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+0.46473791844432144 +0.9769929014039193 +0.897888394956425 +0.712109655007771 +0.32181270388970745 +0.2514978196711735 diff --git a/src/MissingValues.Benchmarks/MissingValues.Benchmarks.csproj b/src/MissingValues.Benchmarks/MissingValues.Benchmarks.csproj index 8100393..74f2f05 100644 --- a/src/MissingValues.Benchmarks/MissingValues.Benchmarks.csproj +++ b/src/MissingValues.Benchmarks/MissingValues.Benchmarks.csproj @@ -15,4 +15,20 @@ + + + + + + + PreserveNewest + + + PreserveNewest + + + PreserveNewest + + + diff --git a/src/MissingValues.Benchmarks/Program.cs b/src/MissingValues.Benchmarks/Program.cs index 2995c6a..9fed5fc 100644 --- a/src/MissingValues.Benchmarks/Program.cs +++ b/src/MissingValues.Benchmarks/Program.cs @@ -1,5 +1,14 @@ using MissingValues.Benchmarks; using BenchmarkDotNet.Running; +using MissingValues; +using System.Numerics; +using System.Text; +using System.Globalization; +using System.Diagnostics; +using System.Runtime.Intrinsics.X86; +using System.Runtime.CompilerServices; +using System.Runtime.Intrinsics; +using System.Windows.Markup; BenchmarkRunner.Run( new Type[] @@ -7,11 +16,13 @@ typeof(UInt256Benchmarks.MathOperators), typeof(UInt256Benchmarks.Formatting), typeof(UInt256Benchmarks.Parsing), - typeof(UInt256Benchmarks.Operations), + typeof(UInt256Benchmarks.Operations), typeof(UInt512Benchmarks.MathOperators), typeof(UInt512Benchmarks.Formatting), typeof(UInt512Benchmarks.Parsing), - typeof(UInt512Benchmarks.Operations) + typeof(UInt512Benchmarks.Operations), + typeof(QuadBenchmarks.MathOperators), + typeof(QuadBenchmarks.Parser), } ); diff --git a/src/MissingValues.Benchmarks/QuadBenchmarks.cs b/src/MissingValues.Benchmarks/QuadBenchmarks.cs new file mode 100644 index 0000000..2ee91e2 --- /dev/null +++ b/src/MissingValues.Benchmarks/QuadBenchmarks.cs @@ -0,0 +1,186 @@ +using BenchmarkDotNet.Attributes; +using System; +using System.Collections.Generic; +using System.Globalization; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Benchmarks +{ + public class QuadBenchmarks + { + private static readonly Random rnd = new Random(7); + + [MemoryDiagnoser] + public class MathOperators + { + private Quad q; + private double d; + private float f; + + private static readonly Quad Two = new Quad(0x4000_0000_0000_0000, 0x0000_0000_0000_0000); + + [Params(10L, 100L, 1000L)] + public long E { get; set; } + + [GlobalSetup] + public void Setup() + { + f = rnd.NextSingle() * E; + d = rnd.NextDouble() * E; + q = (Quad)rnd.NextDouble() * E * E; + } + + [Benchmark] + public float Addition_Op__Single() + { + float sum = f; + for (int i = 0, length = (int)E; i < length; i++) + { + sum += f; + } + return sum; + } + [Benchmark] + public double Addition_Op__Double() + { + double sum = d; + for (int i = 0, length = (int)E; i < length; i++) + { + sum += d; + } + return sum; + } + [Benchmark] + public Quad Addition_Op__Quad() + { + Quad sum = q; + for (int i = 0, length = (int)E; i < length; i++) + { + sum += q; + } + return sum; + } + + [Benchmark] + public float Multiplication_Op__Single() + { + float sum = f; + for (int i = 0, length = (int)E; i < length; i++) + { + sum *= f; + } + return sum; + } + [Benchmark] + public double Multiplication_Op__Double() + { + double sum = d; + for (int i = 0, length = (int)E; i < length; i++) + { + sum *= d; + } + return sum; + } + [Benchmark] + public Quad Multiplication_Op__Quad() + { + Quad sum = q; + for (int i = 0, length = (int)E; i < length; i++) + { + sum *= q; + } + return sum; + } + + [Benchmark] + public float Division_Op__Single() + { + float sum = f; + for (int i = 0, length = (int)E; i < length; i++) + { + sum /= 2F; + } + return sum; + } + [Benchmark] + public double Division_Op__Double() + { + double sum = d; + for (int i = 0, length = (int)E; i < length; i++) + { + sum /= 2d; + } + return sum; + } + [Benchmark] + public Quad Division_Op__Quad() + { + Quad sum = q; + for (int i = 0, length = (int)E; i < length; i++) + { + sum /= Two; + } + return sum; + } + } + [MemoryDiagnoser] + public class Parser + { + private string[] _lines; + + [Params(@"Data/canada.txt", @"Data/mesh.txt", @"Data/synthetic.txt")] + public string FileName { get; set; } + public int LineCount { get; set; } + public ReadOnlySpan Lines => new(_lines); + private NumberFormatInfo _numberFormatInfo = NumberFormatInfo.InvariantInfo; + + [GlobalSetup] + public void Setup() + { + _lines = File.ReadAllLines(FileName); + LineCount = _lines.Length; + } + + [Benchmark] + public Span SingleParse() + { + Span result = new float[_lines.Length]; + + for (int i = 0; i < LineCount; i++) + { + result[i] = float.Parse(_lines[i], _numberFormatInfo); + } + + return result; + } + + [Benchmark] + public Span DoubleParse() + { + Span result = new double[_lines.Length]; + + for (int i = 0; i < LineCount; i++) + { + result[i] = double.Parse(_lines[i], _numberFormatInfo); + } + + return result; + } + + [Benchmark] + public Span QuadParse() + { + Span result = new Quad[_lines.Length]; + + for (int i = 0; i < LineCount; i++) + { + result[i] = Quad.Parse(_lines[i], _numberFormatInfo); + } + + return result; + } + } + } +} diff --git a/src/MissingValues.Benchmarks/UInt256Benchmarks.cs b/src/MissingValues.Benchmarks/UInt256Benchmarks.cs index ae4b492..8fcafc5 100644 --- a/src/MissingValues.Benchmarks/UInt256Benchmarks.cs +++ b/src/MissingValues.Benchmarks/UInt256Benchmarks.cs @@ -10,7 +10,7 @@ namespace MissingValues.Benchmarks { public class UInt256Benchmarks { - static Random rnd = new Random(7); + static readonly Random rnd = new Random(7); [MemoryDiagnoser] public class MathOperators diff --git a/src/MissingValues.Tests/Int256Test.GenericMath.cs b/src/MissingValues.Tests/Core/Int256Test.GenericMath.cs similarity index 99% rename from src/MissingValues.Tests/Int256Test.GenericMath.cs rename to src/MissingValues.Tests/Core/Int256Test.GenericMath.cs index cbc9554..6b4a9c3 100644 --- a/src/MissingValues.Tests/Int256Test.GenericMath.cs +++ b/src/MissingValues.Tests/Core/Int256Test.GenericMath.cs @@ -8,7 +8,7 @@ using Int = MissingValues.Int256; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class Int256Test { diff --git a/src/MissingValues.Tests/Int256Test.cs b/src/MissingValues.Tests/Core/Int256Test.cs similarity index 99% rename from src/MissingValues.Tests/Int256Test.cs rename to src/MissingValues.Tests/Core/Int256Test.cs index 09f6e99..776e9e2 100644 --- a/src/MissingValues.Tests/Int256Test.cs +++ b/src/MissingValues.Tests/Core/Int256Test.cs @@ -9,7 +9,7 @@ using Int = MissingValues.Int256; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class Int256Test { diff --git a/src/MissingValues.Tests/Int512Test.GenericMath.cs b/src/MissingValues.Tests/Core/Int512Test.GenericMath.cs similarity index 99% rename from src/MissingValues.Tests/Int512Test.GenericMath.cs rename to src/MissingValues.Tests/Core/Int512Test.GenericMath.cs index b0d9b13..1eb1673 100644 --- a/src/MissingValues.Tests/Int512Test.GenericMath.cs +++ b/src/MissingValues.Tests/Core/Int512Test.GenericMath.cs @@ -8,7 +8,7 @@ using Int = MissingValues.Int512; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class Int512Test { @@ -364,7 +364,7 @@ public static void AdditiveIdentityTest() public static void MultiplicativeIdentityTest() { Assert.Equal(One, MathConstantsHelper.MultiplicativeIdentityHelper()); - } + } #endregion #region IBinaryInteger @@ -681,7 +681,7 @@ public static void AbsTest() Assert.Throws(() => NumberBaseHelper.Abs(MinValue)); } [Fact] - public static void CreateCheckedToInt256Test() + public static void CreateCheckedToInt512Test() { NumberBaseHelper.CreateChecked(byte.MaxValue).Should().Be(ByteMaxValue); NumberBaseHelper.CreateChecked(short.MaxValue).Should().Be(Int16MaxValue); @@ -698,7 +698,7 @@ public static void CreateCheckedToInt256Test() NumberBaseHelper.CreateChecked(Int512MinValueAsDouble).Should().Be(MinValue); } [Fact] - public static void CreateSaturatingToInt256Test() + public static void CreateSaturatingToInt512Test() { NumberBaseHelper.CreateSaturating(byte.MaxValue).Should().Be(ByteMaxValue); NumberBaseHelper.CreateSaturating(short.MaxValue).Should().Be(Int16MaxValue); @@ -715,7 +715,7 @@ public static void CreateSaturatingToInt256Test() NumberBaseHelper.CreateSaturating(Int512MinValueAsDouble).Should().Be(MinValue); } [Fact] - public static void CreateTruncatingToInt256Test() + public static void CreateTruncatingToInt512Test() { NumberBaseHelper.CreateTruncating(byte.MaxValue).Should().Be(ByteMaxValue); NumberBaseHelper.CreateTruncating(short.MaxValue).Should().Be(Int16MaxValue); @@ -733,7 +733,7 @@ public static void CreateTruncatingToInt256Test() } [Fact] - public static void CreateCheckedFromInt256Test() + public static void CreateCheckedFromInt512Test() { NumberBaseHelper.CreateChecked(ByteMaxValue).Should().Be(byte.MaxValue); NumberBaseHelper.CreateChecked(Int16MaxValue).Should().Be(short.MaxValue); @@ -750,7 +750,7 @@ public static void CreateCheckedFromInt256Test() NumberBaseHelper.CreateChecked(MinValue).Should().Be(Int512MinValueAsDouble); } [Fact] - public static void CreateSaturatingFromInt256Test() + public static void CreateSaturatingFromInt512Test() { NumberBaseHelper.CreateSaturating(ByteMaxValue).Should().Be(byte.MaxValue); NumberBaseHelper.CreateSaturating(Int16MaxValue).Should().Be(short.MaxValue); @@ -767,7 +767,7 @@ public static void CreateSaturatingFromInt256Test() NumberBaseHelper.CreateSaturating(MinValue).Should().Be(Int512MinValueAsDouble); } [Fact] - public static void CreateTruncatingFromInt256Test() + public static void CreateTruncatingFromInt512Test() { NumberBaseHelper.CreateTruncating(ByteMaxValue).Should().Be(byte.MaxValue); NumberBaseHelper.CreateTruncating(Int16MaxValue).Should().Be(short.MaxValue); diff --git a/src/MissingValues.Tests/Int512Test.cs b/src/MissingValues.Tests/Core/Int512Test.cs similarity index 99% rename from src/MissingValues.Tests/Int512Test.cs rename to src/MissingValues.Tests/Core/Int512Test.cs index 76b20a5..1dc562b 100644 --- a/src/MissingValues.Tests/Int512Test.cs +++ b/src/MissingValues.Tests/Core/Int512Test.cs @@ -9,7 +9,7 @@ using Int = MissingValues.Int512; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class Int512Test { diff --git a/src/MissingValues.Tests/Core/QuadTest.GenericMath.cs b/src/MissingValues.Tests/Core/QuadTest.GenericMath.cs new file mode 100644 index 0000000..ec58555 --- /dev/null +++ b/src/MissingValues.Tests/Core/QuadTest.GenericMath.cs @@ -0,0 +1,761 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +using Float = MissingValues.Quad; + +namespace MissingValues.Tests.Core +{ + public partial class QuadTest + { + #region Generic Math Operators + [Theory] + [MemberData(nameof(UnaryNegationOperationTheoryData))] + public static void op_UnaryNegationTest(Float self, Float result) + { + MathOperatorsHelper.UnaryNegationOperation(self) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(AdditionOperationTheoryData))] + public static void op_AdditionTest(Float left, Float right, Float result) + { + MathOperatorsHelper.AdditionOperation(left, right) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(IncrementOperationTheoryData))] + public static void op_IncrementTest(Float self, Float result) + { + MathOperatorsHelper.IncrementOperation(self) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(SubtractionOperationTheoryData))] + public static void op_SubtractionTest(Float left, Float right, Float result) + { + MathOperatorsHelper.SubtractionOperation(left, right) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(DecrementOperationTheoryData))] + public static void