MulMod64Benchmarks.GpuCompatibleDeferred: .NET 8.0(Runtime=.NET 8.0) [Input=ZeroOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 2.009 ns, StdErr = 0.001 ns (0.05%), N = 15, StdDev = 0.004 ns
Min = 2.001 ns, Q1 = 2.007 ns, Median = 2.010 ns, Q3 = 2.013 ns, Max = 2.015 ns
IQR = 0.006 ns, LowerFence = 1.998 ns, UpperFence = 2.022 ns
ConfidenceInterval = [2.005 ns; 2.014 ns] (CI 99.9%), Margin = 0.004 ns (0.21% of Mean)
Skewness = -0.31, Kurtosis = 1.94, MValue = 2
-------------------- Histogram --------------------
[1.999 ns ; 2.017 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                                     | Input             | Mean       | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|------------------------------------------- |------------------ |-----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ExtensionBaseline                          | CrossWordBlend    |   3.606 ns | 0.0030 ns | 0.0025 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleMulModExtension               | CrossWordBlend    |  22.870 ns | 0.1463 ns | 0.1297 ns |  6.34 |    0.04 |         - |          NA |
| GpuCompatibleMulModSimplifiedExtension     | CrossWordBlend    |  22.780 ns | 0.4463 ns | 0.8600 ns |  6.32 |    0.23 |         - |          NA |
| InlineUInt128Operands                      | CrossWordBlend    |  22.218 ns | 0.0319 ns | 0.0266 ns |  6.16 |    0.01 |         - |          NA |
| InlineUInt128OperandsWithReductionFirst    | CrossWordBlend    |  22.626 ns | 0.0553 ns | 0.0517 ns |  6.27 |    0.02 |         - |          NA |
| InlineUInt128OperandsWithOperandReduction  | CrossWordBlend    |  22.548 ns | 0.0487 ns | 0.0432 ns |  6.25 |    0.01 |         - |          NA |
| InlineUInt128WithLocals                    | CrossWordBlend    |  22.226 ns | 0.0464 ns | 0.0434 ns |  6.16 |    0.01 |         - |          NA |
| InlineUInt128WithLocalsAndOperandReduction | CrossWordBlend    |  29.746 ns | 0.1206 ns | 0.1128 ns |  8.24 |    0.03 |         - |          NA |
| MultiplyHighDecomposition                  | CrossWordBlend    |  23.685 ns | 0.0547 ns | 0.0457 ns |  6.57 |    0.01 |         - |          NA |
| GpuCompatibleBaseline                      | CrossWordBlend    |  24.422 ns | 0.4805 ns | 0.9257 ns |  6.86 |    0.28 |         - |          NA |
| GpuCompatibleDeferred                      | CrossWordBlend    | 146.559 ns | 0.1736 ns | 0.1539 ns | 40.63 |    0.05 |         - |          NA |
|                                            |                   |            |           |           |       |         |           |             |
| ExtensionBaseline                          | MixedBitPattern   |   3.564 ns | 0.0059 ns | 0.0052 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleMulModExtension               | MixedBitPattern   |  64.800 ns | 0.3399 ns | 0.3179 ns | 18.17 |    0.09 |         - |          NA |
| GpuCompatibleMulModSimplifiedExtension     | MixedBitPattern   |  59.165 ns | 0.4243 ns | 0.3969 ns | 16.60 |    0.11 |         - |          NA |
| InlineUInt128Operands                      | MixedBitPattern   |  30.539 ns | 0.1396 ns | 0.1306 ns |  8.57 |    0.03 |         - |          NA |
| InlineUInt128OperandsWithReductionFirst    | MixedBitPattern   |  31.237 ns | 0.1013 ns | 0.0898 ns |  8.76 |    0.03 |         - |          NA |
| InlineUInt128OperandsWithOperandReduction  | MixedBitPattern   |  30.210 ns | 0.1323 ns | 0.1237 ns |  8.48 |    0.04 |         - |          NA |
| InlineUInt128WithLocals                    | MixedBitPattern   |  30.882 ns | 0.1155 ns | 0.1023 ns |  8.66 |    0.03 |         - |          NA |
| InlineUInt128WithLocalsAndOperandReduction | MixedBitPattern   |  38.013 ns | 0.1240 ns | 0.1160 ns | 10.67 |    0.03 |         - |          NA |
| MultiplyHighDecomposition                  | MixedBitPattern   |  30.114 ns | 0.1006 ns | 0.0840 ns |  8.45 |    0.02 |         - |          NA |
| GpuCompatibleBaseline                      | MixedBitPattern   |  61.850 ns | 0.1293 ns | 0.1010 ns | 17.36 |    0.04 |         - |          NA |
| GpuCompatibleDeferred                      | MixedBitPattern   | 255.555 ns | 0.3206 ns | 0.2842 ns | 71.70 |    0.14 |         - |          NA |
|                                            |                   |            |           |           |       |         |           |             |
| ExtensionBaseline                          | NearFullRange     |   3.583 ns | 0.0105 ns | 0.0098 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleMulModExtension               | NearFullRange     |   5.708 ns | 0.0520 ns | 0.0486 ns |  1.59 |    0.02 |         - |          NA |
| GpuCompatibleMulModSimplifiedExtension     | NearFullRange     |   5.952 ns | 0.1253 ns | 0.1172 ns |  1.66 |    0.04 |         - |          NA |
| InlineUInt128Operands                      | NearFullRange     |  27.159 ns | 0.0936 ns | 0.0781 ns |  7.58 |    0.03 |         - |          NA |
| InlineUInt128OperandsWithReductionFirst    | NearFullRange     |   4.357 ns | 0.0205 ns | 0.0182 ns |  1.22 |    0.00 |         - |          NA |
| InlineUInt128OperandsWithOperandReduction  | NearFullRange     |   4.319 ns | 0.0158 ns | 0.0140 ns |  1.21 |    0.00 |         - |          NA |
| InlineUInt128WithLocals                    | NearFullRange     |  27.137 ns | 0.1028 ns | 0.0962 ns |  7.57 |    0.03 |         - |          NA |
| InlineUInt128WithLocalsAndOperandReduction | NearFullRange     |  12.187 ns | 0.1527 ns | 0.1429 ns |  3.40 |    0.04 |         - |          NA |
| MultiplyHighDecomposition                  | NearFullRange     |   5.221 ns | 0.0265 ns | 0.0248 ns |  1.46 |    0.01 |         - |          NA |
| GpuCompatibleBaseline                      | NearFullRange     |   7.267 ns | 0.0168 ns | 0.0158 ns |  2.03 |    0.01 |         - |          NA |
| GpuCompatibleDeferred                      | NearFullRange     |  21.390 ns | 0.0212 ns | 0.0198 ns |  5.97 |    0.02 |         - |          NA |
|                                            |                   |            |           |           |       |         |           |             |
| ExtensionBaseline                          | PrimeSizedModulus |   3.593 ns | 0.0039 ns | 0.0037 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleMulModExtension               | PrimeSizedModulus |  52.766 ns | 0.3086 ns | 0.2887 ns | 14.69 |    0.08 |         - |          NA |
| GpuCompatibleMulModSimplifiedExtension     | PrimeSizedModulus |  50.490 ns | 0.1977 ns | 0.1752 ns | 14.05 |    0.05 |         - |          NA |
| InlineUInt128Operands                      | PrimeSizedModulus |  31.409 ns | 0.0984 ns | 0.0920 ns |  8.74 |    0.03 |         - |          NA |
| InlineUInt128OperandsWithReductionFirst    | PrimeSizedModulus |  32.176 ns | 0.3427 ns | 0.3206 ns |  8.96 |    0.09 |         - |          NA |
| InlineUInt128OperandsWithOperandReduction  | PrimeSizedModulus |  31.786 ns | 0.1483 ns | 0.1387 ns |  8.85 |    0.04 |         - |          NA |
| InlineUInt128WithLocals                    | PrimeSizedModulus |  31.351 ns | 0.1016 ns | 0.0849 ns |  8.73 |    0.02 |         - |          NA |
| InlineUInt128WithLocalsAndOperandReduction | PrimeSizedModulus |  40.459 ns | 0.2541 ns | 0.2377 ns | 11.26 |    0.07 |         - |          NA |
| MultiplyHighDecomposition                  | PrimeSizedModulus |  31.950 ns | 0.1510 ns | 0.1339 ns |  8.89 |    0.04 |         - |          NA |
| GpuCompatibleBaseline                      | PrimeSizedModulus |  55.114 ns | 0.7359 ns | 0.6524 ns | 15.34 |    0.18 |         - |          NA |
| GpuCompatibleDeferred                      | PrimeSizedModulus | 294.486 ns | 4.3400 ns | 4.0597 ns | 81.97 |    1.14 |         - |          NA |
|                                            |                   |            |           |           |       |         |           |             |
| ExtensionBaseline                          | SparseOperands    |   3.555 ns | 0.0087 ns | 0.0082 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleMulModExtension               | SparseOperands    |   5.671 ns | 0.0043 ns | 0.0036 ns |  1.60 |    0.00 |         - |          NA |
| GpuCompatibleMulModSimplifiedExtension     | SparseOperands    |   5.239 ns | 0.0103 ns | 0.0096 ns |  1.47 |    0.00 |         - |          NA |
| InlineUInt128Operands                      | SparseOperands    |   3.563 ns | 0.0217 ns | 0.0203 ns |  1.00 |    0.01 |         - |          NA |
| InlineUInt128OperandsWithReductionFirst    | SparseOperands    |   4.617 ns | 0.0095 ns | 0.0089 ns |  1.30 |    0.00 |         - |          NA |
| InlineUInt128OperandsWithOperandReduction  | SparseOperands    |   4.282 ns | 0.0193 ns | 0.0181 ns |  1.20 |    0.01 |         - |          NA |
| InlineUInt128WithLocals                    | SparseOperands    |   3.566 ns | 0.0154 ns | 0.0144 ns |  1.00 |    0.00 |         - |          NA |
| InlineUInt128WithLocalsAndOperandReduction | SparseOperands    |  15.100 ns | 0.0776 ns | 0.0726 ns |  4.25 |    0.03 |         - |          NA |
| MultiplyHighDecomposition                  | SparseOperands    |   5.204 ns | 0.0223 ns | 0.0208 ns |  1.46 |    0.01 |         - |          NA |
| GpuCompatibleBaseline                      | SparseOperands    |   7.261 ns | 0.0065 ns | 0.0057 ns |  2.04 |    0.00 |         - |          NA |
| GpuCompatibleDeferred                      | SparseOperands    |  18.182 ns | 0.0233 ns | 0.0182 ns |  5.12 |    0.01 |         - |          NA |
|                                            |                   |            |           |           |       |         |           |             |
| ExtensionBaseline                          | ZeroOperands      |   3.599 ns | 0.0069 ns | 0.0065 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleMulModExtension               | ZeroOperands      |   1.976 ns | 0.0053 ns | 0.0049 ns |  0.55 |    0.00 |         - |          NA |
| GpuCompatibleMulModSimplifiedExtension     | ZeroOperands      |   1.986 ns | 0.0048 ns | 0.0045 ns |  0.55 |    0.00 |         - |          NA |
| InlineUInt128Operands                      | ZeroOperands      |   3.542 ns | 0.0125 ns | 0.0117 ns |  0.98 |    0.00 |         - |          NA |
| InlineUInt128OperandsWithReductionFirst    | ZeroOperands      |   4.286 ns | 0.0178 ns | 0.0167 ns |  1.19 |    0.01 |         - |          NA |
| InlineUInt128OperandsWithOperandReduction  | ZeroOperands      |   4.256 ns | 0.0116 ns | 0.0097 ns |  1.18 |    0.00 |         - |          NA |
| InlineUInt128WithLocals                    | ZeroOperands      |   3.586 ns | 0.0293 ns | 0.0274 ns |  1.00 |    0.01 |         - |          NA |
| InlineUInt128WithLocalsAndOperandReduction | ZeroOperands      |  11.863 ns | 0.0499 ns | 0.0466 ns |  3.30 |    0.01 |         - |          NA |
| MultiplyHighDecomposition                  | ZeroOperands      |   5.171 ns | 0.0320 ns | 0.0299 ns |  1.44 |    0.01 |         - |          NA |
| GpuCompatibleBaseline                      | ZeroOperands      |   3.587 ns | 0.0091 ns | 0.0085 ns |  1.00 |    0.00 |         - |          NA |
| GpuCompatibleDeferred                      | ZeroOperands      |   2.009 ns | 0.0043 ns | 0.0040 ns |  0.56 |    0.00 |         - |          NA |

// * Hints *
Outliers
  MulMod64Benchmarks.ExtensionBaseline: .NET 8.0                          -> 2 outliers were removed (4.92 ns, 5.01 ns)
  MulMod64Benchmarks.GpuCompatibleMulModExtension: .NET 8.0               -> 1 outlier  was  removed, 2 outliers were detected (23.75 ns, 25.37 ns)
  MulMod64Benchmarks.GpuCompatibleMulModSimplifiedExtension: .NET 8.0     -> 2 outliers were removed, 3 outliers were detected (22.07 ns, 26.53 ns, 26.65 ns)
  MulMod64Benchmarks.InlineUInt128Operands: .NET 8.0                      -> 2 outliers were removed (23.62 ns, 23.64 ns)
  MulMod64Benchmarks.InlineUInt128OperandsWithOperandReduction: .NET 8.0  -> 1 outlier  was  removed (24.42 ns)
  MulMod64Benchmarks.MultiplyHighDecomposition: .NET 8.0                  -> 2 outliers were removed (25.12 ns, 25.31 ns)
  MulMod64Benchmarks.GpuCompatibleBaseline: .NET 8.0                      -> 1 outlier  was  removed (28.50 ns)
  MulMod64Benchmarks.GpuCompatibleDeferred: .NET 8.0                      -> 1 outlier  was  removed (148.92 ns)
  MulMod64Benchmarks.ExtensionBaseline: .NET 8.0                          -> 1 outlier  was  removed (5.07 ns)
  MulMod64Benchmarks.InlineUInt128OperandsWithReductionFirst: .NET 8.0    -> 1 outlier  was  removed (32.96 ns)
  MulMod64Benchmarks.InlineUInt128WithLocals: .NET 8.0                    -> 1 outlier  was  removed (32.57 ns)
  MulMod64Benchmarks.MultiplyHighDecomposition: .NET 8.0                  -> 2 outliers were removed (32.46 ns, 33.49 ns)
  MulMod64Benchmarks.GpuCompatibleBaseline: .NET 8.0                      -> 3 outliers were removed (64.17 ns..64.56 ns)
  MulMod64Benchmarks.GpuCompatibleDeferred: .NET 8.0                      -> 1 outlier  was  removed (259.51 ns)
  MulMod64Benchmarks.InlineUInt128Operands: .NET 8.0                      -> 2 outliers were removed (29.01 ns, 29.49 ns)
  MulMod64Benchmarks.InlineUInt128OperandsWithReductionFirst: .NET 8.0    -> 1 outlier  was  removed (5.72 ns)
  MulMod64Benchmarks.InlineUInt128OperandsWithOperandReduction: .NET 8.0  -> 1 outlier  was  removed (5.73 ns)
  MulMod64Benchmarks.GpuCompatibleMulModSimplifiedExtension: .NET 8.0     -> 1 outlier  was  removed, 3 outliers were detected (51.41 ns, 51.47 ns, 52.10 ns)
  MulMod64Benchmarks.InlineUInt128Operands: .NET 8.0                      -> 1 outlier  was  detected (32.44 ns)
  MulMod64Benchmarks.InlineUInt128WithLocals: .NET 8.0                    -> 2 outliers were removed (33.47 ns, 34.46 ns)
  MulMod64Benchmarks.MultiplyHighDecomposition: .NET 8.0                  -> 1 outlier  was  removed (33.93 ns)
  MulMod64Benchmarks.GpuCompatibleBaseline: .NET 8.0                      -> 1 outlier  was  removed, 2 outliers were detected (55.31 ns, 59.36 ns)
  MulMod64Benchmarks.GpuCompatibleMulModExtension: .NET 8.0               -> 2 outliers were removed (6.96 ns, 6.96 ns)
  MulMod64Benchmarks.InlineUInt128WithLocalsAndOperandReduction: .NET 8.0 -> 2 outliers were detected (16.25 ns, 16.25 ns)
  MulMod64Benchmarks.GpuCompatibleBaseline: .NET 8.0                      -> 1 outlier  was  removed (8.58 ns)
  MulMod64Benchmarks.GpuCompatibleDeferred: .NET 8.0                      -> 3 outliers were removed (19.93 ns..20.25 ns)
  MulMod64Benchmarks.InlineUInt128OperandsWithReductionFirst: .NET 8.0    -> 2 outliers were detected (5.55 ns, 5.55 ns)
  MulMod64Benchmarks.InlineUInt128OperandsWithOperandReduction: .NET 8.0  -> 2 outliers were removed (5.59 ns, 5.60 ns)










Mul64Benchmarks.BigIntegerReference: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 34.286 ns, StdErr = 0.027 ns (0.08%), N = 14, StdDev = 0.101 ns
Min = 34.030 ns, Q1 = 34.296 ns, Median = 34.312 ns, Q3 = 34.340 ns, Max = 34.400 ns
IQR = 0.044 ns, LowerFence = 34.229 ns, UpperFence = 34.407 ns
ConfidenceInterval = [34.173 ns; 34.400 ns] (CI 99.9%), Margin = 0.114 ns (0.33% of Mean)
Skewness = -1.33, Kurtosis = 3.69, MValue = 2
-------------------- Histogram --------------------
[33.975 ns ; 34.455 ns) | @@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                      | Input              | Mean      | Error     | StdDev    | Ratio | RatioSD | Gen0   | Allocated | Alloc Ratio |
|---------------------------- |------------------- |----------:|----------:|----------:|------:|--------:|-------:|----------:|------------:|
| HighWordAccumulatedInLocals | AllBitsSet         |  1.568 ns | 0.0113 ns | 0.0100 ns |  1.00 |    0.00 |      - |         - |          NA |
| FoldedHighReturnValue       | AllBitsSet         |  1.583 ns | 0.0140 ns | 0.0124 ns |  1.01 |    0.01 |      - |         - |          NA |
| GpuFriendlyLayout           | AllBitsSet         |  3.682 ns | 0.0090 ns | 0.0080 ns |  2.35 |    0.02 |      - |         - |          NA |
| BigIntegerReference         | AllBitsSet         | 86.087 ns | 0.3381 ns | 0.2997 ns | 54.92 |    0.36 | 0.0162 |     136 B |          NA |
|                             |                    |           |           |           |       |         |        |           |             |
| HighWordAccumulatedInLocals | HighWordOnly       |  1.495 ns | 0.0079 ns | 0.0070 ns |  1.00 |    0.00 |      - |         - |          NA |
| FoldedHighReturnValue       | HighWordOnly       |  1.542 ns | 0.0127 ns | 0.0119 ns |  1.03 |    0.01 |      - |         - |          NA |
| GpuFriendlyLayout           | HighWordOnly       |  3.679 ns | 0.0087 ns | 0.0082 ns |  2.46 |    0.01 |      - |         - |          NA |
| BigIntegerReference         | HighWordOnly       | 78.860 ns | 0.2640 ns | 0.2470 ns | 52.74 |    0.32 | 0.0153 |     128 B |          NA |
|                             |                    |           |           |           |       |         |        |           |             |
| HighWordAccumulatedInLocals | InterleavedHighLow |  1.526 ns | 0.0126 ns | 0.0112 ns |  1.00 |    0.00 |      - |         - |          NA |
| FoldedHighReturnValue       | InterleavedHighLow |  1.575 ns | 0.0062 ns | 0.0055 ns |  1.03 |    0.01 |      - |         - |          NA |
| GpuFriendlyLayout           | InterleavedHighLow |  3.719 ns | 0.0716 ns | 0.0906 ns |  2.45 |    0.08 |      - |         - |          NA |
| BigIntegerReference         | InterleavedHighLow | 87.367 ns | 0.4155 ns | 0.3684 ns | 57.24 |    0.56 | 0.0210 |     176 B |          NA |
|                             |                    |           |           |           |       |         |        |           |             |
| HighWordAccumulatedInLocals | LowWordMax         |  1.506 ns | 0.0071 ns | 0.0066 ns |  1.00 |    0.00 |      - |         - |          NA |
| FoldedHighReturnValue       | LowWordMax         |  1.581 ns | 0.0068 ns | 0.0063 ns |  1.05 |    0.01 |      - |         - |          NA |
| GpuFriendlyLayout           | LowWordMax         |  3.684 ns | 0.0091 ns | 0.0076 ns |  2.45 |    0.01 |      - |         - |          NA |
| BigIntegerReference         | LowWordMax         | 74.418 ns | 0.3286 ns | 0.2913 ns | 49.43 |    0.27 | 0.0172 |     144 B |          NA |
|                             |                    |           |           |           |       |         |        |           |             |
| HighWordAccumulatedInLocals | ShiftHeavyMixed    |  1.481 ns | 0.0028 ns | 0.0026 ns |  1.00 |    0.00 |      - |         - |          NA |
| FoldedHighReturnValue       | ShiftHeavyMixed    |  1.562 ns | 0.0079 ns | 0.0074 ns |  1.06 |    0.00 |      - |         - |          NA |
| GpuFriendlyLayout           | ShiftHeavyMixed    |  3.707 ns | 0.0409 ns | 0.0362 ns |  2.50 |    0.02 |      - |         - |          NA |
| BigIntegerReference         | ShiftHeavyMixed    | 81.020 ns | 0.7542 ns | 0.7054 ns | 54.71 |    0.49 | 0.0181 |     152 B |          NA |
|                             |                    |           |           |           |       |         |        |           |             |
| HighWordAccumulatedInLocals | TinyOperands       |  1.503 ns | 0.0118 ns | 0.0110 ns |  1.00 |    0.00 |      - |         - |          NA |
| FoldedHighReturnValue       | TinyOperands       |  1.546 ns | 0.0073 ns | 0.0068 ns |  1.03 |    0.01 |      - |         - |          NA |
| GpuFriendlyLayout           | TinyOperands       |  3.683 ns | 0.0210 ns | 0.0176 ns |  2.45 |    0.02 |      - |         - |          NA |
| BigIntegerReference         | TinyOperands       | 34.286 ns | 0.1138 ns | 0.1009 ns | 22.80 |    0.16 |      - |         - |          NA |

