Performance Optimizations

[georgwiese]

This PR gets rid of 2 table lookups and 1 gate in the GreaterThanChip by range-checking using the existing gadget, as suggested in #14.

This increases the required value for k from 12 to 14 for the MNIST-Tiny model, but has no effect on the "real-world" models. For those models, proofs are ~13% faster and the size of the verifier is now small enough to fit into an Ethereum smart contract! 🥳

I also tested switching to the V1 floor planner. Unfortunatey, it has a ~30% proving-time overhead and only reduces k for the MNIST-Tiny model (to 13). So, I undid this change (but keeping the proper implementation of Circuit::without_witness() needed for the V1 floor planner). Once zcash/halo2#547 is resolved, proof-time synthesis of should not be necessary anymore and we can move to the V1 planner.

The benchmarks show an increase of proving time for MINST-Tiny (because of the higher value of k) and a decrease in proving time otherwise:

benches/key_generation_mnist_tiny
                        time:   [2.3072 s 2.3643 s 2.4244 s]
                        change: [+150.63% +159.31% +168.44%] (p = 0.00 < 0.05)
                        Performance has regressed.
benches/proof_generation_mnist_tiny
                        time:   [3.6469 s 3.6879 s 3.7302 s]
                        change: [+126.81% +134.23% +142.59%] (p = 0.00 < 0.05)
                        Performance has regressed.
benches/verification_mnist_tiny
                        time:   [13.714 ms 14.260 ms 14.699 ms]
                        change: [-2.8173% +3.7090% +11.500%] (p = 0.34 > 0.05)
                        No change in performance detected.
benches/proof_generation_mnist_small
                        time:   [6.7773 s 6.8724 s 6.9471 s]
                        change: [-15.671% -13.926% -12.071%] (p = 0.00 < 0.05)
                        Performance has improved.
benches/verification_mnist_small
                        time:   [13.835 ms 14.369 ms 15.008 ms]
                        change: [-9.8799% -3.8734% +2.3501%] (p = 0.27 > 0.05)
                        No change in performance detected.
benches/proof_generation_mnist_medium
                        time:   [6.9457 s 7.0208 s 7.0903 s]
                        change: [-15.176% -13.268% -11.329%] (p = 0.00 < 0.05)
                        Performance has improved.
benches/verification_mnist_medium
                        time:   [13.778 ms 14.315 ms 15.028 ms]
                        change: [-8.8268% -4.0115% +1.3125%] (p = 0.17 > 0.05)
                        No change in performance detected.