Reconfigurable array for transcendental functions calculation

Abstract

Expanding transcendental functions in a series of Shift-and-Add operations is an alternative to Taylor or Chebyshev series expansions when fixed-point arithmetic with reduced wordlength is required. Typically, reconfigurable arrays do not provide architectural support for shift operations. Instead, shift operations are emulated by either multiplexing logic or multiplication by a power of 2. In this paper we describe the architecture of a reconfigurable array that can natively support shift operations. Rather than augmenting the reconfigurable fabric with dedicated shift units, the interconnection network is extended with shift capabilities. This is conceptually possible since a shift operation is a rearrangement and not a combination of the signals. Layers of computing tiles supporting Shift-and-Add/Subtract and Add-and-Select operations are interleaved with interconnect layers. On such a reconfigurable array, a variety of transcendental functions can be efficiently implemented.