require "bignum"

local function euler(n, r, s, t)
    -- Decimal precision.
    local e10 = math.floor(n / 0.6)

    -- Binary precision.
    local e2 = math.round((1 + n / 0.6) / 0.30103)

    -- Start with mpfr for the logs.
    mpfr.init(e2)
    local b = mpfr.log(new bigrat(16, 15, true, false), 2)
    mpfr.mul(b, r)
    local a = mpfr.setVar(1, b)
    mpfr.log(new bigrat(25, 24, true, false), b)
    mpfr.mul(b, s)
    mpfr.addVar(a, b)
    mpfr.log(new bigrat(81, 80, true, false), b)
    mpfr.mul(b, t)
    local u = mpfr.setVar(3, b)
    mpfr.addVar(a, u)
    mpfr.neg(a)

    -- Switch to mpf for the basic arithmetic.
    mpf.init(e2)
    a = mpf.liftVar(1, a)
    b = mpf.set(b, 1)
    mpf.setVar(u, a)
    local v = mpf.setVar(4, b)
    local k = 0
    local n2 = mpf.set(5, n * n)
    local k2 = mpf.set(6, 0)
    repeat
        mpf.add(k2, (k << 1) + 1)
        k += 1
        mpf.mulVar(b, n2)
        mpf.divVar(b, k2)
        mpf.mulVar(a, n2)
        mpf.div(a, k)
        mpf.addVar(a, b)
        mpf.div(a, k)
        mpf.addVar(u, a)
        mpf.addVar(v, b)
        local e = mpf.frx(a, true)
    until math.abs(e) >= e2
    mpf.divVar(u, v)
    local st = mpf.getStr(u, 10, 100)
    print($"gamma {st} (maxerr. 1e-{e10})")
    print($"k = {k}\n")
    for i = 1, 6 do
        mpfr.clear(i)
        mpf.clear(i)
    end
end

euler(60, 41, 30, 18)
euler(4800, 85, 62, 37)
euler(9375, 91, 68, 40)
euler(18750, 98, 73, 43)