picomath

Lua

log_factorial.lua

function log_factorial(n)
    assert(n >= 0, "Invalid input")
    if n > 254 then
        x = n + 1
        return (x - 0.5)*math.log(x) - x + 0.5*math.log(2*math.pi) + 1.0/(12.0*x)
    else
        lf = {
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            0.000000000000000,
            0.693147180559945,
            1.791759469228055,
            3.178053830347946,
            4.787491742782046,
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        }
        return lf[1+n]
    end
end