op_DecrementTest(Float self, Float result) + { + MathOperatorsHelper.DecrementOperation(self) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(MultiplicationOperationTheoryData))] + public static void op_MultiplicationTest(Float left, Float right, Float result) + { + MathOperatorsHelper.MultiplicationOperation(left, right) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(DivisionOperationTheoryData))] + public static void op_DivisionTest(Float left, Float right, Float result) + { + MathOperatorsHelper.DivisionOperation(left, right) + .Should().Be(result) + .And.BeBitwiseEquivalentTo(result); + } + [Theory] + [MemberData(nameof(GreaterThanTheoryData))] + public static void op_GreaterThanTest(Float left, Float right, bool result) + { + ComparisonOperatorsHelper.GreaterThanOperation(left, right) + .Should().Be(result); + } + [Theory] + [MemberData(nameof(GreaterThanTheoryData))] + [MemberData(nameof(EqualToTheoryData))] + public static void op_GreaterThanOrEqualTest(Float left, Float right, bool result) + { + ComparisonOperatorsHelper.GreaterThanOrEqualOperation(left, right) + .Should().Be(result); + } + [Theory] + [MemberData(nameof(LessThanTheoryData))] + public static void op_LessThanTest(Float left, Float right, bool result) + { + ComparisonOperatorsHelper.LessThanOperation(left, right) + .Should().Be(result); + } + [Theory] + [MemberData(nameof(LessThanTheoryData))] + [MemberData(nameof(EqualToTheoryData))] + public static void op_LessThanOrEqualTest(Float left, Float right, bool result) + { + ComparisonOperatorsHelper.LessThanOrEqualOperation(left, right) + .Should().Be(result); + } + [Theory] + [MemberData(nameof(EqualToTheoryData))] + public static void op_EqualToTest(Float left, Float right, bool result) + { + EqualityOperatorsHelper.EqualityOperation(left, right) + .Should().Be(result); + } + [Theory] + [MemberData(nameof(NotEqualToTheoryData))] + public static void op_NotEqualToTest(Float left, Float right, bool result) + { + EqualityOperatorsHelper.InequalityOperation(left, right) + .Should().Be(result); + } + #endregion + + #region Identities + [Fact] + public static void AdditiveIdentityTest() + { + Assert.Equal(Zero, MathConstantsHelper.AdditiveIdentityHelper()); + } + + [Fact] + public static void MultiplicativeIdentityTest() + { + Assert.Equal(One, MathConstantsHelper.MultiplicativeIdentityHelper()); + } + #endregion + + #region IFloatingPoint + [Theory] + [MemberData(nameof(RoundAwayFromZeroTheoryData))] + [MemberData(nameof(RoundToEvenTheoryData))] + [MemberData(nameof(RoundToNegativeInfinityTheoryData))] + [MemberData(nameof(RoundToPositiveInfinityTheoryData))] + [MemberData(nameof(RoundToZeroTheoryData))] + public static void RoundTest(Float self, int digits, MidpointRounding midpointRounding, Float result) + { + Float.Round(self, digits, midpointRounding).Should().Be(result); + } + #endregion + + #region IFloatingPointConstants + [Fact] + public static void ConstantPiTest() + { + Assert.Equal(Float.Pi, MathConstantsHelper.Pi()); + } + [Fact] + public static void ConstantTauTest() + { + Assert.Equal(Float.Tau, MathConstantsHelper.Tau()); + } + [Fact] + public static void ConstantETest() + { + Assert.Equal(Float.E, MathConstantsHelper.E()); + } + #endregion + + #region IMinMaxValue + [Fact] + public static void MaxValueTest() + { + MaxValue.Should().Be(MathConstantsHelper.MaxValue()); + } + + [Fact] + public static void MinValueTest() + { + MinValue.Should().Be(MathConstantsHelper.MinValue()); + } + #endregion + + #region ISignedNumber + [Fact] + public static void NegativeOneTest() + { + MathConstantsHelper.NegativeOne().Should().Be(NegativeOne); + } + #endregion + + #region INumber + [Fact] + public static void ClampTest() + { + NumberHelper.Clamp(Float.NegativeInfinity, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(Float.MinValue, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(NegativeOne, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(-GreatestSubnormal, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(-Float.Epsilon, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(NegativeZero, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(Float.NaN, One, Thousand) + .Should().Be(Float.NaN); + NumberHelper.Clamp(Zero, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(Float.Epsilon, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(GreatestSubnormal, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(One, One, Thousand) + .Should().Be(One); + NumberHelper.Clamp(Float.MaxValue, One, Thousand) + .Should().Be(Thousand); + NumberHelper.Clamp(Float.PositiveInfinity, One, Thousand) + .Should().Be(Thousand); + } + [Fact] + public static void CopySignTest() + { + NumberHelper.CopySign(One, NegativeOne) + .Should().Be(NegativeOne); + NumberHelper.CopySign(NegativeOne, One) + .Should().Be(One); + NumberHelper.CopySign(Thousand, NegativeOne) + .Should().Be(NegativeThousand); + NumberHelper.CopySign(NegativeHundred, NegativeOne) + .Should().Be(NegativeHundred); + } + [Fact] + public static void MaxTest() + { + NumberHelper.Max(Float.NegativeInfinity, One) + .Should().Be(One); + NumberHelper.Max(Float.MinValue, One) + .Should().Be(One); + NumberHelper.Max(NegativeOne, One) + .Should().Be(One); + NumberHelper.Max(-GreatestSubnormal, One) + .Should().Be(One); + NumberHelper.Max(-Float.Epsilon, One) + .Should().Be(One); + NumberHelper.Max(NegativeZero, One) + .Should().Be(One); + NumberHelper.Max(Float.NaN, One) + .Should().Be(Float.NaN); + NumberHelper.Max(Zero, One) + .Should().Be(One); + NumberHelper.Max(Float.Epsilon, One) + .Should().Be(One); + NumberHelper.Max(GreatestSubnormal, One) + .Should().Be(One); + NumberHelper.Max(One, One) + .Should().Be(One); + NumberHelper.Max(Float.MaxValue, One) + .Should().Be(Float.MaxValue); + NumberHelper.Max(Float.PositiveInfinity, One) + .Should().Be(Float.PositiveInfinity); + } + [Fact] + public static void MaxNumberTest() + { + NumberHelper.MaxNumber(Float.NegativeInfinity, One) + .Should().Be(One); + NumberHelper.MaxNumber(Float.MinValue, One) + .Should().Be(One); + NumberHelper.MaxNumber(NegativeOne, One) + .Should().Be(One); + NumberHelper.MaxNumber(-GreatestSubnormal, One) + .Should().Be(One); + NumberHelper.MaxNumber(-Float.Epsilon, One) + .Should().Be(One); + NumberHelper.MaxNumber(NegativeZero, One) + .Should().Be(One); + NumberHelper.MaxNumber(Float.NaN, One) + .Should().Be(One); + NumberHelper.MaxNumber(Zero, One) + .Should().Be(One); + NumberHelper.MaxNumber(Float.Epsilon, One) + .Should().Be(One); + NumberHelper.MaxNumber(GreatestSubnormal, One) + .Should().Be(One); + NumberHelper.MaxNumber(One, One) + .Should().Be(One); + NumberHelper.MaxNumber(Float.MaxValue, One) + .Should().Be(Float.MaxValue); + NumberHelper.MaxNumber(Float.PositiveInfinity, One) + .Should().Be(Float.PositiveInfinity); + } + [Fact] + public static void MinTest() + { + NumberHelper.Min(Float.NegativeInfinity, One) + .Should().Be(Float.NegativeInfinity); + NumberHelper.Min(Float.MinValue, One) + .Should().Be(Float.MinValue); + NumberHelper.Min(NegativeOne, One) + .Should().Be(NegativeOne); + NumberHelper.Min(-GreatestSubnormal, One) + .Should().Be(-GreatestSubnormal); + NumberHelper.Min(-Float.Epsilon, One) + .Should().Be(-Float.Epsilon); + NumberHelper.Min(NegativeZero, One) + .Should().Be(NegativeZero); + NumberHelper.Min(Float.NaN, One) + .Should().Be(Float.NaN); + NumberHelper.Min(Zero, One) + .Should().Be(Zero); + NumberHelper.Min(Float.Epsilon, One) + .Should().Be(Float.Epsilon); + NumberHelper.Min(GreatestSubnormal, One) + .Should().Be(GreatestSubnormal); + NumberHelper.Min(One, One) + .Should().Be(One); + NumberHelper.Min(Float.MaxValue, One) + .Should().Be(One); + NumberHelper.Min(Float.PositiveInfinity, One) + .Should().Be(One); + } + [Fact] + public static void MinNumberTest() + { + NumberHelper.MinNumber(Float.NegativeInfinity, One) + .Should().Be(Float.NegativeInfinity); + NumberHelper.MinNumber(Float.MinValue, One) + .Should().Be(Float.MinValue); + NumberHelper.MinNumber(NegativeOne, One) + .Should().Be(NegativeOne); + NumberHelper.MinNumber(-GreatestSubnormal, One) + .Should().Be(-GreatestSubnormal); + NumberHelper.MinNumber(-Float.Epsilon, One) + .Should().Be(-Float.Epsilon); + NumberHelper.MinNumber(NegativeZero, One) + .Should().Be(NegativeZero); + NumberHelper.MinNumber(Float.NaN, One) + .Should().Be(One); + NumberHelper.MinNumber(Zero, One) + .Should().Be(Zero); + NumberHelper.MinNumber(Float.Epsilon, One) + .Should().Be(Float.Epsilon); + NumberHelper.MinNumber(GreatestSubnormal, One) + .Should().Be(GreatestSubnormal); + NumberHelper.MinNumber(One, One) + .Should().Be(One); + NumberHelper.MinNumber(Float.MaxValue, One) + .Should().Be(One); + NumberHelper.MinNumber(Float.PositiveInfinity, One) + .Should().Be(One); + } + [Fact] + public static void SignTest() + { + NumberHelper.Sign(One) + .Should().Be(1); + NumberHelper.Sign(NegativeOne) + .Should().Be(-1); + NumberHelper.Sign(Ten) + .Should().Be(1); + NumberHelper.Sign(NegativeTen) + .Should().Be(-1); + NumberHelper.Sign(Zero) + .Should().Be(0); + NumberHelper.Sign(NegativeZero) + .Should().Be(0); + } + #endregion + + #region INumberBase + [Fact] + public static void OneTest() + { + Assert.Equal(One, NumberBaseHelper.One); + } + [Fact] + public static void ZeroTest() + { + Assert.Equal(Zero, NumberBaseHelper.Zero); + } + [Fact] + public static void RadixTest() + { + Assert.Equal(Radix, NumberBaseHelper.Radix); + } + [Fact] + public static void AbsTest() + { + NumberBaseHelper.Abs(One).Should().Be(One); + NumberBaseHelper.Abs(NegativeOne).Should().Be(One); + NumberBaseHelper.Abs(NegativeHalf).Should().Be(Half); + NumberBaseHelper.Abs(NegativeQuarter).Should().Be(Quarter); + NumberBaseHelper.Abs(NegativeZero).Should().Be(Zero); + NumberBaseHelper.Abs(Float.NegativeInfinity).Should().Be(Float.PositiveInfinity); + } + [Fact] + public static void CreateCheckedFromQuadTest() + { + NumberBaseHelper.CreateChecked(ByteMaxValue).Should().Be(byte.MaxValue); + NumberBaseHelper.CreateChecked(Int16MaxValue).Should().Be(short.MaxValue); + NumberBaseHelper.CreateChecked(Int32MaxValue).Should().Be(int.MaxValue); + NumberBaseHelper.CreateChecked(Int64MaxValue).Should().Be(long.MaxValue); + NumberBaseHelper.CreateChecked(UInt128MaxValue).Should().Be(UInt128.MaxValue); + NumberBaseHelper.CreateChecked(UInt256MaxValue).Should().Be(UInt256.MaxValue); + NumberBaseHelper.CreateChecked(UInt512MaxValue).Should().Be(UInt512.MaxValue); + + NumberBaseHelper.CreateChecked(Half).Should().Be((Half)0.5f); + NumberBaseHelper.CreateChecked(Half).Should().Be(0.5f); + NumberBaseHelper.CreateChecked(Half).Should().Be(0.5d); + } + [Fact] + public static void CreateSaturatingFromQuadTest() + { + NumberBaseHelper.CreateSaturating(ByteMaxValue).Should().Be(byte.MaxValue); + NumberBaseHelper.CreateSaturating(Int16MaxValue).Should().Be(short.MaxValue); + NumberBaseHelper.CreateSaturating(Int32MaxValue).Should().Be(int.MaxValue); + NumberBaseHelper.CreateSaturating(Int64MaxValue).Should().Be(long.MaxValue); + NumberBaseHelper.CreateSaturating(UInt128MaxValue).Should().Be(UInt128.MaxValue); + NumberBaseHelper.CreateSaturating(UInt256MaxValue).Should().Be(UInt256.MaxValue); + NumberBaseHelper.CreateSaturating(UInt512MaxValue).Should().Be(UInt512.MaxValue); + + NumberBaseHelper.CreateSaturating(Half).Should().Be((Half)0.5f); + NumberBaseHelper.CreateSaturating(Half).Should().Be(0.5f); + NumberBaseHelper.CreateSaturating(Half).Should().Be(0.5d); + } + [Fact] + public static void