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n_cosh.c revision 1.1 
      1 /*      $NetBSD: n_cosh.c,v 1.1 1995/10/10 23:36:42 ragge Exp $ */
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. All advertising materials mentioning features or use of this software
     15  *    must display the following acknowledgement:
     16  *	This product includes software developed by the University of
     17  *	California, Berkeley and its contributors.
     18  * 4. Neither the name of the University nor the names of its contributors
     19  *    may be used to endorse or promote products derived from this software
     20  *    without specific prior written permission.
     21  *
     22  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     23  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     24  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     25  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     26  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     27  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     28  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     29  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     30  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     31  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     32  * SUCH DAMAGE.
     33  */
     34 
     35 #ifndef lint
     36 static char sccsid[] = "@(#)cosh.c	8.1 (Berkeley) 6/4/93";
     37 #endif /* not lint */
     38 
     39 /* COSH(X)
     40  * RETURN THE HYPERBOLIC COSINE OF X
     41  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
     42  * CODED IN C BY K.C. NG, 1/8/85;
     43  * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
     44  *
     45  * Required system supported functions :
     46  *	copysign(x,y)
     47  *	scalb(x,N)
     48  *
     49  * Required kernel function:
     50  *	exp(x)
     51  *	exp__E(x,c)	...return exp(x+c)-1-x for |x|<0.3465
     52  *
     53  * Method :
     54  *	1. Replace x by |x|.
     55  *	2.
     56  *		                                        [ exp(x) - 1 ]^2
     57  *	    0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
     58  *			       			           2*exp(x)
     59  *
     60  *		                                   exp(x) +  1/exp(x)
     61  *	    0.3465   <= x <= 22      :  cosh(x) := -------------------
     62  *			       			           2
     63  *	    22       <= x <= lnovfl  :  cosh(x) := exp(x)/2
     64  *	    lnovfl   <= x <= lnovfl+log(2)
     65  *				     :  cosh(x) := exp(x)/2 (avoid overflow)
     66  *	    log(2)+lnovfl <  x <  INF:  overflow to INF
     67  *
     68  *	Note: .3465 is a number near one half of ln2.
     69  *
     70  * Special cases:
     71  *	cosh(x) is x if x is +INF, -INF, or NaN.
     72  *	only cosh(0)=1 is exact for finite x.
     73  *
     74  * Accuracy:
     75  *	cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
     76  *	In a test run with 768,000 random arguments on a VAX, the maximum
     77  *	observed error was 1.23 ulps (units in the last place).
     78  *
     79  * Constants:
     80  * The hexadecimal values are the intended ones for the following constants.
     81  * The decimal values may be used, provided that the compiler will convert
     82  * from decimal to binary accurately enough to produce the hexadecimal values
     83  * shown.
     84  */
     85 
     86 #include "mathimpl.h"
     87 
     88 vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
     89 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
     90 vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
     91 
     92 ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
     93 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
     94 ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
     95 
     96 #ifdef vccast
     97 #define   mln2hi    vccast(mln2hi)
     98 #define   mln2lo    vccast(mln2lo)
     99 #define   lnovfl    vccast(lnovfl)
    100 #endif
    101 
    102 #if defined(vax)||defined(tahoe)
    103 static max = 126                      ;
    104 #else	/* defined(vax)||defined(tahoe) */
    105 static max = 1023                     ;
    106 #endif	/* defined(vax)||defined(tahoe) */
    107 
    108 double cosh(x)
    109 double x;
    110 {
    111 	static const double half=1.0/2.0,
    112 		one=1.0, small=1.0E-18; /* fl(1+small)==1 */
    113 	double t;
    114 
    115 #if !defined(vax)&&!defined(tahoe)
    116 	if(x!=x) return(x);	/* x is NaN */
    117 #endif	/* !defined(vax)&&!defined(tahoe) */
    118 	if((x=copysign(x,one)) <= 22)
    119 	    if(x<0.3465)
    120 		if(x<small) return(one+x);
    121 		else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
    122 
    123 	    else /* for x lies in [0.3465,22] */
    124 	        { t=exp(x); return((t+one/t)*half); }
    125 
    126 	if( lnovfl <= x && x <= (lnovfl+0.7))
    127         /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
    128          * and return 2^max*exp(x) to avoid unnecessary overflow
    129          */
    130 	    return(scalb(exp((x-mln2hi)-mln2lo), max));
    131 
    132 	else
    133 	    return(exp(x)*half);	/* for large x,  cosh(x)=exp(x)/2 */
    134 }
    135