VERIFICATION OF FIXED-POINT ARITHMETIC

One method of verifying a calculation comprises: receiving a plurality of multiplicand fixed-point values representing respective natural numbers, wherein the multiplicand fixed-point values have respective multiplicand scaling factors; receiving a product fixed-point value representing a respective natural number, wherein the product fixed-point value has a product scaling factor; and determining whether the product fixed-point value is a correctly truncated result of multiplying the multiplicand fixed-point values together by: determining whether the difference between (a) the product of the product fixed-point value and the inverse of a combined scaling factor and (b) the product of the multiplicand fixed-point values is within a range bounded by the negation of an inverse of the combined scaling factor and the inverse of the combined scaling factor, wherein the combined scaling factor is equal to the product of the multiplicand scaling factors divided by the product scaling factor.