CreateTruncatingFromQuadTest() + { + NumberBaseHelper.CreateTruncating(ByteMaxValue).Should().Be(byte.MaxValue); + NumberBaseHelper.CreateTruncating(Int16MaxValue).Should().Be(short.MaxValue); + NumberBaseHelper.CreateTruncating(Int32MaxValue).Should().Be(int.MaxValue); + NumberBaseHelper.CreateTruncating(Int64MaxValue).Should().Be(long.MaxValue); + NumberBaseHelper.CreateTruncating(UInt128MaxValue).Should().Be(UInt128.MaxValue); + NumberBaseHelper.CreateTruncating(UInt256MaxValue).Should().Be(UInt256.MaxValue); + NumberBaseHelper.CreateTruncating(UInt512MaxValue).Should().Be(UInt512.MaxValue); + + NumberBaseHelper.CreateTruncating(Half).Should().Be((Half)0.5f); + NumberBaseHelper.CreateTruncating(Half).Should().Be(0.5f); + NumberBaseHelper.CreateTruncating(Half).Should().Be(0.5d); + } + [Fact] + public static void CreateCheckedToQuadTest() + { + NumberBaseHelper.CreateChecked(byte.MaxValue).Should().Be(ByteMaxValue); + NumberBaseHelper.CreateChecked(short.MaxValue).Should().Be(Int16MaxValue); + NumberBaseHelper.CreateChecked(int.MaxValue).Should().Be(Int32MaxValue); + NumberBaseHelper.CreateChecked(long.MaxValue).Should().Be(Int64MaxValue); + NumberBaseHelper.CreateChecked(UInt128.MaxValue).Should().Be(UInt128MaxValue); + NumberBaseHelper.CreateChecked(UInt256.MaxValue).Should().Be(UInt256MaxValue); + NumberBaseHelper.CreateChecked(UInt512.MaxValue).Should().Be(UInt512MaxValue); + + NumberBaseHelper.CreateChecked((Half)0.5f).Should().Be(Half); + NumberBaseHelper.CreateChecked(0.5f).Should().Be(Half); + NumberBaseHelper.CreateChecked(0.5d).Should().Be(Half); + } + [Fact] + public static void CreateSaturatingToQuadTest() + { + NumberBaseHelper.CreateChecked(byte.MaxValue).Should().Be(ByteMaxValue); + NumberBaseHelper.CreateChecked(short.MaxValue).Should().Be(Int16MaxValue); + NumberBaseHelper.CreateChecked(int.MaxValue).Should().Be(Int32MaxValue); + NumberBaseHelper.CreateChecked(long.MaxValue).Should().Be(Int64MaxValue); + NumberBaseHelper.CreateChecked(UInt128.MaxValue).Should().Be(UInt128MaxValue); + NumberBaseHelper.CreateChecked(UInt256.MaxValue).Should().Be(UInt256MaxValue); + NumberBaseHelper.CreateChecked(UInt512.MaxValue).Should().Be(UInt512MaxValue); + + NumberBaseHelper.CreateChecked((Half)0.5f).Should().Be(Half); + NumberBaseHelper.CreateChecked(0.5f).Should().Be(Half); + NumberBaseHelper.CreateChecked(0.5d).Should().Be(Half); + } + [Fact] + public static void CreateTruncatingToQuadTest() + { + NumberBaseHelper.CreateChecked(byte.MaxValue).Should().Be(ByteMaxValue); + NumberBaseHelper.CreateChecked(short.MaxValue).Should().Be(Int16MaxValue); + NumberBaseHelper.CreateChecked(int.MaxValue).Should().Be(Int32MaxValue); + NumberBaseHelper.CreateChecked(long.MaxValue).Should().Be(Int64MaxValue); + NumberBaseHelper.CreateChecked(UInt128.MaxValue).Should().Be(UInt128MaxValue); + NumberBaseHelper.CreateChecked(UInt256.MaxValue).Should().Be(UInt256MaxValue); + NumberBaseHelper.CreateChecked(UInt512.MaxValue).Should().Be(UInt512MaxValue); + + NumberBaseHelper.CreateChecked((Half)0.5f).Should().Be(Half); + NumberBaseHelper.CreateChecked(0.5f).Should().Be(Half); + NumberBaseHelper.CreateChecked(0.5d).Should().Be(Half); + } + [Fact] + public static void IsCanonicalTest() + { + NumberBaseHelper.IsCanonical(One).Should().BeTrue(); + } + [Fact] + public static void IsComplexNumberTest() + { + NumberBaseHelper.IsComplexNumber(One).Should().BeFalse(); + } + [Fact] + public static void IsEvenIntegerTest() + { + NumberBaseHelper.IsEvenInteger(Half).Should().BeFalse(); + NumberBaseHelper.IsEvenInteger(One).Should().BeFalse(); + NumberBaseHelper.IsEvenInteger(Two).Should().BeTrue(); + NumberBaseHelper.IsEvenInteger(Three).Should().BeFalse(); + NumberBaseHelper.IsEvenInteger(Four).Should().BeTrue(); + NumberBaseHelper.IsEvenInteger(NegativeOne).Should().BeFalse(); + NumberBaseHelper.IsEvenInteger(NegativeTwo).Should().BeTrue(); + NumberBaseHelper.IsEvenInteger(NegativeThree).Should().BeFalse(); + NumberBaseHelper.IsEvenInteger(NegativeFour).Should().BeTrue(); + } + [Fact] + public static void IsFiniteTest() + { + NumberBaseHelper.IsFinite(One).Should().BeTrue(); + NumberBaseHelper.IsFinite(NegativeOne).Should().BeTrue(); + NumberBaseHelper.IsFinite(Float.NaN).Should().BeFalse(); + NumberBaseHelper.IsFinite(Float.PositiveInfinity).Should().BeFalse(); + NumberBaseHelper.IsFinite(Float.NegativeInfinity).Should().BeFalse(); + } + [Fact] + public static void IsImaginaryNumberTest() + { + NumberBaseHelper.IsImaginaryNumber(One).Should().BeFalse(); + } + [Fact] + public static void IsInfinityTest() + { + NumberBaseHelper.IsInfinity(One).Should().BeFalse(); + NumberBaseHelper.IsInfinity(NegativeOne).Should().BeFalse(); + NumberBaseHelper.IsInfinity(Float.NaN).Should().BeFalse(); + NumberBaseHelper.IsInfinity(Float.PositiveInfinity).Should().BeTrue(); + NumberBaseHelper.IsInfinity(Float.NegativeInfinity).Should().BeTrue(); + } + [Fact] + public static void IsIntegerTest() + { + NumberBaseHelper.IsInteger(Quarter).Should().BeFalse(); + NumberBaseHelper.IsInteger(Half).Should().BeFalse(); + NumberBaseHelper.IsInteger(Thousand).Should().BeTrue(); + NumberBaseHelper.IsInteger(One).Should().BeTrue(); + NumberBaseHelper.IsInteger(GreaterThanOneSmallest).Should().BeFalse(); + NumberBaseHelper.IsInteger(SmallestSubnormal).Should().BeFalse(); + NumberBaseHelper.IsInteger(NegativeOne).Should().BeTrue(); + NumberBaseHelper.IsInteger(NegativeThousand).Should().BeTrue(); + NumberBaseHelper.IsInteger(NegativeHalf).Should().BeFalse(); + NumberBaseHelper.IsInteger(NegativeQuarter).Should().BeFalse(); + NumberBaseHelper.IsInteger(Float.NaN).Should().BeFalse(); + NumberBaseHelper.IsInteger(Float.PositiveInfinity).Should().BeFalse(); + NumberBaseHelper.IsInteger(Float.NegativeInfinity).Should().BeFalse(); + } + [Fact] + public static void IsNaNTest() + { + NumberBaseHelper.IsNaN(One).Should().BeFalse(); + NumberBaseHelper.IsNaN(NegativeOne).Should().BeFalse(); + NumberBaseHelper.IsNaN(Float.NaN).Should().BeTrue(); + NumberBaseHelper.IsNaN(Float.PositiveInfinity).Should().BeFalse(); + NumberBaseHelper.IsNaN(Float.NegativeInfinity).Should().BeFalse(); + } + [Fact] + public static void IsNegativeTest() + { + NumberBaseHelper.IsNegative(One).Should().BeFalse(); + NumberBaseHelper.IsNegative(GreatestSubnormal).Should().BeFalse(); + NumberBaseHelper.IsNegative(Float.PositiveInfinity).Should().BeFalse(); + NumberBaseHelper.IsNegative(Float.NaN).Should().BeTrue(); + NumberBaseHelper.IsNegative(NegativeOne).Should().BeTrue(); + NumberBaseHelper.IsNegative(Float.NegativeInfinity).Should().BeTrue(); + } + [Fact] + public static void IsNegativeInfinityTest() + { + NumberBaseHelper.IsNegativeInfinity(One).Should().BeFalse(); + NumberBaseHelper.IsNegativeInfinity(NegativeOne).Should().BeFalse(); + NumberBaseHelper.IsNegativeInfinity(Float.NaN).Should().BeFalse(); + NumberBaseHelper.IsNegativeInfinity(Float.PositiveInfinity).Should().BeFalse(); + NumberBaseHelper.IsNegativeInfinity(Float.NegativeInfinity).Should().BeTrue(); + } + [Fact] + public static void IsNormalTest() + { + NumberBaseHelper.IsNormal(GreatestSubnormal).Should().BeFalse(); + NumberBaseHelper.IsNormal(SmallestSubnormal).Should().BeFalse(); + NumberBaseHelper.IsNormal(MaxValue).Should().BeTrue(); + NumberBaseHelper.IsNormal(MinValue).Should().BeTrue(); + NumberBaseHelper.IsNormal(One).Should().BeTrue(); + } + [Fact] + public static void IsOddIntegerTest() + { + NumberBaseHelper.IsOddInteger(Half).Should().BeFalse(); + NumberBaseHelper.IsOddInteger(One).Should().BeTrue(); + NumberBaseHelper.IsOddInteger(Two).Should().BeFalse(); + NumberBaseHelper.IsOddInteger(Three).Should().BeTrue(); + NumberBaseHelper.IsOddInteger(Four).Should().BeFalse(); + NumberBaseHelper.IsOddInteger(NegativeOne).Should().BeTrue(); + NumberBaseHelper.IsOddInteger(NegativeTwo).Should().BeFalse(); + NumberBaseHelper.IsOddInteger(NegativeThree).Should().BeTrue(); + NumberBaseHelper.IsOddInteger(NegativeFour).Should().BeFalse(); + } + [Fact] + public static void IsPositiveTest() + { + NumberBaseHelper.IsPositive(One).Should().BeTrue(); + NumberBaseHelper.IsPositive(GreatestSubnormal).Should().BeTrue(); + NumberBaseHelper.IsPositive(Float.PositiveInfinity).Should().BeTrue(); + NumberBaseHelper.IsPositive(Float.NaN).Should().BeFalse(); + NumberBaseHelper.IsPositive(NegativeOne).Should().BeFalse(); + NumberBaseHelper.IsPositive(Float.NegativeInfinity).Should().BeFalse(); + } + [Fact] + public static void IsPositiveInfinityTest() + { + NumberBaseHelper.IsPositiveInfinity(One).Should().BeFalse(); + NumberBaseHelper.IsPositiveInfinity(NegativeOne).Should().BeFalse(); + NumberBaseHelper.IsPositiveInfinity(Float.NaN).Should().BeFalse(); + NumberBaseHelper.IsPositiveInfinity(Float.PositiveInfinity).Should().BeTrue(); + NumberBaseHelper.IsPositiveInfinity(Float.NegativeInfinity).Should().BeFalse(); + } + [Fact] + public static void IsRealNumberTest() + { + NumberBaseHelper.IsRealNumber(GreatestSubnormal).Should().BeTrue(); + NumberBaseHelper.IsRealNumber(MaxValue).Should().BeTrue(); + NumberBaseHelper.IsRealNumber(NegativeThousand).Should().BeTrue(); + NumberBaseHelper.IsRealNumber(Float.PositiveInfinity).Should().BeTrue(); + NumberBaseHelper.IsRealNumber(Float.NegativeInfinity).Should().BeTrue(); + NumberBaseHelper.IsRealNumber(Float.NaN).Should().BeFalse(); + } + [Fact] + public static void IsSubnormalTest() + { + NumberBaseHelper.IsSubnormal(GreatestSubnormal).Should().BeTrue(); + NumberBaseHelper.IsSubnormal(SmallestSubnormal).Should().BeTrue(); + NumberBaseHelper.IsSubnormal(MaxValue).Should().BeFalse(); + NumberBaseHelper.IsSubnormal(MinValue).Should().BeFalse(); + NumberBaseHelper.IsSubnormal(One).Should().BeFalse(); + } + [Fact] + public static void IsZeroTest() + { + NumberBaseHelper.IsZero(One).Should().BeFalse(); + NumberBaseHelper.IsZero(Float.Epsilon).Should().BeFalse(); + NumberBaseHelper.IsZero(Zero).Should().BeTrue(); + NumberBaseHelper.IsZero(NegativeZero).Should().BeTrue(); + } + [Fact] + public static void MaxMagnitudeTest() + { + NumberBaseHelper.MaxMagnitude(Float.NegativeInfinity, One) + .Should().Be(Float.NegativeInfinity); + NumberBaseHelper.MaxMagnitude(Float.MinValue, One) + .Should().Be(Float.MinValue); + NumberBaseHelper.MaxMagnitude(NegativeOne, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(-GreatestSubnormal, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(-Float.Epsilon, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(NegativeZero, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(Float.NaN, One) + .Should().Be(Float.NaN); + NumberBaseHelper.MaxMagnitude(Zero, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(Float.Epsilon, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(GreatestSubnormal, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(One, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitude(Float.MaxValue, One) + .Should().Be(Float.MaxValue); + NumberBaseHelper.MaxMagnitude(Float.PositiveInfinity, One) + .Should().Be(Float.PositiveInfinity); + } + [Fact] + public static void MaxMagnitudeNumberTest() + { + NumberBaseHelper.MaxMagnitudeNumber(Float.NegativeInfinity, One) + .Should().Be(Float.NegativeInfinity); + NumberBaseHelper.MaxMagnitudeNumber(Float.MinValue, One) + .Should().Be(Float.MinValue); + NumberBaseHelper.MaxMagnitudeNumber(NegativeOne, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(-GreatestSubnormal, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(-Float.Epsilon, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(NegativeZero, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(Float.NaN, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(Zero, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(Float.Epsilon, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(GreatestSubnormal, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(One, One) + .Should().Be(One); + NumberBaseHelper.MaxMagnitudeNumber(Float.MaxValue, One) + .Should().Be(Float.MaxValue); + NumberBaseHelper.MaxMagnitudeNumber(Float.PositiveInfinity, One) + .Should().Be(Float.PositiveInfinity); + } + [Fact] + public