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#include "libm.h" // for FORCE_EVAL
#include <math.h> // for log, sqrt, asinh, log1p
#include <stdint.h> // for uint64_t
/* 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;
}
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