Optimize shift operations for BigInteger

[kzrnm]

Fix #112564

This pull request includes the following changes:

• Added tests for RotateLeft, RotateRight and the unsigned right shift(>>>).
• Fixed shifting for negative numbers (The unsigned right shift operator (>>>) of BigInteger behaves strangely #112564)
• Optimized performance

Benchmark

BenchmarkDotNet v0.13.12, Windows 11 (10.0.26100.3194)
13th Gen Intel Core i5-13500, 1 CPU, 20 logical and 14 physical cores
.NET SDK 10.0.100-alpha.1.25077.2
  [Host]     : .NET 10.0.0 (10.0.25.7313), X64 RyuJIT AVX2
  Job-XLUTTB : .NET 10.0.0 (42.42.42.42424), X64 RyuJIT AVX2
  Job-KGFXGU : .NET 10.0.0 (42.42.42.42424), X64 RyuJIT AVX2

Method	Toolchain	Mean	Ratio	Gen0	Gen1	Gen2	Allocated	Alloc Ratio
PositiveLeftShift	\main\corerun.exe	13.920 ms	1.00	62.5000	62.5000	62.5000	33 MB	1.00
PositiveLeftShift	\pr\corerun.exe	9.485 ms	0.68	156.2500	156.2500	156.2500	33 MB	1.00
NegativeLeftShift	\main\corerun.exe	13.567 ms	1.00	78.1250	78.1250	78.1250	33 MB	1.00
NegativeLeftShift	\pr\corerun.exe	9.134 ms	0.67	156.2500	156.2500	156.2500	33 MB	1.00
PositiveRightShift	\main\corerun.exe	16.709 ms	1.00	125.0000	125.0000	125.0000	31 MB	1.00
PositiveRightShift	\pr\corerun.exe	12.411 ms	0.74	187.5000	187.5000	187.5000	31 MB	1.00
NegativeRightShift	\main\corerun.exe	21.708 ms	1.00	125.0000	125.0000	125.0000	31 MB	1.00
NegativeRightShift	\pr\corerun.exe	12.291 ms	0.57	187.5000	187.5000	187.5000	31 MB	1.00
PositiveUnsignedRightShift	\main\corerun.exe	15.083 ms	1.00	125.0000	125.0000	125.0000	31 MB	1.00
PositiveUnsignedRightShift	\pr\corerun.exe	12.585 ms	0.84	187.5000	187.5000	187.5000	31 MB	1.00
NegativeUnsignedRightShift	\main\corerun.exe	18.347 ms	1.00	125.0000	125.0000	125.0000	31 MB	1.00
NegativeUnsignedRightShift	\pr\corerun.exe	14.719 ms	0.81	187.5000	187.5000	187.5000	31 MB	1.00
PositiveRotateLeft	\main\corerun.exe	15.150 ms	1.00	125.0000	125.0000	125.0000	32 MB	1.00
PositiveRotateLeft	\pr\corerun.exe	13.825 ms	0.90	187.5000	187.5000	187.5000	32 MB	1.00
NegativeRotateLeft	\main\corerun.exe	19.346 ms	1.00	125.0000	125.0000	125.0000	32 MB	1.00
NegativeRotateLeft	\pr\corerun.exe	18.920 ms	0.97	187.5000	187.5000	187.5000	32 MB	1.00
PositiveRotateRight	\main\corerun.exe	14.727 ms	1.00	125.0000	125.0000	125.0000	32 MB	1.00
PositiveRotateRight	\pr\corerun.exe	14.222 ms	0.97	187.5000	187.5000	187.5000	32 MB	1.00
NegativeRotateRight	\main\corerun.exe	16.936 ms	1.00	125.0000	125.0000	125.0000	32 MB	1.00
NegativeRotateRight	\pr\corerun.exe	16.650 ms	0.98	187.5000	187.5000	187.5000	32 MB	1.00

benchmark code

using BenchmarkDotNet.Attributes;
using BenchmarkDotNet.Configs;
using System.Numerics;

[MemoryDiagnoser(false)]
[HideColumns("Job", "Error", "StdDev", "Median", "RatioSD")]
public class ShiftTest
{
    const int shiftSize = (1 << 23) + 13;
    BigInteger positive, negative;

    [GlobalSetup]
    public void Setup()
    {
        var bytes = new byte[1 << 25];
        new Random(227).NextBytes(bytes);
        positive = new BigInteger(bytes, isUnsigned: true);
        negative = -positive;
    }

    [Benchmark] public BigInteger PositiveLeftShift() => positive << shiftSize;
    [Benchmark] public BigInteger NegativeLeftShift() => negative << shiftSize;

    [Benchmark] public BigInteger PositiveRightShift() => positive >> shiftSize;
    [Benchmark] public BigInteger NegativeRightShift() => negative >> shiftSize;

    [Benchmark] public BigInteger PositiveUnsignedRightShift() => positive >>> shiftSize;
    [Benchmark] public BigInteger NegativeUnsignedRightShift() => negative >>> shiftSize;

    [Benchmark] public BigInteger PositiveRotateLeft() => BigInteger.RotateLeft(positive, shiftSize);
    [Benchmark] public BigInteger NegativeRotateLeft() => BigInteger.RotateLeft(negative, shiftSize);

    [Benchmark] public BigInteger PositiveRotateRight() => BigInteger.RotateRight(positive, shiftSize);
    [Benchmark] public BigInteger NegativeRotateRight() => BigInteger.RotateRight(negative, shiftSize);
}

[EgorBo]

If it accepts a non-readonly span - what is dangerous with it? We typically name such things with "Inplace"

[kzrnm]

I followed the existing DangerousMakeTwosComplement. I have no strong preference for the naming convention, but if DangerousMakeOnesComplement is to be renamed, then DangerousMakeTwosComplement should be renamed as well.

runtime/src/libraries/System.Runtime.Numerics/src/System/Numerics/NumericsHelpers.cs

Line 100 in 8de6e01

public static void DangerousMakeTwosComplement(Span<uint> d)

[EgorBo]

np. It just that it's the code that converts an immutable data into mutable span is what actually dangerous 🙂

[huoyaoyuan]

Fixed shifting for negative numbers

This is indeed behavioral change, could require design decision and breaking change announcement.

[kzrnm]

I noticed other compatibility-related problem, so I will esubmit new PR.

[huoyaoyuan]

I noticed other compatibility-related problem, so I will esubmit new PR.

I'd suggest to confirm the proposed behavioral change in the issue first.