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