1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms are permitted 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. 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. 21 */ 22 23 #ifndef lint 24 static char sccsid[] = "@(#)asinh.c 5.3 (Berkeley) 06/30/88"; 25 #endif /* not lint */ 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 */ 59 60 #if defined(vax)||defined(tahoe) /* VAX/TAHOE D format */ 61 #ifdef vax 62 #define _0x(A,B) 0x/**/A/**/B 63 #else /* vax */ 64 #define _0x(A,B) 0x/**/B/**/A 65 #endif /* vax */ 66 /* static double */ 67 /* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ 68 /* ln2lo = 1.6465949582897081279E-12 ; Hex 2^-39 * .E7BCD5E4F1D9CC */ 69 static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)}; 70 static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)}; 71 #define ln2hi (*(double*)ln2hix) 72 #define ln2lo (*(double*)ln2lox) 73 #else /* defined(vax)||defined(tahoe) */ 74 static double 75 ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ 76 ln2lo = 1.9082149292705877000E-10 ; /*Hex 2^-33 * 1.A39EF35793C76 */ 77 #endif /* defined(vax)||defined(tahoe) */ 78 79 double asinh(x) 80 double x; 81 { 82 double copysign(),log1p(),sqrt(),t,s; 83 static double small=1.0E-10, /* fl(1+small*small) == 1 */ 84 big =1.0E20, /* fl(1+big) == big */ 85 one =1.0 ; 86 87 #if !defined(vax)&&!defined(tahoe) 88 if(x!=x) return(x); /* x is NaN */ 89 #endif /* !defined(vax)&&!defined(tahoe) */ 90 if((t=copysign(x,one))>small) 91 if(t<big) { 92 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } 93 else /* if |x| > big */ 94 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} 95 else /* if |x| < small */ 96 return(x); 97 } 98