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Strength Reduction

C# port of Rust strength_reduce

Overview

This library implements integer division and modulo via "arithmetic strength reduction".

Why?

Modern processors can do multiplication and shifts much faster than division, and "arithmetic strength reduction" is an algorithm to transform divisions into multiplications and shifts. Compilers already perform this optimization for divisors that are known at compile time; this library enables this optimization for divisors that are only known at runtime. From strength_reduce README

Available types

  • StrengthReduceU8
  • StrengthReduceU16
  • StrengthReduceU32
  • StrengthReduceU64

Example usage

Works the best when there is repeated division of the same divisor. For more example see StrengthReductionTest folder

[Test]
public void TestByte()
{
    const byte max = byte.MaxValue;
    byte[] divisors = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, max - 1, max };
    byte[] numerators = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 };
    foreach (var divisor in divisors)
    {
        var reduced = new StrengthReduceU8(divisor);
        foreach (var numerator in numerators)
        {
            Console.WriteLine($"Testing {numerator} / {divisor}");
            var expectedDiv = (byte)(numerator / divisor);
            var expectedRem = (byte)(numerator % divisor);
            var reducedDiv = numerator / reduced;
            var reducedRem = numerator % reduced;
            var (reducedCombinedDiv, reducedCombinedRem) = StrengthReduceU8.DivRem(numerator, reduced);
            Assert.AreEqual(expectedDiv, reducedDiv);
            Assert.AreEqual(expectedRem, reducedRem);
            Assert.AreEqual(expectedDiv, reducedCombinedDiv);
            Assert.AreEqual(expectedRem, reducedCombinedRem);
        }
    }
}

Benchmarks

Benchmark ran with BenchmarkDotNet

Method Mean Error StdDev
BenchStrengthReduceByteOneByte 2.860 ns 0.0044 ns 0.0039 ns
BenchStrengthReduceU16OneU16 3.833 ns 0.0208 ns 0.0194 ns
BenchBaselineOneU64 5.291 ns 0.0099 ns 0.0088 ns
BenchBaselineOneU16 5.294 ns 0.0300 ns 0.0266 ns
BenchBaselineOneByte 5.297 ns 0.0063 ns 0.0059 ns
BenchBaselineOneU32 5.302 ns 0.0729 ns 0.0682 ns
BenchStrengthReduceU32OneU32 5.824 ns 0.0607 ns 0.0568 ns
BenchStrengthReduceU64OneU64 64.970 ns 1.2642 ns 1.0557 ns
BenchStrengthReduceByte 164.748 ns 1.1126 ns 1.0408 ns
BenchStrengthReduceU16 221.468 ns 4.4146 ns 9.1169 ns
BenchStrengthReduceU32 248.601 ns 3.8517 ns 3.4144 ns
BenchStrengthReduceU64 1,775.256 ns 20.8042 ns 19.4603 ns
BenchBaselineByte 3,152.957 ns 20.2562 ns 18.9477 ns
BenchBaselineU16 3,195.399 ns 4.2095 ns 3.7316 ns
BenchBaselineU64 3,196.124 ns 2.2190 ns 2.0757 ns
BenchBaselineU32 3,202.035 ns 4.4703 ns 3.9628 ns