// * Hints *
Outliers
  Mul64Benchmarks.HighWordAccumulatedInLocals: .NET 8.0 -> 1 outlier  was  removed (2.85 ns)
  Mul64Benchmarks.FoldedHighReturnValue: .NET 8.0       -> 1 outlier  was  removed (2.90 ns)
  Mul64Benchmarks.GpuFriendlyLayout: .NET 8.0           -> 1 outlier  was  removed (4.99 ns)
  Mul64Benchmarks.BigIntegerReference: .NET 8.0         -> 1 outlier  was  removed (88.71 ns)
  Mul64Benchmarks.HighWordAccumulatedInLocals: .NET 8.0 -> 1 outlier  was  removed (2.76 ns)
  Mul64Benchmarks.HighWordAccumulatedInLocals: .NET 8.0 -> 1 outlier  was  removed, 2 outliers were detected (2.74 ns, 2.80 ns)
  Mul64Benchmarks.FoldedHighReturnValue: .NET 8.0       -> 1 outlier  was  removed (2.83 ns)
  Mul64Benchmarks.GpuFriendlyLayout: .NET 8.0           -> 6 outliers were removed (5.61 ns..5.93 ns)
  Mul64Benchmarks.BigIntegerReference: .NET 8.0         -> 1 outlier  was  removed, 2 outliers were detected (87.97 ns, 90.14 ns)
  Mul64Benchmarks.GpuFriendlyLayout: .NET 8.0           -> 2 outliers were removed (4.95 ns, 4.98 ns)
  Mul64Benchmarks.BigIntegerReference: .NET 8.0         -> 1 outlier  was  removed (77.42 ns)
  Mul64Benchmarks.GpuFriendlyLayout: .NET 8.0           -> 1 outlier  was  removed (5.36 ns)
  Mul64Benchmarks.BigIntegerReference: .NET 8.0         -> 2 outliers were detected (81.47 ns, 81.49 ns)
  Mul64Benchmarks.GpuFriendlyLayout: .NET 8.0           -> 2 outliers were removed (5.01 ns, 5.07 ns)
  Mul64Benchmarks.BigIntegerReference: .NET 8.0         -> 1 outlier  was  removed, 4 outliers were detected (35.93 ns..36.11 ns, 36.33 ns)
  











MulHighBenchmarks.SchoolbookVariant: .NET 8.0(Runtime=.NET 8.0) [Input=ShiftHeavy]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.748 ns, StdErr = 0.004 ns (0.48%), N = 15, StdDev = 0.014 ns
Min = 0.722 ns, Q1 = 0.736 ns, Median = 0.752 ns, Q3 = 0.758 ns, Max = 0.767 ns
IQR = 0.021 ns, LowerFence = 0.704 ns, UpperFence = 0.790 ns
ConfidenceInterval = [0.734 ns; 0.763 ns] (CI 99.9%), Margin = 0.015 ns (1.98% of Mean)
Skewness = -0.37, Kurtosis = 1.77, MValue = 2
-------------------- Histogram --------------------
[0.715 ns ; 0.742 ns) | @@@@@
[0.742 ns ; 0.775 ns) | @@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                | Input           | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------------- |---------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| CurrentImplementation | AllBitsSet      | 0.7577 ns | 0.0082 ns | 0.0072 ns |  1.00 |    0.00 |         - |          NA |
| UInt128BuiltIn        | AllBitsSet      | 0.0641 ns | 0.0036 ns | 0.0033 ns |  0.08 |    0.00 |         - |          NA |
| GpuUInt128Style       | AllBitsSet      | 0.8643 ns | 0.0078 ns | 0.0065 ns |  1.14 |    0.01 |         - |          NA |
| ShiftThenMultiply     | AllBitsSet      | 0.9894 ns | 0.0074 ns | 0.0070 ns |  1.30 |    0.02 |         - |          NA |
| SchoolbookVariant     | AllBitsSet      | 0.7414 ns | 0.0064 ns | 0.0060 ns |  0.98 |    0.01 |         - |          NA |
|                       |                 |           |           |           |       |         |           |             |
| CurrentImplementation | HighPowersOfTwo | 0.7352 ns | 0.0097 ns | 0.0081 ns |  1.00 |    0.00 |         - |          NA |
| UInt128BuiltIn        | HighPowersOfTwo | 0.0674 ns | 0.0031 ns | 0.0029 ns |  0.09 |    0.00 |         - |          NA |
| GpuUInt128Style       | HighPowersOfTwo | 0.8584 ns | 0.0235 ns | 0.0208 ns |  1.17 |    0.03 |         - |          NA |
| ShiftThenMultiply     | HighPowersOfTwo | 1.1421 ns | 0.0455 ns | 0.0447 ns |  1.55 |    0.07 |         - |          NA |
| SchoolbookVariant     | HighPowersOfTwo | 0.7459 ns | 0.0115 ns | 0.0107 ns |  1.01 |    0.02 |         - |          NA |
|                       |                 |           |           |           |       |         |           |             |
| CurrentImplementation | IncludesZero    | 0.7497 ns | 0.0173 ns | 0.0154 ns |  1.00 |    0.00 |         - |          NA |
| UInt128BuiltIn        | IncludesZero    | 0.0541 ns | 0.0039 ns | 0.0036 ns |  0.07 |    0.00 |         - |          NA |
| GpuUInt128Style       | IncludesZero    | 0.8538 ns | 0.0038 ns | 0.0034 ns |  1.14 |    0.02 |         - |          NA |
| ShiftThenMultiply     | IncludesZero    | 0.9270 ns | 0.0056 ns | 0.0053 ns |  1.24 |    0.03 |         - |          NA |
| SchoolbookVariant     | IncludesZero    | 0.7442 ns | 0.0128 ns | 0.0120 ns |  1.00 |    0.02 |         - |          NA |
|                       |                 |           |           |           |       |         |           |             |
| CurrentImplementation | LowHighWord     | 0.7296 ns | 0.0074 ns | 0.0069 ns |  1.00 |    0.00 |         - |          NA |
| UInt128BuiltIn        | LowHighWord     | 0.0576 ns | 0.0029 ns | 0.0027 ns |  0.08 |    0.00 |         - |          NA |
| GpuUInt128Style       | LowHighWord     | 0.8576 ns | 0.0057 ns | 0.0053 ns |  1.18 |    0.01 |         - |          NA |
| ShiftThenMultiply     | LowHighWord     | 0.9195 ns | 0.0060 ns | 0.0053 ns |  1.26 |    0.01 |         - |          NA |
| SchoolbookVariant     | LowHighWord     | 0.7441 ns | 0.0120 ns | 0.0112 ns |  1.02 |    0.02 |         - |          NA |
|                       |                 |           |           |           |       |         |           |             |
| CurrentImplementation | Mixed           | 0.7365 ns | 0.0146 ns | 0.0136 ns |  1.00 |    0.00 |         - |          NA |
| UInt128BuiltIn        | Mixed           | 0.0634 ns | 0.0048 ns | 0.0038 ns |  0.09 |    0.01 |         - |          NA |
| GpuUInt128Style       | Mixed           | 0.8693 ns | 0.0088 ns | 0.0073 ns |  1.18 |    0.02 |         - |          NA |
| ShiftThenMultiply     | Mixed           | 1.2042 ns | 0.0100 ns | 0.0089 ns |  1.64 |    0.03 |         - |          NA |
| SchoolbookVariant     | Mixed           | 0.7395 ns | 0.0070 ns | 0.0065 ns |  1.00 |    0.01 |         - |          NA |
|                       |                 |           |           |           |       |         |           |             |
| CurrentImplementation | ShiftHeavy      | 0.7747 ns | 0.0240 ns | 0.0213 ns |  1.00 |    0.00 |         - |          NA |
| UInt128BuiltIn        | ShiftHeavy      | 0.0591 ns | 0.0032 ns | 0.0030 ns |  0.08 |    0.00 |         - |          NA |
| GpuUInt128Style       | ShiftHeavy      | 0.8625 ns | 0.0068 ns | 0.0064 ns |  1.11 |    0.03 |         - |          NA |
| ShiftThenMultiply     | ShiftHeavy      | 1.1909 ns | 0.0073 ns | 0.0061 ns |  1.54 |    0.05 |         - |          NA |
| SchoolbookVariant     | ShiftHeavy      | 0.7485 ns | 0.0148 ns | 0.0139 ns |  0.97 |    0.03 |         - |          NA |

// * Warnings *
MultimodalDistribution
  MulHighBenchmarks.UInt128BuiltIn: .NET 8.0 -> It seems that the distribution is bimodal (mValue = 3.5)
  MulHighBenchmarks.UInt128BuiltIn: .NET 8.0 -> It seems that the distribution can have several modes (mValue = 3.14)

// * Hints *
Outliers
  MulHighBenchmarks.CurrentImplementation: .NET 8.0 -> 1 outlier  was  removed (2.06 ns)
  MulHighBenchmarks.GpuUInt128Style: .NET 8.0       -> 2 outliers were removed (2.23 ns, 2.23 ns)
  MulHighBenchmarks.CurrentImplementation: .NET 8.0 -> 2 outliers were removed, 3 outliers were detected (2.00 ns, 2.05 ns, 2.06 ns)
  MulHighBenchmarks.GpuUInt128Style: .NET 8.0       -> 1 outlier  was  removed (2.21 ns)
  MulHighBenchmarks.ShiftThenMultiply: .NET 8.0     -> 1 outlier  was  detected (2.28 ns)
  MulHighBenchmarks.CurrentImplementation: .NET 8.0 -> 1 outlier  was  removed (2.11 ns)
  MulHighBenchmarks.UInt128BuiltIn: .NET 8.0        -> 1 outlier  was  detected (1.34 ns)
  MulHighBenchmarks.GpuUInt128Style: .NET 8.0       -> 1 outlier  was  removed, 2 outliers were detected (2.14 ns, 2.16 ns)
  MulHighBenchmarks.ShiftThenMultiply: .NET 8.0     -> 3 outliers were detected (2.19 ns..2.20 ns)
  MulHighBenchmarks.ShiftThenMultiply: .NET 8.0     -> 1 outlier  was  removed, 3 outliers were detected (2.19 ns, 2.19 ns, 2.21 ns)
  MulHighBenchmarks.UInt128BuiltIn: .NET 8.0        -> 3 outliers were removed, 4 outliers were detected (1.35 ns, 1.38 ns..1.41 ns)
  MulHighBenchmarks.GpuUInt128Style: .NET 8.0       -> 2 outliers were removed, 3 outliers were detected (2.14 ns, 2.19 ns, 2.22 ns)
  MulHighBenchmarks.ShiftThenMultiply: .NET 8.0     -> 1 outlier  was  removed (2.52 ns)
  MulHighBenchmarks.CurrentImplementation: .NET 8.0 -> 1 outlier  was  removed, 3 outliers were detected (2.03 ns, 2.03 ns, 2.12 ns)
  MulHighBenchmarks.UInt128BuiltIn: .NET 8.0        -> 1 outlier  was  detected (1.35 ns)
  MulHighBenchmarks.GpuUInt128Style: .NET 8.0       -> 2 outliers were detected (2.14 ns, 2.14 ns)
  MulHighBenchmarks.ShiftThenMultiply: .NET 8.0     -> 2 outliers were removed (2.50 ns, 2.50 ns)











GpuPow2ModBenchmarks.ProcessSingleBits: .NET 8.0(Runtime=.NET 8.0) [Input=Small(...)dulus [25]]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 85.393 ns, StdErr = 0.062 ns (0.07%), N = 14, StdDev = 0.232 ns
Min = 85.090 ns, Q1 = 85.174 ns, Median = 85.434 ns, Q3 = 85.594 ns, Max = 85.735 ns
IQR = 0.420 ns, LowerFence = 84.543 ns, UpperFence = 86.225 ns
ConfidenceInterval = [85.131 ns; 85.655 ns] (CI 99.9%), Margin = 0.262 ns (0.31% of Mean)
Skewness = 0, Kurtosis = 1.2, MValue = 2
-------------------- Histogram --------------------
[84.963 ns ; 85.862 ns) | @@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                 | Input                | Mean         | Error      | StdDev     | Ratio | Allocated | Alloc Ratio |
|----------------------- |--------------------- |-------------:|-----------:|-----------:|------:|----------:|------------:|
| ProcessEightBitWindows | FullW(...)dulus [33] | 21,481.71 ns |  61.853 ns |  57.857 ns |  1.00 |         - |          NA |
| ProcessSingleBits      | FullW(...)dulus [33] | 50,967.07 ns | 219.430 ns | 205.255 ns |  2.37 |         - |          NA |
|                        |                      |              |            |            |       |           |             |
| ProcessEightBitWindows | Large(...)dulus [28] |  7,874.85 ns |  23.410 ns |  20.752 ns |  1.00 |         - |          NA |
| ProcessSingleBits      | Large(...)dulus [28] |  8,851.95 ns |  21.146 ns |  18.745 ns |  1.12 |         - |          NA |
|                        |                      |              |            |            |       |           |             |
| ProcessEightBitWindows | Mediu(...)dulus [26] |    264.97 ns |   0.225 ns |   0.211 ns |  1.00 |         - |          NA |
| ProcessSingleBits      | Mediu(...)dulus [26] |    265.98 ns |   0.389 ns |   0.345 ns |  1.00 |         - |          NA |
|                        |                      |              |            |            |       |           |             |
| ProcessEightBitWindows | Small(...)dulus [25] |     82.97 ns |   0.049 ns |   0.044 ns |  1.00 |         - |          NA |
| ProcessSingleBits      | Small(...)dulus [25] |     85.39 ns |   0.262 ns |   0.232 ns |  1.03 |         - |          NA |

// * Hints *
Outliers
  GpuPow2ModBenchmarks.ProcessEightBitWindows: .NET 8.0 -> 1 outlier  was  removed (7.95 us)
  GpuPow2ModBenchmarks.ProcessSingleBits: .NET 8.0      -> 1 outlier  was  removed (8.93 us)
  GpuPow2ModBenchmarks.ProcessSingleBits: .NET 8.0      -> 1 outlier  was  removed (269.27 ns)
  GpuPow2ModBenchmarks.ProcessEightBitWindows: .NET 8.0 -> 1 outlier  was  removed (85.06 ns)
  GpuPow2ModBenchmarks.ProcessSingleBits: .NET 8.0      -> 1 outlier  was  removed (88.89 ns)















GpuUInt128AddBenchmarks.CarryInExpression: .NET 8.0(Runtime=.NET 8.0) [Input=MixedOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.474 ns, StdErr = 0.003 ns (0.54%), N = 15, StdDev = 0.010 ns
Min = 0.460 ns, Q1 = 0.466 ns, Median = 0.470 ns, Q3 = 0.483 ns, Max = 0.491 ns
IQR = 0.017 ns, LowerFence = 0.441 ns, UpperFence = 0.508 ns
ConfidenceInterval = [0.463 ns; 0.485 ns] (CI 99.9%), Margin = 0.011 ns (2.25% of Mean)
Skewness = 0.25, Kurtosis = 1.52, MValue = 2
-------------------- Histogram --------------------
[0.460 ns ; 0.470 ns) | @@@@@@@@
[0.470 ns ; 0.485 ns) | @@@@@
[0.485 ns ; 0.497 ns) | @@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                   | Input         | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|------------------------- |-------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| CarryMaterialisedInLocal | AllBitsSet    | 0.4737 ns | 0.0032 ns | 0.0027 ns |  1.00 |    0.00 |         - |          NA |
| CarryInExpression        | AllBitsSet    | 0.4676 ns | 0.0120 ns | 0.0113 ns |  0.98 |    0.02 |         - |          NA |
|                          |               |           |           |           |       |         |           |             |
| CarryMaterialisedInLocal | CarryIntoHigh | 0.4586 ns | 0.0084 ns | 0.0079 ns |  1.00 |    0.00 |         - |          NA |
| CarryInExpression        | CarryIntoHigh | 0.4907 ns | 0.0092 ns | 0.0086 ns |  1.07 |    0.03 |         - |          NA |
|                          |               |           |           |           |       |         |           |             |
| CarryMaterialisedInLocal | IncrementLow  | 0.4653 ns | 0.0096 ns | 0.0090 ns |  1.00 |    0.00 |         - |          NA |
| CarryInExpression        | IncrementLow  | 0.5082 ns | 0.0170 ns | 0.0151 ns |  1.09 |    0.04 |         - |          NA |
|                          |               |           |           |           |       |         |           |             |
| CarryMaterialisedInLocal | MixedOperands | 0.4628 ns | 0.0098 ns | 0.0091 ns |  1.00 |    0.00 |         - |          NA |
| CarryInExpression        | MixedOperands | 0.4741 ns | 0.0107 ns | 0.0100 ns |  1.02 |    0.03 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128AddBenchmarks.CarryMaterialisedInLocal: .NET 8.0 -> 2 outliers were removed (1.77 ns, 1.78 ns)
  GpuUInt128AddBenchmarks.CarryInExpression: .NET 8.0        -> 1 outlier  was  removed (1.93 ns)
  GpuUInt128AddBenchmarks.CarryMaterialisedInLocal: .NET 8.0 -> 1 outlier  was  detected (1.72 ns)











GpuUInt128BinaryGcdBenchmarks.TemporaryStructPerIteration: .NET 8.0(Runtime=.NET 8.0) [Input=SmallOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 5.987 ns, StdErr = 0.003 ns (0.05%), N = 13, StdDev = 0.011 ns
Min = 5.968 ns, Q1 = 5.981 ns, Median = 5.988 ns, Q3 = 5.992 ns, Max = 6.005 ns
IQR = 0.011 ns, LowerFence = 5.965 ns, UpperFence = 6.009 ns
ConfidenceInterval = [5.975 ns; 6.000 ns] (CI 99.9%), Margin = 0.013 ns (0.21% of Mean)
Skewness = -0.19, Kurtosis = 2.12, MValue = 2
-------------------- Histogram --------------------
[5.962 ns ; 6.011 ns) | @@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                      | Input         | Mean       | Error     | StdDev    | Median     | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------------------- |-------------- |-----------:|----------:|----------:|-----------:|------:|--------:|----------:|------------:|
| ReusedVariables             | HighEntropy   | 195.593 ns | 0.4527 ns | 0.4234 ns | 195.557 ns |  1.00 |    0.00 |         - |          NA |
| TemporaryStructPerIteration | HighEntropy   | 186.615 ns | 1.8451 ns | 1.7259 ns | 186.575 ns |  0.95 |    0.01 |         - |          NA |
|                             |               |            |           |           |            |       |         |           |             |
| ReusedVariables             | HighWordOnly  | 196.218 ns | 0.9524 ns | 0.8909 ns | 196.453 ns |  1.00 |    0.00 |         - |          NA |
| TemporaryStructPerIteration | HighWordOnly  | 185.849 ns | 0.2859 ns | 0.2535 ns | 185.776 ns |  0.95 |    0.00 |         - |          NA |
|                             |               |            |           |           |            |       |         |           |             |
| ReusedVariables             | LowWordHeavy  | 157.787 ns | 0.1786 ns | 0.1583 ns | 157.783 ns |  1.00 |    0.00 |         - |          NA |
| TemporaryStructPerIteration | LowWordHeavy  | 143.686 ns | 0.3787 ns | 0.3542 ns | 143.548 ns |  0.91 |    0.00 |         - |          NA |
|                             |               |            |           |           |            |       |         |           |             |
| ReusedVariables             | SmallOperands |   7.317 ns | 0.3025 ns | 0.8919 ns |   7.600 ns |  1.00 |    0.00 |         - |          NA |
| TemporaryStructPerIteration | SmallOperands |   5.987 ns | 0.0128 ns | 0.0107 ns |   5.988 ns |  0.95 |    0.06 |         - |          NA |

