lib/libm/noieee_src/n_asinh.c

   1 /*      $NetBSD: n_asinh.c,v 1.7 2008/04/29 15:10:02 uwe Exp $  */
   2 /*
   3  * Copyright (c) 1985, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  * 3. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 #if 0
  33 static char sccsid[] = "@(#)asinh.c     8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* ASINH(X)
  38  * RETURN THE INVERSE HYPERBOLIC SINE OF X
  39  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  40  * CODED IN C BY K.C. NG, 2/16/85;
  41  * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
  42  *
  43  * Required system supported functions :
  44  *      copysign(x,y)
  45  *      sqrt(x)
  46  *
  47  * Required kernel function:
  48  *      log1p(x)                ...return log(1+x)
  49  *
  50  * Method :
  51  *      Based on
  52  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  53  *      we have
  54  *      asinh(x) := x  if  1+x*x=1,
  55  *               := sign(x)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
  56  *               := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )
  57  *
  58  * Accuracy:
  59  *      asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
  60  *      In a test run with 52,000 random arguments on a VAX, the maximum
  61  *      observed error was 1.58 ulps (units in the last place).
  62  *
  63  * Constants:
  64  * The hexadecimal values are the intended ones for the following constants.
  65  * The decimal values may be used, provided that the compiler will convert
  66  * from decimal to binary accurately enough to produce the hexadecimal values
  67  * shown.
  68  */
  69 #define _LIBM_STATIC
  70 #include "mathimpl.h"
  71
  72 vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
  73 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
  74
  75 ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
  76 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
  77
  78 #ifdef vccast
  79 #define    ln2hi    vccast(ln2hi)
  80 #define    ln2lo    vccast(ln2lo)
  81 #endif
  82
  83 double
  84 asinh(double x)
  85 {
  86         double t,s;
  87         static const double     small=1.0E-10,  /* fl(1+small*small) == 1 */
  88                                 big  =1.0E20,   /* fl(1+big) == big */
  89                                 one  =1.0   ;
  90
  91 #if !defined(__vax__)&&!defined(tahoe)
  92         if(x!=x) return(x);     /* x is NaN */
  93 #endif  /* !defined(__vax__)&&!defined(tahoe) */
  94         if((t=copysign(x,one))>small)
  95             if(t<big) {
  96                 s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
  97             else        /* if |x| > big */
  98                 {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
  99         else    /* if |x| < small */
 100             return(x);
 101 }