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Marek Lemańczyk committed
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using FluentAssertions;
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using PerfectNumbers.Core.Gpu;
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using Xunit;
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[Trait("Category", "Fast")]
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public class GpuUInt128Tests
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{
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[Fact]
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public void Mul_matches_UInt128()
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{
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var random = new Random(0);
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for (var i = 0; i < 100; i++)
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{
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var high1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var high2 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low2 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var a = new GpuUInt128(high1, low1);
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var b = new GpuUInt128(high2, low2);
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var expected = (UInt128)new GpuUInt128(high1, low1) * (UInt128)new GpuUInt128(high2, low2);
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a = a.Mul(b);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void MulMod_matches_UInt128()
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{
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var random = new Random(1);
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for (var i = 0; i < 100; i++)
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{
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var high1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var high2 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low2 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var a = new GpuUInt128((UInt128)new GpuUInt128(high1, low1) % (UInt128)modulus);
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var b = new GpuUInt128((UInt128)new GpuUInt128(high2, low2) % (UInt128)modulus);
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var expected = MulModReference((UInt128)a, (UInt128)b, (UInt128)modulus);
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a = a.MulMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void MulMod_with_ulong_matches_UInt128()
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{
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var random = new Random(5);
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for (var i = 0; i < 100; i++)
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{
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var high1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var a = new GpuUInt128((UInt128)new GpuUInt128(high1, low1) % (UInt128)modulus);
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ulong bRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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UInt128 bBig = (UInt128)bRaw % (UInt128)modulus;
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ulong b = (ulong)bBig;
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var expected = MulModReference((UInt128)a, bBig, (UInt128)modulus);
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a = a.MulMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void MulMod_with_ulong_modulus_matches_UInt128()
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{
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var random = new Random(11);
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for (var i = 0; i < 100; i++)
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{
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ulong modulus = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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ulong aRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong bRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong aVal = aRaw % modulus;
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ulong bVal = bRaw % modulus;
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var a = new GpuUInt128(aVal);
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var b = new GpuUInt128(bVal);
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UInt128 expected = ((UInt128)aVal * bVal) % modulus;
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a = a.MulMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void MulModBigInteger_matches_UInt128()
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{
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var random = new Random(13);
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for (var i = 0; i < 20; i++)
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{
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var high1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low1 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var high2 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var low2 = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var a = new GpuUInt128((UInt128)new GpuUInt128(high1, low1) % (UInt128)modulus);
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var b = new GpuUInt128((UInt128)new GpuUInt128(high2, low2) % (UInt128)modulus);
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var expected = MulModReference((UInt128)a, (UInt128)b, (UInt128)modulus);
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var result = new GpuUInt128(a.High, a.Low);
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result = result.MulModBigInteger(b, modulus);
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((UInt128)result).Should().Be(expected);
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}
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}
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[Fact]
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public void SquareMod_matches_UInt128()
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{
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var random = new Random(8);
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for (var i = 0; i < 100; i++)
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{
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var valueHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var valueLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var a = new GpuUInt128((UInt128)new GpuUInt128(valueHigh, valueLow) % (UInt128)modulus);
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var expected = MulModReference((UInt128)a, (UInt128)a, (UInt128)modulus);
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a = a.SquareMod(modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void ModPow_matches_BigInteger()
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{
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var random = new Random(2);
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for (var i = 0; i < 20; i++)
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{
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var baseHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var baseLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var expHigh = 0UL;
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var expLow = (ulong)random.Next(1, int.MaxValue);
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var value = new GpuUInt128((UInt128)new GpuUInt128(baseHigh, baseLow) % (UInt128)modulus);
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var exponent = new GpuUInt128(expHigh, expLow);
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var expected = (UInt128)System.Numerics.BigInteger.ModPow((System.Numerics.BigInteger)(UInt128)value, (System.Numerics.BigInteger)(UInt128)exponent, (System.Numerics.BigInteger)(UInt128)modulus);
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value = value.ModPow(exponent, modulus);
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((UInt128)value).Should().Be(expected);
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}
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}
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[Fact]
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public void ModPow_with_ulong_matches_BigInteger()
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{
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var random = new Random(9);
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for (var i = 0; i < 20; i++)
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{
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var baseHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var baseLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong exponent = (ulong)random.Next(1, int.MaxValue);
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var value = new GpuUInt128((UInt128)new GpuUInt128(baseHigh, baseLow) % (UInt128)modulus);
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var expected = (UInt128)System.Numerics.BigInteger.ModPow((System.Numerics.BigInteger)(UInt128)value, exponent, (System.Numerics.BigInteger)(UInt128)modulus);
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value = value.ModPow(exponent, modulus);
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((UInt128)value).Should().Be(expected);
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}
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}
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[Fact]
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public void SubMod_matches_UInt128()
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{
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var random = new Random(3);
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for (var i = 0; i < 100; i++)
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{
