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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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/* 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 <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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static const double one = 1.0, huge = 1e300; |
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static const double zero = 0.0; |
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double |
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atanh(double x) |
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{ |
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double t; |
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int32_t hx,ix; |
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u_int32_t lx; |
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EXTRACT_WORDS(hx,lx,x); |
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ix = hx&0x7fffffff; |
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✗✓ |
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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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✗✓ |
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if(ix==0x3ff00000) |
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return x/zero; |
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✓✓✓✗
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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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✓✓ |
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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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✓✓ |
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if(hx>=0) return t; else return -t; |
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} |
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DEF_STD(atanh); |
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LDBL_MAYBE_UNUSED_CLONE(atanh); |