2 * Copyright (c) 1985, 1993
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33 * @(#)asinh.c 8.1 (Berkeley) 6/4/93
37 * RETURN THE INVERSE HYPERBOLIC SINE OF X
38 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
39 * CODED IN C BY K.C. NG, 2/16/85;
40 * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
42 * Required system supported functions :
46 * Required kernel function:
47 * log1p(x) ...return log(1+x)
51 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
53 * asinh(x) := x if 1+x*x=1,
54 * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else
55 * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
58 * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
59 * In a test run with 52,000 random arguments on a VAX, the maximum
60 * observed error was 1.58 ulps (units in the last place).
63 * The hexadecimal values are the intended ones for the following constants.
64 * The decimal values may be used, provided that the compiler will convert
65 * from decimal to binary accurately enough to produce the hexadecimal values
70 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
71 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
73 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
74 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
77 #define ln2hi vccast(ln2hi)
78 #define ln2lo vccast(ln2lo)
85 const static double small=1.0E-10, /* fl(1+small*small) == 1 */
86 big =1.0E20, /* fl(1+big) == big */
89 #if !defined(vax)&&!defined(tahoe)
90 if(x!=x) return(x); /* x is NaN */
91 #endif /* !defined(vax)&&!defined(tahoe) */
92 if((t=copysign(x,one))>small)
94 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
95 else /* if |x| > big */
96 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
97 else /* if |x| < small */