lib/libm/noieee_src/n_cosh.c

   1 /*      $NetBSD: n_cosh.c,v 1.9 2014/10/10 20:58:09 martin 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. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 #if 0
  33 static char sccsid[] = "@(#)cosh.c      8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* COSH(X)
  38  * RETURN THE HYPERBOLIC COSINE OF X
  39  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  40  * CODED IN C BY K.C. NG, 1/8/85;
  41  * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
  42  *
  43  * Required system supported functions :
  44  *      copysign(x,y)
  45  *      scalb(x,N)
  46  *
  47  * Required kernel function:
  48  *      exp(x)
  49  *      exp__E(x,c)     ...return exp(x+c)-1-x for |x|<0.3465
  50  *
  51  * Method :
  52  *      1. Replace x by |x|.
  53  *      2.
  54  *                                                      [ exp(x) - 1 ]^2
  55  *          0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
  56  *                                                         2*exp(x)
  57  *
  58  *                                                 exp(x) +  1/exp(x)
  59  *          0.3465   <= x <= 22      :  cosh(x) := -------------------
  60  *                                                         2
  61  *          22       <= x <= lnovfl  :  cosh(x) := exp(x)/2
  62  *          lnovfl   <= x <= lnovfl+log(2)
  63  *                                   :  cosh(x) := exp(x)/2 (avoid overflow)
  64  *          log(2)+lnovfl <  x <  INF:  overflow to INF
  65  *
  66  *      Note: .3465 is a number near one half of ln2.
  67  *
  68  * Special cases:
  69  *      cosh(x) is x if x is +INF, -INF, or NaN.
  70  *      only cosh(0)=1 is exact for finite x.
  71  *
  72  * Accuracy:
  73  *      cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
  74  *      In a test run with 768,000 random arguments on a VAX, the maximum
  75  *      observed error was 1.23 ulps (units in the last place).
  76  *
  77  * Constants:
  78  * The hexadecimal values are the intended ones for the following constants.
  79  * The decimal values may be used, provided that the compiler will convert
  80  * from decimal to binary accurately enough to produce the hexadecimal values
  81  * shown.
  82  */
  83
  84 #define _LIBM_STATIC
  85 #include "../src/namespace.h"
  86 #include "mathimpl.h"
  87
  88 #ifdef __weak_alias
  89 __weak_alias(cosh, _cosh);
  90 __weak_alias(_coshl, _cosh);
  91 __weak_alias(coshf, _coshf);
  92 #endif
  93
  94 vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
  95 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
  96 vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
  97
  98 ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
  99 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
 100 ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
 101
 102 #ifdef vccast
 103 #define   mln2hi    vccast(mln2hi)
 104 #define   mln2lo    vccast(mln2lo)
 105 #define   lnovfl    vccast(lnovfl)
 106 #endif
 107
 108 #if defined(__vax__)||defined(tahoe)
 109 #define EXPMAX 126
 110 #else
 111 #define EXPMAX 1023
 112 #endif  /* defined(__vax__)||defined(tahoe) */
 113
 114 double
 115 cosh(double x)
 116 {
 117         static const double half=1.0/2.0,
 118                 one=1.0, small=1.0E-18; /* fl(1+small)==1 */
 119         double t;
 120
 121 #if !defined(__vax__)&&!defined(tahoe)
 122         if(x!=x) return(x);     /* x is NaN */
 123 #endif  /* !defined(__vax__)&&!defined(tahoe) */
 124         if((x=copysign(x,one)) <= 22) {
 125             if(x<0.3465) {
 126                 if(x<small) { return(one+x); }
 127                 else {t=x+__exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
 128
 129             } else /* for x lies in [0.3465,22] */
 130                 { t=exp(x); return((t+one/t)*half); }
 131         }
 132
 133         if( lnovfl <= x && x <= (lnovfl+0.7))
 134         /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(EXPMAX+1))
 135          * and return 2^EXPMAX*exp(x) to avoid unnecessary overflow
 136          */
 137             return(scalb(exp((x-mln2hi)-mln2lo), EXPMAX));
 138
 139         else
 140             return(exp(x)*half);        /* for large x,  cosh(x)=exp(x)/2 */
 141 }
 142
 143 float
 144 coshf(float x)
 145 {
 146         return(cosh((double)x));
 147 }