add Berkeley specific header

[unix-history] / usr / src / lib / libm / common_source / sinh.c

/*
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms are permitted
* provided that this notice is preserved and that due credit is given
* to the University of California at Berkeley. The name of the University
* may not be used to endorse or promote products derived from this
* software without specific prior written permission. This software
* is provided ``as is'' without express or implied warranty.
*
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
*/

#ifndef lint
static char sccsid[] = "@(#)sinh.c      5.2 (Berkeley) %G%";
#endif /* not lint */

/* SINH(X)
* RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85.
*
* Required system supported functions :
*      copysign(x,y)
*      scalb(x,N)
*
* Required kernel functions:
*      expm1(x)        ...return exp(x)-1
*
* Method :
*      1. reduce x to non-negative by sinh(-x) = - sinh(x).
*      2. 
*
*                                            expm1(x) + expm1(x)/(expm1(x)+1)
*          0 <= x <= lnovfl     : sinh(x) := --------------------------------
*                                                            2
*     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
* lnovfl+ln2 <  x <  INF        :  overflow to INF
*      
*
* Special cases:
*      sinh(x) is x if x is +INF, -INF, or NaN.
*      only sinh(0)=0 is exact for finite argument.
*
* Accuracy:
*      sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
*      a test run with 1,024,000 random arguments on a VAX, the maximum
*      observed error was 1.93 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.
*/
#if defined(vax)||defined(tahoe)
#ifdef vax
#define _0x(A,B)        0x/**/A/**/B
#else   /* vax */
#define _0x(A,B)        0x/**/B/**/A
#endif  /* vax */
/* static double */
/* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
/* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
/* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
static long    mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)};
static long    mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)};
static long    lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)};
#define   mln2hi    (*(double*)mln2hix)
#define   mln2lo    (*(double*)mln2lox)
#define   lnovfl    (*(double*)lnovflx)
#else   /* defined(vax)||defined(tahoe) */
static double 
mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
#endif  /* defined(vax)||defined(tahoe) */

#if defined(vax)||defined(tahoe)
static max = 126                      ;
#else   /* defined(vax)||defined(tahoe) */
static max = 1023                     ;
#endif  /* defined(vax)||defined(tahoe) */


double sinh(x)
double x;
{
       static double  one=1.0, half=1.0/2.0 ;
       double expm1(), t, scalb(), copysign(), sign;
#if !defined(vax)&&!defined(tahoe)
       if(x!=x) return(x);     /* x is NaN */
#endif  /* !defined(vax)&&!defined(tahoe) */
       sign=copysign(one,x);
       x=copysign(x,one);
       if(x<lnovfl)
           {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}

       else if(x <= lnovfl+0.7)
               /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 
                       to avoid unnecessary overflow */
           return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));

       else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
           return( expm1(x)*sign );
}