Performance improvements

[Shane32]

System

BenchmarkDotNet v0.13.12, Windows 10 (10.0.19045.4291/22H2/2022Update)
13th Gen Intel Core i9-13900K, 1 CPU, 32 logical and 24 physical cores
.NET SDK 8.0.202
  [Host]     : .NET 8.0.3 (8.0.324.11423), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.3 (8.0.324.11423), X64 RyuJIT AVX2

Before

Method	Mean	Error	StdDev	Gen0	Gen1	Allocated
CreateQRCode	245.4 us	4.88 us	5.80 us	17.0898	0.2441	317.99 KB
CreateQRCodeLong	7,531.1 us	34.13 us	31.92 us	265.6250	15.6250	4920.13 KB

After

Method	Mean	Error	StdDev	Gen0	Allocated
CreateQRCode	100.7 us	0.26 us	0.22 us	1.2207	23.18 KB
CreateQRCodeLong	1,842.1 us	3.19 us	2.83 us	23.4375	433.53 KB

Notes

Most of the performance improvements in this PR fall into a few categories:

• Use BitArray instead of string
• Eliminate concatenation and instead write/copy into buffers using offsets and counts
• Preallocation of arrays/lists to proper length
• Eliminate array allocation when unnecessary (e.g. don't call AddRange)
• Eliminate LINQ use
• Improve lookup tables / dictionaries

Progress

So far about half the code has been converted to use BitArray. There is still a notable amount of code that still uses strings that remains to be optimized. Also the Polynom class/constructor is heavily used and should be optimized.

[Shane32]

FYI, I have not yet gone back through all my changes to add comments and perform a self-review, etc.

[Shane32]

By the way, I plan to attempt using ArrayPool for further optimizations but not in this PR.

[Shane32]

@codebude I think this PR has enough changes. The GitHub comparison should be reasonable enough to follow. I would like to follow up with some other PRs:

• Improve readability (code comments, rename variables, split into multiple files, etc)
• Fix bug (?) with string handling
• Utilize ArrayPool and other memory optimizations

[Shane32]

The benchmarks are updated in the PR description, showing 60-75% memory reduction and 100-400% speed increase. Notably, Gen1 collections have been reduced enough that BenchmarkDotNet has stopped listing them!

Most likely further PRs will further reduce memory requirements, but not increase speed.

[Shane32]

I'm not planning to re-engineer the mathematics, like to use vector math or anything. While I'm sure it's possible, that's not my forte.

[Shane32]

Benchmarks updated. New test results shaved 10us (10%) from short test and 20us (1%) from long test.

[Shane32]

Eliminating foreach across a BitArray and implementing IEquatable for Point cut down memory requirements for small QR codes by an additional 80%, and an additional 60% for large QR codes.

[codebude]

Benchmarks updated. New test results shaved 10us (10%) from short test and 20us (1%) from long test.

But memory usage improved massively. :-)

[Shane32]

While all beneficial changes, the memory usage didn't change due to the arithmetic/ref/pointer changes; it measured as identical. The memory usage changes were due to foreach across a BitArray internally cast a bool to an object causing a heap allocation for each bit. Ditto for List<Point>.Contains due to Point not implementing IEquatable. These were accessed across some 'hot' code, and so many unnecessary heap allocations were made.

[gfoidl]

A few nits, otherwise LGTM 👍🏻

[codebude]

Merged. Thanks for your great work @Shane32 & @gfoidl ! 👏