A Dual-Purpose Real/Complex Logarithmic Number System ALU

—The real Logarithmic Number System (LNS) allows fast and inexpensive multiplication and division but more expensive addition and subtraction as precision increases. Recent advances in higher-order and multipartite table methods, together with cotransformation, allow real LNS ALUs to be implemented effectively on FPGAs for a wide variety of medium-precision special-purpose applications. The Complex LNS (CLNS) is a generalization of LNS which represents complex values in logpolar form. CLNS is a more compact representation than traditional rectangular methods, reducing the cost of busses and memory in intensive complex-number applications like the FFT; however, prior CLNS implementations were either slow CORDIC-based or expensive 2D-table-based approaches. This paper attempts to leverage the recent advances made in realvalued LNS units for the more specialized context of CLNS. This paper proposes a novel approach to reduce the cost of CLNS addition by re-using a conventional real-valu...

• Type: Conference
• Year: 2009
• Where: ARITH
• Authors: Mark G. Arnold, Sylvain Collange
• Keywords: Applied Computing, ARITH 2009, CLNS, Real Lns, Real-valued Lns