| #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; | |
| } |