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| | #include "libm.h"
#ifdef LONG_DOUBLE_IS_BINARY64
long double atanhl(long double x)
{
return atanh(x);
}
#elif defined(LONG_DOUBLE_IS_X87_EXTENDED) || defined(LONG_DOUBLE_IS_BINARY128)
/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
long double atanhl(long double x)
{
union ldshape u = {x};
unsigned e = u.i.se & 0x7fff;
unsigned s = u.i.se >> 15;
/* |x| */
u.i.se = e;
x = u.f;
if (e < 0x3ff - 1) {
if (e < 0x3ff - LDBL_MANT_DIG/2) {
/* handle underflow */
if (e == 0)
FORCE_EVAL((float)x);
} else {
/* |x| < 0.5, up to 1.7ulp error */
x = 0.5*log1pl(2*x + 2*x*x/(1-x));
}
} else {
/* avoid overflow */
x = 0.5*log1pl(2*(x/(1-x)));
}
return s ? -x : x;
}
#endif
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