Optimize keys of the memoization cache

[Garrett-Pz]

Remove MemoizeMode::FragsIndex and update remaining memoization cache keys to Vec<usize>, which are faster to hash. Specifically, MemoizeMode::CanonIndex now assigns every canonical labeling computed by canonize::canonize a unique usize canonical identifier. An assembly state's memoization cache key is now a sorted list of canonical IDs corresponding to its fragments.

[jdaymude]

Benchmark results vs. `v0.5.1` as a baseline

These include universal improvement on bench_bounds, with 10–78% improvements on coconut_55.

bench_enumerate/gdb13_1201/extend
                        time:   [25.486 ms 25.491 ms 25.498 ms]
                        change: [-4.6190% -4.5691% -4.5195%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/gdb13_1201/grow-erode
                        time:   [12.274 ms 12.277 ms 12.281 ms]
                        change: [-1.8223% -1.7759% -1.7296%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/gdb17_200/extend
                        time:   [360.91 ms 360.95 ms 361.00 ms]
                        change: [-6.6960% -6.6389% -6.5851%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/gdb17_200/grow-erode
                        time:   [111.29 ms 111.34 ms 111.39 ms]
                        change: [-7.3102% -7.2459% -7.1855%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/checks/extend
                        time:   [138.10 ms 138.20 ms 138.31 ms]
                        change: [-8.5431% -8.4401% -8.3307%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/checks/grow-erode
                        time:   [31.168 ms 31.176 ms 31.183 ms]
                        change: [-6.2755% -6.2053% -6.1403%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/coconut_55/extend
                        time:   [1.2053 s 1.2056 s 1.2059 s]
                        change: [-5.5101% -5.4728% -5.4351%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_enumerate/coconut_55/grow-erode
                        time:   [266.08 ms 266.15 ms 266.22 ms]
                        change: [-6.7591% -6.7172% -6.6778%] (p = 0.00 < 0.05)
                        Performance has improved.

bench_canonize/gdb13_1201/nauty
                        time:   [112.12 ms 112.19 ms 112.26 ms]
                        change: [+3.1710% +3.2530% +3.3417%] (p = 0.00 < 0.05)
                        Performance has regressed.
bench_canonize/gdb13_1201/tree-nauty
                        time:   [53.620 ms 53.646 ms 53.669 ms]
                        change: [+1.3378% +1.3993% +1.4565%] (p = 0.00 < 0.05)
                        Performance has regressed.
bench_canonize/gdb17_200/nauty
                        time:   [2.7710 s 2.7731 s 2.7751 s]
                        change: [+1.2370% +1.3351% +1.4315%] (p = 0.00 < 0.05)
                        Performance has regressed.
bench_canonize/gdb17_200/tree-nauty
                        time:   [1.0822 s 1.0841 s 1.0859 s]
                        change: [+0.3011% +0.4913% +0.6714%] (p = 0.00 < 0.05)
                        Change within noise threshold.
bench_canonize/checks/nauty
                        time:   [1.2000 s 1.2085 s 1.2172 s]
                        change: [-3.8419% -3.1775% -2.4189%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_canonize/checks/tree-nauty
                        time:   [407.28 ms 407.93 ms 408.62 ms]
                        change: [-0.0287% +0.1828% +0.3798%] (p = 0.10 > 0.05)
                        No change in performance detected.
bench_canonize/coconut_55/nauty
                        time:   [11.745 s 11.838 s 11.931 s]
                        change: [-3.5294% -2.7080% -1.9284%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_canonize/coconut_55/tree-nauty
                        time:   [3.9905 s 3.9937 s 3.9967 s]
                        change: [+0.0226% +0.1428% +0.2604%] (p = 0.03 < 0.05)
                        Change within noise threshold.

