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3de6acd5 ZAL |
1 | /* |
2 | * Copyright (c) 1985 Regents of the University of California. | |
3 | * | |
4 | * Use and reproduction of this software are granted in accordance with | |
5 | * the terms and conditions specified in the Berkeley Software License | |
6 | * Agreement (in particular, this entails acknowledgement of the programs' | |
7 | * source, and inclusion of this notice) with the additional understanding | |
8 | * that all recipients should regard themselves as participants in an | |
9 | * ongoing research project and hence should feel obligated to report | |
10 | * their experiences (good or bad) with these elementary function codes, | |
11 | * using "sendbug 4bsd-bugs@BERKELEY", to the authors. | |
12 | */ | |
13 | ||
14 | #ifndef lint | |
a62df508 | 15 | static char sccsid[] = |
0e01cbea | 16 | "@(#)acosh.c 1.2 (Berkeley) 8/21/85; 1.4 (ucb.elefunt) %G%"; |
3de6acd5 | 17 | #endif not lint |
3de6acd5 ZAL |
18 | /* ACOSH(X) |
19 | * RETURN THE INVERSE HYPERBOLIC COSINE OF X | |
20 | * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) | |
21 | * CODED IN C BY K.C. NG, 2/16/85; | |
22 | * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85. | |
23 | * | |
24 | * Required system supported functions : | |
25 | * sqrt(x) | |
26 | * | |
27 | * Required kernel function: | |
28 | * log1p(x) ...return log(1+x) | |
29 | * | |
30 | * Method : | |
31 | * Based on | |
32 | * acosh(x) = log [ x + sqrt(x*x-1) ] | |
33 | * we have | |
34 | * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else | |
35 | * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . | |
36 | * These formulae avoid the over/underflow complication. | |
37 | * | |
38 | * Special cases: | |
39 | * acosh(x) is NaN with signal if x<1. | |
40 | * acosh(NaN) is NaN without signal. | |
41 | * | |
42 | * Accuracy: | |
43 | * acosh(x) returns the exact inverse hyperbolic cosine of x nearly | |
44 | * rounded. In a test run with 512,000 random arguments on a VAX, the | |
45 | * maximum observed error was 3.30 ulps (units of the last place) at | |
46 | * x=1.0070493753568216 . | |
47 | * | |
48 | * Constants: | |
49 | * The hexadecimal values are the intended ones for the following constants. | |
50 | * The decimal values may be used, provided that the compiler will convert | |
51 | * from decimal to binary accurately enough to produce the hexadecimal values | |
52 | * shown. | |
53 | */ | |
54 | ||
e0085737 | 55 | #if (defined(VAX)||defined(TAHOE)) /* VAX D format */ |
0e01cbea ZAL |
56 | #ifdef VAX |
57 | #define _0x(A,B) 0x/**/A/**/B | |
58 | #else /* VAX */ | |
59 | #define _0x(A,B) 0x/**/B/**/A | |
60 | #endif /* VAX */ | |
3de6acd5 ZAL |
61 | /* static double */ |
62 | /* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ | |
63 | /* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */ | |
0e01cbea ZAL |
64 | static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)}; |
65 | static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)}; | |
3de6acd5 ZAL |
66 | #define ln2hi (*(double*)ln2hix) |
67 | #define ln2lo (*(double*)ln2lox) | |
68 | #else /* IEEE double */ | |
69 | static double | |
70 | ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ | |
71 | ln2lo = 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */ | |
72 | #endif | |
73 | ||
74 | double acosh(x) | |
75 | double x; | |
76 | { | |
77 | double log1p(),sqrt(),t,big=1.E20; /* big+1==big */ | |
78 | ||
e0085737 | 79 | #if (!defined(VAX)&&!defined(TAHOE)) |
3de6acd5 ZAL |
80 | if(x!=x) return(x); /* x is NaN */ |
81 | #endif | |
82 | ||
83 | /* return log1p(x) + log(2) if x is large */ | |
84 | if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} | |
85 | ||
86 | t=sqrt(x-1.0); | |
87 | return(log1p(t*(t+sqrt(x+1.0)))); | |
88 | } |