Floating-Point FPGA (FPFPGA) Architecture and Modeling (A paper review) Jason Luu ECE University of Toronto Oct 27, 2009

Motivation Goal: Build faster, cheaper, lower power FPGAs How? Fixed-Functionality (hard) blocks! ▫FPGA reconfigurability comes at the price of area, delay, and power ▫Some reconfigurability is unnecessary, remove it for savings

What to Make Hard? What hard blocks to use? ▫If not used, block is wasted ▫Industry suggests including memories and multipliers ▫Paper suggests adding floating-point units (FPU) Given a hard block, how fractured should it be? ▫Eg. Stratix III FPGA multipliers can be configured in a set of four 18x18 multipliers or one 36x36 multiplier ▫How fractured should the FPU be?

Introducing FPFPGA Contains soft and hard blocks ▫Soft blocks are composed of standard LUTs, FFs ▫Hard blocks are FPUs called Coarse-grained units (CGU) CGU characteristics: ▫Floating-point (FP) adds and multiplies only ▫Bus-based LUT operations using “wordblock” ▫Dedicated output registers ▫Accessible to soft blocks and vice-versa

Architecture of FPFPGA

CGU

CGU parameters # of each type of FP block Bus Width Number of Input Buses Number of Output Buses Number of Feedback Paths

Modeling Methodology Need to measure how “good” FPFPGA is Use empirical measurement method FPFPGA Benchmark Circuit Commercial CAD FLow Measure Quality of Results Very Nice! Commercial tools are unaware of FPFPGA, authors introduce “VEB” as solution

Virtual Embedded Block (VEB) Flow Manually map benchmark circuit into ▫CGU ▫Soft logic Put VEB representing CGU into commercial CAD tool Compile Gather area and timing measurements

VEB Create standard cell ASIC CGU and get area/timing numbers Implement area and timing of ASIC CGU using soft logic of commercial FPGA (different functionality, similar silicon timing, area, and pin demand) Assumes all internal paths == critical path to simplify timing of soft logic implementation

VEB

VEB Details Model delay with carry-chains Model area with shift registers Use LUT inputs and outputs for pin demand Note: Area and delay models use independent resources

VEB Placement Challenge Hard block locations are fixed on an FPGA Commercials tools can’t do that for VEB since it’s just a group of clustered soft logic constrained to be placed in a particular relative distance from each other Solution: ▫Let commercial tools place VEB anywhere ▫Then manually place VEB to fixed locations

VEB Quality 11% delay error when modeling embedded multiplier (non-fp to compare with existing multiplier) Area is accurate (no number given) Important repeatability hint: Must determine timing post-bitstream because of significant false paths (most CGUs do not use the longest path and this is detected post-bitstream)

Benchmarks 32-bit single-precision floating-point 8 benchmarks ▫5 Core computation blocks ▫1 application ▫2 synthetic

Experimental Settings Xilinx Virtex 2: XC2V FF CGUs each implemented as a VEB ▫Each CGU takes up 122 Logic Cells 2 FP multipliers, 2 FP adders, 5 wordblocks ▫In the order: W M A W W M A W W 4 input buses 3 output buses 3 feedback registers

Results Average area reduced by 25x Average delay reduced by ▫3.6x for single precision ▫4.3x for double precision Results are comparable to Kuon FPGA vs ASIC measurements Critical path of all circuits is in FPU

Reason for Good Results Removed reconfiguration bits (area reduction) Efficient directional routing Embedded FP operators

Contributions Exploration of FPGA architectures with embedded floating-point cores VEB methodology to leverage commercial tools to explore new embedded hard blocks even when commercial tools are unaware of those new hard blocks

Weaknesses Significant amounts of speculation ▫Try to claim scope for stuff that should be in future work Especially weak was the paper’s analysis of a FPFPGA compiler which is outside of scope and should be listed as such

My 2 Cents Primary advantage of FPFPGA vs GPU in the floating-point high computation domain is low latency Several applications demand very low latency and very high computational power ▫Plant monitoring of high-speed reactions ▫Financial automatic buy-sell algorithms Secondary advantage is energy consumed to perform the same computations.

My 2 Cents Comparison unfair ▫Most FPGA designers would convert floating- point to fixed point and not leave it as floating- point  Double precision fp add requires 701 slices  Fixed point add 64 LUTs == 16 slices Critical path is in FPU suggests benchmark circuits are unusually geared to use FPU cores and this is admitted by the authors