• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.7
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• pp.21-28
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• 2017

Practical models for FPGA architectures which include performance- and/or density-enhancing components such as carry chains, wide function multiplexers, and memory/multiplier blocks are being applied to academic FPGA placement tools which used to rely on simple imaginary models. Previously the techniques such as pre-packing and multi-layer density analysis are proposed to remedy issues related to such practical models, and the wire length is effectively minimized during initial analytic placement. Since timing should be optimized rather than wire length, most previous work takes into account the timing constraints. However, instead of the initial analytic placement, the timing-driven techniques are mostly applied to subsequent steps such as placement legalization and iterative improvement. This paper incorporates the timing driven techniques, which check if the placement meets the timing constraints given in the standard SDC format, and minimize the detected violations, with the existing analytic placer which implements pre-packing and multi-layer density analysis. First of all, a static timing analyzer has been used to check the timing of the wire-length minimized placement results. In order to minimize the detected violations, a function to minimize the largest arrival time at end points is added to the objective function of the analytic placer. Since each clock has a different period, the function is proposed to be evaluated for each clock, and added to the objective function. Since this function can unnecessarily reduce the unviolated paths, a new function which calculates and minimizes the largest negative slack at end points is also proposed, and compared. Since the existing legalization which is non-timing driven is used before the timing analysis, any improvement on timing is entirely due to the functions added to the objective function. The experiments on twelve industrial examples show that the minimum arrival time function improves the worst negative slack by 15% on average whereas the minimum worst negative slack function improves the negative slacks by additional 6% on average.