// * Warnings *
MultimodalDistribution
  GpuUInt128BinaryGcdBenchmarks.ReusedVariables: .NET 8.0 -> It seems that the distribution is bimodal (mValue = 3.71)

// * Hints *
Outliers
  GpuUInt128BinaryGcdBenchmarks.ReusedVariables: .NET 8.0             -> 2 outliers were detected (195.08 ns, 197.31 ns)
  GpuUInt128BinaryGcdBenchmarks.TemporaryStructPerIteration: .NET 8.0 -> 1 outlier  was  removed (189.36 ns)
  GpuUInt128BinaryGcdBenchmarks.ReusedVariables: .NET 8.0             -> 1 outlier  was  removed (160.52 ns)
  GpuUInt128BinaryGcdBenchmarks.TemporaryStructPerIteration: .NET 8.0 -> 2 outliers were removed (7.32 ns, 7.34 ns)










GpuUInt128Montgomery64Benchmarks.GpuStructMontgomeryMultiply: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 24.869 ns, StdErr = 0.004 ns (0.01%), N = 12, StdDev = 0.013 ns
Min = 24.843 ns, Q1 = 24.865 ns, Median = 24.868 ns, Q3 = 24.877 ns, Max = 24.890 ns
IQR = 0.012 ns, LowerFence = 24.847 ns, UpperFence = 24.895 ns
ConfidenceInterval = [24.852 ns; 24.885 ns] (CI 99.9%), Margin = 0.016 ns (0.07% of Mean)
Skewness = -0.44, Kurtosis = 2.4, MValue = 2
-------------------- Histogram --------------------
[24.835 ns ; 24.898 ns) | @@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                      | Input          | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------------------- |--------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ExtensionMontgomeryMultiply | DenseOperands  |  3.663 ns | 0.0130 ns | 0.0115 ns |  1.00 |    0.00 |         - |          NA |
| GpuStructMontgomeryMultiply | DenseOperands  | 24.904 ns | 0.0410 ns | 0.0383 ns |  6.80 |    0.02 |         - |          NA |
|                             |                |           |           |           |       |         |           |             |
| ExtensionMontgomeryMultiply | MixedMagnitude |  3.636 ns | 0.0060 ns | 0.0056 ns |  1.00 |    0.00 |         - |          NA |
| GpuStructMontgomeryMultiply | MixedMagnitude | 24.886 ns | 0.0175 ns | 0.0155 ns |  6.84 |    0.01 |         - |          NA |
|                             |                |           |           |           |       |         |           |             |
| ExtensionMontgomeryMultiply | NearModulus    |  3.651 ns | 0.0172 ns | 0.0143 ns |  1.00 |    0.00 |         - |          NA |
| GpuStructMontgomeryMultiply | NearModulus    | 24.893 ns | 0.0408 ns | 0.0382 ns |  6.82 |    0.04 |         - |          NA |
|                             |                |           |           |           |       |         |           |             |
| ExtensionMontgomeryMultiply | TinyOperands   |  3.639 ns | 0.0051 ns | 0.0048 ns |  1.00 |    0.00 |         - |          NA |
| GpuStructMontgomeryMultiply | TinyOperands   | 24.869 ns | 0.0164 ns | 0.0128 ns |  6.83 |    0.01 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128Montgomery64Benchmarks.ExtensionMontgomeryMultiply: .NET 8.0 -> 1 outlier  was  removed (4.98 ns)
  GpuUInt128Montgomery64Benchmarks.GpuStructMontgomeryMultiply: .NET 8.0 -> 1 outlier  was  removed (26.27 ns)
  GpuUInt128Montgomery64Benchmarks.ExtensionMontgomeryMultiply: .NET 8.0 -> 2 outliers were removed (5.00 ns, 5.02 ns)
  GpuUInt128Montgomery64Benchmarks.GpuStructMontgomeryMultiply: .NET 8.0 -> 3 outliers were removed (26.21 ns..26.24 ns)










GpuUInt128Mul64Benchmarks.HighProductInline: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 1.602 ns, StdErr = 0.001 ns (0.07%), N = 15, StdDev = 0.004 ns
Min = 1.592 ns, Q1 = 1.601 ns, Median = 1.602 ns, Q3 = 1.605 ns, Max = 1.607 ns
IQR = 0.003 ns, LowerFence = 1.596 ns, UpperFence = 1.609 ns
ConfidenceInterval = [1.597 ns; 1.606 ns] (CI 99.9%), Margin = 0.005 ns (0.29% of Mean)
Skewness = -1.02, Kurtosis = 2.8, MValue = 2
-------------------- Histogram --------------------
[1.590 ns ; 1.609 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method                         | Input        | Mean     | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|------------------------------- |------------- |---------:|----------:|----------:|------:|----------:|------------:|
| HighProductMaterialisedInLocal | AllBitsSet   | 1.551 ns | 0.0116 ns | 0.0109 ns |  1.00 |         - |          NA |
| HighProductInline              | AllBitsSet   | 1.631 ns | 0.0164 ns | 0.0145 ns |  1.05 |         - |          NA |
|                                |              |          |           |           |       |           |             |
| HighProductMaterialisedInLocal | HighByLow    | 1.532 ns | 0.0056 ns | 0.0046 ns |  1.00 |         - |          NA |
| HighProductInline              | HighByLow    | 1.594 ns | 0.0064 ns | 0.0060 ns |  1.04 |         - |          NA |
|                                |              |          |           |           |       |           |             |
| HighProductMaterialisedInLocal | LowWordMax   | 1.548 ns | 0.0042 ns | 0.0035 ns |  1.00 |         - |          NA |
| HighProductInline              | LowWordMax   | 1.623 ns | 0.0062 ns | 0.0048 ns |  1.05 |         - |          NA |
|                                |              |          |           |           |       |           |             |
| HighProductMaterialisedInLocal | TinyOperands | 1.529 ns | 0.0077 ns | 0.0069 ns |  1.00 |         - |          NA |
| HighProductInline              | TinyOperands | 1.602 ns | 0.0047 ns | 0.0044 ns |  1.05 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128Mul64Benchmarks.HighProductInline: .NET 8.0              -> 1 outlier  was  removed (2.99 ns)
  GpuUInt128Mul64Benchmarks.HighProductMaterialisedInLocal: .NET 8.0 -> 2 outliers were removed, 3 outliers were detected (2.79 ns, 2.82 ns, 2.84 ns)
  GpuUInt128Mul64Benchmarks.HighProductMaterialisedInLocal: .NET 8.0 -> 2 outliers were removed, 3 outliers were detected (2.82 ns, 2.84 ns, 2.84 ns)
  GpuUInt128Mul64Benchmarks.HighProductInline: .NET 8.0              -> 3 outliers were removed (2.93 ns..2.96 ns)
  GpuUInt128Mul64Benchmarks.HighProductMaterialisedInLocal: .NET 8.0 -> 1 outlier  was  removed (2.82 ns)
  GpuUInt128Mul64Benchmarks.HighProductInline: .NET 8.0              -> 2 outliers were detected (2.87 ns, 2.87 ns)









GpuUInt128MulModBenchmarks.AllocatePerIteration: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 4.659 ns, StdErr = 0.003 ns (0.06%), N = 14, StdDev = 0.011 ns
Min = 4.645 ns, Q1 = 4.650 ns, Median = 4.659 ns, Q3 = 4.667 ns, Max = 4.675 ns
IQR = 0.018 ns, LowerFence = 4.623 ns, UpperFence = 4.694 ns
ConfidenceInterval = [4.647 ns; 4.671 ns] (CI 99.9%), Margin = 0.012 ns (0.26% of Mean)
Skewness = 0.12, Kurtosis = 1.35, MValue = 2
-------------------- Histogram --------------------
[4.639 ns ; 4.681 ns) | @@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method               | Input           | Mean       | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|--------------------- |---------------- |-----------:|----------:|----------:|------:|--------:|----------:|------------:|
| InPlaceMulMod        | HighWordModulus | 192.794 ns | 0.5762 ns | 0.5390 ns |  1.00 |    0.00 |         - |          NA |
| AllocatePerIteration | HighWordModulus | 184.322 ns | 1.0378 ns | 0.9708 ns |  0.96 |    0.00 |         - |          NA |
|                      |                 |            |           |           |       |         |           |             |
| InPlaceMulMod        | LowWordHeavy    |   6.883 ns | 0.0163 ns | 0.0153 ns |  1.00 |    0.00 |         - |          NA |
| AllocatePerIteration | LowWordHeavy    | 116.993 ns | 0.3416 ns | 0.2853 ns | 17.00 |    0.06 |         - |          NA |
|                      |                 |            |           |           |       |         |           |             |
| InPlaceMulMod        | MixedMagnitude  | 201.468 ns | 1.0945 ns | 0.9703 ns |  1.00 |    0.00 |         - |          NA |
| AllocatePerIteration | MixedMagnitude  | 138.684 ns | 1.0645 ns | 0.9437 ns |  0.69 |    0.00 |         - |          NA |
|                      |                 |            |           |           |       |         |           |             |
| InPlaceMulMod        | TinyOperands    |   7.146 ns | 0.0140 ns | 0.0125 ns |  1.00 |    0.00 |         - |          NA |
| AllocatePerIteration | TinyOperands    |   4.659 ns | 0.0119 ns | 0.0106 ns |  0.65 |    0.00 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128MulModBenchmarks.AllocatePerIteration: .NET 8.0 -> 2 outliers were removed, 3 outliers were detected (118.15 ns, 119.88 ns, 120.37 ns)
  GpuUInt128MulModBenchmarks.InPlaceMulMod: .NET 8.0        -> 1 outlier  was  removed (205.87 ns)
  GpuUInt128MulModBenchmarks.AllocatePerIteration: .NET 8.0 -> 1 outlier  was  removed (143.71 ns)
  GpuUInt128MulModBenchmarks.InPlaceMulMod: .NET 8.0        -> 1 outlier  was  removed (8.46 ns)
  GpuUInt128MulModBenchmarks.AllocatePerIteration: .NET 8.0 -> 1 outlier  was  removed (6.25 ns)










GpuUInt128MulModByLimbBenchmarks.InPlaceReduction: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 12.915 ns, StdErr = 0.009 ns (0.07%), N = 15, StdDev = 0.034 ns
Min = 12.851 ns, Q1 = 12.901 ns, Median = 12.919 ns, Q3 = 12.938 ns, Max = 12.985 ns
IQR = 0.037 ns, LowerFence = 12.844 ns, UpperFence = 12.994 ns
ConfidenceInterval = [12.879 ns; 12.951 ns] (CI 99.9%), Margin = 0.036 ns (0.28% of Mean)
Skewness = -0.01, Kurtosis = 2.51, MValue = 2
-------------------- Histogram --------------------
[12.833 ns ; 13.003 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method           | Input            | Mean     | Error    | StdDev   | Ratio | Allocated | Alloc Ratio |
|----------------- |----------------- |---------:|---------:|---------:|------:|----------:|------------:|
| LegacyAllocating | HighWordDominant | 12.69 ns | 0.026 ns | 0.023 ns |  1.00 |         - |          NA |
| InPlaceReduction | HighWordDominant | 17.88 ns | 0.059 ns | 0.055 ns |  1.41 |         - |          NA |
|                  |                  |          |          |          |       |           |             |
| LegacyAllocating | MixedMagnitude   | 16.26 ns | 0.134 ns | 0.119 ns |  1.00 |         - |          NA |
| InPlaceReduction | MixedMagnitude   | 25.14 ns | 0.086 ns | 0.076 ns |  1.55 |         - |          NA |
|                  |                  |          |          |          |       |           |             |
| LegacyAllocating | TinyOperands     | 10.74 ns | 0.035 ns | 0.029 ns |  1.00 |         - |          NA |
| InPlaceReduction | TinyOperands     | 12.92 ns | 0.036 ns | 0.034 ns |  1.20 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128MulModByLimbBenchmarks.LegacyAllocating: .NET 8.0 -> 1 outlier  was  removed (14.07 ns)
  GpuUInt128MulModByLimbBenchmarks.LegacyAllocating: .NET 8.0 -> 1 outlier  was  removed (18.20 ns)
  GpuUInt128MulModByLimbBenchmarks.InPlaceReduction: .NET 8.0 -> 1 outlier  was  removed (26.84 ns)
  GpuUInt128MulModByLimbBenchmarks.LegacyAllocating: .NET 8.0 -> 2 outliers were removed (12.48 ns, 12.82 ns)










GpuUInt128NativeModuloBenchmarks.DeferredNativeModulo: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 18.149 ns, StdErr = 0.003 ns (0.02%), N = 13, StdDev = 0.011 ns
Min = 18.138 ns, Q1 = 18.140 ns, Median = 18.148 ns, Q3 = 18.153 ns, Max = 18.178 ns
IQR = 0.012 ns, LowerFence = 18.121 ns, UpperFence = 18.171 ns
ConfidenceInterval = [18.136 ns; 18.162 ns] (CI 99.9%), Margin = 0.013 ns (0.07% of Mean)
Skewness = 1.21, Kurtosis = 3.97, MValue = 2
-------------------- Histogram --------------------
[18.132 ns ; 18.184 ns) | @@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method               | Input          | Mean       | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|--------------------- |--------------- |-----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ImmediateModulo      | DenseOperands  |  38.127 ns | 0.7045 ns | 0.6590 ns |  1.00 |    0.00 |         - |          NA |
| DeferredNativeModulo | DenseOperands  | 298.926 ns | 0.5983 ns | 0.4996 ns |  7.83 |    0.14 |         - |          NA |
|                      |                |            |           |           |       |         |           |             |
| ImmediateModulo      | MixedMagnitude |  58.555 ns | 0.4244 ns | 0.3970 ns |  1.00 |    0.00 |         - |          NA |
| DeferredNativeModulo | MixedMagnitude | 255.624 ns | 0.1145 ns | 0.1015 ns |  4.36 |    0.03 |         - |          NA |
|                      |                |            |           |           |       |         |           |             |
| ImmediateModulo      | NearModulus    |  54.691 ns | 0.0499 ns | 0.0442 ns |  1.00 |    0.00 |         - |          NA |
| DeferredNativeModulo | NearModulus    | 293.280 ns | 0.4286 ns | 0.4009 ns |  5.36 |    0.01 |         - |          NA |
|                      |                |            |           |           |       |         |           |             |
| ImmediateModulo      | TinyOperands   |   7.278 ns | 0.0065 ns | 0.0058 ns |  1.00 |    0.00 |         - |          NA |
| DeferredNativeModulo | TinyOperands   |  18.149 ns | 0.0132 ns | 0.0110 ns |  2.49 |    0.00 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128NativeModuloBenchmarks.DeferredNativeModulo: .NET 8.0 -> 2 outliers were removed (303.48 ns, 306.88 ns)
  GpuUInt128NativeModuloBenchmarks.DeferredNativeModulo: .NET 8.0 -> 1 outlier  was  removed (258.04 ns)
  GpuUInt128NativeModuloBenchmarks.ImmediateModulo: .NET 8.0      -> 1 outlier  was  removed (56.38 ns)
  GpuUInt128NativeModuloBenchmarks.ImmediateModulo: .NET 8.0      -> 1 outlier  was  removed (8.67 ns)
  GpuUInt128NativeModuloBenchmarks.DeferredNativeModulo: .NET 8.0 -> 2 outliers were removed (19.49 ns, 19.50 ns)










GpuUInt128ScalarMulModBenchmarks.SpecializedScalar: .NET 8.0(Runtime=.NET 8.0) [Input=TinyOperands]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 154.154 ns, StdErr = 0.059 ns (0.04%), N = 14, StdDev = 0.222 ns
Min = 153.796 ns, Q1 = 154.000 ns, Median = 154.182 ns, Q3 = 154.294 ns, Max = 154.519 ns
IQR = 0.294 ns, LowerFence = 153.559 ns, UpperFence = 154.736 ns
ConfidenceInterval = [153.903 ns; 154.405 ns] (CI 99.9%), Margin = 0.251 ns (0.16% of Mean)
Skewness = 0.02, Kurtosis = 1.76, MValue = 2
-------------------- Histogram --------------------
[153.675 ns ; 154.640 ns) | @@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method            | Input            | Mean     | Error   | StdDev  | Ratio | Allocated | Alloc Ratio |
|------------------ |----------------- |---------:|--------:|--------:|------:|----------:|------------:|
| StructAllocating  | HighWordDominant | 193.7 ns | 0.63 ns | 0.59 ns |  1.00 |         - |          NA |
| SpecializedScalar | HighWordDominant | 192.1 ns | 0.42 ns | 0.35 ns |  0.99 |         - |          NA |
|                   |                  |          |         |         |       |           |             |
| StructAllocating  | MixedMagnitude   | 180.7 ns | 0.39 ns | 0.36 ns |  1.00 |         - |          NA |
| SpecializedScalar | MixedMagnitude   | 168.5 ns | 0.59 ns | 0.55 ns |  0.93 |         - |          NA |
|                   |                  |          |         |         |       |           |             |
| StructAllocating  | TinyOperands     | 164.0 ns | 0.28 ns | 0.23 ns |  1.00 |         - |          NA |
| SpecializedScalar | TinyOperands     | 154.2 ns | 0.25 ns | 0.22 ns |  0.94 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128ScalarMulModBenchmarks.SpecializedScalar: .NET 8.0 -> 2 outliers were removed (195.07 ns, 197.17 ns)
  GpuUInt128ScalarMulModBenchmarks.StructAllocating: .NET 8.0  -> 1 outlier  was  detected (181.51 ns)
  GpuUInt128ScalarMulModBenchmarks.StructAllocating: .NET 8.0  -> 2 outliers were removed (166.87 ns, 167.12 ns)
  GpuUInt128ScalarMulModBenchmarks.SpecializedScalar: .NET 8.0 -> 1 outlier  was  removed (157.40 ns)










GpuUInt128SubModScalarBenchmarks.LegacyTemporaries: .NET 8.0(Runtime=.NET 8.0) [Input=UnderflowAddsModulus]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.722 ns, StdErr = 0.002 ns (0.31%), N = 15, StdDev = 0.009 ns
Min = 0.710 ns, Q1 = 0.718 ns, Median = 0.722 ns, Q3 = 0.728 ns, Max = 0.741 ns
IQR = 0.011 ns, LowerFence = 0.702 ns, UpperFence = 0.744 ns
ConfidenceInterval = [0.713 ns; 0.732 ns] (CI 99.9%), Margin = 0.009 ns (1.29% of Mean)
Skewness = 0.26, Kurtosis = 2.3, MValue = 2
-------------------- Histogram --------------------
[0.705 ns ; 0.730 ns) | @@@@@@@@@@@
[0.730 ns ; 0.746 ns) | @@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]   : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  .NET 8.0 : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Job=.NET 8.0  Runtime=.NET 8.0

| Method            | Input                | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|------------------ |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| CurrentInPlace    | HighWordBorrow       | 0.5112 ns | 0.0093 ns | 0.0087 ns |  1.00 |    0.00 |         - |          NA |
| LegacyTemporaries | HighWordBorrow       | 0.5308 ns | 0.0044 ns | 0.0042 ns |  1.04 |    0.02 |         - |          NA |
|                   |                      |           |           |           |       |         |           |             |
| CurrentInPlace    | LargeLowWord         | 0.5092 ns | 0.0055 ns | 0.0052 ns |  1.00 |    0.00 |         - |          NA |
| LegacyTemporaries | LargeLowWord         | 0.5144 ns | 0.0064 ns | 0.0060 ns |  1.01 |    0.02 |         - |          NA |
|                   |                      |           |           |           |       |         |           |             |
| CurrentInPlace    | UnderflowAddsModulus | 0.7169 ns | 0.0040 ns | 0.0035 ns |  1.00 |    0.00 |         - |          NA |
| LegacyTemporaries | UnderflowAddsModulus | 0.7224 ns | 0.0093 ns | 0.0087 ns |  1.01 |    0.01 |         - |          NA |

// * Hints *
Outliers
  GpuUInt128SubModScalarBenchmarks.CurrentInPlace: .NET 8.0 -> 1 outlier  was  removed, 3 outliers were detected (1.98 ns, 1.98 ns, 2.00 ns)