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var valueHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var valueLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var subHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var subLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var a = new GpuUInt128((UInt128)new GpuUInt128(valueHigh, valueLow) % (UInt128)modulus);
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var b = new GpuUInt128((UInt128)new GpuUInt128(subHigh, subLow) % (UInt128)modulus);
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UInt128 expected = ((UInt128)a + (UInt128)modulus - (UInt128)b) % (UInt128)modulus;
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a = a.SubMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void SubMod_with_ulong_matches_UInt128()
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{
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var random = new Random(6);
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for (var i = 0; i < 100; i++)
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{
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var valueHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var valueLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var a = new GpuUInt128((UInt128)new GpuUInt128(valueHigh, valueLow) % (UInt128)modulus);
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ulong subRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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UInt128 bBig = (UInt128)subRaw % (UInt128)modulus;
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ulong b = (ulong)bBig;
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UInt128 expected = ((UInt128)a + (UInt128)modulus - bBig) % (UInt128)modulus;
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a = a.SubMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void AddMod_matches_UInt128()
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{
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var random = new Random(4);
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for (var i = 0; i < 100; i++)
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{
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var valueHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var valueLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var addHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var addLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var a = new GpuUInt128((UInt128)new GpuUInt128(valueHigh, valueLow) % (UInt128)modulus);
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var b = new GpuUInt128((UInt128)new GpuUInt128(addHigh, addLow) % (UInt128)modulus);
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UInt128 expected = ((UInt128)a + (UInt128)b) % (UInt128)modulus;
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a = a.AddMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void AddMod_with_ulong_modulus_matches_UInt128()
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{
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var random = new Random(12);
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for (var i = 0; i < 100; i++)
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{
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ulong modulus = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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ulong aRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong bRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong aVal = aRaw % modulus;
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ulong bVal = bRaw % modulus;
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var a = new GpuUInt128(aVal);
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var b = new GpuUInt128(bVal);
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UInt128 expected = ((UInt128)aVal + bVal) % modulus;
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a = a.AddMod(b, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void AddMod_with_ulong_operand_and_modulus_matches_UInt128()
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{
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var random = new Random(13);
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for (var i = 0; i < 100; i++)
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{
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ulong modulus = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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ulong aRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong bRaw = ((ulong)random.Next() << 32) | (uint)random.Next();
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ulong aVal = aRaw % modulus;
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ulong bVal = bRaw % modulus;
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var a = new GpuUInt128(aVal);
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UInt128 expected = ((UInt128)aVal + bVal) % modulus;
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a = a.AddMod(bVal, modulus);
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((UInt128)a).Should().Be(expected);
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}
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}
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[Fact]
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public void ModInv_matches_BigInteger()
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{
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var random = new Random(7);
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for (var i = 0; i < 20; i++)
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{
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var modHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var modLow = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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var modulus = new GpuUInt128(modHigh, modLow);
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var valueHigh = ((ulong)random.Next() << 32) | (uint)random.Next();
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var valueLow = ((ulong)random.Next() << 32) | (uint)random.Next();
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var value = new GpuUInt128((UInt128)new GpuUInt128(valueHigh, valueLow) % (UInt128)modulus);
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if (value.IsZero)
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{
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value = value.Add(1UL);
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}
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var expected = (UInt128)System.Numerics.BigInteger.ModPow((System.Numerics.BigInteger)(UInt128)value, (System.Numerics.BigInteger)(UInt128)modulus - 2, (System.Numerics.BigInteger)(UInt128)modulus);
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value = value.ModInv(modulus);
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((UInt128)value).Should().Be(expected);
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}
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}
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[Fact]
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public void ModInv_with_ulong_modulus_matches_BigInteger()
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{
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var random = new Random(8);
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for (var i = 0; i < 20; i++)
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{
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ulong modulus = ((ulong)random.Next() << 32) | (uint)random.Next() | 1UL;
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ulong raw = ((ulong)random.Next() << 32) | (uint)random.Next();
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var value = new GpuUInt128((UInt128)(raw % modulus));
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if (value.IsZero)
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{
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value = value.Add(1UL);
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}
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var expected = (UInt128)System.Numerics.BigInteger.ModPow((System.Numerics.BigInteger)(UInt128)value, (System.Numerics.BigInteger)modulus - 2, (System.Numerics.BigInteger)modulus);
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value = value.ModInv(modulus);
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((UInt128)value).Should().Be(expected);
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}
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}
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private static UInt128 MulModReference(UInt128 a, UInt128 b, UInt128 modulus)
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{
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UInt128 result = 0;
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UInt128 x = a;
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UInt128 y = b;
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while (y != 0)
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{
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if ((y & 1) != 0)
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{
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result += x;
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if (result >= modulus)
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{
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result -= modulus;
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}
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}
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x <<= 1;
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if (x >= modulus)
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{
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x -= modulus;
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}
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y >>= 1;
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}
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return result;
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}
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}
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