Liquid: Fast placement prototyping through steepest gradient descent movement

FPGA design compilation takes too much time to allow efficient design turnaround times. The largest runtime consuming steps of the compilation are placement and routing. To speed up the FPGA placement process, analytical placement techniques have become more popular in the last decade. Analytical techniques produce a placement in two steps, a placement prototyping step and a refinement step. In this work we focus on fast FPGA placement prototyping. Placement prototypes are also used to obtain fast accurate timing estimations and speed up the design cycle. In conventional analytical placement prototyping techniques the placement problem is formulated as a linear system which is solved several times to find a good legal placement. The most time consuming step of that process is solving the linear system. We show that it is not necessary to exactly solve this system, but that it is sufficient to optimize the placement following the steepest gradient descent in between legalization phases. This technique is implemented in our new placement tool called Liquid. In Liquid each block's position is updated several times following an accelerated gradient simulation. We compare this new technique with conventional analytical placement. The Titan23 designs and the Stratix IV FPGA are used for benchmarking. The net effect is that the runtime can be reduced by 2× on average compared to conventional analytical placement without losing any quality.