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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_atanh.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* atanhl(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
*
* Special cases:
* atanhl(x) is NaN if |x| > 1 with signal;
* atanhl(NaN) is that NaN with no signal;
* atanhl(+-1) is +-INF with signal.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double atanhl(long double x)
{
return atanh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double huge = 1e4900L;
long double atanhl(long double x)
{
long double t;
int32_t ix;
uint32_t se,i0,i1;
GET_LDOUBLE_WORDS(se, i0, i1, x);
ix = se & 0x7fff;
if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31)) > 0x3fff)
/* |x| > 1 */
return (x-x)/(x-x);
if (ix == 0x3fff)
return x/0.0;
if (ix < 0x3fe3 && huge+x > 0.0) /* x < 2**-28 */
return x;
SET_LDOUBLE_EXP(x, ix);
if (ix < 0x3ffe) { /* x < 0.5 */
t = x + x;
t = 0.5*log1pl(t + t*x/(1.0 - x));
} else
t = 0.5*log1pl((x + x)/(1.0 - x));
if (se <= 0x7fff)
return t;
return -t;
}
#endif
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