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9b525f39 | 1 | /* |
06b452f6 | 2 | * Copyright (c) 1985 Regents of the University of California. |
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3 | * All rights reserved. |
4 | * | |
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5 | * Redistribution and use in source and binary forms, with or without |
6 | * modification, are permitted provided that the following conditions | |
7 | * are met: | |
8 | * 1. Redistributions of source code must retain the above copyright | |
9 | * notice, this list of conditions and the following disclaimer. | |
10 | * 2. Redistributions in binary form must reproduce the above copyright | |
11 | * notice, this list of conditions and the following disclaimer in the | |
12 | * documentation and/or other materials provided with the distribution. | |
13 | * 3. All advertising materials mentioning features or use of this software | |
14 | * must display the following acknowledgement: | |
15 | * This product includes software developed by the University of | |
16 | * California, Berkeley and its contributors. | |
17 | * 4. Neither the name of the University nor the names of its contributors | |
18 | * may be used to endorse or promote products derived from this software | |
19 | * without specific prior written permission. | |
9b525f39 | 20 | * |
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21 | * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND |
22 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
23 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
24 | * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE | |
25 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
26 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
27 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
28 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
29 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
30 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
31 | * SUCH DAMAGE. | |
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32 | */ |
33 | ||
34 | #ifndef lint | |
af359dea | 35 | static char sccsid[] = "@(#)tanh.c 5.5 (Berkeley) 10/9/90"; |
9b525f39 | 36 | #endif /* not lint */ |
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37 | |
38 | /* TANH(X) | |
39 | * RETURN THE HYPERBOLIC TANGENT OF X | |
40 | * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) | |
41 | * CODED IN C BY K.C. NG, 1/8/85; | |
42 | * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. | |
43 | * | |
44 | * Required system supported functions : | |
45 | * copysign(x,y) | |
46 | * finite(x) | |
47 | * | |
48 | * Required kernel function: | |
49 | * expm1(x) ...exp(x)-1 | |
50 | * | |
51 | * Method : | |
52 | * 1. reduce x to non-negative by tanh(-x) = - tanh(x). | |
53 | * 2. | |
54 | * 0 < x <= 1.e-10 : tanh(x) := x | |
55 | * -expm1(-2x) | |
56 | * 1.e-10 < x <= 1 : tanh(x) := -------------- | |
57 | * expm1(-2x) + 2 | |
58 | * 2 | |
59 | * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- | |
60 | * expm1(2x) + 2 | |
61 | * 22.0 < x <= INF : tanh(x) := 1. | |
62 | * | |
63 | * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. | |
64 | * | |
65 | * Special cases: | |
66 | * tanh(NaN) is NaN; | |
67 | * only tanh(0)=0 is exact for finite argument. | |
68 | * | |
69 | * Accuracy: | |
70 | * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. | |
71 | * In a test run with 1,024,000 random arguments on a VAX, the maximum | |
72 | * observed error was 2.22 ulps (units in the last place). | |
73 | */ | |
74 | ||
75 | double tanh(x) | |
76 | double x; | |
77 | { | |
78 | static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; | |
79 | double expm1(), t, copysign(), sign; | |
80 | int finite(); | |
81 | ||
859dc438 | 82 | #if !defined(vax)&&!defined(tahoe) |
06b452f6 | 83 | if(x!=x) return(x); /* x is NaN */ |
859dc438 | 84 | #endif /* !defined(vax)&&!defined(tahoe) */ |
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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 | {big+x; return(copysign(x,sign));} | |
95 | else if(finite(x)) | |
96 | return (sign+1.0E-37); /* raise the INEXACT flag */ | |
97 | else | |
98 | return(sign); /* x is +- INF */ | |
99 | } |