1 /* 2 * Copyright (c) 1985, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 */ 7 8 #ifndef lint 9 static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 06/04/93"; 10 #endif /* not lint */ 11 12 /* ASINH(X) 13 * RETURN THE INVERSE HYPERBOLIC SINE OF X 14 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 15 * CODED IN C BY K.C. NG, 2/16/85; 16 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. 17 * 18 * Required system supported functions : 19 * copysign(x,y) 20 * sqrt(x) 21 * 22 * Required kernel function: 23 * log1p(x) ...return log(1+x) 24 * 25 * Method : 26 * Based on 27 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 28 * we have 29 * asinh(x) := x if 1+x*x=1, 30 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else 31 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) 32 * 33 * Accuracy: 34 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. 35 * In a test run with 52,000 random arguments on a VAX, the maximum 36 * observed error was 1.58 ulps (units in the last place). 37 * 38 * Constants: 39 * The hexadecimal values are the intended ones for the following constants. 40 * The decimal values may be used, provided that the compiler will convert 41 * from decimal to binary accurately enough to produce the hexadecimal values 42 * shown. 43 */ 44 #include "mathimpl.h" 45 46 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) 47 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) 48 49 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) 50 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) 51 52 #ifdef vccast 53 #define ln2hi vccast(ln2hi) 54 #define ln2lo vccast(ln2lo) 55 #endif 56 57 double asinh(x) 58 double x; 59 { 60 double t,s; 61 const static double small=1.0E-10, /* fl(1+small*small) == 1 */ 62 big =1.0E20, /* fl(1+big) == big */ 63 one =1.0 ; 64 65 #if !defined(vax)&&!defined(tahoe) 66 if(x!=x) return(x); /* x is NaN */ 67 #endif /* !defined(vax)&&!defined(tahoe) */ 68 if((t=copysign(x,one))>small) 69 if(t<big) { 70 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); } 71 else /* if |x| > big */ 72 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} 73 else /* if |x| < small */ 74 return(x); 75 } 76