lib/libm/noieee_src/n_tanh.c

   1 /*      $NetBSD: n_tanh.c,v 1.6 2003/08/07 16:44:52 agc 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[] = "@(#)tanh.c      8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* TANH(X)
  38  * RETURN THE HYPERBOLIC TANGENT OF X
  39  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
  40  * CODED IN C BY K.C. NG, 1/8/85;
  41  * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
  42  *
  43  * Required system supported functions :
  44  *      copysign(x,y)
  45  *      finite(x)
  46  *
  47  * Required kernel function:
  48  *      expm1(x)        ...exp(x)-1
  49  *
  50  * Method :
  51  *      1. reduce x to non-negative by tanh(-x) = - tanh(x).
  52  *      2.
  53  *          0      <  x <=  1.e-10 :  tanh(x) := x
  54  *                                                -expm1(-2x)
  55  *          1.e-10 <  x <=  1      :  tanh(x) := --------------
  56  *                                               expm1(-2x) + 2
  57  *                                                        2
  58  *          1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
  59  *                                                    expm1(2x) + 2
  60  *          22.0   <  x <= INF     :  tanh(x) := 1.
  61  *
  62  *      Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
  63  *
  64  * Special cases:
  65  *      tanh(NaN) is NaN;
  66  *      only tanh(0)=0 is exact for finite argument.
  67  *
  68  * Accuracy:
  69  *      tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
  70  *      In a test run with 1,024,000 random arguments on a VAX, the maximum
  71  *      observed error was 2.22 ulps (units in the last place).
  72  */
  73
  74 #include "mathimpl.h"
  75
  76 double
  77 tanh(double x)
  78 {
  79         static const double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
  80         double t, sign;
  81
  82 #if !defined(__vax__)&&!defined(tahoe)
  83         if(x!=x) return(x);     /* x is NaN */
  84 #endif  /* !defined(__vax__)&&!defined(tahoe) */
  85
  86         sign=copysign(one,x);
  87         x=copysign(x,one);
  88         if(x < 22.0)
  89             if( x > one )
  90                 return(copysign(one-two/(expm1(x+x)+two),sign));
  91             else if ( x > small )
  92                 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
  93             else                /* raise the INEXACT flag for non-zero x */
  94                 { t = big+x; return(copysign(x,sign));} /* ??? -ragge */
  95         else if(finite(x))
  96             return (sign+1.0E-37); /* raise the INEXACT flag */
  97         else
  98             return(sign);       /* x is +- INF */
  99 }