1#include "libm.h" 2 3/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ 4double asinh(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 12 /* |x| */ 13 u.i &= (uint64_t)-1 / 2; 14 x = u.f; 15 16 if (e >= 0x3ff + 26) { 17 /* |x| >= 0x1p26 or inf or nan */ 18 x = log(x) + 0.693147180559945309417232121458176568; 19 } else if (e >= 0x3ff + 1) { 20 /* |x| >= 2 */ 21 x = log(2 * x + 1 / (sqrt(x * x + 1) + x)); 22 } else if (e >= 0x3ff - 26) { 23 /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ 24 x = log1p(x + x * x / (sqrt(x * x + 1) + 1)); 25 } else { 26 /* |x| < 0x1p-26, raise inexact if x != 0 */ 27 FORCE_EVAL(x + 0x1p120f); 28 } 29 return s ? -x : x; 30} 31