1 #include "libm.h" 2 3 /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ 4 double asinh(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 10 /* |x| */ 11 u.i &= (uint64_t)-1/2; 12 x = u.f; 13 14 if (e >= 0x3ff + 26) { 15 /* |x| >= 0x1p26 or inf or nan */ 16 x = log(x) + 0.693147180559945309417232121458176568; 17 } else if (e >= 0x3ff + 1) { 18 /* |x| >= 2 */ 19 x = log(2*x + 1/(sqrt(x*x+1)+x)); 20 } else if (e >= 0x3ff - 26) { 21 /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ 22 x = log1p(x + x*x/(sqrt(x*x+1)+1)); 23 } else { 24 /* |x| < 0x1p-26, raise inexact if x != 0 */ 25 FORCE_EVAL(x + 0x1p120f); 26 } 27 return s ? -x : x; 28 } 29