usr/src/lib/libast/common/uwin/asinh.c

   1 #include "FEATURE/uwin"
   2
   3 #if !_UWIN || _lib_asinh
   4
   5 void _STUB_asinh(){}
   6
   7 #else
   8
   9 /*
  10  * Copyright (c) 1985, 1993
  11  *      The Regents of the University of California.  All rights reserved.
  12  *
  13  * Redistribution and use in source and binary forms, with or without
  14  * modification, are permitted provided that the following conditions
  15  * are met:
  16  * 1. Redistributions of source code must retain the above copyright
  17  *    notice, this list of conditions and the following disclaimer.
  18  * 2. Redistributions in binary form must reproduce the above copyright
  19  *    notice, this list of conditions and the following disclaimer in the
  20  *    documentation and/or other materials provided with the distribution.
  21  * 3. Neither the name of the University nor the names of its contributors
  22  *    may be used to endorse or promote products derived from this software
  23  *    without specific prior written permission.
  24  *
  25  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  26  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  27  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  28  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  29  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  30  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  31  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  32  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  33  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  34  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  35  * SUCH DAMAGE.
  36  */
  37
  38 static char sccsid[] = "@(#)asinh.c     8.1 (Berkeley) 6/4/93";
  39
  40 /* ASINH(X)
  41  * RETURN THE INVERSE HYPERBOLIC SINE OF X
  42  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  43  * CODED IN C BY K.C. NG, 2/16/85;
  44  * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
  45  *
  46  * Required system supported functions :
  47  *      copysign(x,y)
  48  *      sqrt(x)
  49  *
  50  * Required kernel function:
  51  *      log1p(x)                ...return log(1+x)
  52  *
  53  * Method :
  54  *      Based on
  55  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  56  *      we have
  57  *      asinh(x) := x  if  1+x*x=1,
  58  *               := sign(x)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
  59  *               := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
  60  *
  61  * Accuracy:
  62  *      asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
  63  *      In a test run with 52,000 random arguments on a VAX, the maximum
  64  *      observed error was 1.58 ulps (units in the last place).
  65  *
  66  * Constants:
  67  * The hexadecimal values are the intended ones for the following constants.
  68  * The decimal values may be used, provided that the compiler will convert
  69  * from decimal to binary accurately enough to produce the hexadecimal values
  70  * shown.
  71  */
  72 #include "mathimpl.h"
  73
  74 vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
  75 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
  76
  77 ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
  78 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
  79
  80 #ifdef vccast
  81 #define    ln2hi    vccast(ln2hi)
  82 #define    ln2lo    vccast(ln2lo)
  83 #endif
  84
  85 extern double asinh(x)
  86 double x;
  87 {
  88         double t,s;
  89         const static double     small=1.0E-10,  /* fl(1+small*small) == 1 */
  90                                 big  =1.0E20,   /* fl(1+big) == big */
  91                                 one  =1.0   ;
  92
  93 #if !defined(vax)&&!defined(tahoe)
  94         if(x!=x) return(x);     /* x is NaN */
  95 #endif  /* !defined(vax)&&!defined(tahoe) */
  96         if((t=copysign(x,one))>small)
  97             if(t<big) {
  98                 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
  99             else        /* if |x| > big */
 100                 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
 101         else    /* if |x| < small */
 102             return(x);
 103 }
 104
 105 #endif