140 lines
3.0 KiB
C
140 lines
3.0 KiB
C
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/* @(#)e_atanh.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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/*
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FUNCTION
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<<atanh>>, <<atanhf>>---inverse hyperbolic tangent
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INDEX
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atanh
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INDEX
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atanhf
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ANSI_SYNOPSIS
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#include <math.h>
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double atanh(double <[x]>);
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float atanhf(float <[x]>);
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TRAD_SYNOPSIS
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#include <math.h>
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double atanh(<[x]>)
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double <[x]>;
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float atanhf(<[x]>)
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float <[x]>;
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DESCRIPTION
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<<atanh>> calculates the inverse hyperbolic tangent of <[x]>.
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<<atanhf>> is identical, other than taking and returning
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<<float>> values.
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RETURNS
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<<atanh>> and <<atanhf>> return the calculated value.
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If
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@ifnottex
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|<[x]>|
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@end ifnottex
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@tex
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$|x|$
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@end tex
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is greater than 1, the global <<errno>> is set to <<EDOM>> and
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the result is a NaN. A <<DOMAIN error>> is reported.
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If
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@ifnottex
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|<[x]>|
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@end ifnottex
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@tex
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$|x|$
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@end tex
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is 1, the global <<errno>> is set to <<EDOM>>; and the result is
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infinity with the same sign as <<x>>. A <<SING error>> is reported.
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You can modify the error handling for these routines using
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<<matherr>>.
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PORTABILITY
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Neither <<atanh>> nor <<atanhf>> are ANSI C.
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QUICKREF
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atanh - pure
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atanhf - pure
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*/
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/* atanh(x)
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* Method :
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* 1.Reduced x to positive by atanh(-x) = -atanh(x)
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* 2.For x>=0.5
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* 1 2x x
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* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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* 2 1 - x 1 - x
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*
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* For x<0.5
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* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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*
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* Special cases:
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* atanh(x) is NaN if |x| > 1 with signal;
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* atanh(NaN) is that NaN with no signal;
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* atanh(+-1) is +-INF with signal.
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*
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*/
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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static const double one = 1.0, huge = 1e300;
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#else
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static double one = 1.0, huge = 1e300;
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#endif
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#ifdef __STDC__
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static const double zero = 0.0;
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#else
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static double zero = 0.0;
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#endif
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#ifdef __STDC__
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double atanh(double x)
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#else
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double atanh(x)
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double x;
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#endif
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{
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double t;
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__int32_t hx,ix;
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__uint32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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ix = hx&0x7fffffff;
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if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
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return (x-x)/(x-x);
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if(ix==0x3ff00000)
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return x/zero;
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if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
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SET_HIGH_WORD(x,ix);
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if(ix<0x3fe00000) { /* x < 0.5 */
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t = x+x;
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t = 0.5*log1p(t+t*x/(one-x));
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} else
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t = 0.5*log1p((x+x)/(one-x));
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if(hx>=0) return t; else return -t;
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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