66 lines
1.6 KiB
C
66 lines
1.6 KiB
C
/* @(#)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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/* atanhl(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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* atanhl(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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* atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
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*
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* Special cases:
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* atanhl(x) is NaN if |x| > 1 with signal;
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* atanhl(NaN) is that NaN with no signal;
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* atanhl(+-1) is +-INF with signal.
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*
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*/
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#include <openlibm_math.h>
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#include "math_private.h"
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static const long double one = 1.0L, huge = 1e4900L;
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static const long double zero = 0.0L;
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long double
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atanhl(long double x)
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{
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long double t;
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u_int32_t jx, ix;
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ieee_quad_shape_type u;
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u.value = x;
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jx = u.parts32.mswhi;
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ix = jx & 0x7fffffff;
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u.parts32.mswhi = ix;
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if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
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{
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if (u.value == one)
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return x/zero;
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else
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return (x-x)/(x-x);
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}
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if(ix<0x3fc60000 && (huge+x)>zero) return x; /* x < 2^-57 */
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if(ix<0x3ffe0000) { /* x < 0.5 */
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t = u.value+u.value;
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t = 0.5*log1pl(t+t*u.value/(one-u.value));
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} else
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t = 0.5*log1pl((u.value+u.value)/(one-u.value));
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if(jx & 0x80000000) return -t; else return t;
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}
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