MontgomeryMultiplyBenchmarks.OptimizedImplementation: Job-KEFHMK(Runtime=.NET 8.0, IterationCount=10, LaunchCount=1, WarmupCount=1) [BatchSize=1024]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 3.752 us, StdErr = 0.001 us (0.02%), N = 10, StdDev = 0.002 us
Min = 3.746 us, Q1 = 3.751 us, Median = 3.752 us, Q3 = 3.753 us, Max = 3.755 us
IQR = 0.001 us, LowerFence = 3.750 us, UpperFence = 3.755 us
ConfidenceInterval = [3.748 us; 3.755 us] (CI 99.9%), Margin = 0.004 us (0.10% of Mean)
Skewness = -0.72, Kurtosis = 2.54, MValue = 2
-------------------- Histogram --------------------
[3.745 us ; 3.756 us) | @@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-KEFHMK : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=10  LaunchCount=1
WarmupCount=1

| Method                  | BatchSize | Mean       | Error    | StdDev   | Ratio | Allocated | Alloc Ratio |
|------------------------ |---------- |-----------:|---------:|---------:|------:|----------:|------------:|
| OriginalImplementation  | 64        |   247.0 ns |  2.70 ns |  1.60 ns |  1.00 |         - |          NA |
| OptimizedImplementation | 64        |   234.9 ns |  0.83 ns |  0.55 ns |  0.95 |         - |          NA |
|                         |           |            |          |          |       |           |             |
| OriginalImplementation  | 256       |   974.2 ns |  5.34 ns |  2.79 ns |  1.00 |         - |          NA |
| OptimizedImplementation | 256       |   942.6 ns |  3.33 ns |  2.20 ns |  0.97 |         - |          NA |
|                         |           |            |          |          |       |           |             |
| OriginalImplementation  | 1024      | 3,940.6 ns | 51.22 ns | 33.88 ns |  1.00 |         - |          NA |
| OptimizedImplementation | 1024      | 3,751.6 ns |  3.73 ns |  2.47 ns |  0.95 |         - |          NA |

// * Hints *
Outliers
  MontgomeryMultiplyBenchmarks.OriginalImplementation: Runtime=.NET 8.0, IterationCount=10, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (256.77 ns)
  MontgomeryMultiplyBenchmarks.OriginalImplementation: Runtime=.NET 8.0, IterationCount=10, LaunchCount=1, WarmupCount=1  -> 2 outliers were removed, 4 outliers were detected (971.28 ns, 972.29 ns, 984.85 ns, 1.00 us)
  MontgomeryMultiplyBenchmarks.OptimizedImplementation: Runtime=.NET 8.0, IterationCount=10, LaunchCount=1, WarmupCount=1 -> 2 outliers were detected (3.75 us, 3.75 us)










Pow2MontgomeryModBenchmarks.BigIntegerMod: Job-OPHYZY(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Scale=Large]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 562.781 us, StdErr = 0.497 us (0.09%), N = 5, StdDev = 1.111 us
Min = 561.136 us, Q1 = 562.598 us, Median = 562.681 us, Q3 = 563.338 us, Max = 564.153 us
IQR = 0.739 us, LowerFence = 561.489 us, UpperFence = 564.447 us
ConfidenceInterval = [558.502 us; 567.061 us] (CI 99.9%), Margin = 4.279 us (0.76% of Mean)
Skewness = -0.25, Kurtosis = 1.44, MValue = 2
-------------------- Histogram --------------------
[560.283 us ; 565.006 us) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-OPHYZY : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method                 | Scale | Mean       | Error     | StdDev    | Ratio | RatioSD | Gen0   | Allocated | Alloc Ratio |
|----------------------- |------ |-----------:|----------:|----------:|------:|--------:|-------:|----------:|------------:|
| Baseline               | Small |  36.359 us | 0.5443 us | 0.1414 us |  1.00 |    0.00 |      - |         - |          NA |
| BaselineWithKnownCycle | Small |  26.040 us | 0.2308 us | 0.0357 us |  0.72 |    0.00 |      - |         - |          NA |
| LeftToRight            | Small |  39.112 us | 1.1095 us | 0.1717 us |  1.08 |    0.00 |      - |         - |          NA |
| Batched4               | Small |  38.740 us | 0.4199 us | 0.1090 us |  1.07 |    0.01 |      - |         - |          NA |
| SlidingWindow          | Small |  52.822 us | 0.1447 us | 0.0376 us |  1.45 |    0.01 |      - |         - |          NA |
| BinaryMod              | Small |  24.746 us | 0.3291 us | 0.0855 us |  0.68 |    0.00 |      - |         - |          NA |
| PrecomputedTableMod    | Small |  30.177 us | 0.8010 us | 0.2080 us |  0.83 |    0.00 |      - |         - |          NA |
| BigIntegerMod          | Small |  17.207 us | 0.0480 us | 0.0074 us |  0.47 |    0.00 |      - |         - |          NA |
|                        |       |            |           |           |       |         |        |           |             |
| Baseline               | Large | 117.316 us | 1.1253 us | 0.2922 us |  1.00 |    0.00 |      - |         - |          NA |
| BaselineWithKnownCycle | Large |   9.528 us | 0.0969 us | 0.0252 us |  0.08 |    0.00 |      - |         - |          NA |
| LeftToRight            | Large | 126.384 us | 3.8246 us | 0.9932 us |  1.08 |    0.01 |      - |         - |          NA |
| Batched4               | Large | 120.110 us | 0.5397 us | 0.1402 us |  1.02 |    0.00 |      - |         - |          NA |
| SlidingWindow          | Large | 124.134 us | 0.2362 us | 0.0365 us |  1.06 |    0.00 |      - |         - |          NA |
| BinaryMod              | Large | 295.289 us | 3.5017 us | 0.9094 us |  2.52 |    0.01 |      - |         - |          NA |
| PrecomputedTableMod    | Large | 289.804 us | 1.9896 us | 0.5167 us |  2.47 |    0.01 |      - |         - |          NA |
| BigIntegerMod          | Large | 562.781 us | 4.2794 us | 1.1114 us |  4.80 |    0.02 | 1.9531 |   20480 B |          NA |

// * Hints *
Outliers
  Pow2MontgomeryModBenchmarks.BaselineWithKnownCycle: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (25.99 us, 26.54 us)
  Pow2MontgomeryModBenchmarks.LeftToRight: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1            -> 1 outlier  was  removed (39.65 us)
  Pow2MontgomeryModBenchmarks.Batched4: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1               -> 1 outlier  was  detected (38.56 us)
  Pow2MontgomeryModBenchmarks.BigIntegerMod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1          -> 1 outlier  was  removed (17.25 us)
  Pow2MontgomeryModBenchmarks.Baseline: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1               -> 1 outlier  was  detected (116.89 us)
  Pow2MontgomeryModBenchmarks.SlidingWindow: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1          -> 1 outlier  was  removed (124.35 us)
  Pow2MontgomeryModBenchmarks.BigIntegerMod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1          -> 1 outlier  was  detected (561.14 us)










Pow2MontgomeryModCycleComputationBenchmarks.MontgomeryWithGpuCycleComputation: Job-DXKTIZ(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Scale=Large]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 12.908 us, StdErr = 0.013 us (0.10%), N = 5, StdDev = 0.030 us
Min = 12.875 us, Q1 = 12.884 us, Median = 12.916 us, Q3 = 12.916 us, Max = 12.949 us
IQR = 0.033 us, LowerFence = 12.834 us, UpperFence = 12.965 us
ConfidenceInterval = [12.794 us; 13.022 us] (CI 99.9%), Margin = 0.114 us (0.88% of Mean)
Skewness = 0.17, Kurtosis = 1.15, MValue = 2
-------------------- Histogram --------------------
[12.853 us ; 12.972 us) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-DXKTIZ : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method                            | Scale | Mean          | Error       | StdDev     | Ratio    | RatioSD | Allocated | Alloc Ratio |
|---------------------------------- |------ |--------------:|------------:|-----------:|---------:|--------:|----------:|------------:|
| MontgomeryWithoutCycle            | Small |     35.407 us |   0.3530 us |  0.0917 us |     1.00 |    0.00 |         - |          NA |
| MontgomeryWithPrecomputedCycle    | Small |     25.808 us |   0.1513 us |  0.0393 us |     0.73 |    0.00 |         - |          NA |
| MontgomeryWithGpuCycleComputation | Small | 54,088.467 us | 399.4765 us | 61.8194 us | 1,527.49 |    3.33 |      40 B |          NA |
|                                   |       |               |             |            |          |         |           |             |
| MontgomeryWithoutCycle            | Large |    117.327 us |   1.4583 us |  0.3787 us |     1.00 |    0.00 |         - |          NA |
| MontgomeryWithPrecomputedCycle    | Large |      9.119 us |   0.1517 us |  0.0394 us |     0.08 |    0.00 |         - |          NA |
| MontgomeryWithGpuCycleComputation | Large |     12.908 us |   0.1137 us |  0.0295 us |     0.11 |    0.00 |         - |          NA |

// * Hints *
Outliers
  Pow2MontgomeryModCycleComputationBenchmarks.MontgomeryWithGpuCycleComputation: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (54.26 ms)










ResidueComputationBenchmarks.ModMethodModulo: DefaultJob [Exponent=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 3.355 ns, StdErr = 0.003 ns (0.08%), N = 15, StdDev = 0.011 ns
Min = 3.338 ns, Q1 = 3.347 ns, Median = 3.353 ns, Q3 = 3.366 ns, Max = 3.371 ns
IQR = 0.019 ns, LowerFence = 3.319 ns, UpperFence = 3.394 ns
ConfidenceInterval = [3.343 ns; 3.366 ns] (CI 99.9%), Margin = 0.012 ns (0.35% of Mean)
Skewness = 0.15, Kurtosis = 1.5, MValue = 2
-------------------- Histogram --------------------
[3.333 ns ; 3.377 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method          | Exponent   | Mean     | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |----------- |---------:|----------:|----------:|------:|----------:|------------:|
| LegacyModulo    | 3          | 2.412 ns | 0.0088 ns | 0.0078 ns |  1.00 |         - |          NA |
| ModMethodModulo | 3          | 2.799 ns | 0.0109 ns | 0.0091 ns |  1.16 |         - |          NA |
|                 |            |          |           |           |       |           |             |
| LegacyModulo    | 8191       | 2.405 ns | 0.0110 ns | 0.0092 ns |  1.00 |         - |          NA |
| ModMethodModulo | 8191       | 2.842 ns | 0.0149 ns | 0.0139 ns |  1.18 |         - |          NA |
|                 |            |          |           |           |       |           |             |
| LegacyModulo    | 131071     | 2.416 ns | 0.0117 ns | 0.0110 ns |  1.00 |         - |          NA |
| ModMethodModulo | 131071     | 3.111 ns | 0.0138 ns | 0.0129 ns |  1.29 |         - |          NA |
|                 |            |          |           |           |       |           |             |
| LegacyModulo    | 2147483647 | 2.427 ns | 0.0051 ns | 0.0046 ns |  1.00 |         - |          NA |
| ModMethodModulo | 2147483647 | 3.355 ns | 0.0116 ns | 0.0108 ns |  1.38 |         - |          NA |

// * Hints *
Outliers
  ResidueComputationBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (3.74 ns)
  ResidueComputationBenchmarks.ModMethodModulo: Default -> 2 outliers were removed (4.10 ns, 4.14 ns)
  ResidueComputationBenchmarks.LegacyModulo: Default    -> 2 outliers were removed (3.75 ns, 3.78 ns)
  ResidueComputationBenchmarks.ModMethodModulo: Default -> 2 outliers were detected (4.09 ns, 4.10 ns)
  ResidueComputationBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (3.73 ns)










		MersenneDivisorCycleLengthGpuBenchmarks.UnrolledHexImplementation: Job-VMUOXT(Runtime=.NET 8.0, IterationCount=3, LaunchCount=1, WarmupCount=1) [Divisor=8388607]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 4.591 ms, StdErr = 0.001 ms (0.02%), N = 3, StdDev = 0.002 ms
Min = 4.590 ms, Q1 = 4.591 ms, Median = 4.591 ms, Q3 = 4.592 ms, Max = 4.593 ms
IQR = 0.002 ms, LowerFence = 4.588 ms, UpperFence = 4.594 ms
ConfidenceInterval = [4.564 ms; 4.619 ms] (CI 99.9%), Margin = 0.028 ms (0.60% of Mean)
Skewness = 0.06, Kurtosis = 0.67, MValue = 2
-------------------- Histogram --------------------
[4.588 ms ; 4.594 ms) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-VMUOXT : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=3  LaunchCount=1
WarmupCount=1

| Method                       | Divisor | Mean             | Error           | StdDev         | Ratio | RatioSD | Allocated | Alloc Ratio |
|----------------------------- |-------- |-----------------:|----------------:|---------------:|------:|--------:|----------:|------------:|
| CurrentImplementation        | 17      |         6.741 ns |      20.3809 ns |      1.1171 ns |  1.00 |    0.00 |         - |          NA |
| DoWhileImplementation        | 17      |         5.877 ns |       1.2875 ns |      0.0706 ns |  0.89 |    0.14 |         - |          NA |
| DoubleSubtractImplementation | 17      |         6.300 ns |       0.7151 ns |      0.0392 ns |  0.95 |    0.14 |         - |          NA |
| UInt128ModuloImplementation  | 17      |        42.355 ns |       2.8645 ns |      0.1570 ns |  6.39 |    0.97 |         - |          NA |
| UnrolledPairImplementation   | 17      |         6.789 ns |       0.0964 ns |      0.0053 ns |  1.02 |    0.16 |         - |          NA |
| UnrolledQuadImplementation   | 17      |         5.834 ns |       2.6198 ns |      0.1436 ns |  0.88 |    0.13 |         - |          NA |
| UnrolledOctImplementation    | 17      |         5.445 ns |       0.3855 ns |      0.0211 ns |  0.82 |    0.12 |         - |          NA |
| UnrolledHexImplementation    | 17      |         4.833 ns |       0.1499 ns |      0.0082 ns |  0.73 |    0.11 |         - |          NA |
|                              |         |                  |                 |                |       |         |           |             |
| CurrentImplementation        | 31      |         9.469 ns |       0.4837 ns |      0.0265 ns |  1.00 |    0.00 |         - |          NA |
| DoWhileImplementation        | 31      |         9.409 ns |       0.3854 ns |      0.0211 ns |  0.99 |    0.00 |         - |          NA |
| DoubleSubtractImplementation | 31      |         8.476 ns |       0.6979 ns |      0.0383 ns |  0.90 |    0.01 |         - |          NA |
| UInt128ModuloImplementation  | 31      |        45.255 ns |       0.5181 ns |      0.0284 ns |  4.78 |    0.01 |         - |          NA |
| UnrolledPairImplementation   | 31      |         7.372 ns |       0.1373 ns |      0.0075 ns |  0.78 |    0.00 |         - |          NA |
| UnrolledQuadImplementation   | 31      |         5.988 ns |       0.6249 ns |      0.0343 ns |  0.63 |    0.00 |         - |          NA |
| UnrolledOctImplementation    | 31      |         5.779 ns |       1.5591 ns |      0.0855 ns |  0.61 |    0.01 |         - |          NA |
| UnrolledHexImplementation    | 31      |         5.127 ns |       0.3423 ns |      0.0188 ns |  0.54 |    0.00 |         - |          NA |
|                              |         |                  |                 |                |       |         |           |             |
| CurrentImplementation        | 8191    |       684.638 ns |       9.7897 ns |      0.5366 ns |  1.00 |    0.00 |         - |          NA |
| DoWhileImplementation        | 8191    |       681.509 ns |      97.6324 ns |      5.3516 ns |  1.00 |    0.01 |         - |          NA |
| DoubleSubtractImplementation | 8191    |       685.454 ns |     130.5754 ns |      7.1573 ns |  1.00 |    0.01 |         - |          NA |
| UInt128ModuloImplementation  | 8191    |     3,292.450 ns |     165.4176 ns |      9.0671 ns |  4.81 |    0.01 |         - |          NA |
| UnrolledPairImplementation   | 8191    |       640.489 ns |      91.3047 ns |      5.0047 ns |  0.94 |    0.01 |         - |          NA |
| UnrolledQuadImplementation   | 8191    |       610.716 ns |      63.5287 ns |      3.4822 ns |  0.89 |    0.00 |         - |          NA |
| UnrolledOctImplementation    | 8191    |       582.150 ns |     124.1510 ns |      6.8051 ns |  0.85 |    0.01 |         - |          NA |
| UnrolledHexImplementation    | 8191    |       552.836 ns |      30.3518 ns |      1.6637 ns |  0.81 |    0.00 |         - |          NA |
|                              |         |                  |                 |                |       |         |           |             |
| CurrentImplementation        | 131071  |    55,781.576 ns |   3,739.5389 ns |    204.9767 ns |  1.00 |    0.00 |         - |          NA |
| DoWhileImplementation        | 131071  |    55,696.390 ns |   1,069.4099 ns |     58.6180 ns |  1.00 |    0.00 |         - |          NA |
| DoubleSubtractImplementation | 131071  |    56,267.609 ns |   3,211.0457 ns |    176.0083 ns |  1.01 |    0.00 |         - |          NA |
| UInt128ModuloImplementation  | 131071  |    71,508.525 ns |   2,910.0609 ns |    159.5103 ns |  1.28 |    0.00 |         - |          NA |
| UnrolledPairImplementation   | 131071  |    52,647.972 ns |   5,477.0651 ns |    300.2164 ns |  0.94 |    0.00 |         - |          NA |
| UnrolledQuadImplementation   | 131071  |    52,175.284 ns |   4,709.0765 ns |    258.1204 ns |  0.94 |    0.01 |         - |          NA |
| UnrolledOctImplementation    | 131071  |    50,453.831 ns |   9,204.4196 ns |    504.5253 ns |  0.90 |    0.01 |         - |          NA |
| UnrolledHexImplementation    | 131071  |    50,516.549 ns |   1,290.6332 ns |     70.7440 ns |  0.91 |    0.00 |         - |          NA |
|                              |         |                  |                 |                |       |         |           |             |
| CurrentImplementation        | 524287  |   100,190.804 ns |   2,701.2789 ns |    148.0662 ns |  1.00 |    0.00 |         - |          NA |
| DoWhileImplementation        | 524287  |   100,180.701 ns |   2,021.5359 ns |    110.8072 ns |  1.00 |    0.00 |         - |          NA |
| DoubleSubtractImplementation | 524287  |   100,945.190 ns |   8,500.9006 ns |    465.9630 ns |  1.01 |    0.01 |         - |          NA |
| UInt128ModuloImplementation  | 524287  |   132,443.294 ns |   1,489.1490 ns |     81.6253 ns |  1.32 |    0.00 |         - |          NA |
| UnrolledPairImplementation   | 524287  |    95,646.906 ns |   2,659.2089 ns |    145.7602 ns |  0.95 |    0.00 |         - |          NA |
| UnrolledQuadImplementation   | 524287  |    98,377.401 ns |     700.5979 ns |     38.4021 ns |  0.98 |    0.00 |         - |          NA |
| UnrolledOctImplementation    | 524287  |    96,018.392 ns |     634.3117 ns |     34.7688 ns |  0.96 |    0.00 |         - |          NA |
| UnrolledHexImplementation    | 524287  |    94,820.581 ns |   4,302.7771 ns |    235.8497 ns |  0.95 |    0.00 |         - |          NA |
|                              |         |                  |                 |                |       |         |           |             |
| CurrentImplementation        | 2097151 |   572,102.567 ns |  12,462.9791 ns |    683.1379 ns |  1.00 |    0.00 |         - |          NA |
| DoWhileImplementation        | 2097151 |   597,706.585 ns |  12,005.6116 ns |    658.0681 ns |  1.04 |    0.00 |         - |          NA |
| DoubleSubtractImplementation | 2097151 |   579,587.128 ns | 486,254.8709 ns | 26,653.2703 ns |  1.01 |    0.05 |         - |          NA |
| UInt128ModuloImplementation  | 2097151 |   730,129.924 ns |  18,007.6131 ns |    987.0580 ns |  1.28 |    0.00 |       1 B |          NA |
| UnrolledPairImplementation   | 2097151 |   541,683.750 ns |  23,917.6353 ns |  1,311.0063 ns |  0.95 |    0.00 |         - |          NA |
| UnrolledQuadImplementation   | 2097151 |   530,161.597 ns |  10,170.0594 ns |    557.4553 ns |  0.93 |    0.00 |         - |          NA |
| UnrolledOctImplementation    | 2097151 |   541,356.250 ns |   4,299.7940 ns |    235.6862 ns |  0.95 |    0.00 |         - |          NA |
| UnrolledHexImplementation    | 2097151 |   530,835.382 ns |  18,773.6811 ns |  1,029.0488 ns |  0.93 |    0.00 |         - |          NA |
|                              |         |                  |                 |                |       |         |           |             |
| CurrentImplementation        | 8388607 | 4,945,688.281 ns |  80,178.6194 ns |  4,394.8607 ns |  1.00 |    0.00 |       3 B |        1.00 |
| DoWhileImplementation        | 8388607 | 4,950,188.542 ns | 126,375.4630 ns |  6,927.0656 ns |  1.00 |    0.00 |       3 B |        1.00 |
| DoubleSubtractImplementation | 8388607 | 4,915,241.406 ns | 198,944.9215 ns | 10,904.8425 ns |  0.99 |    0.00 |       3 B |        1.00 |
| UInt128ModuloImplementation  | 8388607 | 6,165,180.208 ns | 345,499.7285 ns | 18,938.0060 ns |  1.25 |    0.00 |       6 B |        2.00 |
| UnrolledPairImplementation   | 8388607 | 4,778,103.125 ns |  48,098.6391 ns |  2,636.4487 ns |  0.97 |    0.00 |       3 B |        1.00 |
| UnrolledQuadImplementation   | 8388607 | 4,748,245.052 ns | 221,915.6436 ns | 12,163.9452 ns |  0.96 |    0.00 |       3 B |        1.00 |
| UnrolledOctImplementation    | 8388607 | 4,674,474.219 ns | 171,733.6592 ns |  9,413.3014 ns |  0.95 |    0.00 |       3 B |        1.00 |
| UnrolledHexImplementation    | 8388607 | 4,591,312.500 ns |  27,677.3865 ns |  1,517.0909 ns |  0.93 |    0.00 |       3 B |        1.00 |










