#include "libm.h" /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ double atanh(double x) { union {double f; uint64_t i;} u = {.f = x}; unsigned e = u.i >> 52 & 0x7ff; unsigned s = u.i >> 63; /* |x| */ u.i &= (uint64_t)-1/2; x = u.f; if (e < 0x3ff - 1) { /* |x| < 0.5, up to 1.7ulp error */ x = 0.5*log1p(2*x + 2*x*x/(1-x)); } else { x = 0.5*log1p(2*x/(1-x)); } return s ? -x : x; }