100 lines
3.6 KiB
C
100 lines
3.6 KiB
C
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/*
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)tanh.c 5.5 (Berkeley) 10/9/90";
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#endif /* not lint */
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/* TANH(X)
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* RETURN THE HYPERBOLIC TANGENT OF X
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* DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 1/8/85;
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* REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85.
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*
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* Required system supported functions :
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* copysign(x,y)
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* finite(x)
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*
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* Required kernel function:
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* expm1(x) ...exp(x)-1
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*
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* Method :
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* 1. reduce x to non-negative by tanh(-x) = - tanh(x).
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* 2.
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* 0 < x <= 1.e-10 : tanh(x) := x
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* -expm1(-2x)
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* 1.e-10 < x <= 1 : tanh(x) := --------------
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* expm1(-2x) + 2
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* 2
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* 1 <= x <= 22.0 : tanh(x) := 1 - ---------------
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* expm1(2x) + 2
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* 22.0 < x <= INF : tanh(x) := 1.
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*
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* Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
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*
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* Special cases:
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* tanh(NaN) is NaN;
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* only tanh(0)=0 is exact for finite argument.
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*
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* Accuracy:
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* tanh(x) returns the exact hyperbolic tangent of x nealy rounded.
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* In a test run with 1,024,000 random arguments on a VAX, the maximum
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* observed error was 2.22 ulps (units in the last place).
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*/
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double tanh(x)
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double x;
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{
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static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10;
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double expm1(), t, copysign(), sign;
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int finite();
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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sign=copysign(one,x);
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x=copysign(x,one);
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if(x < 22.0)
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if( x > one )
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return(copysign(one-two/(expm1(x+x)+two),sign));
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else if ( x > small )
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{t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));}
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else /* raise the INEXACT flag for non-zero x */
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{big+x; return(copysign(x,sign));}
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else if(finite(x))
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return (sign+1.0E-37); /* raise the INEXACT flag */
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else
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return(sign); /* x is +- INF */
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}
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