Mod8ULongBenchmarks.ExtensionMethod: Job-MSCCQK(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551488]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.011 ns, StdErr = 0.000 ns (3.51%), N = 5, StdDev = 0.001 ns
Min = 0.010 ns, Q1 = 0.011 ns, Median = 0.011 ns, Q3 = 0.012 ns, Max = 0.012 ns
IQR = 0.001 ns, LowerFence = 0.009 ns, UpperFence = 0.013 ns
ConfidenceInterval = [0.008 ns; 0.014 ns] (CI 99.9%), Margin = 0.003 ns (30.26% of Mean)
Skewness = -0.29, Kurtosis = 1.23, MValue = 2
-------------------- Histogram --------------------
[0.009 ns ; 0.010 ns) | @
[0.010 ns ; 0.012 ns) | @@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-MSCCQK : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Median    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 8                    | 0.0224 ns | 0.0199 ns | 0.0031 ns | 0.0234 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8                    | 0.0344 ns | 0.0296 ns | 0.0046 ns | 0.0345 ns |  1.55 |    0.26 |         - |          NA |
|                 |                      |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8191                 | 0.0000 ns | 0.0000 ns | 0.0000 ns | 0.0000 ns |     ? |       ? |         - |           ? |
| ExtensionMethod | 8191                 | 0.0296 ns | 0.0199 ns | 0.0052 ns | 0.0305 ns |     ? |       ? |         - |           ? |
|                 |                      |           |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 0.0069 ns | 0.0102 ns | 0.0026 ns | 0.0072 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.0114 ns | 0.0044 ns | 0.0011 ns | 0.0114 ns |  2.00 |    1.26 |         - |          NA |
|                 |                      |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647           | 0.0117 ns | 0.0041 ns | 0.0011 ns | 0.0111 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.0106 ns | 0.0021 ns | 0.0003 ns | 0.0107 ns |  0.90 |    0.11 |         - |          NA |
|                 |                      |           |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709551488 | 0.1073 ns | 0.4465 ns | 0.1160 ns | 0.0256 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 18446744073709551488 | 0.0109 ns | 0.0033 ns | 0.0009 ns | 0.0107 ns |  0.31 |    0.25 |         - |          NA |

// * Warnings *
BaselineCustomAnalyzer
  Summary -> A question mark '?' symbol indicates that it was not possible to compute the (Ratio, RatioSD, Alloc Ratio) column(s) because the baseline value is too close to zero.
ZeroMeasurement
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.32 ns, 1.35 ns)
  Mod8ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.35 ns)
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.52 ns)
  Mod8ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.29 ns)
  Mod8ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.29 ns, 1.29 ns)










Mod10_8_5_3Benchmarks.ModMethodModulo: DefaultJob [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 2.164 ns, StdErr = 0.002 ns (0.08%), N = 14, StdDev = 0.007 ns
Min = 2.151 ns, Q1 = 2.159 ns, Median = 2.165 ns, Q3 = 2.166 ns, Max = 2.176 ns
IQR = 0.007 ns, LowerFence = 2.149 ns, UpperFence = 2.177 ns
ConfidenceInterval = [2.156 ns; 2.171 ns] (CI 99.9%), Margin = 0.008 ns (0.35% of Mean)
Skewness = -0.26, Kurtosis = 2.21, MValue = 2
-------------------- Histogram --------------------
[2.147 ns ; 2.180 ns) | @@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method          | Value      | Mean     | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |---------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3          | 1.138 ns | 0.0057 ns | 0.0053 ns |  1.00 |    0.00 |         - |          NA |
| LegacyModulo    | 3          | 2.834 ns | 0.0066 ns | 0.0061 ns |  2.49 |    0.01 |         - |          NA |
| ModMethodModulo | 3          | 1.630 ns | 0.0083 ns | 0.0074 ns |  1.43 |    0.01 |         - |          NA |
|                 |            |          |           |           |       |         |           |             |
| ModuloOperator  | 8191       | 1.143 ns | 0.0062 ns | 0.0058 ns |  1.00 |    0.00 |         - |          NA |
| LegacyModulo    | 8191       | 3.038 ns | 0.0090 ns | 0.0084 ns |  2.66 |    0.02 |         - |          NA |
| ModMethodModulo | 8191       | 1.635 ns | 0.0033 ns | 0.0031 ns |  1.43 |    0.01 |         - |          NA |
|                 |            |          |           |           |       |         |           |             |
| ModuloOperator  | 131071     | 1.134 ns | 0.0043 ns | 0.0041 ns |  1.00 |    0.00 |         - |          NA |
| LegacyModulo    | 131071     | 3.067 ns | 0.0347 ns | 0.0289 ns |  2.70 |    0.03 |         - |          NA |
| ModMethodModulo | 131071     | 1.875 ns | 0.0055 ns | 0.0049 ns |  1.65 |    0.01 |         - |          NA |
|                 |            |          |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 1.141 ns | 0.0044 ns | 0.0042 ns |  1.00 |    0.00 |         - |          NA |
| LegacyModulo    | 2147483647 | 3.039 ns | 0.0100 ns | 0.0094 ns |  2.66 |    0.01 |         - |          NA |
| ModMethodModulo | 2147483647 | 2.164 ns | 0.0076 ns | 0.0067 ns |  1.90 |    0.01 |         - |          NA |

// * Hints *
Outliers
  Mod10_8_5_3Benchmarks.ModMethodModulo: Default -> 1 outlier  was  removed (2.93 ns)
  Mod10_8_5_3Benchmarks.LegacyModulo: Default    -> 1 outlier  was  detected (4.30 ns)
  Mod10_8_5_3Benchmarks.ModuloOperator: Default  -> 1 outlier  was  detected (2.41 ns)
  Mod10_8_5_3Benchmarks.LegacyModulo: Default    -> 2 outliers were removed (4.46 ns, 4.57 ns)
  Mod10_8_5_3Benchmarks.ModMethodModulo: Default -> 1 outlier  was  removed (3.17 ns)
  Mod10_8_5_3Benchmarks.LegacyModulo: Default    -> 1 outlier  was  detected (4.29 ns)
  Mod10_8_5_3Benchmarks.ModMethodModulo: Default -> 1 outlier  was  removed (3.48 ns)










Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: DefaultJob [Value=18446744073709551598]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 4.289 ns, StdErr = 0.002 ns (0.05%), N = 15, StdDev = 0.008 ns
Min = 4.279 ns, Q1 = 4.282 ns, Median = 4.286 ns, Q3 = 4.296 ns, Max = 4.305 ns
IQR = 0.013 ns, LowerFence = 4.263 ns, UpperFence = 4.315 ns
ConfidenceInterval = [4.281 ns; 4.298 ns] (CI 99.9%), Margin = 0.009 ns (0.20% of Mean)
Skewness = 0.42, Kurtosis = 1.76, MValue = 2
-------------------- Histogram --------------------
[4.275 ns ; 4.310 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method          | Value                | Mean     | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |---------:|----------:|----------:|------:|--------:|----------:|------------:|
| LegacyModulo    | 3                    | 2.413 ns | 0.0132 ns | 0.0123 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 3                    | 2.790 ns | 0.0058 ns | 0.0049 ns |  1.16 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 6                    | 2.378 ns | 0.0156 ns | 0.0146 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 6                    | 3.135 ns | 0.0503 ns | 0.0471 ns |  1.32 |    0.02 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 128                  | 2.358 ns | 0.0047 ns | 0.0040 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 128                  | 2.775 ns | 0.0174 ns | 0.0163 ns |  1.18 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 256                  | 2.363 ns | 0.0051 ns | 0.0048 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 256                  | 3.005 ns | 0.0059 ns | 0.0049 ns |  1.27 |    0.00 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 2047                 | 2.370 ns | 0.0104 ns | 0.0092 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 2047                 | 3.033 ns | 0.0078 ns | 0.0069 ns |  1.28 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 8191                 | 2.361 ns | 0.0048 ns | 0.0045 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 8191                 | 3.070 ns | 0.0113 ns | 0.0101 ns |  1.30 |    0.00 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 65535                | 2.400 ns | 0.0142 ns | 0.0133 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 65535                | 3.032 ns | 0.0141 ns | 0.0132 ns |  1.26 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 131071               | 2.355 ns | 0.0056 ns | 0.0044 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 131071               | 3.206 ns | 0.0096 ns | 0.0089 ns |  1.36 |    0.00 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 2147483647           | 2.458 ns | 0.0105 ns | 0.0093 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 2147483647           | 3.441 ns | 0.0357 ns | 0.0334 ns |  1.40 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709550591 | 2.371 ns | 0.0037 ns | 0.0029 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709550591 | 4.247 ns | 0.0159 ns | 0.0149 ns |  1.79 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709551104 | 2.368 ns | 0.0093 ns | 0.0087 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709551104 | 3.716 ns | 0.0137 ns | 0.0128 ns |  1.57 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709551360 | 2.367 ns | 0.0030 ns | 0.0027 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709551360 | 4.264 ns | 0.0074 ns | 0.0069 ns |  1.80 |    0.00 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709551488 | 2.374 ns | 0.0027 ns | 0.0024 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709551488 | 4.344 ns | 0.0135 ns | 0.0119 ns |  1.83 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709551552 | 2.368 ns | 0.0043 ns | 0.0038 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709551552 | 4.272 ns | 0.0128 ns | 0.0113 ns |  1.80 |    0.01 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709551584 | 2.366 ns | 0.0035 ns | 0.0031 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709551584 | 3.717 ns | 0.0064 ns | 0.0057 ns |  1.57 |    0.00 |         - |          NA |
|                 |                      |          |           |           |       |         |           |             |
| LegacyModulo    | 18446744073709551598 | 2.412 ns | 0.0202 ns | 0.0179 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 18446744073709551598 | 4.289 ns | 0.0086 ns | 0.0080 ns |  1.78 |    0.01 |         - |          NA |

// * Hints *
Outliers
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 2 outliers were removed, 3 outliers were detected (4.06 ns, 4.09 ns, 4.10 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 2 outliers were detected (4.32 ns, 4.35 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 2 outliers were removed, 3 outliers were detected (3.62 ns, 3.64 ns, 3.65 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 2 outliers were removed, 3 outliers were detected (4.28 ns, 4.31 ns, 4.35 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (3.69 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 1 outlier  was  removed, 4 outliers were detected (4.31 ns..4.31 ns, 4.34 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 1 outlier  was  removed, 2 outliers were detected (4.33 ns, 4.39 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 3 outliers were removed, 5 outliers were detected (3.62 ns, 3.63 ns, 3.64 ns..3.64 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (3.80 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 3 outliers were removed (3.71 ns..3.73 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 1 outlier  was  detected (4.98 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed, 2 outliers were detected (3.64 ns, 3.65 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (3.66 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 1 outlier  was  removed, 2 outliers were detected (5.60 ns, 5.65 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed, 2 outliers were detected (3.63 ns, 3.65 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 1 outlier  was  removed (5.74 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed, 2 outliers were detected (3.64 ns, 3.66 ns)
  Mod10_8_5_3PropertiesBenchmarks.ModMethodModulo: Default -> 1 outlier  was  removed (5.04 ns)
  Mod10_8_5_3PropertiesBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (3.74 ns)











Mod10_8_5_3StepsBenchmarks.ModMethodModulo: DefaultJob [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 3.649 ns, StdErr = 0.006 ns (0.18%), N = 15, StdDev = 0.025 ns
Min = 3.614 ns, Q1 = 3.633 ns, Median = 3.643 ns, Q3 = 3.662 ns, Max = 3.697 ns
IQR = 0.028 ns, LowerFence = 3.591 ns, UpperFence = 3.705 ns
ConfidenceInterval = [3.623 ns; 3.675 ns] (CI 99.9%), Margin = 0.026 ns (0.73% of Mean)
Skewness = 0.58, Kurtosis = 2.35, MValue = 2
-------------------- Histogram --------------------
[3.607 ns ; 3.711 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method          | Value      | Mean      | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|----------:|------------:|
| LegacyModulo    | 3          | 12.052 ns | 0.0425 ns | 0.0332 ns |  1.00 |         - |          NA |
| ModMethodModulo | 3          |  3.576 ns | 0.0900 ns | 0.0842 ns |  0.30 |         - |          NA |
|                 |            |           |           |           |       |           |             |
| LegacyModulo    | 8191       | 11.891 ns | 0.0333 ns | 0.0295 ns |  1.00 |         - |          NA |
| ModMethodModulo | 8191       |  3.682 ns | 0.0963 ns | 0.1031 ns |  0.31 |         - |          NA |
|                 |            |           |           |           |       |           |             |
| LegacyModulo    | 131071     | 13.401 ns | 0.1983 ns | 0.1854 ns |  1.00 |         - |          NA |
| ModMethodModulo | 131071     |  3.773 ns | 0.0437 ns | 0.0409 ns |  0.28 |         - |          NA |
|                 |            |           |           |           |       |           |             |
| LegacyModulo    | 2147483647 | 12.114 ns | 0.0669 ns | 0.0593 ns |  1.00 |         - |          NA |
| ModMethodModulo | 2147483647 |  3.649 ns | 0.0265 ns | 0.0248 ns |  0.30 |         - |          NA |

// * Hints *
Outliers
  Mod10_8_5_3StepsBenchmarks.LegacyModulo: Default    -> 3 outliers were removed (13.57 ns..13.83 ns)
  Mod10_8_5_3StepsBenchmarks.ModMethodModulo: Default -> 1 outlier  was  detected (4.67 ns)
  Mod10_8_5_3StepsBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (13.30 ns)
  Mod10_8_5_3StepsBenchmarks.ModMethodModulo: Default -> 3 outliers were detected (4.68 ns..4.80 ns)
  Mod10_8_5_3StepsBenchmarks.LegacyModulo: Default    -> 3 outliers were detected (14.17 ns..14.51 ns)
  Mod10_8_5_3StepsBenchmarks.LegacyModulo: Default    -> 1 outlier  was  removed (13.86 ns)










Mod10UInt128Benchmarks.ModWithLoopModulo: DefaultJob [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 2.216 ns, StdErr = 0.002 ns (0.09%), N = 15, StdDev = 0.008 ns
Min = 2.202 ns, Q1 = 2.211 ns, Median = 2.216 ns, Q3 = 2.220 ns, Max = 2.232 ns
IQR = 0.009 ns, LowerFence = 2.197 ns, UpperFence = 2.234 ns
ConfidenceInterval = [2.208 ns; 2.225 ns] (CI 99.9%), Margin = 0.009 ns (0.39% of Mean)
Skewness = 0.34, Kurtosis = 2.34, MValue = 2
-------------------- Histogram --------------------
[2.198 ns ; 2.236 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method               | Value      | Mean     | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|--------------------- |----------- |---------:|----------:|----------:|------:|----------:|------------:|
| StandardModulo       | 3          | 3.378 ns | 0.0137 ns | 0.0128 ns |  1.00 |         - |          NA |
| ModWithHighLowModulo | 3          | 1.804 ns | 0.0072 ns | 0.0067 ns |  0.53 |         - |          NA |
| ModWithLoopModulo    | 3          | 2.204 ns | 0.0105 ns | 0.0098 ns |  0.65 |         - |          NA |
|                      |            |          |           |           |       |           |             |
| StandardModulo       | 8191       | 3.269 ns | 0.0064 ns | 0.0057 ns |  1.00 |         - |          NA |
| ModWithHighLowModulo | 8191       | 1.798 ns | 0.0084 ns | 0.0078 ns |  0.55 |         - |          NA |
| ModWithLoopModulo    | 8191       | 2.234 ns | 0.0090 ns | 0.0080 ns |  0.68 |         - |          NA |
|                      |            |          |           |           |       |           |             |
| StandardModulo       | 131071     | 3.248 ns | 0.0118 ns | 0.0104 ns |  1.00 |         - |          NA |
| ModWithHighLowModulo | 131071     | 1.817 ns | 0.0056 ns | 0.0052 ns |  0.56 |         - |          NA |
| ModWithLoopModulo    | 131071     | 2.268 ns | 0.0118 ns | 0.0110 ns |  0.70 |         - |          NA |
|                      |            |          |           |           |       |           |             |
| StandardModulo       | 2147483647 | 3.281 ns | 0.0085 ns | 0.0080 ns |  1.00 |         - |          NA |
| ModWithHighLowModulo | 2147483647 | 1.779 ns | 0.0061 ns | 0.0057 ns |  0.54 |         - |          NA |
| ModWithLoopModulo    | 2147483647 | 2.216 ns | 0.0087 ns | 0.0081 ns |  0.68 |         - |          NA |

// * Hints *
Outliers
  Mod10UInt128Benchmarks.StandardModulo: Default       -> 1 outlier  was  removed, 2 outliers were detected (4.56 ns, 4.58 ns)
  Mod10UInt128Benchmarks.ModWithLoopModulo: Default    -> 1 outlier  was  removed, 2 outliers were detected (3.49 ns, 3.53 ns)
  Mod10UInt128Benchmarks.StandardModulo: Default       -> 1 outlier  was  removed (4.63 ns)
  Mod10UInt128Benchmarks.ModWithHighLowModulo: Default -> 1 outlier  was  detected (3.08 ns)










Mod10UIntBenchmarks.ExtensionMethod: Job-MVZCXR(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.037 ns, StdErr = 0.000 ns (1.31%), N = 4, StdDev = 0.001 ns
Min = 0.036 ns, Q1 = 0.037 ns, Median = 0.038 ns, Q3 = 0.038 ns, Max = 0.038 ns
IQR = 0.001 ns, LowerFence = 0.036 ns, UpperFence = 0.039 ns
ConfidenceInterval = [0.031 ns; 0.044 ns] (CI 99.9%), Margin = 0.006 ns (16.98% of Mean)
Skewness = -0.69, Kurtosis = 1.27, MValue = 2
-------------------- Histogram --------------------
[0.035 ns ; 0.037 ns) | @
[0.037 ns ; 0.039 ns) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-MVZCXR : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Median    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 10         | 0.0407 ns | 0.0148 ns | 0.0038 ns | 0.0405 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 10         | 0.7727 ns | 2.5823 ns | 0.6706 ns | 1.2387 ns | 19.59 |   17.15 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.3224 ns | 0.0016 ns | 0.0004 ns | 0.3227 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.0448 ns | 0.0038 ns | 0.0010 ns | 0.0451 ns |  0.14 |    0.00 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.2382 ns | 0.4473 ns | 0.1162 ns | 0.2598 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.0405 ns | 0.0112 ns | 0.0017 ns | 0.0408 ns |  0.14 |    0.02 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0555 ns | 0.0558 ns | 0.0145 ns | 0.0615 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.0372 ns | 0.0063 ns | 0.0010 ns | 0.0377 ns |  0.76 |    0.23 |         - |          NA |

// * Hints *
Outliers
  Mod10UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.30 ns)
  Mod10UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.31 ns)
  Mod10UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.30 ns, 1.31 ns)










Mod10ULongBenchmarks.ModMethodModulo: DefaultJob [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.741 ns, StdErr = 0.000 ns (0.07%), N = 14, StdDev = 0.002 ns
Min = 0.738 ns, Q1 = 0.739 ns, Median = 0.741 ns, Q3 = 0.742 ns, Max = 0.745 ns
IQR = 0.003 ns, LowerFence = 0.735 ns, UpperFence = 0.746 ns
ConfidenceInterval = [0.739 ns; 0.743 ns] (CI 99.9%), Margin = 0.002 ns (0.28% of Mean)
Skewness = 0.17, Kurtosis = 2.03, MValue = 2
-------------------- Histogram --------------------
[0.737 ns ; 0.746 ns) | @@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method          | Value      | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| LegacyModulo    | 3          | 0.2591 ns | 0.0053 ns | 0.0050 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 3          | 0.7503 ns | 0.0274 ns | 0.0257 ns |  2.90 |    0.14 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| LegacyModulo    | 8191       | 0.2597 ns | 0.0061 ns | 0.0057 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 8191       | 0.7320 ns | 0.0042 ns | 0.0039 ns |  2.82 |    0.06 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| LegacyModulo    | 131071     | 0.2605 ns | 0.0060 ns | 0.0047 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 131071     | 0.7346 ns | 0.0063 ns | 0.0053 ns |  2.82 |    0.05 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| LegacyModulo    | 2147483647 | 0.2598 ns | 0.0022 ns | 0.0019 ns |  1.00 |    0.00 |         - |          NA |
| ModMethodModulo | 2147483647 | 0.7411 ns | 0.0021 ns | 0.0019 ns |  2.85 |    0.02 |         - |          NA |