static void MinMagnitudeTest() + { + NumberBaseHelper.MinMagnitude(Float.NegativeInfinity, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitude(Float.MinValue, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitude(NegativeOne, One) + .Should().Be(NegativeOne); + NumberBaseHelper.MinMagnitude(-GreatestSubnormal, One) + .Should().Be(-GreatestSubnormal); + NumberBaseHelper.MinMagnitude(-Float.Epsilon, One) + .Should().Be(-Float.Epsilon); + NumberBaseHelper.MinMagnitude(NegativeZero, One) + .Should().Be(NegativeZero); + NumberBaseHelper.MinMagnitude(Float.NaN, One) + .Should().Be(Float.NaN); + NumberBaseHelper.MinMagnitude(Zero, One) + .Should().Be(Zero); + NumberBaseHelper.MinMagnitude(Float.Epsilon, One) + .Should().Be(Float.Epsilon); + NumberBaseHelper.MinMagnitude(GreatestSubnormal, One) + .Should().Be(GreatestSubnormal); + NumberBaseHelper.MinMagnitude(One, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitude(Float.MaxValue, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitude(Float.PositiveInfinity, One) + .Should().Be(One); + } + [Fact] + public static void MinMagnitudeNumberTest() + { + NumberBaseHelper.MinMagnitudeNumber(Float.NegativeInfinity, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitudeNumber(Float.MinValue, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitudeNumber(NegativeOne, One) + .Should().Be(NegativeOne); + NumberBaseHelper.MinMagnitudeNumber(-GreatestSubnormal, One) + .Should().Be(-GreatestSubnormal); + NumberBaseHelper.MinMagnitudeNumber(-Float.Epsilon, One) + .Should().Be(-Float.Epsilon); + NumberBaseHelper.MinMagnitudeNumber(NegativeZero, One) + .Should().Be(NegativeZero); + NumberBaseHelper.MinMagnitudeNumber(Float.NaN, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitudeNumber(Zero, One) + .Should().Be(Zero); + NumberBaseHelper.MinMagnitudeNumber(Float.Epsilon, One) + .Should().Be(Float.Epsilon); + NumberBaseHelper.MinMagnitudeNumber(GreatestSubnormal, One) + .Should().Be(GreatestSubnormal); + NumberBaseHelper.MinMagnitudeNumber(One, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitudeNumber(Float.MaxValue, One) + .Should().Be(One); + NumberBaseHelper.MinMagnitudeNumber(Float.PositiveInfinity, One) + .Should().Be(One); + } + #endregion + } +} diff --git a/src/MissingValues.Tests/Core/QuadTest.TheoryData.cs b/src/MissingValues.Tests/Core/QuadTest.TheoryData.cs new file mode 100644 index 0000000..7d85625 --- /dev/null +++ b/src/MissingValues.Tests/Core/QuadTest.TheoryData.cs @@ -0,0 +1,761 @@ +using System; +using System.Collections.Generic; +using System.Diagnostics.Contracts; +using System.Globalization; +using System.Xml; + +namespace MissingValues.Tests.Core +{ + public partial class QuadTest + { +#pragma warning disable S3263 // Static fields should appear in the order they must be initialized + private static (string, bool, Quad)[] _tryParseData = + { + ("2,0", true, Two), + ("-2", true, NegativeTwo), + ("0", true, Zero), + (NumberFormatInfo.CurrentInfo.PositiveInfinitySymbol, true, Quad.PositiveInfinity), + (NumberFormatInfo.CurrentInfo.NegativeInfinitySymbol, true, Quad.NegativeInfinity), + (NumberFormatInfo.CurrentInfo.NaNSymbol, true, Quad.NaN), + ("256,4995", true, Values.CreateQuad(0x4007_007F_DF3B_645A, 0x1CAC_0831_26E9_78D5)), + ("471581881", true, Values.CreateQuad(0x401B_C1BC_4B90_0000, 0x0000_0000_0000_0000)), + ("1,93561113", true, Values.CreateQuad(0x3FFF_EF84_3605_1FA4, 0x8B0F_3D34_BECE_8762)), + ("9715574,2", true, Values.CreateQuad(0x4016_287E_EC66_6666, 0x6666_6666_6666_6666)), + ("0,51438427732005011792", true, Values.CreateQuad(0x3FFE_075D_6041_5519, 0x72D0_0AD3_7DB4_57E9)), + ("0,04201133209656899095", true, Values.CreateQuad(0x3FFA_5828_262D_512C, 0x8840_B3B3_D424_5947)), + ("7,7E777", true, Values.CreateQuad(0x4A17_0F28_5D1D_4C84, 0xA11F_6899_101B_A9A4)), + ("-7,7E-777", true, Values.CreateQuad(0xB5EC_BFCE_3AF6_4E08, 0x42C8_5750_BEBD_A572)), + ("1A", false, default), + }; + + private static (Quad, Quad)[] _unaryNegationOperationData = + { + (One, NegativeOne), + (Two, NegativeTwo), + (Ten, NegativeTen), + (Hundred, NegativeHundred), + (Thousand, NegativeThousand) + }; + private static (Quad, Quad)[] _incrementOperationData = + { + (NegativeTwo, NegativeOne), + (NegativeOne, Zero), + (Zero, One), + (One, Two), + }; + private static (Quad, Quad)[] _decrementOperationData = + { + (NegativeOne, NegativeTwo), + (Zero, NegativeOne), + (One, Zero), + (Two, One), + }; + + private static (Quad, Quad, Quad)[] _additionOperationData = + { + (One, One, Two), + (One, NegativeOne, Zero), + (One, NegativeTwo, NegativeOne), + (Quad.PositiveInfinity, Quad.One, Quad.PositiveInfinity), + (Quad.NegativeInfinity, Quad.One, Quad.NegativeInfinity), + (Quad.PositiveInfinity, Quad.PositiveInfinity, Quad.PositiveInfinity), + (Quad.NegativeInfinity, Quad.NegativeInfinity, Quad.NegativeInfinity), + }; + private static (Quad, Quad, Quad)[] _subtractionOperationData = + { + (One, One, Zero), + (One, NegativeOne, Two), + (One, Two, NegativeOne), + (Quad.PositiveInfinity, Quad.PositiveInfinity, Quad.NaN), + (Quad.NegativeInfinity, Quad.NegativeInfinity, Quad.NaN), + }; + private static (Quad, Quad, Quad)[] _multiplicationOperationData = + { + (One, One, One), + (One, NegativeOne, NegativeOne), + (Ten, Ten, Hundred), + (NegativeHundred, Ten, NegativeThousand), + (Zero, NegativeThousand, NegativeZero), + (Zero, Quad.PositiveInfinity, Quad.NaN), + (NegativeZero, Quad.NegativeInfinity, Quad.NaN), + (Quad.PositiveInfinity, Zero, Quad.NaN), + (Quad.NegativeInfinity, NegativeZero, Quad.NaN), + }; + private static (Quad, Quad, Quad)[] _divisionOperationData = + { + (Ten, Ten, One), + (Hundred, Ten, Ten), + (NegativeThousand, Ten, NegativeHundred), + (Zero, Zero, Quad.NaN), + (One, Zero, Quad.PositiveInfinity), + (NegativeOne, Zero, Quad.NegativeInfinity), + (Quad.PositiveInfinity, Quad.PositiveInfinity, Quad.NaN), + (Quad.NegativeInfinity, Quad.NegativeInfinity, Quad.NaN), + }; + + private static (byte, Quad)[] _castFromByteData = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (byte.MaxValue, ByteMaxValue), + }; + private static (ushort, Quad)[] _castFromUInt16Data = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (byte.MaxValue, ByteMaxValue), + (ushort.MaxValue, UInt16MaxValue), + }; + private static (uint, Quad)[] _castFromUInt32Data = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (byte.MaxValue, ByteMaxValue), + (ushort.MaxValue, UInt16MaxValue), + (uint.MaxValue, UInt32MaxValue), + }; + private static (ulong, Quad)[] _castFromUInt64Data = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (byte.MaxValue, ByteMaxValue), + (ushort.MaxValue, UInt16MaxValue), + (uint.MaxValue, UInt32MaxValue), + (ulong.MaxValue, UInt64MaxValue), + }; + private static (UInt128, Quad)[] _castFromUInt128Data = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (byte.MaxValue, ByteMaxValue), + (ushort.MaxValue, UInt16MaxValue), + (uint.MaxValue, UInt32MaxValue), + (ulong.MaxValue, UInt64MaxValue), + }; + private static (UInt256, Quad)[] _castFromUInt256Data = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (byte.MaxValue, ByteMaxValue), + (ushort.MaxValue, UInt16MaxValue), + (uint.MaxValue, UInt32MaxValue), + (ulong.MaxValue, UInt64MaxValue), + }; + private static (UInt512, Quad)[] _castFromUInt512Data = + { + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (byte.MaxValue, ByteMaxValue), + (ushort.MaxValue, UInt16MaxValue), + (uint.MaxValue, UInt32MaxValue), + (ulong.MaxValue, UInt64MaxValue), + }; + private static (sbyte, Quad)[] _castFromSByteData = + { + (sbyte.MinValue, SByteMinValue), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (sbyte.MaxValue, SByteMaxValue), + }; + private static (short, Quad)[] _castFromInt16Data = + { + (short.MinValue, Int16MinValue), + (sbyte.MinValue, SByteMinValue), + (-1000, NegativeThousand), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (sbyte.MaxValue, SByteMaxValue), + (short.MaxValue, Int16MaxValue), + }; + private static (int, Quad)[] _castFromInt32Data = + { + (int.MinValue, Int32MinValue), + (short.MinValue, Int16MinValue), + (sbyte.MinValue, SByteMinValue), + (-1000, NegativeThousand), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (sbyte.MaxValue, SByteMaxValue), + (short.MaxValue, Int16MaxValue), + (int.MaxValue, Int32MaxValue), + }; + private static (long, Quad)[] _castFromInt64Data = + { + (long.MinValue, Int64MinValue), + (int.MinValue, Int32MinValue), + (short.MinValue, Int16MinValue), + (sbyte.MinValue, SByteMinValue), + (-1000, NegativeThousand), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (sbyte.MaxValue, SByteMaxValue), + (short.MaxValue, Int16MaxValue), + (int.MaxValue, Int32MaxValue), + (long.MaxValue, Int64MaxValue), + }; + private static (Int128, Quad)[] _castFromInt128Data = + { + (long.MinValue, Int64MinValue), + (int.MinValue, Int32MinValue), + (short.MinValue, Int16MinValue), + (sbyte.MinValue, SByteMinValue), + (-1000, NegativeThousand), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (sbyte.MaxValue, SByteMaxValue), + (short.MaxValue, Int16MaxValue), + (int.MaxValue, Int32MaxValue), + (long.MaxValue, Int64MaxValue), + }; + private static (Int256, Quad)[] _castFromInt256Data = + { + (long.MinValue, Int64MinValue), + (int.MinValue, Int32MinValue), + (short.MinValue, Int16MinValue), + (sbyte.MinValue, SByteMinValue), + (-1000, NegativeThousand), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (sbyte.MaxValue, SByteMaxValue), + (short.MaxValue, Int16MaxValue), + (int.MaxValue, Int32MaxValue), + (long.MaxValue, Int64MaxValue), + }; + private static (Int512, Quad)[] _castFromInt512Data = + { + (long.MinValue, Int64MinValue), + (int.MinValue, Int32MinValue), + (short.MinValue, Int16MinValue), + (sbyte.MinValue, SByteMinValue), + (-1000, NegativeThousand), + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + (1000, Thousand), + (sbyte.MaxValue, SByteMaxValue), + (short.MaxValue, Int16MaxValue), + (int.MaxValue, Int32MaxValue), + (long.MaxValue, Int64MaxValue), + }; + private static (Half, Quad)[] _castFromHalfData = + { + (System.Half.NegativeOne, NegativeOne), + (System.Half.NegativeZero, NegativeZero), + (System.Half.Zero, Zero), + (System.Half.One, One), + ((Half)10, Ten), + ((Half)100, Hundred), + ((Half)1000, Thousand), + }; + private static (float, Quad)[] _castFromSingleData = + { + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + }; + private static (double, Quad)[] _castFromDoubleData = + { + (-100, NegativeHundred), + (-10, NegativeTen), + (-2, NegativeTwo), + (-1, NegativeOne), + (0, Zero), + (1, One), + (2, Two), + (10, Ten), + (100, Hundred), + }; + + private static (Quad, byte)[] _castToByteData = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (ByteMaxValue, byte.MaxValue), + }; + private static (Quad, ushort)[] _castToUInt16Data = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (Thousand, 1000), + (ByteMaxValue, byte.MaxValue), + (UInt16MaxValue, ushort.MaxValue), + }; + private static (Quad, uint)[] _castToUInt32Data = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (Thousand, 1000), + (ByteMaxValue, byte.MaxValue), + (UInt16MaxValue, ushort.MaxValue), + (UInt32MaxValue, uint.MaxValue), + }; + private static (Quad, ulong)[] _castToUInt64Data = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Thousand, 