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_acosh(x)

    28  * Method :

    29  *      Based on

    30  *              acosh(x) = log [ x + sqrt(x*x-1) ]

    31  *      we have

    32  *              acosh(x) := log(x)+ln2, if x is large; else

    33  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else

    34  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.

    35  *

    36  * Special cases:

    37  *      acosh(x) is NaN with signal if x<1.

    38  *      acosh(NaN) is NaN without signal.

    39  */

    40 

    41 #include "fdlibm.h"

    42 

    43 #ifdef __STDC__

    44 static const double

    45 #else

    46 static double

    47 #endif

    48 one     = 1.0,

    49 ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

    50 

    51 #ifdef __STDC__

    52         double __ieee754_acosh(double x)

    53 #else

    54         double __ieee754_acosh(x)

    55         double x;

    56 #endif

    57 {

    58         double t;

    59         int hx;

    60         hx = __HI(x);

    61         if(hx<0x3ff00000) {             /* x < 1 */

    62             return (x-x)/(x-x);

    63         } else if(hx >=0x41b00000) {    /* x > 2**28 */

    64             if(hx >=0x7ff00000) {       /* x is inf of NaN */

    65                 return x+x;

    66             } else

    67                 return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */

    68         } else if(((hx-0x3ff00000)|__LO(x))==0) {

    69             return 0.0;                 /* acosh(1) = 0 */

    70         } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */

    71             t=x*x;

    72             return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));

    73         } else {                        /* 1<x<2 */

    74             t = x-one;

    75             return log1p(t+sqrt(2.0*t+t*t));

    76         }

    77 }