// * Hints *
Outliers
  Mod10ULongBenchmarks.ModMethodModulo: Default -> 1 outlier  was  detected (1.99 ns)
  Mod10ULongBenchmarks.LegacyModulo: Default    -> 3 outliers were removed (1.60 ns..1.70 ns)
  Mod10ULongBenchmarks.ModMethodModulo: Default -> 2 outliers were removed (2.01 ns, 2.02 ns)
  Mod10ULongBenchmarks.LegacyModulo: Default    -> 2 outliers were removed (1.53 ns, 1.53 ns)
  Mod10ULongBenchmarks.ModMethodModulo: Default -> 1 outlier  was  removed (2.03 ns)










Mod11_7_5_3Benchmarks.CombinedMethod: DefaultJob [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 8.968 ns, StdErr = 0.013 ns (0.15%), N = 15, StdDev = 0.051 ns
Min = 8.881 ns, Q1 = 8.936 ns, Median = 8.958 ns, Q3 = 9.006 ns, Max = 9.052 ns
IQR = 0.070 ns, LowerFence = 8.832 ns, UpperFence = 9.110 ns
ConfidenceInterval = [8.914 ns; 9.022 ns] (CI 99.9%), Margin = 0.054 ns (0.60% of Mean)
Skewness = 0.14, Kurtosis = 1.81, MValue = 2
-------------------- Histogram --------------------
[8.854 ns ; 9.079 ns) | @@@@@@@@@@@@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  DefaultJob : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2


| Method         | Value      | Mean     | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|--------------- |----------- |---------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator | 3          | 1.611 ns | 0.0100 ns | 0.0089 ns |  1.00 |    0.00 |         - |          NA |
| CombinedMethod | 3          | 2.095 ns | 0.0079 ns | 0.0074 ns |  1.30 |    0.01 |         - |          NA |
|                |            |          |           |           |       |         |           |             |
| ModuloOperator | 8191       | 1.563 ns | 0.0030 ns | 0.0026 ns |  1.00 |    0.00 |         - |          NA |
| CombinedMethod | 8191       | 4.926 ns | 0.0089 ns | 0.0083 ns |  3.15 |    0.01 |         - |          NA |
|                |            |          |           |           |       |         |           |             |
| ModuloOperator | 131071     | 1.561 ns | 0.0039 ns | 0.0034 ns |  1.00 |    0.00 |         - |          NA |
| CombinedMethod | 131071     | 7.098 ns | 0.0493 ns | 0.0437 ns |  4.55 |    0.03 |         - |          NA |
|                |            |          |           |           |       |         |           |             |
| ModuloOperator | 2147483647 | 1.572 ns | 0.0088 ns | 0.0082 ns |  1.00 |    0.00 |         - |          NA |
| CombinedMethod | 2147483647 | 8.968 ns | 0.0542 ns | 0.0507 ns |  5.70 |    0.04 |         - |          NA |

// * Hints *
Outliers
  Mod11_7_5_3Benchmarks.ModuloOperator: Default -> 1 outlier  was  removed (2.94 ns)
  Mod11_7_5_3Benchmarks.ModuloOperator: Default -> 1 outlier  was  removed, 2 outliers were detected (2.82 ns, 2.97 ns)
  Mod11_7_5_3Benchmarks.ModuloOperator: Default -> 1 outlier  was  removed (2.84 ns)
  Mod11_7_5_3Benchmarks.CombinedMethod: Default -> 1 outlier  was  removed (8.86 ns)










Mod11UInt128Benchmarks.ExtensionMethod: Job-KKLXVZ(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551360]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.666 ns, StdErr = 0.001 ns (0.16%), N = 5, StdDev = 0.002 ns
Min = 0.662 ns, Q1 = 0.666 ns, Median = 0.666 ns, Q3 = 0.668 ns, Max = 0.668 ns
IQR = 0.002 ns, LowerFence = 0.663 ns, UpperFence = 0.671 ns
ConfidenceInterval = [0.657 ns; 0.675 ns] (CI 99.9%), Margin = 0.009 ns (1.38% of Mean)
Skewness = -0.64, Kurtosis = 1.59, MValue = 2
-------------------- Histogram --------------------
[0.660 ns ; 0.670 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-KKLXVZ : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 11                   | 2.8719 ns | 0.0334 ns | 0.0052 ns |  1.00 |         - |          NA |
| ExtensionMethod | 11                   | 0.6721 ns | 0.0522 ns | 0.0081 ns |  0.23 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 8191                 | 2.8715 ns | 0.0116 ns | 0.0030 ns |  1.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.6765 ns | 0.0322 ns | 0.0084 ns |  0.24 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.8534 ns | 0.0410 ns | 0.0064 ns |  1.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.6760 ns | 0.0252 ns | 0.0066 ns |  0.24 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.8716 ns | 0.0578 ns | 0.0150 ns |  1.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.6614 ns | 0.0245 ns | 0.0064 ns |  0.23 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 18446744073709551360 | 2.8715 ns | 0.0104 ns | 0.0016 ns |  1.00 |         - |          NA |
| ExtensionMethod | 18446744073709551360 | 0.6661 ns | 0.0092 ns | 0.0024 ns |  0.23 |         - |          NA |

// * Hints *
Outliers
  Mod11UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (4.14 ns, 4.16 ns)
  Mod11UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.94 ns, 1.96 ns)
  Mod11UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (4.12 ns, 4.14 ns)
  Mod11UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (4.16 ns)
  Mod11UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.92 ns)










Mod11UIntBenchmarks.ExtensionMethod: Job-WJRSHE(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 3.170 ns, StdErr = 0.001 ns (0.02%), N = 5, StdDev = 0.001 ns
Min = 3.168 ns, Q1 = 3.169 ns, Median = 3.170 ns, Q3 = 3.170 ns, Max = 3.171 ns
IQR = 0.002 ns, LowerFence = 3.166 ns, UpperFence = 3.173 ns
ConfidenceInterval = [3.165 ns; 3.174 ns] (CI 99.9%), Margin = 0.005 ns (0.15% of Mean)
Skewness = -0.02, Kurtosis = 1.06, MValue = 2
-------------------- Histogram --------------------
[3.167 ns ; 3.172 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-WJRSHE : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 11         | 0.0299 ns | 0.0035 ns | 0.0009 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11         | 0.2862 ns | 0.0248 ns | 0.0064 ns |  9.60 |    0.49 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0333 ns | 0.0119 ns | 0.0018 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.9571 ns | 0.0370 ns | 0.0096 ns | 28.88 |    1.46 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0393 ns | 0.0054 ns | 0.0014 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.9218 ns | 0.0444 ns | 0.0069 ns | 23.21 |    0.79 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0367 ns | 0.0027 ns | 0.0004 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 3.1696 ns | 0.0047 ns | 0.0012 ns | 86.34 |    1.03 |         - |          NA |

// * Hints *
Outliers
  Mod11UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.30 ns)
  Mod11UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (2.17 ns, 2.19 ns)
  Mod11UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.29 ns, 1.30 ns)










Mod11UIntBenchmarks.ExtensionMethod: Job-WJRSHE(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 3.170 ns, StdErr = 0.001 ns (0.02%), N = 5, StdDev = 0.001 ns
Min = 3.168 ns, Q1 = 3.169 ns, Median = 3.170 ns, Q3 = 3.170 ns, Max = 3.171 ns
IQR = 0.002 ns, LowerFence = 3.166 ns, UpperFence = 3.173 ns
ConfidenceInterval = [3.165 ns; 3.174 ns] (CI 99.9%), Margin = 0.005 ns (0.15% of Mean)
Skewness = -0.02, Kurtosis = 1.06, MValue = 2
-------------------- Histogram --------------------
[3.167 ns ; 3.172 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-WJRSHE : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 11         | 0.0299 ns | 0.0035 ns | 0.0009 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11         | 0.2862 ns | 0.0248 ns | 0.0064 ns |  9.60 |    0.49 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0333 ns | 0.0119 ns | 0.0018 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.9571 ns | 0.0370 ns | 0.0096 ns | 28.88 |    1.46 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0393 ns | 0.0054 ns | 0.0014 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.9218 ns | 0.0444 ns | 0.0069 ns | 23.21 |    0.79 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0367 ns | 0.0027 ns | 0.0004 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 3.1696 ns | 0.0047 ns | 0.0012 ns | 86.34 |    1.03 |         - |          NA |

// * Hints *
Outliers
  Mod11UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.30 ns)
  Mod11UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (2.17 ns, 2.19 ns)
  Mod11UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.29 ns, 1.30 ns)










Mod11UIntBenchmarks.ExtensionMethod: Job-WJRSHE(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 3.170 ns, StdErr = 0.001 ns (0.02%), N = 5, StdDev = 0.001 ns
Min = 3.168 ns, Q1 = 3.169 ns, Median = 3.170 ns, Q3 = 3.170 ns, Max = 3.171 ns
IQR = 0.002 ns, LowerFence = 3.166 ns, UpperFence = 3.173 ns
ConfidenceInterval = [3.165 ns; 3.174 ns] (CI 99.9%), Margin = 0.005 ns (0.15% of Mean)
Skewness = -0.02, Kurtosis = 1.06, MValue = 2
-------------------- Histogram --------------------
[3.167 ns ; 3.172 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-WJRSHE : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 11         | 0.0299 ns | 0.0035 ns | 0.0009 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11         | 0.2862 ns | 0.0248 ns | 0.0064 ns |  9.60 |    0.49 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0333 ns | 0.0119 ns | 0.0018 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.9571 ns | 0.0370 ns | 0.0096 ns | 28.88 |    1.46 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0393 ns | 0.0054 ns | 0.0014 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.9218 ns | 0.0444 ns | 0.0069 ns | 23.21 |    0.79 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0367 ns | 0.0027 ns | 0.0004 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 3.1696 ns | 0.0047 ns | 0.0012 ns | 86.34 |    1.03 |         - |          NA |

// * Hints *
Outliers
  Mod11UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.30 ns)
  Mod11UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (2.17 ns, 2.19 ns)
  Mod11UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.29 ns, 1.30 ns)










Mod128UIntBenchmarks.ExtensionMethod: Job-YWWRGO(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=4294967295]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.016 ns, StdErr = 0.002 ns (10.50%), N = 5, StdDev = 0.004 ns
Min = 0.012 ns, Q1 = 0.012 ns, Median = 0.015 ns, Q3 = 0.017 ns, Max = 0.021 ns
IQR = 0.004 ns, LowerFence = 0.006 ns, UpperFence = 0.024 ns
ConfidenceInterval = [0.002 ns; 0.030 ns] (CI 99.9%), Margin = 0.014 ns (90.38% of Mean)
Skewness = 0.44, Kurtosis = 1.31, MValue = 2
-------------------- Histogram --------------------
[0.012 ns ; 0.018 ns) | @@@@
[0.018 ns ; 0.024 ns) | @
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-YWWRGO : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Median    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3          | 0.0191 ns | 0.0229 ns | 0.0035 ns | 0.0201 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 3          | 0.0163 ns | 0.0075 ns | 0.0020 ns | 0.0172 ns |  0.85 |    0.16 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 5          | 0.0136 ns | 0.0195 ns | 0.0051 ns | 0.0125 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 5          | 0.0123 ns | 0.0102 ns | 0.0016 ns | 0.0129 ns |  0.86 |    0.28 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 6          | 0.0122 ns | 0.0221 ns | 0.0034 ns | 0.0123 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 6          | 0.0064 ns | 0.0088 ns | 0.0023 ns | 0.0065 ns |  0.52 |    0.18 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8          | 0.0140 ns | 0.0077 ns | 0.0012 ns | 0.0141 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8          | 0.0130 ns | 0.0221 ns | 0.0057 ns | 0.0112 ns |  0.99 |    0.41 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 10         | 0.0181 ns | 0.0066 ns | 0.0010 ns | 0.0184 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 10         | 0.0152 ns | 0.0029 ns | 0.0008 ns | 0.0157 ns |  0.84 |    0.08 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 11         | 0.0179 ns | 0.0100 ns | 0.0026 ns | 0.0183 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11         | 0.0111 ns | 0.0132 ns | 0.0034 ns | 0.0128 ns |  0.65 |    0.26 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 32         | 0.0170 ns | 0.0091 ns | 0.0024 ns | 0.0172 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 32         | 0.0180 ns | 0.0095 ns | 0.0025 ns | 0.0191 ns |  1.06 |    0.06 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 64         | 0.0145 ns | 0.0039 ns | 0.0010 ns | 0.0144 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 64         | 0.9496 ns | 0.0173 ns | 0.0027 ns | 0.9506 ns | 67.21 |    3.57 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 128        | 0.0125 ns | 0.0069 ns | 0.0011 ns | 0.0128 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 128        | 0.0228 ns | 0.0910 ns | 0.0141 ns | 0.0167 ns |  1.84 |    1.12 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 256        | 0.0108 ns | 0.0050 ns | 0.0008 ns | 0.0105 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 256        | 0.1192 ns | 0.0209 ns | 0.0054 ns | 0.1166 ns | 11.22 |    1.07 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0127 ns | 0.0043 ns | 0.0011 ns | 0.0128 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.0002 ns | 0.0013 ns | 0.0002 ns | 0.0002 ns |  0.02 |    0.01 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8191       | 0.0135 ns | 0.0081 ns | 0.0013 ns | 0.0138 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191       | 0.1209 ns | 0.0127 ns | 0.0033 ns | 0.1219 ns |  9.00 |    1.06 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0148 ns | 0.0116 ns | 0.0030 ns | 0.0145 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.0140 ns | 0.0072 ns | 0.0019 ns | 0.0136 ns |  0.97 |    0.20 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 131071     | 0.0104 ns | 0.0136 ns | 0.0035 ns | 0.0118 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071     | 0.0153 ns | 0.0064 ns | 0.0017 ns | 0.0155 ns |  1.64 |    0.66 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0138 ns | 0.0112 ns | 0.0029 ns | 0.0130 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.0200 ns | 0.0138 ns | 0.0036 ns | 0.0189 ns |  1.52 |    0.47 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294966271 | 0.0135 ns | 0.0054 ns | 0.0008 ns | 0.0132 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294966271 | 0.0141 ns | 0.0090 ns | 0.0023 ns | 0.0145 ns |  1.04 |    0.21 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294966784 | 0.0257 ns | 0.0317 ns | 0.0082 ns | 0.0230 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294966784 | 0.0129 ns | 0.0094 ns | 0.0015 ns | 0.0132 ns |  0.58 |    0.14 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967040 | 0.0180 ns | 0.0219 ns | 0.0057 ns | 0.0147 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967040 | 0.0060 ns | 0.0178 ns | 0.0046 ns | 0.0044 ns |  0.35 |    0.26 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967168 | 0.0096 ns | 0.0105 ns | 0.0027 ns | 0.0105 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967168 | 0.1193 ns | 0.0437 ns | 0.0114 ns | 0.1171 ns | 14.13 |    7.74 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967232 | 0.0116 ns | 0.0077 ns | 0.0020 ns | 0.0113 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967232 | 0.0153 ns | 0.0110 ns | 0.0017 ns | 0.0146 ns |  1.30 |    0.27 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967264 | 0.0124 ns | 0.0007 ns | 0.0001 ns | 0.0124 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967264 | 0.0090 ns | 0.0037 ns | 0.0010 ns | 0.0090 ns |  0.72 |    0.08 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967278 | 0.0105 ns | 0.0135 ns | 0.0035 ns | 0.0091 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967278 | 0.0131 ns | 0.0093 ns | 0.0024 ns | 0.0139 ns |  1.39 |    0.56 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967295 | 0.0170 ns | 0.0110 ns | 0.0029 ns | 0.0155 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967295 | 0.0156 ns | 0.0141 ns | 0.0037 ns | 0.0151 ns |  0.95 |    0.32 |         - |          NA |

// * Warnings *
ZeroMeasurement
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.31 ns)
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.28 ns, 1.29 ns)
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.32 ns)
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.29 ns)
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.28 ns, 1.28 ns)
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.27 ns)
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (2.22 ns, 2.23 ns)
  Mod128UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.36 ns)
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.30 ns)
  Mod128UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.28 ns)










Mod128ULongBenchmarks.ExtensionMethod: Job-EFEXGV(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=4294967295]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.012 ns, StdErr = 0.001 ns (11.66%), N = 5, StdDev = 0.003 ns
Min = 0.009 ns, Q1 = 0.009 ns, Median = 0.012 ns, Q3 = 0.014 ns, Max = 0.017 ns
IQR = 0.004 ns, LowerFence = 0.003 ns, UpperFence = 0.020 ns
ConfidenceInterval = [-0.000 ns; 0.024 ns] (CI 99.9%), Margin = 0.012 ns (100.42% of Mean)
Skewness = 0.24, Kurtosis = 1.13, MValue = 2
-------------------- Histogram --------------------
[0.009 ns ; 0.014 ns) | @@@@
[0.014 ns ; 0.019 ns) | @
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-EFEXGV : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Median    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3          | 0.0227 ns | 0.0167 ns | 0.0043 ns | 0.0226 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 3          | 0.0113 ns | 0.0150 ns | 0.0039 ns | 0.0092 ns |  0.51 |    0.20 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 5          | 0.0124 ns | 0.0235 ns | 0.0061 ns | 0.0148 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 5          | 0.0149 ns | 0.0145 ns | 0.0038 ns | 0.0124 ns |  1.47 |    0.73 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 6          | 0.0087 ns | 0.0058 ns | 0.0015 ns | 0.0088 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 6          | 0.0152 ns | 0.0104 ns | 0.0027 ns | 0.0150 ns |  1.78 |    0.43 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8          | 0.0101 ns | 0.0135 ns | 0.0035 ns | 0.0103 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8          | 0.0110 ns | 0.0076 ns | 0.0020 ns | 0.0114 ns |  1.25 |    0.58 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 10         | 0.0146 ns | 0.0161 ns | 0.0042 ns | 0.0173 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 10         | 0.0152 ns | 0.0169 ns | 0.0044 ns | 0.0161 ns |  1.12 |    0.53 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 11         | 0.0141 ns | 0.0141 ns | 0.0037 ns | 0.0133 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11         | 0.0100 ns | 0.0080 ns | 0.0021 ns | 0.0106 ns |  0.74 |    0.21 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 32         | 0.0090 ns | 0.0118 ns | 0.0018 ns | 0.0095 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 32         | 0.0128 ns | 0.0067 ns | 0.0017 ns | 0.0135 ns |  1.43 |    0.25 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 64         | 0.0184 ns | 0.0120 ns | 0.0031 ns | 0.0175 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 64         | 0.0094 ns | 0.0056 ns | 0.0015 ns | 0.0087 ns |  0.51 |    0.07 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 128        | 0.0141 ns | 0.0094 ns | 0.0024 ns | 0.0127 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 128        | 0.0105 ns | 0.0237 ns | 0.0062 ns | 0.0089 ns |  0.80 |    0.53 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 256        | 0.0096 ns | 0.0091 ns | 0.0014 ns | 0.0101 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 256        | 0.0106 ns | 0.0141 ns | 0.0037 ns | 0.0124 ns |  1.04 |    0.33 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0251 ns | 0.0332 ns | 0.0086 ns | 0.0201 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.0080 ns | 0.0091 ns | 0.0024 ns | 0.0090 ns |  0.33 |    0.08 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8191       | 0.0120 ns | 0.0116 ns | 0.0030 ns | 0.0113 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191       | 0.0099 ns | 0.0084 ns | 0.0022 ns | 0.0096 ns |  0.85 |    0.20 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0113 ns | 0.0071 ns | 0.0011 ns | 0.0112 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.0101 ns | 0.0084 ns | 0.0022 ns | 0.0100 ns |  0.90 |    0.27 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 131071     | 0.0137 ns | 0.0129 ns | 0.0033 ns | 0.0115 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071     | 0.0068 ns | 0.0059 ns | 0.0009 ns | 0.0069 ns |  0.51 |    0.19 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0190 ns | 0.0447 ns | 0.0116 ns | 0.0160 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.0109 ns | 0.0118 ns | 0.0031 ns | 0.0114 ns |  0.78 |    0.55 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294966271 | 0.0165 ns | 0.0185 ns | 0.0048 ns | 0.0186 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294966271 | 0.0119 ns | 0.0065 ns | 0.0017 ns | 0.0115 ns |  0.82 |    0.42 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294966784 | 0.0089 ns | 0.0090 ns | 0.0014 ns | 0.0095 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294966784 | 0.5901 ns | 2.0424 ns | 0.5304 ns | 0.9747 ns | 51.92 |   58.78 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967040 | 0.0110 ns | 0.0136 ns | 0.0021 ns | 0.0115 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967040 | 0.0118 ns | 0.0066 ns | 0.0017 ns | 0.0124 ns |  1.09 |    0.32 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967168 | 0.0108 ns | 0.0111 ns | 0.0029 ns | 0.0113 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967168 | 0.0062 ns | 0.0092 ns | 0.0024 ns | 0.0062 ns |  0.57 |    0.16 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967232 | 0.0174 ns | 0.0088 ns | 0.0023 ns | 0.0161 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967232 | 0.0094 ns | 0.0045 ns | 0.0007 ns | 0.0096 ns |  0.54 |    0.10 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967264 | 0.0106 ns | 0.0084 ns | 0.0013 ns | 0.0111 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967264 | 0.0107 ns | 0.0087 ns | 0.0022 ns | 0.0097 ns |  1.06 |    0.38 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967278 | 0.0157 ns | 0.0146 ns | 0.0038 ns | 0.0163 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967278 | 0.0173 ns | 0.0484 ns | 0.0075 ns | 0.0167 ns |  1.20 |    0.46 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967295 | 0.0004 ns | 0.0027 ns | 0.0007 ns | 0.0000 ns |     ? |       ? |         - |           ? |
| ExtensionMethod | 4294967295 | 0.0122 ns | 0.0122 ns | 0.0032 ns | 0.0123 ns |     ? |       ? |         - |           ? |

