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n_sinh.c revision 1.1 
      1 /*      $NetBSD: n_sinh.c,v 1.1 1995/10/10 23:37:05 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[] = "@(#)sinh.c	8.1 (Berkeley) 6/4/93";
     37 #endif /* not lint */
     38 
     39 /* SINH(X)
     40  * RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85.
     44  *
     45  * Required system supported functions :
     46  *	copysign(x,y)
     47  *	scalb(x,N)
     48  *
     49  * Required kernel functions:
     50  *	expm1(x)	...return exp(x)-1
     51  *
     52  * Method :
     53  *	1. reduce x to non-negative by sinh(-x) = - sinh(x).
     54  *	2.
     55  *
     56  *	                                      expm1(x) + expm1(x)/(expm1(x)+1)
     57  *	    0 <= x <= lnovfl     : sinh(x) := --------------------------------
     58  *			       		                      2
     59  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
     60  * lnovfl+ln2 <  x <  INF        :  overflow to INF
     61  *
     62  *
     63  * Special cases:
     64  *	sinh(x) is x if x is +INF, -INF, or NaN.
     65  *	only sinh(0)=0 is exact for finite argument.
     66  *
     67  * Accuracy:
     68  *	sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
     69  *	a test run with 1,024,000 random arguments on a VAX, the maximum
     70  *	observed error was 1.93 ulps (units in the last place).
     71  *
     72  * Constants:
     73  * The hexadecimal values are the intended ones for the following constants.
     74  * The decimal values may be used, provided that the compiler will convert
     75  * from decimal to binary accurately enough to produce the hexadecimal values
     76  * shown.
     77  */
     78 
     79 #include "mathimpl.h"
     80 
     81 vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
     82 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
     83 vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
     84 
     85 ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
     86 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
     87 ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
     88 
     89 #ifdef vccast
     90 #define	mln2hi	vccast(mln2hi)
     91 #define	mln2lo	vccast(mln2lo)
     92 #define	lnovfl	vccast(lnovfl)
     93 #endif
     94 
     95 #if defined(vax)||defined(tahoe)
     96 static max = 126                      ;
     97 #else	/* defined(vax)||defined(tahoe) */
     98 static max = 1023                     ;
     99 #endif	/* defined(vax)||defined(tahoe) */
    100 
    101 
    102 double sinh(x)
    103 double x;
    104 {
    105 	static const double  one=1.0, half=1.0/2.0 ;
    106 	double t, sign;
    107 #if !defined(vax)&&!defined(tahoe)
    108 	if(x!=x) return(x);	/* x is NaN */
    109 #endif	/* !defined(vax)&&!defined(tahoe) */
    110 	sign=copysign(one,x);
    111 	x=copysign(x,one);
    112 	if(x<lnovfl)
    113 	    {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
    114 
    115 	else if(x <= lnovfl+0.7)
    116 		/* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
    117 	    		to avoid unnecessary overflow */
    118 	    return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
    119 
    120 	else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
    121 	    return( expm1(x)*sign );
    122 }
    123