Customising floating-point designs

This paper describes a method for customising the representation of floating-point numbers that exploits the flexibility of reconfigurable hardware. The method determines the appropriate size of mantissa and exponent for each operation in a design, so that a cost function with a given error specification for the output relative to a reference representation can be satisfied. Currently our tool, which adopts an iterative implementation of this method, supports single- or double-precision floating-point representation as the reference representation. It produces customised floating-point formats with arbitrary-sized mantissa and exponent. Results show that, for calculations involving large dynamic ranges, our method can achieve significant hardware reduction and speed improvement with respect to a design adopting the reference representation.