| #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; |
| double_t y; |
| |
| /* |x| */ |
| u.i &= (uint64_t)-1 / 2; |
| y = u.f; |
| |
| if (e < 0x3ff - 1) { |
| if (e < 0x3ff - 32) { |
| /* handle underflow */ |
| if (e == 0) |
| FORCE_EVAL((float)y); |
| } else { |
| /* |x| < 0.5, up to 1.7ulp error */ |
| y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y)); |
| } |
| } else { |
| /* avoid overflow */ |
| y = 0.5 * log1p(2 * (y / (1 - y))); |
| } |
| return s ? -y : y; |
| } |