// * Warnings *
BaselineCustomAnalyzer
  Summary -> A question mark '?' symbol indicates that it was not possible to compute the (Ratio, RatioSD, Alloc Ratio) column(s) because the baseline value is too close to zero.
ZeroMeasurement
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.28 ns)
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.28 ns, 1.29 ns)
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.29 ns)
  Mod128ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.32 ns)
  Mod128ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.29 ns)










Mod3UInt128Benchmarks.ExtensionMethod: Job-REHAVU(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551598]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.475 ns, StdErr = 0.002 ns (0.51%), N = 5, StdDev = 0.005 ns
Min = 0.468 ns, Q1 = 0.473 ns, Median = 0.474 ns, Q3 = 0.478 ns, Max = 0.482 ns
IQR = 0.004 ns, LowerFence = 0.467 ns, UpperFence = 0.484 ns
ConfidenceInterval = [0.454 ns; 0.496 ns] (CI 99.9%), Margin = 0.021 ns (4.40% of Mean)
Skewness = 0.07, Kurtosis = 1.35, MValue = 2
-------------------- Histogram --------------------
[0.464 ns ; 0.487 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-REHAVU : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 3                    | 2.9692 ns | 0.0336 ns | 0.0087 ns |  1.00 |         - |          NA |
| ExtensionMethod | 3                    | 0.4549 ns | 0.0199 ns | 0.0052 ns |  0.15 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 8191                 | 2.8871 ns | 0.0411 ns | 0.0064 ns |  1.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.4562 ns | 0.0133 ns | 0.0035 ns |  0.16 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.8850 ns | 0.0209 ns | 0.0054 ns |  1.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.4656 ns | 0.0048 ns | 0.0007 ns |  0.16 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.8841 ns | 0.0396 ns | 0.0103 ns |  1.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.4710 ns | 0.0065 ns | 0.0017 ns |  0.16 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 18446744073709551598 | 2.9329 ns | 0.0549 ns | 0.0143 ns |  1.00 |         - |          NA |
| ExtensionMethod | 18446744073709551598 | 0.4750 ns | 0.0209 ns | 0.0054 ns |  0.16 |         - |          NA |

// * Hints *
Outliers
  Mod3UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (4.21 ns)
  Mod3UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.75 ns)










Mod3UIntBenchmarks.ExtensionMethod: Job-GFHXOG(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.035 ns, StdErr = 0.002 ns (5.03%), N = 5, StdDev = 0.004 ns
Min = 0.031 ns, Q1 = 0.032 ns, Median = 0.035 ns, Q3 = 0.037 ns, Max = 0.040 ns
IQR = 0.005 ns, LowerFence = 0.024 ns, UpperFence = 0.045 ns
ConfidenceInterval = [0.020 ns; 0.050 ns] (CI 99.9%), Margin = 0.015 ns (43.34% of Mean)
Skewness = 0.24, Kurtosis = 1.09, MValue = 2
-------------------- Histogram --------------------
[0.030 ns ; 0.036 ns) | @@@
[0.036 ns ; 0.042 ns) | @@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-GFHXOG : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3          | 0.0320 ns | 0.0636 ns | 0.0165 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 3          | 0.0217 ns | 0.0133 ns | 0.0021 ns |  0.73 |    0.35 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0918 ns | 0.1303 ns | 0.0202 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.0303 ns | 0.0085 ns | 0.0013 ns |  0.34 |    0.08 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0355 ns | 0.0130 ns | 0.0034 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.0597 ns | 0.0564 ns | 0.0146 ns |  1.69 |    0.44 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0309 ns | 0.0098 ns | 0.0025 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.0350 ns | 0.0152 ns | 0.0039 ns |  1.15 |    0.21 |         - |          NA |

// * Hints *
Outliers
  Mod3UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.32 ns)
  Mod3UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.53 ns)
  Mod3UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.31 ns)










Mod3ULongBenchmarks.ExtensionMethod: Job-URMFUY(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551598]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.448 ns, StdErr = 0.005 ns (1.11%), N = 5, StdDev = 0.011 ns
Min = 0.435 ns, Q1 = 0.438 ns, Median = 0.450 ns, Q3 = 0.454 ns, Max = 0.461 ns
IQR = 0.017 ns, LowerFence = 0.412 ns, UpperFence = 0.480 ns
ConfidenceInterval = [0.405 ns; 0.490 ns] (CI 99.9%), Margin = 0.043 ns (9.59% of Mean)
Skewness = -0.07, Kurtosis = 0.92, MValue = 2
-------------------- Histogram --------------------
[0.426 ns ; 0.445 ns) | @@
[0.445 ns ; 0.464 ns) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-URMFUY : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3                    | 0.2640 ns | 0.0123 ns | 0.0019 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 3                    | 0.4406 ns | 0.0119 ns | 0.0031 ns |  1.67 |    0.01 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 8191                 | 0.2599 ns | 0.0158 ns | 0.0041 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.4372 ns | 0.0096 ns | 0.0015 ns |  1.69 |    0.03 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 0.2620 ns | 0.0163 ns | 0.0042 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.4379 ns | 0.0066 ns | 0.0017 ns |  1.67 |    0.03 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647           | 0.2858 ns | 0.1371 ns | 0.0356 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.4355 ns | 0.0127 ns | 0.0033 ns |  1.54 |    0.18 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709551598 | 0.4916 ns | 0.0336 ns | 0.0052 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 18446744073709551598 | 0.4475 ns | 0.0429 ns | 0.0112 ns |  0.92 |    0.02 |         - |          NA |

// * Hints *
Outliers
  Mod3ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.53 ns)
  Mod3ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.70 ns)
  Mod3ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.72 ns)
  Mod3ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.78 ns)










Mod5UInt128Benchmarks.ExtensionMethod: Job-CYVDBZ(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551584]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.467 ns, StdErr = 0.001 ns (0.27%), N = 5, StdDev = 0.003 ns
Min = 0.462 ns, Q1 = 0.467 ns, Median = 0.468 ns, Q3 = 0.469 ns, Max = 0.469 ns
IQR = 0.002 ns, LowerFence = 0.463 ns, UpperFence = 0.472 ns
ConfidenceInterval = [0.456 ns; 0.478 ns] (CI 99.9%), Margin = 0.011 ns (2.30% of Mean)
Skewness = -0.8, Kurtosis = 1.71, MValue = 2
-------------------- Histogram --------------------
[0.460 ns ; 0.471 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-CYVDBZ : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 5                    | 2.8402 ns | 0.0655 ns | 0.0170 ns |  1.00 |         - |          NA |
| ExtensionMethod | 5                    | 0.4706 ns | 0.0269 ns | 0.0070 ns |  0.17 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 8191                 | 2.8744 ns | 0.0511 ns | 0.0079 ns |  1.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.4691 ns | 0.0143 ns | 0.0037 ns |  0.16 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.8699 ns | 0.0563 ns | 0.0146 ns |  1.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.4644 ns | 0.0164 ns | 0.0043 ns |  0.16 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.8950 ns | 0.0268 ns | 0.0069 ns |  1.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.4847 ns | 0.0481 ns | 0.0125 ns |  0.17 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 18446744073709551584 | 2.9267 ns | 0.0559 ns | 0.0145 ns |  1.00 |         - |          NA |
| ExtensionMethod | 18446744073709551584 | 0.4669 ns | 0.0107 ns | 0.0028 ns |  0.16 |         - |          NA |

// * Hints *
Outliers
  Mod5UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (4.25 ns)
  Mod5UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (4.19 ns)
  Mod5UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.75 ns)










Mod5UIntBenchmarks.ExtensionMethod: Job-UKOYIC(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=4294967295]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.029 ns, StdErr = 0.001 ns (4.81%), N = 5, StdDev = 0.003 ns
Min = 0.026 ns, Q1 = 0.027 ns, Median = 0.029 ns, Q3 = 0.031 ns, Max = 0.034 ns
IQR = 0.004 ns, LowerFence = 0.021 ns, UpperFence = 0.038 ns
ConfidenceInterval = [0.017 ns; 0.042 ns] (CI 99.9%), Margin = 0.012 ns (41.40% of Mean)
Skewness = 0.21, Kurtosis = 1.08, MValue = 2
-------------------- Histogram --------------------
[0.025 ns ; 0.030 ns) | @@@
[0.030 ns ; 0.035 ns) | @@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-UKOYIC : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Median    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3          | 0.0547 ns | 0.1192 ns | 0.0185 ns | 0.0541 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 3          | 0.0349 ns | 0.0087 ns | 0.0014 ns | 0.0349 ns |  0.70 |    0.25 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 5          | 0.0296 ns | 0.0047 ns | 0.0012 ns | 0.0303 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 5          | 0.0316 ns | 0.0234 ns | 0.0036 ns | 0.0300 ns |  1.05 |    0.11 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 6          | 0.0671 ns | 0.0674 ns | 0.0175 ns | 0.0745 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 6          | 0.0346 ns | 0.0168 ns | 0.0044 ns | 0.0360 ns |  0.58 |    0.29 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8          | 0.0326 ns | 0.0067 ns | 0.0017 ns | 0.0333 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8          | 0.0294 ns | 0.0040 ns | 0.0006 ns | 0.0292 ns |  0.88 |    0.01 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 10         | 0.0289 ns | 0.0117 ns | 0.0030 ns | 0.0275 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 10         | 0.0306 ns | 0.0030 ns | 0.0008 ns | 0.0304 ns |  1.07 |    0.12 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 11         | 0.1236 ns | 0.4016 ns | 0.1043 ns | 0.0900 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11         | 0.0315 ns | 0.0208 ns | 0.0032 ns | 0.0323 ns |  0.64 |    0.47 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 32         | 0.0840 ns | 0.0343 ns | 0.0089 ns | 0.0855 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 32         | 0.0328 ns | 0.0085 ns | 0.0022 ns | 0.0336 ns |  0.39 |    0.04 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 64         | 0.0721 ns | 0.1529 ns | 0.0237 ns | 0.0754 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 64         | 0.0356 ns | 0.0108 ns | 0.0017 ns | 0.0363 ns |  0.54 |    0.21 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 128        | 0.0272 ns | 0.0062 ns | 0.0016 ns | 0.0276 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 128        | 0.0336 ns | 0.0127 ns | 0.0020 ns | 0.0335 ns |  1.21 |    0.11 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 256        | 0.0285 ns | 0.0143 ns | 0.0037 ns | 0.0288 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 256        | 0.0282 ns | 0.0054 ns | 0.0014 ns | 0.0285 ns |  1.01 |    0.16 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0882 ns | 0.1426 ns | 0.0370 ns | 0.0945 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.0328 ns | 0.0053 ns | 0.0008 ns | 0.0331 ns |  0.49 |    0.21 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 8191       | 0.0303 ns | 0.0044 ns | 0.0011 ns | 0.0305 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191       | 0.0390 ns | 0.0296 ns | 0.0077 ns | 0.0365 ns |  1.29 |    0.28 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0866 ns | 0.0601 ns | 0.0093 ns | 0.0901 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.0305 ns | 0.0199 ns | 0.0052 ns | 0.0291 ns |  0.36 |    0.03 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 131071     | 0.2312 ns | 0.5389 ns | 0.1399 ns | 0.3289 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071     | 0.0270 ns | 0.0161 ns | 0.0042 ns | 0.0285 ns |  0.17 |    0.12 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0306 ns | 0.0057 ns | 0.0015 ns | 0.0298 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.0327 ns | 0.0234 ns | 0.0036 ns | 0.0335 ns |  1.08 |    0.09 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294966271 | 0.0302 ns | 0.0061 ns | 0.0016 ns | 0.0301 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294966271 | 0.0371 ns | 0.0161 ns | 0.0042 ns | 0.0380 ns |  1.23 |    0.16 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294966784 | 0.0683 ns | 0.2301 ns | 0.0356 ns | 0.0646 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294966784 | 0.0359 ns | 0.0205 ns | 0.0032 ns | 0.0366 ns |  0.65 |    0.32 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967040 | 0.0329 ns | 0.0152 ns | 0.0039 ns | 0.0345 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967040 | 0.0327 ns | 0.0105 ns | 0.0027 ns | 0.0327 ns |  1.00 |    0.14 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967168 | 0.0297 ns | 0.0284 ns | 0.0074 ns | 0.0314 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967168 | 0.0322 ns | 0.0223 ns | 0.0034 ns | 0.0335 ns |  1.23 |    0.43 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967232 | 0.0229 ns | 0.0103 ns | 0.0027 ns | 0.0244 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967232 | 0.0306 ns | 0.0041 ns | 0.0011 ns | 0.0307 ns |  1.36 |    0.23 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967264 | 0.0867 ns | 0.1993 ns | 0.0518 ns | 0.0584 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967264 | 0.0288 ns | 0.0072 ns | 0.0019 ns | 0.0291 ns |  0.42 |    0.19 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967278 | 0.0313 ns | 0.0092 ns | 0.0024 ns | 0.0301 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967278 | 0.0465 ns | 0.0510 ns | 0.0079 ns | 0.0453 ns |  1.48 |    0.33 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 4294967295 | 0.0728 ns | 0.0825 ns | 0.0214 ns | 0.0670 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 4294967295 | 0.0295 ns | 0.0122 ns | 0.0032 ns | 0.0292 ns |  0.43 |    0.11 |         - |          NA |

// * Hints *
Outliers
  Mod5UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.52 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.31 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.34 ns)
  Mod5UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.31 ns)
  Mod5UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.30 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.30 ns, 1.52 ns)
  Mod5UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.53 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.31 ns, 1.32 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.32 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.31 ns, 1.31 ns)
  Mod5UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.35 ns, 1.40 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.30 ns, 1.33 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.36 ns)
  Mod5UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.30 ns, 1.31 ns)










Mod5ULongBenchmarks.ExtensionMethod: Job-QVAGLZ(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551584]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.448 ns, StdErr = 0.003 ns (0.67%), N = 5, StdDev = 0.007 ns
Min = 0.437 ns, Q1 = 0.448 ns, Median = 0.448 ns, Q3 = 0.452 ns, Max = 0.455 ns
IQR = 0.005 ns, LowerFence = 0.441 ns, UpperFence = 0.459 ns
ConfidenceInterval = [0.422 ns; 0.474 ns] (CI 99.9%), Margin = 0.026 ns (5.78% of Mean)
Skewness = -0.51, Kurtosis = 1.54, MValue = 2
-------------------- Histogram --------------------
[0.432 ns ; 0.443 ns) | @
[0.443 ns ; 0.457 ns) | @@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-QVAGLZ : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 5                    | 0.2657 ns | 0.0194 ns | 0.0030 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 5                    | 0.4305 ns | 0.0443 ns | 0.0069 ns |  1.62 |    0.04 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 8191                 | 0.2622 ns | 0.0330 ns | 0.0051 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.4404 ns | 0.0068 ns | 0.0011 ns |  1.68 |    0.03 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 0.2640 ns | 0.0141 ns | 0.0037 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.4359 ns | 0.0104 ns | 0.0027 ns |  1.65 |    0.03 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647           | 0.2645 ns | 0.0300 ns | 0.0046 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.4361 ns | 0.0142 ns | 0.0037 ns |  1.65 |    0.04 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709551584 | 0.2696 ns | 0.0195 ns | 0.0051 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 18446744073709551584 | 0.4481 ns | 0.0259 ns | 0.0067 ns |  1.66 |    0.05 |         - |          NA |

// * Hints *
Outliers
  Mod5ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.59 ns)
  Mod5ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.69 ns, 1.72 ns)
  Mod5ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.52 ns, 1.74 ns)
  Mod5ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.70 ns, 1.70 ns)
  Mod5ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.60 ns)
  Mod5ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.70 ns)










Mod6ComparisonBenchmarks.ExtensionMethod: Job-YZTHHU(Runtime=.NET 8.0, IterationCount=3, LaunchCount=1, WarmupCount=1) [StartValue=18446744073709550591]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 1.060 ns, StdErr = 0.001 ns (0.08%), N = 3, StdDev = 0.001 ns
Min = 1.059 ns, Q1 = 1.060 ns, Median = 1.061 ns, Q3 = 1.061 ns, Max = 1.062 ns
IQR = 0.001 ns, LowerFence = 1.058 ns, UpperFence = 1.063 ns
ConfidenceInterval = [1.033 ns; 1.088 ns] (CI 99.9%), Margin = 0.027 ns (2.58% of Mean)
Skewness = -0.23, Kurtosis = 0.67, MValue = 2
-------------------- Histogram --------------------
[1.057 ns ; 1.063 ns) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-YZTHHU : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=3  LaunchCount=1
WarmupCount=1

| Method          | StartValue           | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3                    | 1.0201 ns | 0.0221 ns | 0.0012 ns |  1.00 |    0.00 |         - |          NA |
| DivisionBased   | 3                    | 0.9915 ns | 0.1010 ns | 0.0055 ns |  0.97 |    0.00 |         - |          NA |
| FastDivHigh     | 3                    | 1.6913 ns | 0.1088 ns | 0.0060 ns |  1.66 |    0.00 |         - |          NA |
| ExtensionMethod | 3                    | 1.0605 ns | 0.0498 ns | 0.0027 ns |  1.04 |    0.00 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 1.0351 ns | 0.2104 ns | 0.0115 ns |  1.00 |    0.00 |         - |          NA |
| DivisionBased   | 131071               | 1.0633 ns | 0.3786 ns | 0.0208 ns |  1.03 |    0.02 |         - |          NA |
| FastDivHigh     | 131071               | 1.7062 ns | 0.1798 ns | 0.0099 ns |  1.65 |    0.01 |         - |          NA |
| ExtensionMethod | 131071               | 1.0696 ns | 0.0920 ns | 0.0050 ns |  1.03 |    0.01 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709550591 | 1.0105 ns | 0.0190 ns | 0.0010 ns |  1.00 |    0.00 |         - |          NA |
| DivisionBased   | 18446744073709550591 | 0.9617 ns | 0.1333 ns | 0.0073 ns |  0.95 |    0.01 |         - |          NA |
| FastDivHigh     | 18446744073709550591 | 1.6730 ns | 0.1585 ns | 0.0087 ns |  1.66 |    0.01 |         - |          NA |
| ExtensionMethod | 18446744073709550591 | 1.0604 ns | 0.0273 ns | 0.0015 ns |  1.05 |    0.00 |         - |          NA |










Mod6UInt128Benchmarks.ExtensionMethod: Job-OUNYJB(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551552]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 1.167 ns, StdErr = 0.003 ns (0.24%), N = 5, StdDev = 0.006 ns
Min = 1.162 ns, Q1 = 1.163 ns, Median = 1.164 ns, Q3 = 1.172 ns, Max = 1.176 ns
IQR = 0.009 ns, LowerFence = 1.150 ns, UpperFence = 1.185 ns
ConfidenceInterval = [1.144 ns; 1.191 ns] (CI 99.9%), Margin = 0.024 ns (2.04% of Mean)
Skewness = 0.34, Kurtosis = 0.95, MValue = 2
-------------------- Histogram --------------------
[1.157 ns ; 1.181 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-OUNYJB : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean     | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |---------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 6                    | 2.894 ns | 0.0430 ns | 0.0112 ns |  1.00 |         - |          NA |
| ExtensionMethod | 6                    | 1.180 ns | 0.0513 ns | 0.0079 ns |  0.41 |         - |          NA |
|                 |                      |          |           |           |       |           |             |
| ModuloOperator  | 8191                 | 2.897 ns | 0.0300 ns | 0.0078 ns |  1.00 |         - |          NA |
| ExtensionMethod | 8191                 | 1.164 ns | 0.0139 ns | 0.0036 ns |  0.40 |         - |          NA |
|                 |                      |          |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.911 ns | 0.0209 ns | 0.0054 ns |  1.00 |         - |          NA |
| ExtensionMethod | 131071               | 1.158 ns | 0.0402 ns | 0.0104 ns |  0.40 |         - |          NA |
|                 |                      |          |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.874 ns | 0.0221 ns | 0.0057 ns |  1.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 1.241 ns | 0.0476 ns | 0.0074 ns |  0.43 |         - |          NA |
|                 |                      |          |           |           |       |           |             |
| ModuloOperator  | 18446744073709551552 | 2.908 ns | 0.0120 ns | 0.0031 ns |  1.00 |         - |          NA |
| ExtensionMethod | 18446744073709551552 | 1.167 ns | 0.0238 ns | 0.0062 ns |  0.40 |         - |          NA |

