Improve efficiency of Natural <-> ByteString

[janmasrovira]

I've improved efficiency of encoding/decoding Natural to Bytestring.

With very big numbers, the gains are dramatic. With smaller numbers, the gains are more modest but still relevant.

Benchmarks

1,000,000 digits

Natural -> ByteString

      Shift based:    OK
        1.697 s ±  13 ms
      Word64 based:   OK
        327  μs ±  21 μs
      Word8 based:    OK
        21.7 ms ± 1.2 ms
      Cereal library: OK
        1.874 s ± 3.6 ms

ByteString -> Natural

    ByteString -> Natural
      Shift based:    OK
        13.7 ms ± 889 μs
      Word based:     OK
        671  μs ±  30 μs

500 digits

Natural -> ByteString

    Natural -> ByteString
      Shift based:    OK
        4.99 μs ± 456 ns
      Word64 based:   OK
        267  ns ±  16 ns
      Word8 based:    OK
        1.86 μs ± 170 ns
      Cereal library: OK
        9.72 μs ± 771 ns

ByteString -> Natural

    ByteString -> Natural
      Old:            OK
        4.31 μs ± 411 ns
      New:            OK
        219  ns ±  21 ns

Unfortunately, I haven't measured any gains by measuring the execution time of the nock pipeline.

[lukaszcz]

Unfortunately, I haven't measured any gains by measuring the execution time of the nock pipeline.

Me neither. But after precomputing the hashes, the time difference with compilation to cairo dropped to below 30%. So it's acceptable.

heliax@imac positive % hyperfine -w 1 "juvix compile anoma test001.juvix" "juvix compile cairo test001.juvix"
Benchmark 1: juvix compile anoma test001.juvix
  Time (mean ± σ):      1.448 s ±  0.046 s    [User: 2.232 s, System: 0.252 s]
  Range (min … max):    1.375 s …  1.535 s    10 runs
 
Benchmark 2: juvix compile cairo test001.juvix
  Time (mean ± σ):      1.247 s ±  0.024 s    [User: 1.971 s, System: 0.223 s]
  Range (min … max):    1.200 s …  1.278 s    10 runs
 
Summary
  juvix compile cairo test001.juvix ran
    1.16 ± 0.04 times faster than juvix compile anoma test001.juvix

heliax@imac positive % hyperfine -w 1 "juvix compile anoma test001.juvix --modular" "juvix compile cairo test001.juvix"
Benchmark 1: juvix compile anoma test001.juvix --modular
  Time (mean ± σ):      1.605 s ±  0.043 s    [User: 2.382 s, System: 0.268 s]
  Range (min … max):    1.553 s …  1.677 s    10 runs
 
Benchmark 2: juvix compile cairo test001.juvix
  Time (mean ± σ):      1.260 s ±  0.045 s    [User: 1.975 s, System: 0.222 s]
  Range (min … max):    1.200 s …  1.339 s    10 runs
 
Summary
  juvix compile cairo test001.juvix ran
    1.27 ± 0.06 times faster than juvix compile anoma test001.juvix --modular

Modular compilation slows things down, because we don't filter out unused definitions early in Core anymore. But not so much (and we can't do much about that):

heliax@imac positive % hyperfine -w 1 "juvix compile anoma test001.juvix --modular" "juvix compile anoma test001.juvix" 
Benchmark 1: juvix compile anoma test001.juvix --modular
  Time (mean ± σ):      1.474 s ±  0.037 s    [User: 2.268 s, System: 0.186 s]
  Range (min … max):    1.418 s …  1.543 s    10 runs
 
Benchmark 2: juvix compile anoma test001.juvix
  Time (mean ± σ):      1.310 s ±  0.038 s    [User: 2.024 s, System: 0.161 s]
  Range (min … max):    1.265 s …  1.381 s    10 runs
 
Summary
  juvix compile anoma test001.juvix ran
    1.13 ± 0.04 times faster than juvix compile anoma test001.juvix --modular

heliax@imac positive % hyperfine -w 1 -p "rm -rf .juvix-build" "juvix compile anoma test001.juvix --modular" "juvix compile anoma test001.juvix"
Benchmark 1: juvix compile anoma test001.juvix --modular
  Time (mean ± σ):      5.247 s ±  0.216 s    [User: 8.392 s, System: 0.352 s]
  Range (min … max):    5.046 s …  5.694 s    10 runs
 
Benchmark 2: juvix compile anoma test001.juvix
  Time (mean ± σ):      5.029 s ±  0.235 s    [User: 8.302 s, System: 0.374 s]
  Range (min … max):    4.820 s …  5.468 s    10 runs
 
Summary
  juvix compile anoma test001.juvix ran
    1.04 ± 0.06 times faster than juvix compile anoma test001.juvix --modular