1 #include "libm.h" 2 3 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 atanhl(long double x)4long double atanhl(long double x) 5 { 6 return atanh(x); 7 } 8 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 9 /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ atanhl(long double x)10long double atanhl(long double x) 11 { 12 union ldshape u = {x}; 13 unsigned e = u.i.se & 0x7fff; 14 unsigned s = u.i.se >> 15; 15 16 /* |x| */ 17 u.i.se = e; 18 x = u.f; 19 20 if (e < 0x3ff - 1) { 21 if (e < 0x3ff - LDBL_MANT_DIG/2) { 22 /* handle underflow */ 23 if (e == 0) 24 FORCE_EVAL((float)x); 25 } else { 26 /* |x| < 0.5, up to 1.7ulp error */ 27 x = 0.5*log1pl(2*x + 2*x*x/(1-x)); 28 } 29 } else { 30 /* avoid overflow */ 31 x = 0.5*log1pl(2*(x/(1-x))); 32 } 33 return s ? -x : x; 34 } 35 #endif 36