Apparatus for calculating a first result modal interval dependent on a first modal interval, each said modal interval defined by first and second endpoints each comprising sign, fraction and exponent bit fields, said apparatus comprising: a) a first operand register for holding the first and second endpoints of the first modal interval, and for providing a first operand signal specifying the contents of the first modal interval endpoints' fields; b) a first analysis element for receiving the first operand signal, for creating a first truth table for the first endpoint and a second truth table for the second endpoint, each truth table including a sign bit indicating the sign of the respective endpoint (a1, a2), a not-a-number bit indicating whether the respective endpoint (a1, a2) is Not-a-Number, an infinity bit indicating whether the respective endpoint (a1, a2) is infinity and a zero bit indicating whether the respective endpoint (a1, a2) is zero; c) a first logic array for determining a classification from the first and second truth tables, the classification including an empty bit and a tracking decoration, wherein: when the first and second truth tables indicate that the first and second endpoints have the same sign and a value of infinity, the empty bit is 1 and the tracking decoration indicates an empty or non-empty restriction; when the first and second truth tables indicate that one of the first and second endpoints are not-a-number, the empty bit is 1 and the tracking decoration is the NaN decoration field from the not-a-number endpoint; when the first and second truth tables indicate that both of the first and second endpoints are not-a-number, the empty bit is 1 and the tracking decoration indicates an empty input restriction; otherwise the empty bit is 0 and the tracking decoration is not used; and d) a first computational element receiving the first operand signal and the empty bit value signal, and performing a computation associated with the first computational element using the data encoded in the first operand signal and the empty bit value signal, and providing a result signal encoding the first result modal interval as a result of the computation by the first computational element. a) a first operand register for holding the first and second endpoints of the first modal interval, and for providing a first operand signal specifying the contents of the first modal interval endpoints' fields; b) a first analysis element for receiving the first operand signal, for creating a first truth table for the first endpoint and a second truth table for the second endpoint, each truth table including a sign bit indicating the sign of the respective endpoint (a1, a2), a not-a-number bit indicating whether the respective endpoint (a1, a2) is Not-a-Number, an infinity bit indicating whether the respective endpoint (a1, a2) is infinity and a zero bit indicating whether the respective endpoint (a1, a2) is zero; c) a first logic array for determining a classification from the first and second truth tables, the classification including an empty bit and a tracking decoration, wherein: when the first and second truth tables indicate that the first and second endpoints have the same sign and a value of infinity, the empty bit is 1 and the tracking decoration indicates an empty or non-empty restriction; when the first and second truth tables indicate that one of the first and second endpoints are not-a-number, the empty bit is 1 and the tracking decoration is the NaN decoration field from the not-a-number endpoint; when the first and second truth tables indicate that both of the first and second endpoints are not-a-number, the empty bit is 1 and the tracking decoration indicates an empty input restriction; otherwise the empty bit is 0 and the tracking decoration is not used; and when the first and second truth tables indicate that the first and second endpoints have the same sign and a value of infinity, the empty bit is 1 and the tracking decoration indicates an empty or non-empty restriction; when the first and second truth tables indicate that one of the first and second endpoints are not-a-number, the empty bit is 1 and the tracking decoration is the NaN decoration field from the not-a-number endpoint; when the first and second truth tables indicate that both of the first and second endpoints are not-a-number, the empty bit is 1 and the tracking decoration indicates an empty input restriction; otherwise the empty bit is 0 and the tracking decoration is not used; and d) a first computational element receiving the first operand signal and the empty bit value signal, and performing a computation associated with the first computational element using the data encoded in the first operand signal and the empty bit value signal, and providing a result signal encoding the first result modal interval as a result of the computation by the first computational element.