#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 /* 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