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 ```#include "libm.h" ``` ``` ``` ```/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ ``` ```double asinh(double x) ``` ```{ ``` ``` union {double f; uint64_t i;} u = {.f = x}; ``` ``` unsigned e = u.i >> 52 & 0x7ff; ``` ``` unsigned s = u.i >> 63; ``` ``` ``` ``` /* |x| */ ``` ``` u.i &= (uint64_t)-1/2; ``` ``` x = u.f; ``` ``` ``` ``` if (e >= 0x3ff + 26) { ``` ``` /* |x| >= 0x1p26 or inf or nan */ ``` ``` x = log(x) + 0.693147180559945309417232121458176568; ``` ``` } else if (e >= 0x3ff + 1) { ``` ``` /* |x| >= 2 */ ``` ``` x = log(2*x + 1/(sqrt(x*x+1)+x)); ``` ``` } else if (e >= 0x3ff - 26) { ``` ``` /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ ``` ``` x = log1p(x + x*x/(sqrt(x*x+1)+1)); ``` ``` } else { ``` ``` /* |x| < 0x1p-26, raise inexact if x != 0 */ ``` ``` FORCE_EVAL(x + 0x1p120f); ``` ``` } ``` ``` return s ? -x : x; ``` ```} ```