */
85
86 sign=copysign(one,x);
87 x=copysign(x,one);
88 if(x < 22.0)
89 if( x > one )
90 return(copysign(one-two/(expm1(x+x)+two),sign));
91 else if ( x > small )
92 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
93 else /* raise the INEXACT flag for non-zero x */
94 { t = big+x; return(copysign(x,sign));} /* ??? -ragge */
95 else if(finite(x))
96 return (sign+1.0E-37); /* raise the INEXACT flag */
97 else
98 return(sign); /* x is +- INF */
99 }
100
101 float
tanhf(float x)102 tanhf(float x)
103 {
104 return tanh(x);
105 }
106