# n is an integer, the number of quantization steps of the 4-tuple [w, x, y, z]
def quantize(w, x, y, z, n) :
    if z == None :
        z = 1.0 - w - x - y
    #assert w + x + y + z == 1
    n = int(n)

    v = [w, x, y, z]
    vn = [a * n for a in v]
    vni = [int(a) for a in vn]
    vnf = [a - ai for a, ai in zip(vn, vni)]
    defect = n - sum(vni)

    if defect == 0 :
        cutoff = 1.0
    else :
        defects = vnf[:]
        defects.sort() # could replace with sorting network or min heap or something
        cutoff = defects[-defect]

    def cround(xi, xf) :
        if xf < cutoff :
            return float(xi) / n
        else :
            return float(xi + 1) / n

    return [cround(ai, af) for ai, af in zip(vni, vnf)]