1000), + (ByteMaxValue, byte.MaxValue), + (UInt16MaxValue, ushort.MaxValue), + (UInt32MaxValue, uint.MaxValue), + (UInt64MaxValue, ulong.MaxValue), + }; + private static (Quad, UInt128)[] _castToUInt128Data = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (Thousand, 1000), + (ByteMaxValue, byte.MaxValue), + (UInt16MaxValue, ushort.MaxValue), + (UInt32MaxValue, uint.MaxValue), + (UInt64MaxValue, ulong.MaxValue), + }; + private static (Quad, UInt256)[] _castToUInt256Data = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (Thousand, 1000), + (ByteMaxValue, byte.MaxValue), + (UInt16MaxValue, ushort.MaxValue), + (UInt32MaxValue, uint.MaxValue), + (UInt64MaxValue, ulong.MaxValue), + }; + private static (Quad, UInt512)[] _castToUInt512Data = + { + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (Thousand, 1000), + (ByteMaxValue, byte.MaxValue), + (UInt16MaxValue, ushort.MaxValue), + (UInt32MaxValue, uint.MaxValue), + (UInt64MaxValue, ulong.MaxValue), + }; + private static (Quad, sbyte)[] _castToSByteData = + { + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + }; + private static (Quad, short)[] _castToInt16Data = + { + (Int16MinValue, short.MinValue), + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + (Int16MaxValue, short.MaxValue), + }; + private static (Quad, int)[] _castToInt32Data = + { + (Int32MinValue, int.MinValue), + (Int16MinValue, short.MinValue), + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + (Int16MaxValue, short.MaxValue), + (Int32MaxValue, int.MaxValue), + }; + private static (Quad, long)[] _castToInt64Data = + { + (Int64MinValue, long.MinValue), + (Int32MinValue, int.MinValue), + (Int16MinValue, short.MinValue), + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + (Int16MaxValue, short.MaxValue), + (Int32MaxValue, int.MaxValue), + (Int64MaxValue, long.MaxValue), + }; + private static (Quad, Int128)[] _castToInt128Data = + { + (Int64MinValue, long.MinValue), + (Int32MinValue, int.MinValue), + (Int16MinValue, short.MinValue), + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + (Int16MaxValue, short.MaxValue), + (Int32MaxValue, int.MaxValue), + (Int64MaxValue, long.MaxValue), + }; + private static (Quad, Int256)[] _castToInt256Data = + { + (Int64MinValue, long.MinValue), + (Int32MinValue, int.MinValue), + (Int16MinValue, short.MinValue), + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + (Int16MaxValue, short.MaxValue), + (Int32MaxValue, int.MaxValue), + (Int64MaxValue, long.MaxValue), + }; + private static (Quad, Int512)[] _castToInt512Data = + { + (Int64MinValue, long.MinValue), + (Int32MinValue, int.MinValue), + (Int16MinValue, short.MinValue), + (SByteMinValue, sbyte.MinValue), + (NegativeHundred, -100), + (NegativeTen, -10), + (NegativeTwo, -2), + (NegativeOne, -1), + (Half, 0), + (One, 1), + (Two, 2), + (Ten, 10), + (Hundred, 100), + (SByteMaxValue, sbyte.MaxValue), + (Int16MaxValue, short.MaxValue), + (Int32MaxValue, int.MaxValue), + (Int64MaxValue, long.MaxValue), + }; + private static (Quad, Half)[] _castToHalfData = + { + (NegativeHundred, -(Half)100.0f), + (NegativeTen, -(Half)10.0f), + (NegativeTwo, -(Half)2.0f), + (NegativeOne, -(Half)1.0f), + (NegativeZero, -(Half)0.0f), + (Zero, (Half)0.0f), + (One, System.Half.One), + (Two, (Half)2.0f), + (Ten, (Half)10.0f), + (Hundred, (Half)100.0f), + }; + private static (Quad, float)[] _castToSingleData = + { + (NegativeThousand, -1000.0f), + (NegativeHundred, -100.0f), + (NegativeTen, -10.0f), + (NegativeTwo, -2.0f), + (NegativeOne, -1.0f), + (NegativeZero, -0.0f), + (Zero, 0.0f), + (Half, 0.5f), + (One, 1.0f), + (Two, 2.0f), + (Ten, 10.0f), + (Hundred, 100.0f), + (Thousand, 1000.0f), + }; + private static (Quad, double)[] _castToDoubleData = + { + (NegativeThousand, -1000.0d), + (NegativeHundred, -100.0d), + (NegativeTen, -10.0d), + (NegativeTwo, -2.0d), + (NegativeOne, -1.0d), + (NegativeZero, -0.0d), + (Zero, 0.0d), + (Half, 0.5d), + (One, 1.0d), + (Two, 2.0d), + (Ten, 10.0d), + (Hundred, 100.0d), + (Thousand, 1000.0d), + }; + + private static (Quad, int, MidpointRounding, Quad)[] _roundAwayFromZeroData = + { + (Values.CreateQuad(0x4000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.AwayFromZero, Four), + (Values.CreateQuad(0x4000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.AwayFromZero, Three), + (Values.CreateQuad(0x4000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.AwayFromZero, Three), + (Values.CreateQuad(0x4000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.AwayFromZero, Two), + (Values.CreateQuad(0xC000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.AwayFromZero, NegativeTwo), + (Values.CreateQuad(0xC000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.AwayFromZero, NegativeThree), + (Values.CreateQuad(0xC000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.AwayFromZero, NegativeThree), + (Values.CreateQuad(0xC000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.AwayFromZero, NegativeFour), + }; + private static (Quad, int, MidpointRounding, Quad)[] _roundToEvenData = + { + (Values.CreateQuad(0x4000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToEven, Four), + (Values.CreateQuad(0x4000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToEven, Three), + (Values.CreateQuad(0x4000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToEven, Two), + (Values.CreateQuad(0x4000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToEven, Two), + (Values.CreateQuad(0xC000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToEven, NegativeTwo), + (Values.CreateQuad(0xC000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToEven, NegativeTwo), + (Values.CreateQuad(0xC000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToEven, NegativeThree), + (Values.CreateQuad(0xC000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToEven, NegativeFour), + }; + private static (Quad, int, MidpointRounding, Quad)[] _roundToNegativeInfinityData = + { + (Values.CreateQuad(0x4000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToNegativeInfinity, Three), + (Values.CreateQuad(0x4000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToNegativeInfinity, Two), + (Values.CreateQuad(0x4000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToNegativeInfinity, Two), + (Values.CreateQuad(0x4000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToNegativeInfinity, Two), + (Values.CreateQuad(0xC000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToNegativeInfinity, NegativeThree), + (Values.CreateQuad(0xC000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToNegativeInfinity, NegativeThree), + (Values.CreateQuad(0xC000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToNegativeInfinity, NegativeThree), + (Values.CreateQuad(0xC000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToNegativeInfinity, NegativeFour), + }; + private static (Quad, int, MidpointRounding, Quad)[] _roundToPositiveInfinityData = + { + (Values.CreateQuad(0x4000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToPositiveInfinity, Four), + (Values.CreateQuad(0x4000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToPositiveInfinity, Three), + (Values.CreateQuad(0x4000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToPositiveInfinity, Three), + (Values.CreateQuad(0x4000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToPositiveInfinity, Three), + (Values.CreateQuad(0xC000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToPositiveInfinity, NegativeTwo), + (Values.CreateQuad(0xC000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToPositiveInfinity, NegativeTwo), + (Values.CreateQuad(0xC000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToPositiveInfinity, NegativeTwo), + (Values.CreateQuad(0xC000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToPositiveInfinity, NegativeThree), + }; + private static (Quad, int, MidpointRounding, Quad)[] _roundToZeroData = + { + (Values.CreateQuad(0x4000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToZero, Three), + (Values.CreateQuad(0x4000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToZero, Two), + (Values.CreateQuad(0x4000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToZero, Two), + (Values.CreateQuad(0x4000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToZero, Two), + (Values.CreateQuad(0xC000_0CCC_CCCC_CCCC, 0xCCCC_CCCC_CCCC_CCCD), 0, MidpointRounding.ToZero, NegativeTwo), + (Values.CreateQuad(0xC000_4000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToZero, NegativeTwo), + (Values.CreateQuad(0xC000_6666_6666_6666, 0x6666_6666_6666_6666), 0, MidpointRounding.ToZero, NegativeTwo), + (Values.CreateQuad(0xC000_C000_0000_0000, 0x0000_0000_0000_0000), 0, MidpointRounding.ToZero, NegativeThree), + }; + + private static (Quad, Quad, bool)[] _greaterThanData = + { + (Two, One, true), + (Thousand, NegativeThousand, true), + (NegativeQuarter, NegativeHalf, true), + (Quarter, Half, false), + (Ten, Hundred, false), + (GreaterThanOneSmallest, One, true), + }; + private static (Quad, Quad, bool)[] _lessThanData = + { + (Zero, One, true), + (Zero, Quarter, true), + (NegativeThousand, Thousand, true), + (NegativeOne, NegativeThree, false), + (Hundred, Two, false), + (LessThanOneLargest, One, true), + }; + private static (Quad, Quad, bool)[] _equalToData = + { + (One, One, true), + (Two, Two, true), + (Quad.NaN, Quad.NaN, false), + (GreatestSubnormal, GreatestSubnormal, true), + }; + private static (Quad, Quad, bool)[] _notEqualToData = + { + (One, One, false), + (Quad.NaN, Quad.NaN, true), + (NegativeTwo, Two, true), + (SmallestSubnormal, GreatestSubnormal, true) + }; + + + public static TryParseTheoryData TryParseTheoryData = new(_tryParseData); + + public static UnaryTheoryData UnaryNegationOperationTheoryData = new(_unaryNegationOperationData); + public static UnaryTheoryData IncrementOperationTheoryData = new(_incrementOperationData); + public static UnaryTheoryData DecrementOperationTheoryData = new(_decrementOperationData); + + public static OperationTheoryData AdditionOperationTheoryData = new(_additionOperationData); + public static OperationTheoryData SubtractionOperationTheoryData = new(_subtractionOperationData); + public static OperationTheoryData MultiplicationOperationTheoryData = new(_multiplicationOperationData); + public static OperationTheoryData DivisionOperationTheoryData = new(_divisionOperationData); + + public static CastingTheoryData CastFromByteTheoryData = new(_castFromByteData); + public static CastingTheoryData CastFromUInt16TheoryData = new(_castFromUInt16Data); + public static CastingTheoryData CastFromUInt32TheoryData = new(_castFromUInt32Data); + public static CastingTheoryData CastFromUInt64TheoryData = new(_castFromUInt64Data); + public static CastingTheoryData CastFromUInt128TheoryData = new(_castFromUInt128Data); + public static CastingTheoryData CastFromUInt256TheoryData = new(_castFromUInt256Data); + public static CastingTheoryData CastFromUInt512TheoryData = new(_castFromUInt512Data); + public static CastingTheoryData CastFromSByteTheoryData = new(_castFromSByteData); + public static CastingTheoryData CastFromInt16TheoryData = new(_castFromInt16Data); + public static CastingTheoryData CastFromInt32TheoryData = new(_castFromInt32Data); + public static CastingTheoryData CastFromInt64TheoryData = new(_castFromInt64Data); + public static CastingTheoryData CastFromInt128TheoryData = new(_castFromInt128Data); + public static CastingTheoryData CastFromInt256TheoryData = new(_castFromInt256Data); + public static CastingTheoryData CastFromInt512TheoryData = new(_castFromInt512Data); + public static CastingTheoryData CastFromHalfTheoryData = new(_castFromHalfData); + public static CastingTheoryData CastFromSingleTheoryData = new(_castFromSingleData); + public static CastingTheoryData CastFromDoubleTheoryData = new(_castFromDoubleData); + + public static CastingTheoryData CastToByteTheoryData = new(_castToByteData); + public static CastingTheoryData CastToUInt16TheoryData = new(_castToUInt16Data); + public static CastingTheoryData CastToUInt32TheoryData = new(_castToUInt32Data); + public static CastingTheoryData CastToUInt64TheoryData = new(_castToUInt64Data); + public static CastingTheoryData CastToUInt128TheoryData = new(_castToUInt128Data); + public static CastingTheoryData CastToUInt256TheoryData = new(_castToUInt256Data); + public static CastingTheoryData CastToUInt512TheoryData = new(_castToUInt512Data); + public static CastingTheoryData CastToSByteTheoryData = new(_castToSByteData); + public static CastingTheoryData CastToInt16TheoryData = new(_castToInt16Data); + public static CastingTheoryData CastToInt32TheoryData = new(_castToInt32Data); + public static CastingTheoryData CastToInt64TheoryData = new(_castToInt64Data); + public static CastingTheoryData CastToInt128TheoryData = new(_castToInt128Data); + public static CastingTheoryData CastToInt256TheoryData = new(_castToInt256Data); + public static CastingTheoryData CastToInt512TheoryData = new(_castToInt512Data); + public static CastingTheoryData CastToHalfTheoryData = new(_castToHalfData); + public static CastingTheoryData CastToSingleTheoryData = new(_castToSingleData); + public static CastingTheoryData CastToDoubleTheoryData = new(_castToDoubleData); + + public static RoundTheoryData RoundAwayFromZeroTheoryData = new(_roundAwayFromZeroData); + public static RoundTheoryData RoundToEvenTheoryData = new(_roundToEvenData); + public static RoundTheoryData RoundToNegativeInfinityTheoryData = new(_roundToNegativeInfinityData); + public static RoundTheoryData RoundToPositiveInfinityTheoryData = new(_roundToPositiveInfinityData); + public static RoundTheoryData RoundToZeroTheoryData = new(_roundToZeroData); + + public static ComparisonOperatorsTheoryData GreaterThanTheoryData = new(_greaterThanData); + public static ComparisonOperatorsTheoryData LessThanTheoryData = new(_lessThanData); + public static ComparisonOperatorsTheoryData EqualToTheoryData = new(_equalToData); + public static ComparisonOperatorsTheoryData NotEqualToTheoryData = new(_notEqualToData); +#pragma warning restore S3263 // Static fields should appear in the order they must be initialized + } +} diff --git a/src/MissingValues.Tests/Core/QuadTest.cs b/src/MissingValues.Tests/Core/QuadTest.cs new file mode 100644 index 0000000..993731d --- /dev/null +++ b/src/MissingValues.Tests/Core/QuadTest.cs @@ -0,0 +1,356 @@ +using System; +using System.Collections.Generic; +using System.Diagnostics.Contracts; +using System.Globalization; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Core +{ + public partial class QuadTest + { + public static readonly Quad NegativeThousand = Values.CreateQuad(0xC008_F400_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeHundred = Values.CreateQuad(0xC005_9000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeTen = Values.CreateQuad(0xC002_4000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeFour = Values.CreateQuad(0xC001_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeThree = Values.CreateQuad(0xC000_8000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeTwo = Values.CreateQuad(0xC000_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeOne = Quad.NegativeOne; + public static readonly Quad NegativeHalf = Values.CreateQuad(0xBFFE_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeQuarter = Values.CreateQuad(0xBFFD_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad NegativeZero = Quad.NegativeZero; + public static readonly Quad Zero = Quad.Zero; + public static readonly Quad Quarter = Values.CreateQuad(0x3FFD_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Half = Values.CreateQuad(0x3FFE_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad One = Quad.One; + public static readonly Quad Two = Values.CreateQuad(0x4000_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Three = Values.CreateQuad(0x4000_8000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Four = Values.CreateQuad(0x4001_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Ten = Values.CreateQuad(0x4002_4000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Hundred = Values.CreateQuad(0x4005_9000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Thousand = Values.CreateQuad(0x4008_F400_0000_0000, 0x0000_0000_0000_0000); + + public static readonly Quad GreaterThanOneSmallest = Values.CreateQuad(0x3FFF_0000_0000_0000, 0x0000_0000_0000_0001); + public static readonly Quad LessThanOneLargest = Values.CreateQuad(0x3FFE_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + + public static readonly Quad SmallestSubnormal = Values.CreateQuad(0x0000_0000_0000_0000, 0x0000_0000_0000_0001); + public static readonly Quad GreatestSubnormal = Values.CreateQuad(0x0000_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + + public static readonly Quad MaxValue = Quad.MaxValue; + public static readonly Quad MinValue = Quad.MinValue; + + public static readonly Quad ByteMaxValue = Values.CreateQuad(0x4006_FE00_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad UInt16MaxValue = Values.CreateQuad(0x400E_FFFE_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad UInt32MaxValue = Values.CreateQuad(0x401E_FFFF_FFFE_0000, 0x0000_0000_0000_0000); + public static readonly Quad UInt64MaxValue = Values.CreateQuad(0x403E_FFFF_FFFF_FFFF, 0xFFFE_0000_0000_0000); + public static readonly Quad UInt128MaxValue = Values.CreateQuad(0x407F_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad UInt256MaxValue = Values.CreateQuad(0x40FF_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad UInt512MaxValue = Values.CreateQuad(0x41FF_0000_0000_0000, 0x0000_0000_0000_0000); + + public static readonly Quad SByteMaxValue = Values.CreateQuad(0x4005_FC00_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad SByteMinValue = Values.CreateQuad(0xC006_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Int16MaxValue = Values.CreateQuad(0x400D_FFFC_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Int16MinValue = Values.CreateQuad(0xC00E_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Int32MaxValue = Values.CreateQuad(0x401D_FFFF_FFFC_0000, 0x0000_0000_0000_0000); + public static readonly Quad Int32MinValue = Values.CreateQuad(0xC01E_0000_0000_0000, 0x0000_0000_0000_0000); + public static readonly Quad Int64MaxValue = Values.CreateQuad(0x403D_FFFF_FFFF_FFFF, 0xFFFC_0000_0000_0000); + public static readonly Quad Int64MinValue = Values.CreateQuad(0xC03E_0000_0000_0000, 0x0000_0000_0000_0000); + + public static readonly int Radix = 2; + + + [Fact] + public void Ctor_Empty() + { + var i = new Quad(); + Assert.Equal(Zero, i); + } + + [Theory] + [MemberData(nameof(CastFromByteTheoryData))] + public void Cast_FromByte(byte from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromUInt16TheoryData))] + public void Cast_FromUInt16(ushort from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromUInt32TheoryData))] + public void Cast_FromUInt32(uint from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromUInt64TheoryData))] + public void Cast_FromUInt64(ulong from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromUInt128TheoryData))] + public void Cast_FromUInt128(UInt128 from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromUInt256TheoryData))] + public void Cast_FromUInt256(UInt256 from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromUInt512TheoryData))] + public void Cast_FromUInt512(UInt512 from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromSByteTheoryData))] + public void Cast_FromSByte(sbyte from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromInt16TheoryData))] + public void Cast_FromInt16(short from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromInt32TheoryData))] + public void Cast_FromInt32(int from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromInt64TheoryData))] + public void Cast_FromInt64(long from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromInt128TheoryData))] + public void Cast_FromInt128(Int128 from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromInt256TheoryData))] + public void Cast_FromInt256(Int256 from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromInt512TheoryData))] + public void Cast_FromInt512(Int512 from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromHalfTheoryData))] + public void Cast_FromHalf(Half from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromSingleTheoryData))] + public void Cast_FromSingle(float from, Quad to) + { + ((Quad)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastFromDoubleTheoryData))] + public void Cast_FromDouble(double from, Quad to) + { + ((Quad)from).Should().Be(to); + } + + [Theory] + [MemberData(nameof(CastToByteTheoryData))] + public void Cast_ToByte(Quad from, byte to) + { + ((byte)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToUInt16TheoryData))] + public void Cast_ToUInt16(Quad from, ushort to) + { + ((ushort)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToUInt32TheoryData))] + public void Cast_ToUInt32(Quad from, uint to) + { + ((uint)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToUInt64TheoryData))] + public void Cast_ToUInt64(Quad from, ulong to) + { + ((ulong)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToUInt128TheoryData))] + public void Cast_ToUInt128(Quad from, UInt128 to) + { + ((UInt128)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToUInt256TheoryData))] + public void Cast_ToUInt256(Quad from, UInt256 to) + { + ((UInt256)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToUInt512TheoryData))] + public void Cast_ToUInt512(Quad from, UInt512 to) + { + ((UInt512)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToSByteTheoryData))] + public void Cast_ToSByte(Quad from, sbyte to) + { + ((sbyte)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToInt16TheoryData))] + public void Cast_ToInt16(Quad from, short to) + { + ((short)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToInt32TheoryData))] + public void Cast_ToInt32(Quad from, int to) + { + ((int)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToInt64TheoryData))] + public void Cast_ToInt64(Quad from, long to) + { + ((long)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToInt128TheoryData))] + public void Cast_ToInt128(Quad from, Int128 to) + { + ((Int128)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToInt256TheoryData))] + public void Cast_ToInt256(Quad from, Int256 to) + { + ((Int256)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToInt512TheoryData))] + public void Cast_ToInt512(Quad from, Int512 to) + { + ((Int512)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToHalfTheoryData))] + public void Cast_ToHalf(Quad from, Half to) + { + ((Half)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToSingleTheoryData))] + public void Cast_ToSingle(Quad from, float to) + { + ((float)from).Should().Be(to); + } + [Theory] + [MemberData(nameof(CastToDoubleTheoryData))] + public void Cast_ToDouble(Quad from, double to) + { + ((double)from).Should().Be(to); + } + + [Fact] + public void ToGeneralStringTest() + { + NegativeQuarter.ToString("G33", CultureInfo.InvariantCulture) + .Should().Be("-0.25"); + Half.ToString("G33", CultureInfo.InvariantCulture) + .Should().Be("0.5"); + NegativeHalf.ToString("G33", CultureInfo.InvariantCulture) + .Should().Be("-0.5"); + One.ToString("G33", CultureInfo.InvariantCulture) + .Should().Be("1"); + Thousand.ToString("G33", CultureInfo.InvariantCulture) + .Should().Be("1000"); + NegativeThousand.ToString("G33", CultureInfo.InvariantCulture) + .Should().Be("-1000"); + } + + [Fact] + public