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21585cc4 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[] = |
2893dfdc | 16 | "@(#)asinh.c 1.2 (Berkeley) 8/21/85; 5.1 (ucb.elefunt) %G%"; |
859dc438 | 17 | #endif /* not lint */ |
21585cc4 ZAL |
18 | |
19 | /* ASINH(X) | |
20 | * RETURN THE INVERSE HYPERBOLIC SINE OF X | |
21 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
22 | * CODED IN C BY K.C. NG, 2/16/85; | |
23 | * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. | |
24 | * | |
25 | * Required system supported functions : | |
26 | * copysign(x,y) | |
27 | * sqrt(x) | |
28 | * | |
29 | * Required kernel function: | |
30 | * log1p(x) ...return log(1+x) | |
31 | * | |
32 | * Method : | |
33 | * Based on | |
34 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] | |
35 | * we have | |
36 | * asinh(x) := x if 1+x*x=1, | |
37 | * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else | |
38 | * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) | |
39 | * | |
40 | * Accuracy: | |
41 | * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. | |
42 | * In a test run with 52,000 random arguments on a VAX, the maximum | |
43 | * observed error was 1.58 ulps (units in the last place). | |
44 | * | |
45 | * Constants: | |
46 | * The hexadecimal values are the intended ones for the following constants. | |
47 | * The decimal values may be used, provided that the compiler will convert | |
48 | * from decimal to binary accurately enough to produce the hexadecimal values | |
49 | * shown. | |
50 | */ | |
51 | ||
859dc438 ZAL |
52 | #if defined(vax)||defined(tahoe) /* VAX/TAHOE D format */ |
53 | #ifdef vax | |
0e01cbea | 54 | #define _0x(A,B) 0x/**/A/**/B |
859dc438 | 55 | #else /* vax */ |
0e01cbea | 56 | #define _0x(A,B) 0x/**/B/**/A |
859dc438 | 57 | #endif /* vax */ |
21585cc4 ZAL |
58 | /* static double */ |
59 | /* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ | |
60 | /* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */ | |
0e01cbea ZAL |
61 | static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)}; |
62 | static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)}; | |
21585cc4 ZAL |
63 | #define ln2hi (*(double*)ln2hix) |
64 | #define ln2lo (*(double*)ln2lox) | |
859dc438 | 65 | #else /* defined(vax)||defined(tahoe) */ |
21585cc4 ZAL |
66 | static double |
67 | ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ | |
68 | ln2lo = 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */ | |
859dc438 | 69 | #endif /* defined(vax)||defined(tahoe) */ |
21585cc4 ZAL |
70 | |
71 | double asinh(x) | |
72 | double x; | |
73 | { | |
74 | double copysign(),log1p(),sqrt(),t,s; | |
75 | static double small=1.0E-10, /* fl(1+small*small) == 1 */ | |
76 | big =1.0E20, /* fl(1+big) == big */ | |
77 | one =1.0 ; | |
78 | ||
859dc438 | 79 | #if !defined(vax)&&!defined(tahoe) |
21585cc4 | 80 | if(x!=x) return(x); /* x is NaN */ |
859dc438 | 81 | #endif /* !defined(vax)&&!defined(tahoe) */ |
21585cc4 ZAL |
82 | if((t=copysign(x,one))>small) |
83 | if(t<big) { | |
84 | s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } | |
85 | else /* if |x| > big */ | |
86 | {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} | |
87 | else /* if |x| < small */ | |
88 | return(x); | |
89 | } |