1 

     2 /*

     3  * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.

     4  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

     5  *

     6  * This code is free software; you can redistribute it and/or modify it

     7  * under the terms of the GNU General Public License version 2 only, as

     8  * published by the Free Software Foundation.  Oracle designates this

     9  * particular file as subject to the "Classpath" exception as provided

    10  * by Oracle in the LICENSE file that accompanied this code.

    11  *

    12  * This code is distributed in the hope that it will be useful, but WITHOUT

    13  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

    14  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

    15  * version 2 for more details (a copy is included in the LICENSE file that

    16  * accompanied this code).

    17  *

    18  * You should have received a copy of the GNU General Public License version

    19  * 2 along with this work; if not, write to the Free Software Foundation,

    20  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

    21  *

    22  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

    23  * or visit www.oracle.com if you need additional information or have any

    24  * questions.

    25  */

    26 

    27 /* __ieee754_cosh(x)

    28  * Method :

    29  * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2

    30  *      1. Replace x by |x| (cosh(x) = cosh(-x)).

    31  *      2.

    32  *                                                      [ exp(x) - 1 ]^2

    33  *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------

    34  *                                                         2*exp(x)

    35  *

    36  *                                                exp(x) +  1/exp(x)

    37  *          ln2/2    <= x <= 22     :  cosh(x) := -------------------

    38  *                                                        2

    39  *          22       <= x <= lnovft :  cosh(x) := exp(x)/2

    40  *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)

    41  *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)

    42  *

    43  * Special cases:

    44  *      cosh(x) is |x| if x is +INF, -INF, or NaN.

    45  *      only cosh(0)=1 is exact for finite x.

    46  */

    47 

    48 #include "fdlibm.h"

    49 

    50 #ifdef __STDC__

    51 static const double one = 1.0, half=0.5, huge = 1.0e300;

    52 #else

    53 static double one = 1.0, half=0.5, huge = 1.0e300;

    54 #endif

    55 

    56 #ifdef __STDC__

    57         double __ieee754_cosh(double x)

    58 #else

    59         double __ieee754_cosh(x)

    60         double x;

    61 #endif

    62 {

    63         double t,w;

    64         int ix;

    65         unsigned lx;

    66 

    67     /* High word of |x|. */

    68         ix = __HI(x);

    69         ix &= 0x7fffffff;

    70 

    71     /* x is INF or NaN */

    72         if(ix>=0x7ff00000) return x*x;

    73 

    74     /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */

    75         if(ix<0x3fd62e43) {

    76             t = expm1(fabs(x));

    77             w = one+t;

    78             if (ix<0x3c800000) return w;        /* cosh(tiny) = 1 */

    79             return one+(t*t)/(w+w);

    80         }

    81 

    82     /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */

    83         if (ix < 0x40360000) {

    84                 t = __ieee754_exp(fabs(x));

    85                 return half*t+half/t;

    86         }

    87 

    88     /* |x| in [22, log(maxdouble)] return half*exp(|x|) */

    89         if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));

    90 

    91     /* |x| in [log(maxdouble), overflowthresold] */

    92         lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);

    93         if (ix<0x408633CE ||

    94               ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {

    95             w = __ieee754_exp(half*fabs(x));

    96             t = half*w;

    97             return t*w;

    98         }

    99 

   100     /* |x| > overflowthresold, cosh(x) overflow */

   101         return huge*huge;

   102 }