100 lines
3.6 KiB
C
100 lines
3.6 KiB
C
/*
|
|
* Copyright (c) 1985, 1993
|
|
* The Regents of the University of California. All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* This product includes software developed by the University of
|
|
* California, Berkeley and its contributors.
|
|
* 4. Neither the name of the University nor the names of its contributors
|
|
* may be used to endorse or promote products derived from this software
|
|
* without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*/
|
|
|
|
#ifndef lint
|
|
static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93";
|
|
#endif /* not lint */
|
|
|
|
/* TANH(X)
|
|
* RETURN THE HYPERBOLIC TANGENT OF X
|
|
* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
|
|
* CODED IN C BY K.C. NG, 1/8/85;
|
|
* REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
|
|
*
|
|
* Required system supported functions :
|
|
* copysign(x,y)
|
|
* finite(x)
|
|
*
|
|
* Required kernel function:
|
|
* expm1(x) ...exp(x)-1
|
|
*
|
|
* Method :
|
|
* 1. reduce x to non-negative by tanh(-x) = - tanh(x).
|
|
* 2.
|
|
* 0 < x <= 1.e-10 : tanh(x) := x
|
|
* -expm1(-2x)
|
|
* 1.e-10 < x <= 1 : tanh(x) := --------------
|
|
* expm1(-2x) + 2
|
|
* 2
|
|
* 1 <= x <= 22.0 : tanh(x) := 1 - ---------------
|
|
* expm1(2x) + 2
|
|
* 22.0 < x <= INF : tanh(x) := 1.
|
|
*
|
|
* Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
|
|
*
|
|
* Special cases:
|
|
* tanh(NaN) is NaN;
|
|
* only tanh(0)=0 is exact for finite argument.
|
|
*
|
|
* Accuracy:
|
|
* tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
|
|
* In a test run with 1,024,000 random arguments on a VAX, the maximum
|
|
* observed error was 2.22 ulps (units in the last place).
|
|
*/
|
|
|
|
double tanh(x)
|
|
double x;
|
|
{
|
|
static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
|
|
double expm1(), t, copysign(), sign;
|
|
int finite();
|
|
|
|
#if !defined(vax)&&!defined(tahoe)
|
|
if(x!=x) return(x); /* x is NaN */
|
|
#endif /* !defined(vax)&&!defined(tahoe) */
|
|
|
|
sign=copysign(one,x);
|
|
x=copysign(x,one);
|
|
if(x < 22.0)
|
|
if( x > one )
|
|
return(copysign(one-two/(expm1(x+x)+two),sign));
|
|
else if ( x > small )
|
|
{t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
|
|
else /* raise the INEXACT flag for non-zero x */
|
|
{big+x; return(copysign(x,sign));}
|
|
else if(finite(x))
|
|
return (sign+1.0E-37); /* raise the INEXACT flag */
|
|
else
|
|
return(sign); /* x is +- INF */
|
|
}
|