usr/src/lib/libm/common/C/cosh.c

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 /*
  22  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  23  */
  24 /*
  25  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  26  * Use is subject to license terms.
  27  */
  28
  29 #pragma weak __cosh = cosh
  30
  31 /* INDENT OFF */
  32 /*
  33  * cosh(x)
  34  * Code originated from 4.3bsd.
  35  * Modified by K.C. Ng for SUN 4.0 libm.
  36  * Method :
  37  *      1. Replace x by |x| (cosh(x) = cosh(-x)).
  38  *      2.
  39  *                                       [ exp(x) - 1 ]^2
  40  *  0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
  41  *                                                                    2*exp(x)
  42  *
  43  *                                                 exp(x) +  1/exp(x)
  44  *  0.3465   <= x <= 22      :  cosh(x) := -------------------
  45  *                                                                         2
  46  *  22       <= x <= lnovft  :  cosh(x) := exp(x)/2
  47  *  lnovft   <= x <  INF     :  cosh(x) := scalbn(exp(x-1024*ln2),1023)
  48  *
  49  *      Note: .3465 is a number near one half of ln2.
  50  *
  51  * Special cases:
  52  *      cosh(x) is |x| if x is +INF, -INF, or NaN.
  53  *      only cosh(0)=1 is exact for finite x.
  54  */
  55 /* INDENT ON */
  56
  57 #include "libm.h"
  58
  59 static const double
  60         ln2 = 6.93147180559945286227e-01,
  61         ln2hi = 6.93147180369123816490e-01,
  62         ln2lo = 1.90821492927058770002e-10,
  63         lnovft = 7.09782712893383973096e+02;
  64
  65 double
  66 cosh(double x) {
  67         double t, w;
  68
  69         w = fabs(x);
  70         if (!finite(w))
  71                 return (w * w);
  72         if (w < 0.3465) {
  73                 t = expm1(w);
  74                 w = 1.0 + t;
  75                 if (w != 1.0)
  76                         w = 1.0 + (t * t) / (w + w);
  77                 return (w);
  78         } else if (w < 22.0) {
  79                 t = exp(w);
  80                 return (0.5 * (t + 1.0 / t));
  81         } else if (w <= lnovft) {
  82                 return (0.5 * exp(w));
  83         } else {
  84                 w = (w - 1024 * ln2hi) - 1024 * ln2lo;
  85                 if (w >= ln2)
  86                         return (_SVID_libm_err(x, x, 5));
  87                 else
  88                         return (scalbn(exp(w), 1023));
  89         }
  90 }