4.3BSD - /usr/src/usr.lib/libm/atanh.c

   1: /*
   2:  * Copyright (c) 1985 Regents of the University of California.
   3:  *
   4:  * Use and reproduction of this software are granted  in  accordance  with
   5:  * the terms and conditions specified in  the  Berkeley  Software  License
   6:  * Agreement (in particular, this entails acknowledgement of the programs'
   7:  * source, and inclusion of this notice) with the additional understanding
   8:  * that  all  recipients  should regard themselves as participants  in  an
   9:  * ongoing  research  project and hence should  feel  obligated  to report
  10:  * their  experiences (good or bad) with these elementary function  codes,
  11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
  12:  */
  13: 
  14: #ifndef lint
  15: static char sccsid[] = "@(#)atanh.c	1.2 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* ATANH(X)
  19:  * RETURN THE HYPERBOLIC ARC TANGENT OF X
  20:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  21:  * CODED IN C BY K.C. NG, 1/8/85;
  22:  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
  23:  *
  24:  * Required kernel function:
  25:  *	log1p(x) 	...return log(1+x)
  26:  *
  27:  * Method :
  28:  *	Return
  29:  *                          1              2x                          x
  30:  *		atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  31:  *                          2             1 - x                      1 - x
  32:  *
  33:  * Special cases:
  34:  *	atanh(x) is NaN if |x| > 1 with signal;
  35:  *	atanh(NaN) is that NaN with no signal;
  36:  *	atanh(+-1) is +-INF with signal.
  37:  *
  38:  * Accuracy:
  39:  *	atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
  40:  *	In a test run with 512,000 random arguments on a VAX, the maximum
  41:  *	observed error was 1.87 ulps (units in the last place) at
  42:  *	x= -3.8962076028810414000e-03.
  43:  */
  44: #ifdef VAX
  45: #include <errno.h>
  46: #endif
  47: 
  48: double atanh(x)
  49: double x;
  50: {
  51:     double copysign(),log1p(),z;
  52:     z = copysign(0.5,x);
  53:     x = copysign(x,1.0);
  54: #ifdef VAX
  55:     if (x == 1.0) {
  56:         extern double infnan();
  57:         return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */
  58:     }
  59: #endif
  60:     x = x/(1.0-x);
  61:     return( z*log1p(x+x) );
  62: }

Defined functions

Defined variables