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4c182be8 | 1 | /* |
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2 | * Copyright (c) 1985, 1993 |
3 | * The Regents of the University of California. All rights reserved. | |
4c182be8 | 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. | |
4c182be8 | 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 | |
ad787160 | 35 | static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93"; |
4c182be8 | 36 | #endif /* not lint */ |
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37 | |
38 | /* ASINH(X) | |
39 | * RETURN THE INVERSE HYPERBOLIC SINE OF X | |
40 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
41 | * CODED IN C BY K.C. NG, 2/16/85; | |
42 | * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. | |
43 | * | |
44 | * Required system supported functions : | |
45 | * copysign(x,y) | |
46 | * sqrt(x) | |
47 | * | |
48 | * Required kernel function: | |
49 | * log1p(x) ...return log(1+x) | |
50 | * | |
51 | * Method : | |
52 | * Based on | |
53 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] | |
54 | * we have | |
55 | * asinh(x) := x if 1+x*x=1, | |
56 | * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else | |
57 | * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) | |
58 | * | |
59 | * Accuracy: | |
60 | * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. | |
61 | * In a test run with 52,000 random arguments on a VAX, the maximum | |
62 | * observed error was 1.58 ulps (units in the last place). | |
63 | * | |
64 | * Constants: | |
65 | * The hexadecimal values are the intended ones for the following constants. | |
66 | * The decimal values may be used, provided that the compiler will convert | |
67 | * from decimal to binary accurately enough to produce the hexadecimal values | |
68 | * shown. | |
69 | */ | |
9eda3584 | 70 | #include "mathimpl.h" |
21585cc4 | 71 | |
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72 | vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) |
73 | vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) | |
74 | ||
75 | ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) | |
76 | ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) | |
77 | ||
78 | #ifdef vccast | |
79 | #define ln2hi vccast(ln2hi) | |
80 | #define ln2lo vccast(ln2lo) | |
81 | #endif | |
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82 | |
83 | double asinh(x) | |
84 | double x; | |
85 | { | |
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86 | double t,s; |
87 | const static double small=1.0E-10, /* fl(1+small*small) == 1 */ | |
88 | big =1.0E20, /* fl(1+big) == big */ | |
89 | one =1.0 ; | |
21585cc4 | 90 | |
859dc438 | 91 | #if !defined(vax)&&!defined(tahoe) |
21585cc4 | 92 | if(x!=x) return(x); /* x is NaN */ |
859dc438 | 93 | #endif /* !defined(vax)&&!defined(tahoe) */ |
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94 | if((t=copysign(x,one))>small) |
95 | if(t<big) { | |
96 | s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } | |
97 | else /* if |x| > big */ | |
98 | {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} | |
99 | else /* if |x| < small */ | |
100 | return(x); | |
101 | } |