21 September 2007 Carry length distribution analysis for self-timed asynchronous adders
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Abstract
Due to the synchronization method employed by most modern digital circuits, the maximum propagation delay through an adder unit is typically used to set the system level delay for addition operations. The actual delay of a binary addition computation is fundamentally tied to the longest carry propagation chain created by certain input operands. Although the probability of lengthy carry propagation chains is quite low, modern synchronous adders devote a large portion of their silicon area and energy consumption to speeding up the propagation of carries through the adder. Therefore, considerable die area and system power must be spent optimizing the improbable worst case delay. Using asynchronous self-timed circuits, similar adder performance can be obtained at a fraction of the hardware cost and energy consumption. This paper shows the inadequacy of characterizing self-timed adder performance using the assumption that typical input operands are uniformly randomly distributed, and presents a new self-timed adder characterization benchmark based on the SpecINT 2000 benchmark suite. The SpecINT 2000 benchmark was selected since there is no published carry propagation chain distribution for this modern benchmark suite and the benchmark is well suited for measuring carry propagation chains due to its code size and the fact that it is a non-synthetic benchmark. All totaled, over 4.7 billion addition/subtraction operations resulting from address and data calculations were tabulated to create the SpecINT 2000 Carry Propagation Distribution. This new carry propagation distribution sheds light on the accuracy of existing distributions based on the Dhrystone integer benchmark and demonstrates how measuring self-timed adder performance with a uniformly random input distribution can overestimate self-timed adder performance by over 50 percent.
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Albert A. Liddicoat, Albert A. Liddicoat, Anton Clarkson, Anton Clarkson, Lynne A. Slivovsky, Lynne A. Slivovsky, } "Carry length distribution analysis for self-timed asynchronous adders", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 66970U (21 September 2007); doi: 10.1117/12.735140; https://doi.org/10.1117/12.735140
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