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4c182be8 | 1 | /* |
3de6acd5 | 2 | * Copyright (c) 1985 Regents of the University of California. |
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3 | * All rights reserved. |
4 | * | |
5 | * Redistribution and use in source and binary forms are permitted | |
6 | * provided that this notice is preserved and that due credit is given | |
7 | * to the University of California at Berkeley. The name of the University | |
8 | * may not be used to endorse or promote products derived from this | |
9 | * software without specific prior written permission. This software | |
10 | * is provided ``as is'' without express or implied warranty. | |
11 | * | |
12 | * All recipients should regard themselves as participants in an ongoing | |
13 | * research project and hence should feel obligated to report their | |
14 | * experiences (good or bad) with these elementary function codes, using | |
15 | * the sendbug(8) program, to the authors. | |
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16 | */ |
17 | ||
18 | #ifndef lint | |
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19 | static char sccsid[] = "@(#)acosh.c 5.2 (Berkeley) %G%"; |
20 | #endif /* not lint */ | |
21 | ||
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22 | /* ACOSH(X) |
23 | * RETURN THE INVERSE HYPERBOLIC COSINE OF X | |
24 | * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) | |
25 | * CODED IN C BY K.C. NG, 2/16/85; | |
26 | * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85. | |
27 | * | |
28 | * Required system supported functions : | |
29 | * sqrt(x) | |
30 | * | |
31 | * Required kernel function: | |
32 | * log1p(x) ...return log(1+x) | |
33 | * | |
34 | * Method : | |
35 | * Based on | |
36 | * acosh(x) = log [ x + sqrt(x*x-1) ] | |
37 | * we have | |
38 | * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else | |
39 | * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . | |
40 | * These formulae avoid the over/underflow complication. | |
41 | * | |
42 | * Special cases: | |
43 | * acosh(x) is NaN with signal if x<1. | |
44 | * acosh(NaN) is NaN without signal. | |
45 | * | |
46 | * Accuracy: | |
47 | * acosh(x) returns the exact inverse hyperbolic cosine of x nearly | |
48 | * rounded. In a test run with 512,000 random arguments on a VAX, the | |
49 | * maximum observed error was 3.30 ulps (units of the last place) at | |
50 | * x=1.0070493753568216 . | |
51 | * | |
52 | * Constants: | |
53 | * The hexadecimal values are the intended ones for the following constants. | |
54 | * The decimal values may be used, provided that the compiler will convert | |
55 | * from decimal to binary accurately enough to produce the hexadecimal values | |
56 | * shown. | |
57 | */ | |
58 | ||
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59 | #if defined(vax)||defined(tahoe) /* VAX D format */ |
60 | #ifdef vax | |
0e01cbea | 61 | #define _0x(A,B) 0x/**/A/**/B |
859dc438 | 62 | #else /* vax */ |
0e01cbea | 63 | #define _0x(A,B) 0x/**/B/**/A |
859dc438 | 64 | #endif /* vax */ |
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65 | /* static double */ |
66 | /* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ | |
67 | /* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */ | |
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68 | static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)}; |
69 | static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)}; | |
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70 | #define ln2hi (*(double*)ln2hix) |
71 | #define ln2lo (*(double*)ln2lox) | |
859dc438 | 72 | #else /* defined(vax)||defined(tahoe) */ |
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73 | static double |
74 | ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ | |
75 | ln2lo = 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */ | |
859dc438 | 76 | #endif /* defined(vax)||defined(tahoe) */ |
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77 | |
78 | double acosh(x) | |
79 | double x; | |
80 | { | |
81 | double log1p(),sqrt(),t,big=1.E20; /* big+1==big */ | |
82 | ||
859dc438 | 83 | #if !defined(vax)&&!defined(tahoe) |
3de6acd5 | 84 | if(x!=x) return(x); /* x is NaN */ |
859dc438 | 85 | #endif /* !defined(vax)&&!defined(tahoe) */ |
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86 | |
87 | /* return log1p(x) + log(2) if x is large */ | |
88 | if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} | |
89 | ||
90 | t=sqrt(x-1.0); | |
91 | return(log1p(t*(t+sqrt(x+1.0)))); | |
92 | } |