Decompose input into mantissa m and exponent e such that input = m * 2**e with |m| in [0.5, 1) (or m == 0).

Returns a (mantissa, exponent) tuple. Exponent dtype is int32. Non-finite inputs propagate: NaN → (NaN, 0); ±inf → (±inf, 0); 0 → (0, 0).