text: /*      $NetBSD: n_cosh.c,v 1.2 1997/10/20 14:12:06 ragge Exp $ */
  /*
   * Copyright (c) 1985, 1993
   *	The Regents of the University of California.  All rights reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in the
   *    documentation and/or other materials provided with the distribution.
   * 3. All advertising materials mentioning features or use of this software
   *    must display the following acknowledgement:
   *	This product includes software developed by the University of
   *	California, Berkeley and its contributors.
   * 4. Neither the name of the University nor the names of its contributors
   *    may be used to endorse or promote products derived from this software
   *    without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
   * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
   * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
   * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   */
  
  #ifndef lint
  #if 0
  static char sccsid[] = "@(#)cosh.c	8.1 (Berkeley) 6/4/93";
  #endif
  #endif /* not lint */
  
  /* COSH(X)
   * RETURN THE HYPERBOLIC COSINE OF X
   * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
   * CODED IN C BY K.C. NG, 1/8/85; 
   * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
   *
   * Required system supported functions :
   *	copysign(x,y)
   *	scalb(x,N)
   *
   * Required kernel function:
   *	exp(x) 
   *	exp__E(x,c)	...return exp(x+c)-1-x for |x|<0.3465
   *
   * Method :
   *	1. Replace x by |x|. 
   *	2. 
   *		                                        [ exp(x) - 1 ]^2 
   *	    0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
   *			       			           2*exp(x)
   *
   *		                                   exp(x) +  1/exp(x)
   *	    0.3465   <= x <= 22      :  cosh(x) := -------------------
   *			       			           2
   *	    22       <= x <= lnovfl  :  cosh(x) := exp(x)/2 
   *	    lnovfl   <= x <= lnovfl+log(2)
   *				     :  cosh(x) := exp(x)/2 (avoid overflow)
   *	    log(2)+lnovfl <  x <  INF:  overflow to INF
   *
   *	Note: .3465 is a number near one half of ln2.
   *
   * Special cases:
   *	cosh(x) is x if x is +INF, -INF, or NaN.
   *	only cosh(0)=1 is exact for finite x.
   *
   * Accuracy:
   *	cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
   *	In a test run with 768,000 random arguments on a VAX, the maximum
   *	observed error was 1.23 ulps (units in the last place).
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following constants.
   * The decimal values may be used, provided that the compiler will convert
   * from decimal to binary accurately enough to produce the hexadecimal values
   * shown.
   */
  
  #include "mathimpl.h"
  
  vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
  vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
  vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
  
  ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
  ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
  ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
  
  #ifdef vccast
  #define   mln2hi    vccast(mln2hi)
  #define   mln2lo    vccast(mln2lo)
  #define   lnovfl    vccast(lnovfl)
  #endif
  
  #if defined(vax)||defined(tahoe)
  static max = 126                      ;
  #else	/* defined(vax)||defined(tahoe) */
  static max = 1023                     ;
  #endif	/* defined(vax)||defined(tahoe) */
  
  double cosh(x)
  double x;
  {	
  	static const double half=1.0/2.0,
  		one=1.0, small=1.0E-18; /* fl(1+small)==1 */
  	double t;
  
  #if !defined(vax)&&!defined(tahoe)
  	if(x!=x) return(x);	/* x is NaN */
  #endif	/* !defined(vax)&&!defined(tahoe) */
  	if((x=copysign(x,one)) <= 22)
  	    if(x<0.3465) 
  		if(x<small) return(one+x);
  		else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
  
  	    else /* for x lies in [0.3465,22] */
  	        { t=exp(x); return((t+one/t)*half); }
  
  	if( lnovfl <= x && x <= (lnovfl+0.7)) 
          /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) 
           * and return 2^max*exp(x) to avoid unnecessary overflow 
           */
  	    return(scalb(exp((x-mln2hi)-mln2lo), max)); 
  
  	else 
  	    return(exp(x)*half);	/* for large x,  cosh(x)=exp(x)/2 */
  }
  