sysdeps/generic/cosh.c

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