121026Smiriam /*
221026Smiriam * Copyright (c) 1985 Regents of the University of California.
321026Smiriam *
421026Smiriam * Use and reproduction of this software are granted in accordance with
521026Smiriam * the terms and conditions specified in the Berkeley Software License
621026Smiriam * Agreement (in particular, this entails acknowledgement of the programs'
721026Smiriam * source, and inclusion of this notice) with the additional understanding
821026Smiriam * that all recipients should regard themselves as participants in an
921026Smiriam * ongoing research project and hence should feel obligated to report
1021026Smiriam * their experiences (good or bad) with these elementary function codes,
1121026Smiriam * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
1221026Smiriam */
1321026Smiriam
1421026Smiriam #ifndef lint
15*24337Smiriam static char sccsid[] = "@(#)atanh.c 1.2 (Berkeley) 08/21/85";
1621026Smiriam #endif not lint
1721026Smiriam
1821026Smiriam /* ATANH(X)
1921026Smiriam * RETURN THE HYPERBOLIC ARC TANGENT OF X
2021026Smiriam * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
2121026Smiriam * CODED IN C BY K.C. NG, 1/8/85;
22*24337Smiriam * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
2321026Smiriam *
2421026Smiriam * Required kernel function:
25*24337Smiriam * log1p(x) ...return log(1+x)
2621026Smiriam *
2721026Smiriam * Method :
2821026Smiriam * Return
29*24337Smiriam * 1 2x x
30*24337Smiriam * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
31*24337Smiriam * 2 1 - x 1 - x
3221026Smiriam *
3321026Smiriam * Special cases:
34*24337Smiriam * atanh(x) is NaN if |x| > 1 with signal;
35*24337Smiriam * atanh(NaN) is that NaN with no signal;
3621026Smiriam * atanh(+-1) is +-INF with signal.
3721026Smiriam *
3821026Smiriam * Accuracy:
3921026Smiriam * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
40*24337Smiriam * In a test run with 512,000 random arguments on a VAX, the maximum
41*24337Smiriam * observed error was 1.87 ulps (units in the last place) at
42*24337Smiriam * x= -3.8962076028810414000e-03.
4321026Smiriam */
44*24337Smiriam #ifdef VAX
45*24337Smiriam #include <errno.h>
46*24337Smiriam #endif
4721026Smiriam
atanh(x)4821026Smiriam double atanh(x)
4921026Smiriam double x;
5021026Smiriam {
51*24337Smiriam double copysign(),log1p(),z;
52*24337Smiriam z = copysign(0.5,x);
53*24337Smiriam x = copysign(x,1.0);
54*24337Smiriam #ifdef VAX
55*24337Smiriam if (x == 1.0) {
56*24337Smiriam extern double infnan();
57*24337Smiriam return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */
58*24337Smiriam }
59*24337Smiriam #endif
60*24337Smiriam x = x/(1.0-x);
61*24337Smiriam return( z*log1p(x+x) );
6221026Smiriam }
63