3 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
4 long double atanhl(long double x)
8 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
9 /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
10 long double atanhl(long double x)
12 union ldshape u = {x};
13 unsigned e = u.i.se & 0x7fff;
14 unsigned s = u.i.se >> 15;
21 if (e < 0x3ff - LDBL_MANT_DIG/2) {
22 /* handle underflow */
26 /* |x| < 0.5, up to 1.7ulp error */
27 x = 0.5*log1pl(2*x + 2*x*x/(1-x));
31 x = 0.5*log1pl(2*(x/(1-x)));