A format for representing floating point numbers reduces the overhead typically associated with parsing floating point numbers and thereby provides for significantly improved processing speeds, particularly for bit-serial processors. According to an exemplary single-precision embodiment, numbers are represented using a 36-bit data format. Extra bits in the representation according to the invention allow certain conditions, such as overflow/underflow and the zero-ness of a number, to be detected and asserted quickly. Other conditions, such as denormalization are subsumed into normal processing through the extension of an exponent range in the representation.
Operations that involve denormalized numbers are handled by restructuring the input values for an operation as normalized numbers, and performing calculations on the normalized numbers. As a first step in the process of performing an operation, a determination is made whether input values for the operation contain one or more denormalized numbers. For certain types of operations, a determination is made whether the input values are such that the output value from the operation will be a denormalized number. For each operation in which either the input values or output values comprise a denormalized number, the input values are scaled to produce values that are not denormalized. Once the appropriate factoring has been carried out, the requested operation is performed, using normalized numbers, to produce an intermediate result which is then adjusted to account for the initial scaling.