// * Hints *
Outliers
  Mod6UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (2.53 ns)
  Mod6UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (2.45 ns)
  Mod6UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (4.19 ns)
  Mod6UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (2.51 ns, 2.53 ns)










Mod6UIntBenchmarks.ExtensionMethod: Job-NYQPPY(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.459 ns, StdErr = 0.002 ns (0.52%), N = 5, StdDev = 0.005 ns
Min = 0.450 ns, Q1 = 0.457 ns, Median = 0.461 ns, Q3 = 0.461 ns, Max = 0.464 ns
IQR = 0.005 ns, LowerFence = 0.450 ns, UpperFence = 0.468 ns
ConfidenceInterval = [0.438 ns; 0.479 ns] (CI 99.9%), Margin = 0.021 ns (4.47% of Mean)
Skewness = -0.5, Kurtosis = 1.39, MValue = 2
-------------------- Histogram --------------------
[0.446 ns ; 0.465 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-NYQPPY : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Median    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 6          | 0.0348 ns | 0.0632 ns | 0.0164 ns | 0.0432 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 6          | 0.4328 ns | 0.0241 ns | 0.0063 ns | 0.4352 ns | 19.21 |   18.98 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0277 ns | 0.0118 ns | 0.0031 ns | 0.0287 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.4518 ns | 0.0098 ns | 0.0025 ns | 0.4508 ns | 16.47 |    1.86 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0492 ns | 0.0875 ns | 0.0227 ns | 0.0470 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.4543 ns | 0.0131 ns | 0.0034 ns | 0.4545 ns | 11.10 |    5.23 |         - |          NA |
|                 |            |           |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0385 ns | 0.0097 ns | 0.0025 ns | 0.0394 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.4587 ns | 0.0205 ns | 0.0053 ns | 0.4609 ns | 11.96 |    0.92 |         - |          NA |

// * Hints *
Outliers
  Mod6UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.30 ns)










Mod6ULongBenchmarks.ExtensionMethod: Job-PJWCPL(Runtime=.NET 8.0, IterationCount=3, LaunchCount=1, WarmupCount=1) [Value=18446744073709551615]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.467 ns, StdErr = 0.002 ns (0.39%), N = 3, StdDev = 0.003 ns
Min = 0.465 ns, Q1 = 0.466 ns, Median = 0.466 ns, Q3 = 0.469 ns, Max = 0.471 ns
IQR = 0.003 ns, LowerFence = 0.461 ns, UpperFence = 0.473 ns
ConfidenceInterval = [0.410 ns; 0.525 ns] (CI 99.9%), Margin = 0.057 ns (12.23% of Mean)
Skewness = 0.3, Kurtosis = 0.67, MValue = 2
-------------------- Histogram --------------------
[0.462 ns ; 0.474 ns) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-PJWCPL : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=3  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 3                    | 0.2644 ns | 0.1200 ns | 0.0066 ns |  1.00 |    0.00 |         - |          NA |
| DivisionBased   | 3                    | 0.2767 ns | 0.1131 ns | 0.0062 ns |  1.05 |    0.03 |         - |          NA |
| FastDivHigh     | 3                    | 1.2405 ns | 0.0349 ns | 0.0019 ns |  4.69 |    0.12 |         - |          NA |
| ExtensionMethod | 3                    | 0.4609 ns | 0.0214 ns | 0.0012 ns |  1.74 |    0.04 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 0.2624 ns | 0.0816 ns | 0.0045 ns |  1.00 |    0.00 |         - |          NA |
| DivisionBased   | 131071               | 0.2843 ns | 0.0577 ns | 0.0032 ns |  1.08 |    0.02 |         - |          NA |
| FastDivHigh     | 131071               | 1.0431 ns | 0.0419 ns | 0.0023 ns |  3.98 |    0.06 |         - |          NA |
| ExtensionMethod | 131071               | 0.4671 ns | 0.0199 ns | 0.0011 ns |  1.78 |    0.03 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709551615 | 0.2705 ns | 0.0662 ns | 0.0036 ns |  1.00 |    0.00 |         - |          NA |
| DivisionBased   | 18446744073709551615 | 0.2872 ns | 0.0161 ns | 0.0009 ns |  1.06 |    0.01 |         - |          NA |
| FastDivHigh     | 18446744073709551615 | 1.1667 ns | 0.1333 ns | 0.0073 ns |  4.31 |    0.04 |         - |          NA |
| ExtensionMethod | 18446744073709551615 | 0.4674 ns | 0.0572 ns | 0.0031 ns |  1.73 |    0.01 |         - |          NA |










Mod7UInt128Benchmarks.ExtensionMethod: Job-YIEQKK(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551488]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.676 ns, StdErr = 0.005 ns (0.70%), N = 4, StdDev = 0.010 ns
Min = 0.662 ns, Q1 = 0.676 ns, Median = 0.680 ns, Q3 = 0.681 ns, Max = 0.681 ns
IQR = 0.005 ns, LowerFence = 0.668 ns, UpperFence = 0.688 ns
ConfidenceInterval = [0.614 ns; 0.737 ns] (CI 99.9%), Margin = 0.062 ns (9.10% of Mean)
Skewness = -0.75, Kurtosis = 1.31, MValue = 2
-------------------- Histogram --------------------
[0.654 ns ; 0.672 ns) | @
[0.672 ns ; 0.689 ns) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-YIEQKK : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 7                    | 2.8599 ns | 0.0231 ns | 0.0060 ns |  1.00 |         - |          NA |
| ExtensionMethod | 7                    | 0.6761 ns | 0.0105 ns | 0.0027 ns |  0.24 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 8191                 | 2.8866 ns | 0.0290 ns | 0.0075 ns |  1.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.6747 ns | 0.0207 ns | 0.0032 ns |  0.23 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.8732 ns | 0.0070 ns | 0.0011 ns |  1.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.7218 ns | 0.1429 ns | 0.0371 ns |  0.25 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.8779 ns | 0.0353 ns | 0.0055 ns |  1.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.8820 ns | 0.0091 ns | 0.0024 ns |  0.31 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 18446744073709551488 | 2.9146 ns | 0.0095 ns | 0.0025 ns |  1.00 |         - |          NA |
| ExtensionMethod | 18446744073709551488 | 0.6758 ns | 0.0615 ns | 0.0095 ns |  0.23 |         - |          NA |

// * Hints *
Outliers
  Mod7UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.95 ns)
  Mod7UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (4.19 ns)
  Mod7UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (4.20 ns)
  Mod7UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.94 ns, 1.96 ns)










Mod7UIntBenchmarks.ExtensionMethod: Job-RAOTLX(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 4.579 ns, StdErr = 0.051 ns (1.11%), N = 5, StdDev = 0.113 ns
Min = 4.391 ns, Q1 = 4.554 ns, Median = 4.632 ns, Q3 = 4.654 ns, Max = 4.663 ns
IQR = 0.099 ns, LowerFence = 4.406 ns, UpperFence = 4.802 ns
ConfidenceInterval = [4.143 ns; 5.015 ns] (CI 99.9%), Margin = 0.436 ns (9.52% of Mean)
Skewness = -0.75, Kurtosis = 1.62, MValue = 2
-------------------- Histogram --------------------
[4.304 ns ; 4.478 ns) | @
[4.478 ns ; 4.696 ns) | @@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-RAOTLX : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Ratio  | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|-------:|--------:|----------:|------------:|
| ModuloOperator  | 7          | 0.0354 ns | 0.0124 ns | 0.0032 ns |   1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 7          | 0.2683 ns | 0.0194 ns | 0.0050 ns |   7.63 |    0.78 |         - |          NA |
|                 |            |           |           |           |        |         |           |             |
| ModuloOperator  | 2047       | 0.0276 ns | 0.0131 ns | 0.0034 ns |   1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 1.2166 ns | 0.0164 ns | 0.0025 ns |  45.72 |    5.92 |         - |          NA |
|                 |            |           |           |           |        |         |           |             |
| ModuloOperator  | 65535      | 0.0282 ns | 0.0259 ns | 0.0040 ns |   1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 2.3342 ns | 0.3051 ns | 0.0792 ns |  83.89 |   10.09 |         - |          NA |
|                 |            |           |           |           |        |         |           |             |
| ModuloOperator  | 2147483647 | 0.0422 ns | 0.0224 ns | 0.0058 ns |   1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 4.5787 ns | 0.4360 ns | 0.1132 ns | 110.08 |   13.59 |         - |          NA |

// * Warnings *
ZeroMeasurement
  Mod7UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod7UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.56 ns)
  Mod7UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (2.52 ns)
  Mod7UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.53 ns)
  Mod7UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (5.68 ns)










Mod7ULongBenchmarks.ExtensionMethod: Job-HROZQV(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551552]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.684 ns, StdErr = 0.002 ns (0.29%), N = 5, StdDev = 0.004 ns
Min = 0.676 ns, Q1 = 0.684 ns, Median = 0.686 ns, Q3 = 0.686 ns, Max = 0.687 ns
IQR = 0.002 ns, LowerFence = 0.681 ns, UpperFence = 0.690 ns
ConfidenceInterval = [0.667 ns; 0.701 ns] (CI 99.9%), Margin = 0.017 ns (2.53% of Mean)
Skewness = -0.94, Kurtosis = 1.9, MValue = 2
-------------------- Histogram --------------------
[0.673 ns ; 0.690 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-HROZQV : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 7                    | 0.2739 ns | 0.0040 ns | 0.0006 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 7                    | 0.4329 ns | 0.0044 ns | 0.0007 ns |  1.58 |    0.00 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 8191                 | 0.2699 ns | 0.0152 ns | 0.0039 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.4434 ns | 0.0189 ns | 0.0049 ns |  1.64 |    0.02 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 0.2676 ns | 0.0209 ns | 0.0032 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.4356 ns | 0.0184 ns | 0.0029 ns |  1.63 |    0.03 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647           | 0.2697 ns | 0.0351 ns | 0.0091 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.4380 ns | 0.0087 ns | 0.0023 ns |  1.63 |    0.06 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709551552 | 0.2746 ns | 0.0094 ns | 0.0024 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 18446744073709551552 | 0.6840 ns | 0.0173 ns | 0.0045 ns |  2.49 |    0.03 |         - |          NA |

// * Hints *
Outliers
  Mod7ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.57 ns, 1.58 ns)
  Mod7ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.72 ns)
  Mod7ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.76 ns)
  Mod7ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed, 2 outliers were detected (1.71 ns, 1.74 ns)
  Mod7ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.55 ns)
  Mod7ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.95 ns)










Mod8UInt128Benchmarks.ExtensionMethod: Job-TVOQGP(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551360]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.020 ns, StdErr = 0.000 ns (1.86%), N = 4, StdDev = 0.001 ns
Min = 0.020 ns, Q1 = 0.020 ns, Median = 0.020 ns, Q3 = 0.021 ns, Max = 0.021 ns
IQR = 0.001 ns, LowerFence = 0.019 ns, UpperFence = 0.021 ns
ConfidenceInterval = [0.015 ns; 0.025 ns] (CI 99.9%), Margin = 0.005 ns (23.99% of Mean)
Skewness = 0.64, Kurtosis = 1.22, MValue = 2
-------------------- Histogram --------------------
[0.019 ns ; 0.021 ns) | @@@
[0.021 ns ; 0.022 ns) | @
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-TVOQGP : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 8                    | 2.8637 ns | 0.0567 ns | 0.0088 ns | 1.000 |         - |          NA |
| ExtensionMethod | 8                    | 0.0170 ns | 0.0082 ns | 0.0021 ns | 0.006 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 8191                 | 2.8776 ns | 0.0649 ns | 0.0100 ns | 1.000 |         - |          NA |
| ExtensionMethod | 8191                 | 0.0144 ns | 0.0225 ns | 0.0035 ns | 0.005 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.8954 ns | 0.1186 ns | 0.0308 ns | 1.000 |         - |          NA |
| ExtensionMethod | 131071               | 0.0134 ns | 0.0138 ns | 0.0036 ns | 0.005 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.8903 ns | 0.0272 ns | 0.0071 ns | 1.000 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.0105 ns | 0.0125 ns | 0.0033 ns | 0.004 |         - |          NA |
|                 |                      |           |           |           |       |           |             |
| ModuloOperator  | 18446744073709551360 | 2.8936 ns | 0.0265 ns | 0.0069 ns | 1.000 |         - |          NA |
| ExtensionMethod | 18446744073709551360 | 0.0203 ns | 0.0049 ns | 0.0008 ns | 0.007 |         - |          NA |

// * Warnings *
ZeroMeasurement
  Mod8UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod8UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod8UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (4.20 ns)
  Mod8UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.29 ns)
  Mod8UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (4.14 ns, 4.19 ns)
  Mod8UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.31 ns)
  Mod8UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.30 ns)
  Mod8UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (4.17 ns)
  Mod8UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.32 ns)










Mod8UIntBenchmarks.ExtensionMethod: Job-HSXEMD(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=2147483647]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.015 ns, StdErr = 0.001 ns (9.47%), N = 5, StdDev = 0.003 ns
Min = 0.012 ns, Q1 = 0.014 ns, Median = 0.014 ns, Q3 = 0.017 ns, Max = 0.020 ns
IQR = 0.003 ns, LowerFence = 0.009 ns, UpperFence = 0.022 ns
ConfidenceInterval = [0.003 ns; 0.027 ns] (CI 99.9%), Margin = 0.012 ns (81.51% of Mean)
Skewness = 0.33, Kurtosis = 1.17, MValue = 2
-------------------- Histogram --------------------
[0.010 ns ; 0.015 ns) | @@@
[0.015 ns ; 0.021 ns) | @@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-HSXEMD : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value      | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |----------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 8          | 0.0109 ns | 0.0232 ns | 0.0060 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8          | 0.0032 ns | 0.0095 ns | 0.0025 ns |  0.29 |    0.26 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2047       | 0.0151 ns | 0.0083 ns | 0.0022 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2047       | 0.0113 ns | 0.0101 ns | 0.0016 ns |  0.72 |    0.16 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 65535      | 0.0123 ns | 0.0052 ns | 0.0008 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 65535      | 0.0191 ns | 0.0281 ns | 0.0043 ns |  1.56 |    0.41 |         - |          NA |
|                 |            |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647 | 0.0122 ns | 0.0061 ns | 0.0016 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647 | 0.0150 ns | 0.0122 ns | 0.0032 ns |  1.25 |    0.31 |         - |          NA |

// * Warnings *
ZeroMeasurement
  Mod8UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod8UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod8UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> The method duration is indistinguishable from the empty method duration
  Mod8UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod8UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.31 ns)
  Mod8UIntBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.29 ns)
  Mod8UIntBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.46 ns)










Mod11ULongBenchmarks.ExtensionMethod: Job-SXCLPE(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551488]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 1.152 ns, StdErr = 0.003 ns (0.26%), N = 5, StdDev = 0.007 ns
Min = 1.146 ns, Q1 = 1.148 ns, Median = 1.149 ns, Q3 = 1.154 ns, Max = 1.163 ns
IQR = 0.006 ns, LowerFence = 1.139 ns, UpperFence = 1.163 ns
ConfidenceInterval = [1.126 ns; 1.178 ns] (CI 99.9%), Margin = 0.026 ns (2.23% of Mean)
Skewness = 0.61, Kurtosis = 1.49, MValue = 2
-------------------- Histogram --------------------
[1.141 ns ; 1.168 ns) | @@@@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-SXCLPE : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Ratio | RatioSD | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|------:|--------:|----------:|------------:|
| ModuloOperator  | 11                   | 0.2713 ns | 0.0197 ns | 0.0051 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 11                   | 0.6777 ns | 0.0261 ns | 0.0068 ns |  2.50 |    0.04 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 8191                 | 0.2335 ns | 0.0190 ns | 0.0049 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 8191                 | 0.7509 ns | 0.0363 ns | 0.0056 ns |  3.20 |    0.06 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 131071               | 0.2636 ns | 0.0153 ns | 0.0024 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 131071               | 0.7538 ns | 0.0415 ns | 0.0108 ns |  2.86 |    0.07 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 2147483647           | 0.2647 ns | 0.0061 ns | 0.0009 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.6572 ns | 0.0155 ns | 0.0040 ns |  2.49 |    0.01 |         - |          NA |
|                 |                      |           |           |           |       |         |           |             |
| ModuloOperator  | 18446744073709551488 | 0.2709 ns | 0.0072 ns | 0.0011 ns |  1.00 |    0.00 |         - |          NA |
| ExtensionMethod | 18446744073709551488 | 1.1519 ns | 0.0257 ns | 0.0067 ns |  4.26 |    0.01 |         - |          NA |

// * Hints *
Outliers
  Mod11ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (1.59 ns)
  Mod11ULongBenchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (2.08 ns)
  Mod11ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed, 2 outliers were detected (1.56 ns, 1.56 ns)
  Mod11ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.56 ns)
  Mod11ULongBenchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  removed (1.57 ns)










Mod128UInt128Benchmarks.ExtensionMethod: Job-YHIMPB(Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1) [Value=18446744073709551104]
Runtime = .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2; GC = Concurrent Workstation
Mean = 0.014 ns, StdErr = 0.003 ns (18.86%), N = 5, StdDev = 0.006 ns
Min = 0.007 ns, Q1 = 0.009 ns, Median = 0.017 ns, Q3 = 0.019 ns, Max = 0.019 ns
IQR = 0.011 ns, LowerFence = -0.007 ns, UpperFence = 0.035 ns
ConfidenceInterval = [-0.009 ns; 0.038 ns] (CI 99.9%), Margin = 0.023 ns (162.42% of Mean)
Skewness = -0.29, Kurtosis = 0.81, MValue = 2
-------------------- Histogram --------------------
[0.003 ns ; 0.014 ns) | @@
[0.014 ns ; 0.024 ns) | @@@
---------------------------------------------------

// * Summary *

BenchmarkDotNet v0.13.12, Windows 11 (10.0.22631.5909/23H2/2023Update/SunValley3)
AMD Ryzen 5 5625U with Radeon Graphics, 1 CPU, 12 logical and 6 physical cores
.NET SDK 10.0.100-preview.7.25380.108
  [Host]     : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2
  Job-YHIMPB : .NET 8.0.20 (8.0.2025.41914), X64 RyuJIT AVX2

Runtime=.NET 8.0  IterationCount=5  LaunchCount=1
WarmupCount=1

| Method          | Value                | Mean      | Error     | StdDev    | Median    | Ratio | Allocated | Alloc Ratio |
|---------------- |--------------------- |----------:|----------:|----------:|----------:|------:|----------:|------------:|
| ModuloOperator  | 128                  | 3.4231 ns | 1.2618 ns | 0.3277 ns | 3.3547 ns | 1.000 |         - |          NA |
| ExtensionMethod | 128                  | 0.0246 ns | 0.0585 ns | 0.0152 ns | 0.0294 ns | 0.007 |         - |          NA |
|                 |                      |           |           |           |           |       |           |             |
| ModuloOperator  | 8191                 | 3.0253 ns | 0.1308 ns | 0.0340 ns | 3.0379 ns | 1.000 |         - |          NA |
| ExtensionMethod | 8191                 | 0.0061 ns | 0.0075 ns | 0.0019 ns | 0.0055 ns | 0.002 |         - |          NA |
|                 |                      |           |           |           |           |       |           |             |
| ModuloOperator  | 131071               | 2.9497 ns | 0.0139 ns | 0.0036 ns | 2.9504 ns | 1.000 |         - |          NA |
| ExtensionMethod | 131071               | 0.0043 ns | 0.0205 ns | 0.0053 ns | 0.0009 ns | 0.001 |         - |          NA |
|                 |                      |           |           |           |           |       |           |             |
| ModuloOperator  | 2147483647           | 2.9480 ns | 0.0357 ns | 0.0093 ns | 2.9447 ns | 1.000 |         - |          NA |
| ExtensionMethod | 2147483647           | 0.0189 ns | 0.0131 ns | 0.0020 ns | 0.0185 ns | 0.006 |         - |          NA |
|                 |                      |           |           |           |           |       |           |             |
| ModuloOperator  | 18446744073709551104 | 2.9670 ns | 0.1010 ns | 0.0262 ns | 2.9526 ns | 1.000 |         - |          NA |
| ExtensionMethod | 18446744073709551104 | 0.0143 ns | 0.0233 ns | 0.0060 ns | 0.0174 ns | 0.005 |         - |          NA |

// * Warnings *
ZeroMeasurement
  Mod128UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration
  Mod128UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> The method duration is indistinguishable from the empty method duration

// * Hints *
Outliers
  Mod128UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  detected (1.41 ns)
  Mod128UInt128Benchmarks.ModuloOperator: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1  -> 1 outlier  was  detected (4.44 ns)
  Mod128UInt128Benchmarks.ExtensionMethod: Runtime=.NET 8.0, IterationCount=5, LaunchCount=1, WarmupCount=1 -> 1 outlier  was  removed (1.37 ns)
