Because the set of possible output values of a quantizer is countable, any quantizer can be decomposed into two distinct stages, which can be referred to as the "classification" stage (or "forward quantization" stage) and the "reconstruction" stage (or "inverse quantization" stage), where the classification stage maps the input value to an integer "quantization index" formula_10 and the reconstruction stage maps the index formula_10 to the "reconstruction value" formula_12 that is the output approximation of the input value. For the example uniform quantizer described above, the forward quantization stage can be expressed as