1#include "libm.h" 2 3/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ 4double atanh(double x) { 5 union { 6 double f; 7 uint64_t i; 8 } u = {.f = x}; 9 unsigned e = u.i >> 52 & 0x7ff; 10 unsigned s = u.i >> 63; 11 double_t y; 12 13 /* |x| */ 14 u.i &= (uint64_t)-1 / 2; 15 y = u.f; 16 17 if (e < 0x3ff - 1) { 18 if (e < 0x3ff - 32) { 19 /* handle underflow */ 20 if (e == 0) 21 FORCE_EVAL((float)y); 22 } else { 23 /* |x| < 0.5, up to 1.7ulp error */ 24 y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y)); 25 } 26 } else { 27 /* avoid overflow */ 28 y = 0.5 * log1p(2 * (y / (1 - y))); 29 } 30 return s ? -y : y; 31} 32