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