An apparatus comprises floating-point processing circuitry to perform a floating-point operation with rounding to generate a floating-point result value; and tininess detection circuitry to detect a tininess status indicating whether an outcome of the floating-point operation is tiny. A tiny outcome corresponds to a non-zero number with a magnitude smaller than a minimum non-zero magnitude representable as a normal floating-point number in a floating-point format to be used for the floating-point result value. The tininess detection circuitry comprises hardware circuit logic configured to support both before rounding tininess detection and after rounding tininess detection for detecting the tininess status.