Encoding performance improvements

[jackkleeman]

1. Use a lookup table (3844 pairs of u8s) for turning bytes corresponding to 2 base62 characters into those two characters, reducing the number of div/rem operations needed
2. Avoid branching when handling 21/21 or 11/10 digit cases
3. Avoid binary search when determining digit count, use instead an approximation with correction

Overall improvements on my M2 max are 30-50%, decoding benchmarks unaffected:

encode/standard_new_fixed
                        time:   [21.810 ns 21.865 ns 21.924 ns]
                        change: [−20.781% −18.469% −16.145%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 9 outliers among 100 measurements (9.00%)
  4 (4.00%) low mild
  3 (3.00%) high mild
  2 (2.00%) high severe
encode/standard_new_random
                        time:   [16.702 ns 16.863 ns 17.027 ns]
                        change: [−36.855% −35.101% −33.665%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 16 outliers among 100 measurements (16.00%)
  8 (8.00%) low mild
  5 (5.00%) high mild
  3 (3.00%) high severe
encode/standard_new_random_u64
                        time:   [12.128 ns 12.258 ns 12.373 ns]
                        change: [−31.413% −29.568% −27.826%] (p = 0.00 < 0.05)
                        Performance has improved.
encode/standard_bytes_fixed
                        time:   [8.9859 ns 9.0062 ns 9.0267 ns]
                        change: [−40.511% −38.713% −37.367%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 4 outliers among 100 measurements (4.00%)
  4 (4.00%) high mild
encode/standard_bytes_random
                        time:   [10.264 ns 10.311 ns 10.362 ns]
                        change: [−40.286% −39.525% −38.883%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 4 outliers among 100 measurements (4.00%)
  3 (3.00%) high mild
  1 (1.00%) high severe
encode/standard_bytes_random_u64
                        time:   [4.8844 ns 4.9894 ns 5.0998 ns]
                        change: [−45.120% −43.545% −41.757%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 6 outliers among 100 measurements (6.00%)
  2 (2.00%) low mild
  2 (2.00%) high mild
  2 (2.00%) high severe
encode/standard_buf_fixed
                        time:   [9.1049 ns 9.1667 ns 9.2424 ns]
                        change: [−39.683% −37.537% −35.580%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 4 outliers among 100 measurements (4.00%)
  2 (2.00%) high mild
  2 (2.00%) high severe
encode/standard_buf_random
                        time:   [9.8441 ns 9.8764 ns 9.9082 ns]
                        change: [−40.796% −39.898% −39.266%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 3 outliers among 100 measurements (3.00%)
  2 (2.00%) low mild
  1 (1.00%) high mild
encode/standard_buf_random_u64
                        time:   [4.4342 ns 4.4420 ns 4.4501 ns]
                        change: [−50.769% −49.654% −48.998%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 6 outliers among 100 measurements (6.00%)
  1 (1.00%) low severe
  4 (4.00%) low mild
  1 (1.00%) high mild
encode/alternative_new_fixed
                        time:   [21.840 ns 21.922 ns 22.024 ns]
                        change: [−21.341% −19.820% −18.214%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 4 outliers among 100 measurements (4.00%)
  2 (2.00%) high mild
  2 (2.00%) high severe
encode/alternative_new_random
                        time:   [17.275 ns 17.436 ns 17.593 ns]
                        change: [−32.089% −31.037% −30.045%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 1 outliers among 100 measurements (1.00%)
  1 (1.00%) high mild
encode/alternative_new_random_u64
                        time:   [12.161 ns 12.281 ns 12.410 ns]
                        change: [−25.044% −23.586% −22.151%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 5 outliers among 100 measurements (5.00%)
  4 (4.00%) low mild
  1 (1.00%) high mild
encode/alternative_bytes_fixed
                        time:   [9.0809 ns 9.2128 ns 9.4044 ns]
                        change: [−37.003% −36.148% −35.102%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 5 outliers among 100 measurements (5.00%)
  1 (1.00%) high mild
  4 (4.00%) high severe
encode/alternative_bytes_random
                        time:   [10.398 ns 10.504 ns 10.611 ns]
                        change: [−39.402% −38.730% −38.121%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 3 outliers among 100 measurements (3.00%)
  3 (3.00%) high mild
encode/alternative_bytes_random_u64
                        time:   [4.8215 ns 4.9078 ns 4.9969 ns]
                        change: [−44.269% −42.694% −40.968%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 20 outliers among 100 measurements (20.00%)
  14 (14.00%) low mild
  5 (5.00%) high mild
  1 (1.00%) high severe
encode/alternative_buf_fixed
                        time:   [9.1571 ns 9.1818 ns 9.2060 ns]
                        change: [−37.374% −37.108% −36.842%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 1 outliers among 100 measurements (1.00%)
  1 (1.00%) high mild
encode/alternative_buf_random
                        time:   [9.8021 ns 9.8417 ns 9.8796 ns]
                        change: [−39.731% −39.315% −38.920%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 1 outliers among 100 measurements (1.00%)
  1 (1.00%) high mild
encode/alternative_buf_random_u64
                        time:   [4.5678 ns 4.6589 ns 4.7722 ns]
                        change: [−48.095% −47.371% −46.465%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 9 outliers among 100 measurements (9.00%)
  3 (3.00%) high mild
  6 (6.00%) high severe

[fbernier]

great stuff again. Thanks!