void ToScientificStringTest() + { + NegativeQuarter.ToString("E33", CultureInfo.InvariantCulture) + .Should().Be("-2.5E-1"); + Half.ToString("E33", CultureInfo.InvariantCulture) + .Should().Be("5E-1"); + NegativeHalf.ToString("E33", CultureInfo.InvariantCulture) + .Should().Be("-5E-1"); + One.ToString("E33", CultureInfo.InvariantCulture) + .Should().Be("1E+0"); + Thousand.ToString("E33", CultureInfo.InvariantCulture) + .Should().Be("1E+3"); + NegativeThousand.ToString("E33", CultureInfo.InvariantCulture) + .Should().Be("-1E+3"); + } + + [Fact] + public void ToGeneralFormatStringTest() + { + $"{NegativeQuarter:G33}" + .Should().Be("-0,25"); + $"{Half:G33}" + .Should().Be("0,5"); + $"{NegativeHalf:G33}" + .Should().Be("-0,5"); + $"{One:G33}" + .Should().Be("1"); + $"{Thousand:G33}" + .Should().Be("1000"); + $"{NegativeThousand:G33}" + .Should().Be("-1000"); + } + + [Fact] + public void ToScientificFormatStringTest() + { + $"{NegativeQuarter:E33}" + .Should().Be("-2,5E-1"); + $"{Half:E33}" + .Should().Be("5E-1"); + $"{NegativeHalf:E33}" + .Should().Be("-5E-1"); + $"{One:E33}" + .Should().Be("1E+0"); + $"{Thousand:E33}" + .Should().Be("1E+3"); + $"{NegativeThousand:E33}" + .Should().Be("-1E+3"); + } + + + + [Theory] + [MemberData(nameof(TryParseTheoryData))] + public void TryParseTest(string s, bool success, Quad returnValue) + { + Quad result; + + Quad.TryParse(s, out result).Should().Be(success); + result.Should().Be(returnValue); + } + } +} diff --git a/src/MissingValues.Tests/UInt256Test.GenericMath.cs b/src/MissingValues.Tests/Core/UInt256Test.GenericMath.cs similarity index 99% rename from src/MissingValues.Tests/UInt256Test.GenericMath.cs rename to src/MissingValues.Tests/Core/UInt256Test.GenericMath.cs index 3306852..4016920 100644 --- a/src/MissingValues.Tests/UInt256Test.GenericMath.cs +++ b/src/MissingValues.Tests/Core/UInt256Test.GenericMath.cs @@ -7,7 +7,7 @@ using UInt = MissingValues.UInt256; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class UInt256Test { diff --git a/src/MissingValues.Tests/UInt256Test.cs b/src/MissingValues.Tests/Core/UInt256Test.cs similarity index 99% rename from src/MissingValues.Tests/UInt256Test.cs rename to src/MissingValues.Tests/Core/UInt256Test.cs index f142264..fa1ce76 100644 --- a/src/MissingValues.Tests/UInt256Test.cs +++ b/src/MissingValues.Tests/Core/UInt256Test.cs @@ -7,7 +7,7 @@ using UInt = MissingValues.UInt256; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class UInt256Test { diff --git a/src/MissingValues.Tests/UInt512Test.GenericMath.cs b/src/MissingValues.Tests/Core/UInt512Test.GenericMath.cs similarity index 99% rename from src/MissingValues.Tests/UInt512Test.GenericMath.cs rename to src/MissingValues.Tests/Core/UInt512Test.GenericMath.cs index ba773dc..f2072fd 100644 --- a/src/MissingValues.Tests/UInt512Test.GenericMath.cs +++ b/src/MissingValues.Tests/Core/UInt512Test.GenericMath.cs @@ -7,7 +7,7 @@ using UInt = MissingValues.UInt512; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class UInt512Test { diff --git a/src/MissingValues.Tests/UInt512Test.cs b/src/MissingValues.Tests/Core/UInt512Test.cs similarity index 99% rename from src/MissingValues.Tests/UInt512Test.cs rename to src/MissingValues.Tests/Core/UInt512Test.cs index 1c05181..abb6194 100644 --- a/src/MissingValues.Tests/UInt512Test.cs +++ b/src/MissingValues.Tests/Core/UInt512Test.cs @@ -7,7 +7,7 @@ using UInt = MissingValues.UInt512; -namespace MissingValues.Tests +namespace MissingValues.Tests.Core { public partial class UInt512Test { diff --git a/src/MissingValues.Tests/Helpers/BinaryFloatingPointIeee754Helper.cs b/src/MissingValues.Tests/Helpers/BinaryFloatingPointIeee754Helper.cs new file mode 100644 index 0000000..7ddfc63 --- /dev/null +++ b/src/MissingValues.Tests/Helpers/BinaryFloatingPointIeee754Helper.cs @@ -0,0 +1,12 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Helpers +{ + internal static class BinaryFloatingPointIeee754Helper + { + } +} diff --git a/src/MissingValues.Tests/Helpers/FloatingPoint.cs b/src/MissingValues.Tests/Helpers/FloatingPoint.cs new file mode 100644 index 0000000..14ec260 --- /dev/null +++ b/src/MissingValues.Tests/Helpers/FloatingPoint.cs @@ -0,0 +1,52 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Numerics; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Helpers +{ + internal static class FloatingPoint + where TSelf : IFloatingPoint + { + /// + public static TSelf Ceiling(TSelf x) => TSelf.Ceiling(x); + /// + public static TSelf Floor(TSelf x) => TSelf.Floor(x); + /// + public static TSelf Round(TSelf x) => TSelf.Round(x); + /// + public static TSelf Round(TSelf x, int digits) => TSelf.Round(x, digits); + /// + public static TSelf Round(TSelf x, MidpointRounding mode) => TSelf.Round(x, mode); + /// + public static TSelf Round(TSelf x, int digits, MidpointRounding mode) => TSelf.Round(x, digits, mode); + /// + public static TSelf Truncate(TSelf x) => TSelf.Truncate(x); + /// + public static int GetExponentByteCount(TSelf x) => x.GetExponentByteCount(); + /// + public static int GetExponentShortestBitLength(TSelf x) => x.GetExponentShortestBitLength(); + /// + public static int GetSignificandBitLength(TSelf x) => x.GetSignificandBitLength(); + /// + public static int GetSignificandByteCount(TSelf x) => x.GetSignificandByteCount(); + public static bool TryWriteExponentBigEndian(TSelf x, Span destination, out int bytesWritten) => x.TryWriteExponentBigEndian(destination, out bytesWritten); + public static bool TryWriteExponentLittleEndian(TSelf x, Span destination, out int bytesWritten) => x.TryWriteExponentLittleEndian(destination, out bytesWritten); + public static bool TryWriteSignificandBigEndian(TSelf x, Span destination, out int bytesWritten) => x.TryWriteSignificandBigEndian(destination, out bytesWritten); + public static bool TryWriteSignificandLittleEndian(TSelf x, Span destination, out int bytesWritten) => x.TryWriteSignificandLittleEndian(destination, out bytesWritten); + public static int WriteExponentBigEndian(TSelf x, byte[] destination) => x.WriteExponentBigEndian(destination); + public static int WriteExponentBigEndian(TSelf x, byte[] destination, int startIndex) => x.WriteExponentBigEndian(destination, startIndex); + public static int WriteExponentBigEndian(TSelf x, Span destination) => x.WriteExponentBigEndian(destination); + public static int WriteExponentLittleEndian(TSelf x, byte[] destination) => x.WriteExponentLittleEndian(destination); + public static int WriteExponentLittleEndian(TSelf x, byte[] destination, int startIndex) => x.WriteExponentLittleEndian(destination, startIndex); + public static int WriteExponentLittleEndian(TSelf x, Span destination) => x.WriteExponentLittleEndian(destination); + public static int WriteSignificandBigEndian(TSelf x, byte[] destination) => x.WriteSignificandBigEndian(destination); + public static int WriteSignificandBigEndian(TSelf x, byte[] destination, int startIndex) => x.WriteSignificandBigEndian(destination, startIndex); + public static int WriteSignificandBigEndian(TSelf x, Span destination) => x.WriteSignificandBigEndian(destination); + public static int WriteSignificandLittleEndian(TSelf x, byte[] destination) => x.WriteSignificandLittleEndian(destination); + public static int WriteSignificandLittleEndian(TSelf x, byte[] destination, int startIndex) => x.WriteSignificandLittleEndian(destination, startIndex); + public static int WriteSignificandLittleEndian(TSelf x, Span destination) => x.WriteSignificandLittleEndian(destination); + } +} diff --git a/src/MissingValues.Tests/Helpers/FloatingPointIeee754.cs b/src/MissingValues.Tests/Helpers/FloatingPointIeee754.cs new file mode 100644 index 0000000..75cff1d --- /dev/null +++ b/src/MissingValues.Tests/Helpers/FloatingPointIeee754.cs @@ -0,0 +1,14 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Numerics; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Helpers +{ + internal static class FloatingPointIeee754 + where TSelf : IFloatingPointIeee754 + { + } +} diff --git a/src/MissingValues.Tests/Helpers/FluentAssertionsExtensions.cs b/src/MissingValues.Tests/Helpers/FluentAssertionsExtensions.cs new file mode 100644 index 0000000..9c07859 --- /dev/null +++ b/src/MissingValues.Tests/Helpers/FluentAssertionsExtensions.cs @@ -0,0 +1,54 @@ +using FluentAssertions.Execution; +using FluentAssertions.Numeric; +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Helpers +{ + public static class FluentAssertionsExtensions + { + public static AndConstraint> BeBitwiseEquivalentTo(this ComparableTypeAssertions> assertions, Quad expected, string because = "", params object[] becauseArgs) + { + bool condition; + + if (Quad.IsNaN((Quad)assertions.Subject) && Quad.IsNaN(expected)) + { + condition = true; + } + else + { + condition = Equals(Quad.QuadToUInt128Bits((Quad)assertions.Subject), Quad.QuadToUInt128Bits(expected)); + } + + Execute.Assertion + .ForCondition(condition) + .BecauseOf(because, becauseArgs) + .FailWith("Expected {context:object} to be equal to {0}{reason}, but found {1}.", expected, assertions.Subject); + + return new AndConstraint>((ComparableTypeAssertions)assertions); + } + public static AndConstraint> NotBeBitwiseEquivalentTo(this ComparableTypeAssertions> assertions, Quad expected, string because = "", params object[] becauseArgs) + { + bool condition; + + if (Quad.IsNaN((Quad)assertions.Subject) && Quad.IsNaN(expected)) + { + condition = true; + } + else + { + condition = Equals(Quad.QuadToUInt128Bits((Quad)assertions.Subject), Quad.QuadToUInt128Bits(expected)); + } + + Execute.Assertion + .ForCondition(!condition) + .BecauseOf(because, becauseArgs) + .FailWith("Expected {context:object} to be equal to {0}{reason}, but found {1}.", expected, assertions.Subject); + + return new AndConstraint>((ComparableTypeAssertions)assertions); + } + } +} diff --git a/src/MissingValues.Tests/Helpers/GenericMathOperatorsHelper.cs b/src/MissingValues.Tests/Helpers/GenericMathOperatorsHelper.cs index f79407f..3d49662 100644 --- a/src/MissingValues.Tests/Helpers/GenericMathOperatorsHelper.cs +++ b/src/MissingValues.Tests/Helpers/GenericMathOperatorsHelper.cs @@ -1,6 +1,7 @@ using Microsoft.VisualStudio.TestPlatform.ObjectModel; using System; using System.Collections.Generic; +using System.Diagnostics.Contracts; using System.Linq; using System.Numerics; using System.Text; @@ -31,6 +32,28 @@ public static TSelf CheckedIncrementOperation(TSelf value) { return checked(++value); } + + public static TResult UnaryPlusOperation(TSelf value) + where TSelf : IUnaryPlusOperators + { + return +value; + } + public static TResult CheckedUnaryPlusOperation(TSelf value) + where TSelf : IUnaryPlusOperators + { + return checked(+value); + } + + public static TResult UnaryNegationOperation(TSelf value) + where TSelf : IUnaryNegationOperators + { + return -value; + } + public static TResult CheckedUnaryNegationOperation(TSelf value) + where TSelf : IUnaryNegationOperators + { + return checked(-value); + } public static TResult SubtractionOperation(TSelf left, TOther right) where TSelf : ISubtractionOperators @@ -153,6 +176,7 @@ public static TResult UnsignedRightShiftOperation(TSelf value, TOther shiftAmoun return value >>> shiftAmount; } } + internal static class UnaryOperatorsHelper { public static TResult UnaryPlusOperation(TSelf value) diff --git a/src/MissingValues.Tests/Helpers/MathConstantsHelper.cs b/src/MissingValues.Tests/Helpers/MathConstantsHelper.cs index