uint256: optimize MulMod, MulModWithReciprocal

[AaronChen0]

The api of reduce4 is changed to reduce array copies.

1. The function reduce4 doesn't change the values of its parameters x, m, and mu. So it's fine to pass by pointers.
2. In the case of z == m (They are alias), m is used before z, and z is only written in the last step. So this is fine too.

Benchmark

goos: linux
goarch: amd64
pkg: github.com/holiman/uint256
cpu: AMD Ryzen 7 7735H with Radeon Graphics         
                          │     old     │                 new                 │
                          │   sec/op    │   sec/op     vs base                │
MulMod/small/uint256-16     15.84n ± 2%   15.63n ± 1%   -1.33% (p=0.049 n=10)
MulMod/mod64/uint256-16     29.44n ± 1%   29.09n ± 2%   -1.17% (p=0.030 n=10)
MulMod/mod128/uint256-16    51.92n ± 1%   52.62n ± 2%        ~ (p=0.183 n=10)
MulMod/mod192/uint256-16    66.39n ± 2%   65.42n ± 1%        ~ (p=0.086 n=10)
MulMod/mod256/uint256-16    87.02n ± 2%   77.26n ± 1%  -11.20% (p=0.000 n=10)
MulMod/mod256/uint256r-16   38.07n ± 2%   27.52n ± 2%  -27.70% (p=0.000 n=10)
geomean                     41.79n        38.64n        -7.53%

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (70cbe2b) to head (adec10c).

Additional details and impacted files

@@            Coverage Diff            @@
##            master      #172   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            5         5           
  Lines         1632      1630    -2     
=========================================
- Hits          1632      1630    -2     

[holiman]

LGTM, thanks!

[holiman]

Doesn't repro on my machine though:

goos: linux
goarch: amd64
pkg: github.com/holiman/uint256
cpu: 12th Gen Intel(R) Core(TM) i7-1270P
                         │ bench.mulmod.1 │             bench.mulmod.2              │
                         │     sec/op     │     sec/op      vs base                 │
MulMod/small/uint256-8     36.33n ± 32%     47.02n ± 28%          ~ (p=0.105 n=10)
MulMod/mod64/uint256-8     57.80n ± 15%     65.16n ± 41%          ~ (p=0.143 n=10)
MulMod/mod128/uint256-8    108.5n ±  9%     138.3n ± 45%    +27.47% (p=0.019 n=10)
MulMod/mod192/uint256-8    148.2n ± 18%     230.3n ± 40%          ~ (p=0.063 n=10)
MulMod/mod256/uint256-8    197.3n ± 66%     204.8n ± 53%          ~ (p=0.565 n=10)
MulMod/mod256/uint256r-8   87.19n ± 47%     80.01n ± 35%          ~ (p=0.280 n=10)
MulMod/small/big-8         84.76n ±   ∞ ¹   81.11n ±   ∞ ¹        ~ (p=0.229 n=3+4)

OTOH, my machine has variations going all over the place. I'll trust your numbers more.

[AaronChen0]

You can consider spinning up a ubuntu vps on DigitalOcean or Vultr for testing and delete the machine after finishing testing.