sysdeps/generic/acosh.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[] = "@(#)acosh.c     8.1 (Berkeley) 6/4/93";
  36 #endif /* not lint */
  37
  38 /* ACOSH(X)
  39  * RETURN THE INVERSE HYPERBOLIC COSINE OF X
  40  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
  41  * CODED IN C BY K.C. NG, 2/16/85;
  42  * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
  43  *
  44  * Required system supported functions :
  45  *      sqrt(x)
  46  *
  47  * Required kernel function:
  48  *      log1p(x)                ...return log(1+x)
  49  *
  50  * Method :
  51  *      Based on
  52  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  53  *      we have
  54  *              acosh(x) := log1p(x)+ln2,       if (x > 1.0E20); else
  55  *              acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
  56  *      These formulae avoid the over/underflow complication.
  57  *
  58  * Special cases:
  59  *      acosh(x) is NaN with signal if x<1.
  60  *      acosh(NaN) is NaN without signal.
  61  *
  62  * Accuracy:
  63  *      acosh(x) returns the exact inverse hyperbolic cosine of x nearly
  64  *      rounded. In a test run with 512,000 random arguments on a VAX, the
  65  *      maximum observed error was 3.30 ulps (units of the last place) at
  66  *      x=1.0070493753568216 .
  67  *
  68  * Constants:
  69  * The hexadecimal values are the intended ones for the following constants.
  70  * The decimal values may be used, provided that the compiler will convert
  71  * from decimal to binary accurately enough to produce the hexadecimal values
  72  * shown.
  73  */
  74
  75 #include "mathimpl.h"
  76
  77 vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
  78 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
  79
  80 ic(ln2hi, 6.9314718036912381649E-1,  -1, 1.62E42FEE00000)
  81 ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
  82
  83 #ifdef vccast
  84 #define    ln2hi    vccast(ln2hi)
  85 #define    ln2lo    vccast(ln2lo)
  86 #endif
  87
  88 double acosh(x)
  89 double x;
  90 {
  91         double t,big=1.E20; /* big+1==big */
  92
  93 #if !defined(vax)&&!defined(tahoe)
  94         if(x!=x) return(x);     /* x is NaN */
  95 #endif  /* !defined(vax)&&!defined(tahoe) */
  96
  97     /* return log1p(x) + log(2) if x is large */
  98         if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);}
  99
 100         t=sqrt(x-1.0);
 101         return(log1p(t*(t+sqrt(x+1.0))));
 102 }