projects / unix-history / blame
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| 4c182be8 | 1 | /* |
| 21585cc4 | 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 | |
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6 | * provided that the above copyright notice and this paragraph are |
| 7 | * duplicated in all such forms and that any documentation, | |
| 8 | * advertising materials, and other materials related to such | |
| 9 | * distribution and use acknowledge that the software was developed | |
| 10 | * by the University of California, Berkeley. The name of the | |
| 11 | * University may not be used to endorse or promote products derived | |
| 12 | * from this software without specific prior written permission. | |
| 13 | * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR | |
| 14 | * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED | |
| 15 | * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. | |
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16 | * |
| 17 | * All recipients should regard themselves as participants in an ongoing | |
| 18 | * research project and hence should feel obligated to report their | |
| 19 | * experiences (good or bad) with these elementary function codes, using | |
| 20 | * the sendbug(8) program, to the authors. | |
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21 | */ |
| 22 | ||
| 23 | #ifndef lint | |
| 9eda3584 | 24 | static char sccsid[] = "@(#)asinh.c 5.4 (Berkeley) %G%"; |
| 4c182be8 | 25 | #endif /* not lint */ |
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26 | |
| 27 | /* ASINH(X) | |
| 28 | * RETURN THE INVERSE HYPERBOLIC SINE OF X | |
| 29 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
| 30 | * CODED IN C BY K.C. NG, 2/16/85; | |
| 31 | * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. | |
| 32 | * | |
| 33 | * Required system supported functions : | |
| 34 | * copysign(x,y) | |
| 35 | * sqrt(x) | |
| 36 | * | |
| 37 | * Required kernel function: | |
| 38 | * log1p(x) ...return log(1+x) | |
| 39 | * | |
| 40 | * Method : | |
| 41 | * Based on | |
| 42 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] | |
| 43 | * we have | |
| 44 | * asinh(x) := x if 1+x*x=1, | |
| 45 | * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else | |
| 46 | * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) | |
| 47 | * | |
| 48 | * Accuracy: | |
| 49 | * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. | |
| 50 | * In a test run with 52,000 random arguments on a VAX, the maximum | |
| 51 | * observed error was 1.58 ulps (units in the last place). | |
| 52 | * | |
| 53 | * Constants: | |
| 54 | * The hexadecimal values are the intended ones for the following constants. | |
| 55 | * The decimal values may be used, provided that the compiler will convert | |
| 56 | * from decimal to binary accurately enough to produce the hexadecimal values | |
| 57 | * shown. | |
| 58 | */ | |
| 9eda3584 | 59 | #include "mathimpl.h" |
| 21585cc4 | 60 | |
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61 | vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) |
| 62 | vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) | |
| 63 | ||
| 64 | ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) | |
| 65 | ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) | |
| 66 | ||
| 67 | #ifdef vccast | |
| 68 | #define ln2hi vccast(ln2hi) | |
| 69 | #define ln2lo vccast(ln2lo) | |
| 70 | #endif | |
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71 | |
| 72 | double asinh(x) | |
| 73 | double x; | |
| 74 | { | |
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75 | double t,s; |
| 76 | const static double small=1.0E-10, /* fl(1+small*small) == 1 */ | |
| 77 | big =1.0E20, /* fl(1+big) == big */ | |
| 78 | one =1.0 ; | |
| 21585cc4 | 79 | |
| 859dc438 | 80 | #if !defined(vax)&&!defined(tahoe) |
| 21585cc4 | 81 | if(x!=x) return(x); /* x is NaN */ |
| 859dc438 | 82 | #endif /* !defined(vax)&&!defined(tahoe) */ |
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83 | if((t=copysign(x,one))>small) |
| 84 | if(t<big) { | |
| 85 | s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } | |
| 86 | else /* if |x| > big */ | |
| 87 | {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} | |
| 88 | else /* if |x| < small */ | |
| 89 | return(x); | |
| 90 | } |