bench_bounds/gdb13_1201/no-bounds
                        time:   [51.594 ms 51.898 ms 52.177 ms]
                        change: [-18.206% -17.586% -17.000%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb13_1201/log
                        time:   [50.616 ms 50.954 ms 51.298 ms]
                        change: [-12.608% -11.914% -11.235%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb13_1201/int
                        time:   [46.683 ms 46.971 ms 47.290 ms]
                        change: [-5.0849% -4.2812% -3.4648%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb13_1201/int-vec
                        time:   [46.370 ms 46.600 ms 46.819 ms]
                        change: [-3.1511% -2.3430% -1.5853%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb17_200/no-bounds
                        time:   [321.97 ms 325.46 ms 328.87 ms]
                        change: [-73.857% -73.411% -72.988%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb17_200/log
                        time:   [278.01 ms 280.22 ms 282.43 ms]
                        change: [-63.591% -63.236% -62.897%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb17_200/int
                        time:   [85.457 ms 85.771 ms 86.079 ms]
                        change: [-50.017% -49.692% -49.394%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/gdb17_200/int-vec
                        time:   [66.170 ms 66.450 ms 66.728 ms]
                        change: [-12.857% -12.408% -11.946%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/checks/no-bounds
                        time:   [273.93 ms 284.95 ms 299.64 ms]
                        change: [-75.423% -74.137% -72.607%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/checks/log time:   [181.29 ms 184.68 ms 188.00 ms]
                        change: [-61.079% -60.015% -59.070%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/checks/int time:   [30.459 ms 30.776 ms 31.083 ms]
                        change: [-66.104% -65.128% -64.231%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/checks/int-vec
                        time:   [11.654 ms 11.713 ms 11.782 ms]
                        change: [-26.381% -25.609% -24.784%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/coconut_55/no-bounds
                        time:   [3.5605 s 3.6421 s 3.7182 s]
                        change: [-79.049% -78.471% -77.864%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/coconut_55/log
                        time:   [3.3160 s 3.3668 s 3.4170 s]
                        change: [-76.646% -75.963% -75.237%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/coconut_55/int
                        time:   [321.01 ms 327.36 ms 333.40 ms]
                        change: [-60.115% -58.731% -57.526%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_bounds/coconut_55/int-vec
                        time:   [206.82 ms 210.27 ms 213.21 ms]
                        change: [-12.116% -9.9580% -8.0124%] (p = 0.00 < 0.05)
                        Performance has improved.

bench_memoize/gdb13_1201/no-memoize
                        time:   [23.327 ms 23.736 ms 24.357 ms]
                        change: [-5.7462% +2.8449% +11.869%] (p = 0.54 > 0.05)
                        No change in performance detected.
bench_memoize/gdb13_1201/nauty-index
                        time:   [48.698 ms 49.088 ms 49.502 ms]
                        change: [-4.4699% -3.4780% -2.4538%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_memoize/gdb13_1201/tree-nauty-index
                        time:   [46.309 ms 46.675 ms 47.007 ms]
                        change: [-2.3466% -1.4214% -0.5180%] (p = 0.01 < 0.05)
                        Change within noise threshold.
bench_memoize/gdb17_200/no-memoize
                        time:   [56.901 ms 57.303 ms 57.718 ms]
                        change: [+10.370% +11.362% +12.486%] (p = 0.00 < 0.05)
                        Performance has regressed.
bench_memoize/gdb17_200/nauty-index
                        time:   [69.047 ms 69.321 ms 69.650 ms]
                        change: [-22.020% -21.574% -21.113%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_memoize/gdb17_200/tree-nauty-index
                        time:   [66.070 ms 66.358 ms 66.648 ms]
                        change: [-13.293% -12.790% -12.274%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_memoize/checks/no-memoize
                        time:   [13.199 ms 13.507 ms 13.740 ms]
                        change: [+12.663% +15.558% +18.352%] (p = 0.00 < 0.05)
                        Performance has regressed.
bench_memoize/checks/nauty-index
                        time:   [12.039 ms 12.067 ms 12.095 ms]
                        change: [-46.984% -45.859% -44.806%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_memoize/checks/tree-nauty-index
                        time:   [11.652 ms 11.709 ms 11.781 ms]
                        change: [-28.227% -26.957% -25.865%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_memoize/coconut_55/no-memoize
                        time:   [344.14 ms 351.64 ms 358.15 ms]
                        change: [+9.4051% +13.260% +17.480%] (p = 0.00 < 0.05)
                        Performance has regressed.
bench_memoize/coconut_55/nauty-index
                        time:   [209.28 ms 212.59 ms 215.79 ms]
                        change: [-22.666% -20.899% -19.116%] (p = 0.00 < 0.05)
                        Performance has improved.
bench_memoize/coconut_55/tree-nauty-index
                        time:   [205.01 ms 208.99 ms 212.49 ms]
                        change: [-12.968% -10.648% -8.6130%] (p = 0.00 < 0.05)
                        Performance has improved.

Interestingly, implementing a critical part of this update using the more elegant entry API for Rust maps (see the canonical_id function of commit 7d293a4) is much worse. For example, the entry API version is 22–857% slower on coconut_55 than the direct get/insert implementation, and individual memoization operations are up to twice as slow.