Asymmetric and compressed logarithmic number systems for multimedia coprocessor (invited paper)

The logarithmic number system (LNS) represents a real number with its sign and the logarithm of its absolute value. Inexpensive logarithmic arithmetic has shorter word length than fixed point. Conventional LNS is symmetrical: every reciprocal is representable. This paper proposes asymmetrical LNS (one sixteenth to 2048) with acceptable visual quality for MPEG decoding that saves one bit compared to conventional LNS. Novel compression saves another bit with only slight image degradation and allows 8 by 8 matrices to fit in 64 (not 128) bytes. The proposed LNS inverse discrete cosine transform (IDCT) coprocessor is compatible with conventional byte-sized packed-arithmetic SIMD architectures.