e4da546..f9e9a7f 100644 --- a/src/MissingValues.Tests/Helpers/MathConstantsHelper.cs +++ b/src/MissingValues.Tests/Helpers/MathConstantsHelper.cs @@ -39,5 +39,35 @@ public static TSelf NegativeOne() { return TSelf.NegativeOne; } + public static TSelf Pi() + where TSelf : IFloatingPointConstants + { + return TSelf.Pi; + } + public static TSelf Tau() + where TSelf : IFloatingPointConstants + { + return TSelf.Tau; + } + public static TSelf E() + where TSelf : IFloatingPointConstants + { + return TSelf.E; + } + public static TSelf PositiveInfinity() + where TSelf : IFloatingPointIeee754 + { + return TSelf.PositiveInfinity; + } + public static TSelf NegativeInfinity() + where TSelf : IFloatingPointIeee754 + { + return TSelf.NegativeInfinity; + } + public static TSelf NaN() + where TSelf : IFloatingPointIeee754 + { + return TSelf.NaN; + } } } diff --git a/src/MissingValues.Tests/Helpers/TheoryDataTypes.cs b/src/MissingValues.Tests/Helpers/TheoryDataTypes.cs new file mode 100644 index 0000000..0a2cdd8 --- /dev/null +++ b/src/MissingValues.Tests/Helpers/TheoryDataTypes.cs @@ -0,0 +1,103 @@ +using System; +using System.Collections.Generic; +using System.Diagnostics.Contracts; +using System.Linq; +using System.Numerics; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Helpers +{ + public class NumberTheoryData : TheoryData + where TSelf : INumberBase + { + public NumberTheoryData(IEnumerable data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat); + } + } + } + + public class OperationTheoryData : TheoryData + { + public OperationTheoryData(IEnumerable<(TSelf, TOther, TResult)> data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat.Item1, dat.Item2, dat.Item3); + } + } + } + + public class RoundTheoryData : TheoryData + { + public RoundTheoryData(IEnumerable<(TFloat, int, MidpointRounding, TFloat)> data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat.Item1, dat.Item2, dat.Item3, dat.Item4); + } + } + } + + public class UnaryTheoryData : TheoryData + { + public UnaryTheoryData(IEnumerable<(TSelf, TResult)> data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat.Item1, dat.Item2); + } + } + } + + public class CastingTheoryData : TheoryData + { + public CastingTheoryData(IEnumerable<(TFrom, TTo)> data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat.Item1, dat.Item2); + } + } + } + + public class ComparisonOperatorsTheoryData : TheoryData + { + public ComparisonOperatorsTheoryData(IEnumerable<(TSelf, TOther, bool)> data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat.Item1, dat.Item2, dat.Item3); + } + } + } + + public class TryParseTheoryData : TheoryData + where T : IParsable + { + public TryParseTheoryData(IEnumerable<(string, bool, T)> data) + { + Contract.Assert(data is not null && data.Any()); + + foreach (var dat in data) + { + Add(dat.Item1, dat.Item2, dat.Item3); + } + } + } +} diff --git a/src/MissingValues.Tests/Helpers/Values.cs b/src/MissingValues.Tests/Helpers/Values.cs new file mode 100644 index 0000000..850a784 --- /dev/null +++ b/src/MissingValues.Tests/Helpers/Values.cs @@ -0,0 +1,13 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Tests.Helpers +{ + internal static class Values + { + public static Quad CreateQuad(ulong upper, ulong lower) => Quad.UInt128BitsToQuad(new UInt128(upper, lower)); + } +} diff --git a/src/MissingValues/Int256.cs b/src/MissingValues/Int256.cs index 6f9f886..afe5668 100644 --- a/src/MissingValues/Int256.cs +++ b/src/MissingValues/Int256.cs @@ -296,6 +296,15 @@ public static explicit operator decimal(Int256 value) } return (decimal)(double)(UInt256)(value); } + public static explicit operator Quad(Int256 value) + { + if (IsNegative(value)) + { + value = -value; + return -(Quad)(UInt128)(value); + } + return (Quad)(UInt128)(value); + } public static explicit operator double(Int256 value) { if (IsNegative(value)) diff --git a/src/MissingValues/Int512.cs b/src/MissingValues/Int512.cs index 04249ee..449200a 100644 --- a/src/MissingValues/Int512.cs +++ b/src/MissingValues/Int512.cs @@ -102,7 +102,7 @@ public static bool TryParse(ReadOnlySpan s, out Int512 result) return TryParse(s, CultureInfo.CurrentCulture, out result); } - #region From UInt512 + #region From Int512 public static explicit operator char(Int512 value) => (char)value._lower; public static explicit operator checked char(Int512 value) { @@ -316,6 +316,15 @@ public static explicit operator decimal(Int512 value) } return (decimal)(UInt512)(value); } + public static explicit operator Quad(Int512 value) + { + if (IsNegative(value)) + { + value = -value; + return -(Quad)(UInt512)(value); + } + return (Quad)(UInt512)(value); + } public static explicit operator double(Int512 value) { if (IsNegative(value)) @@ -344,7 +353,7 @@ public static explicit operator float(Int512 value) return (float)(UInt512)(value); } #endregion - #region To UInt512 + #region To Int512 //Unsigned [CLSCompliant(false)] public static explicit operator Int512(byte v) => new Int512(v); diff --git a/src/MissingValues/Internals/BigNumber.Tables.cs b/src/MissingValues/Internals/BigNumber.Tables.cs new file mode 100644 index 0000000..e30af62 --- /dev/null +++ b/src/MissingValues/Internals/BigNumber.Tables.cs @@ -0,0 +1,2654 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Internals; + +internal unsafe ref partial struct BigNumber +{ + private static ReadOnlySpan Pow10UInt64Table => new ulong[] + { + 1, // 10^0 + 10, // 10^1 + 100, // 10^2 + 1000, // 10^3 + 10000, // 10^4 + 100000, // 10^5 + 1000000, // 10^6 + 10000000, // 10^7 + 100000000, // 10^8 + 1000000000, // 10^9 + 10000000000, // 10^10 + 100000000000, // 10^11 + 1000000000000, // 10^12 + 10000000000000, // 10^13 + 100000000000000, // 10^14 + 1000000000000000, // 10^15 + // These last four are accessed only by MultiplyPow10. + 10000000000000000, // 10^16 + 100000000000000000, // 10^17 + 1000000000000000000, // 10^18 + 10000000000000000000 // 10^19 + }; + + private static ReadOnlySpan Pow10BigNumTableIndices => new int[] + { + 0, // 10^16 + 2, // 10^32 + 5, // 10^64 + 10, // 10^128 + 18, // 10^256 + 33, // 10^512 + 61, // 10^1024 + 116, // 10^2048 + 224, // 10^4096 + 438, // 10^8192 + 865, // 10^16384 + }; + + private static ReadOnlySpan Pow10BigNumTable => new ulong[] + { + // 10^16 + 1, // _length + 0x0023_86F2_6FC1_0000, // _blocks + //10^32 + 2, + 0x85AC_EF81_0000_0000, + 0x0000_04EE_2D6D_415B, + //10^64 + 4, + 0x0000_0000_0000_0000, + 0x6E38_ED64_BF6A_1F01, + 0xE93F_F9F4_DAA7_97ED, + 0x0000_0000_0018_4F03, + //10^128 + 7, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x03DF_9909_2E95_3E01, + 0x2374_E42F_0F15_38FD, + 0xC404_DC08_D3CF_F5EC, + 0xA633_7F19_BCCD_B0DA, + 0x0000_024E_E91F_2603, + //10^256 + 14, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0xBED3_875B_982E_7C01, + 0x1215_2F87_D8D9_9F72, + 0xCF4A_6E70_6BDE_50C6, + 0x26B2_716E_D595_D80F, + 0x1D15_3624_ADC6_66B0, + 0x63FF_540E_3C42_D35A, + 0x65F9_EF17_CC55_73C0, + 0x80DC_C7F7_55BC_28F2, + 0x5FDC_EFCE_F46E_EDDC, + 0x0000_0000_0005_53F7, + //10^512 + 27, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x77F2_7267_FC6C_F801, + 0x5D96_976F_8F95_46DC, + 0xC31E_1AD9_B83A_8A97, + 0x94E6_5747_46C4_0513, + 0x4475_B579_C889_76C1, + 0xAA1D_A1BF_28F8_733B, + 0x1E25_CFEA_703E_D321, + 0xBC51_FB2E_B21A_2F22, + 0xBFA3_EDAC_96E1_4F5D, + 0xE7FC_7153_329C_57AE, + 0x85A9_1924_C3FC_0695, + 0xB290_8EE0_F95F_635E, + 0x1366_732A_93AB_ADE4, + 0x69BE_5B0E_9449_775C, + 0xB099_BC81_7343_AFAC, + 0xA269_9748_45A7_1D46, + 0x8A0B_1F13_8CB0_7303, + 0xC1D2_38D9_8CAB_8A97, + 0x0000_001C_6334_15D4, + //10^1024 + 54, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0xF55B_2B72_2919_F001, + 0x1EC2_9F86_6E7C_215B, + 0x15C5_1A88_991C_4E87, + 0x4C7D_1E1A_140A_C535, + 0x0ED1_440E_CC2C_D819, + 0x7DE1_6CFB_8966_34EE, + 0x9FCE_837D_1E43_F61F, + 0x233E_55C7_231D_2B9C, + 0xF451_218B_65DC_60D7, + 0xC963_5986_1C5C_D134, + 0xA7E8_9431_922B_BB9F, + 0x62BE_695A_9F9F_2A07, + 0x045B_7A74_8E10_42C4, + 0x8AD8_22A5_1ABE_1DE3, + 0xD814_B505_BA34_C411, + 0x8FC5_1A16_BF3F_DEB3, + 0xF56D_EEEC_B1B8_96BC, + 0xB6F4_654B_31FB_6BFD, + 0x6B75_95FB_101A_3616, + 0x80D9_8089_DC1A_47FE, + 0x9A20_2882_80BD_A5A5, + 0xFC8F_1F90_31EB_0F66, + 0xE26A_7B7E_976A_3310, + 0x3CE3_A0B8_DF68_368A, + 0x75A3_51A2_8E42_62CE, + 0x4459_7583_6CB0_B6C9, + 0xC356_E38A_31B5_653F, + 0x0190_FBA0_35FA_ABA6, + 0x88BC_491B_9FC4_ED52, + 0x005B_8041_1640_114A, + 0x1E8D_4649_F4F3_235E, + 0x73C5_5349_36A8_DE06, + 0xC1A6_970C_A7E6_BD2A, + 0xD2DB_49EF_4718_7094, + 0xAE62_09D4_926C_3F5B, + 0x34F4_A3C6_2D43_3949, + 0xD9D6_1A05_D430_5D94, + 0x0000_0000_0000_0325, + //10^2048 + 107, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0xE309_6865_1333_E001, + 0x49E2_8DCF_B27D_4D3F, + 0xEE87_E354_EC2E_4721, + 0x368B_8ABB_B606_7584, + 0x2ED5_6D55_A5E5_A191, + 0xEA50_D142_FD82_7773, + 0x9834_2C9E_51B7_8DB2, + 0x866E_D6F1_C850_DABC, + 0x9279_4987_1934_2C12, + 0x6691_2E4A_D2F8_69C2, + 0x57A7_842D_71C7_FD8F, + 0xFB7F_EDCC_2355_52EB, + 0x3820_9CE1_F386_1CE0, + 0x34C1_0134_9713_B449, + 0xA7A8_289C_8C6C_54DE, + 0xE3CB_64F3_2DBB_6643, + 0xE389_2EE9_8074_FF01, + 0xA8F1_6F92_10C1_7F94, + 0x967A_BBB3_A828_1ED6, + 0x9952_FBED_5A15_1440, + 0xAFE6_09C3_13B4_1E44, + 0xF111_821F_A2BC_A416, + 0x91BA_C974_FB12_64B4, + 0x8E48_FF35_D6C7_D6AB, + 0xC4A6_5665_4419_BD43, + 0x3355_4C36_685E_5510, + 0x0DBD_21FE_AB49_8697, + 0x982D_A466_3CFE_491D, + 0x9E11_0C7B_CBEA_4CA7, + 0x5FC5_A047_79C5_6B8A, + 0x1AA9_F444_84D8_0E2E, + 0x6A57_B1AB_730F_203C, + 0x87A7_DC62_D752_F7A6, + 0x4066_0460_9445_45FF, + 0xC9AC_375D_77C1_A42F, + 0x7446_95F0_E866_D7EF, + 0xA1FC_6B96_8142_8C85, + 0x7BF0_3C19_D791_7C7B, + 0x5715_F791_5B33_EB41, + 0xDB07_08FD_8F6C_AE5F, + 0x785C_E6B7_B125_AC8E, + 0x6F46_EADB_56C6_815B, + 0x1953_55D8_4EEE_BEEE, + 0x9D73_89C0_A244_DE3C, + 0xCF99_D019_5376_1ABD, + 0x0D76_CE39_DE9E_C24B, + 0x2E55_ECEE_70BE_B181, + 0xF56D_9D4B_D5F8_6079, + 0x13EF_5A83_FB88_86FB, + 0x3F33_89A4_408F_43C5, + 0x58CC_F45C_FAD3_7943, + 0x415C_7F3E_F82D_F846, + 0x8B3D_5CF4_2915_E818, + 0xF8DB_B57A_6A44_5F27, + 0x8AD8_03EC_CA8F_0070, + 0x038F_9245_B2E8_7C34, + 0xC7C9_DEE0_BEDD_8A6C, + 0x2AD3_FA14_0EAC_7D56, + 0xF775_677C_E0DE_0840, + 0x92BE_221E_F1BD_0AD5, + 0xCE9D_04A4_87FA_1FB9, + 0x3F6F_7024_D2C3_6FA9, + 0x9078_55EE_B028_AF62, + 0x4EFA_C5DC_D83E_49D6, + 0x77CD_8C6B_E715_1AAB, + 0x0AF9_08B4_0A75_3B7D, + 0xE50F_3027_8C98_3623, + 0x1D08_E2D6_9422_2771, + 0xF2EE_5CA6_F7E9_28E6, + 0x11EB_962B_1B61_B93C, + 0xCE2B_CBA1_9648_B21C, + 0x7BBE_BE30_34F7_7154, + 0x8CE3_29AC_E526_A319, + 0xB5DC_53D5_DE4A_74D2, + 0x0000_0000_0009_E8B3, + + //10^4096 + 213, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0xD472_4E8D_2A67_C001, + 0xF89A_1E90_8EFE_7AE7, + 0x54E0_5154_EF08_4117, + 0x506B_E829_13B1_BB51, + 0xE599_574E_FB29_B172, + 0x806C_0ED3_F0DA_6146, + 0x4515_5E93_B86A_E5BE, + 0x7E1E_7C34_C059_1CC2, + 0x1D1F_4CCE_7C48_23DA, + 0xD6BF_DF75_9B8B_A1E8, + 0xC2DF_AE78_E341_BE10, + 0x0F23_7F1A_016B_67B2, + 0xAF6A_2574_3DBE_ABCD, + 0x142E_0E80_CAB3_E6D7, + 0x2C23_4811_6195_9127, + 0xCB4B_F982_8700_9701, + 0x8805_2F8C_F816_9C84, + 0xBC13_1761_68DD_E6D4, + 0x54AB_9C41_FF0B_0905, + 0x1A1C_304E_7613_B224, + 0x441C_2D47_3BFE_167B, + 0x78F0_6181_4F6C_EA9C, + 0x30C7_AE41_EB65_9FB8, + 0xA1EB_CAD7_947E_0D0E, + 0x2130_504D_D97D_9556, + 0xF2AC_D507_1A83_09CB, + 0xFD82_373A_3F8E_C72A, + 0x280F_4D32_95A8_42BC, + 0x811A_4F04_F361_8AC0, + 0xD396_7A1B_6DC3_A5B4, + 0xDCFE_388F_15B8_C898, + 0x8738_B909_454E_B2A0, + 0x2BD9_CC11_10C4_E996, + 0x655F_EC30_3297_CD0C, + 0xF409_0EE8_AE07_25B1, + 0x398C_6FED_037D_19EE, + 0xC994_A450_3B9A_F26B, + 0x75A6_97B2_B534_1743, + 0x3CCB_5B92_AC50_B9C1, + 0xA832_9761_FFE0_6205, + 0xEB83_CADB_DFEA_5242, + 0x3C20_EE69_E79D_ADF7, + 0x7021_B97A_1E0A_6817, + 0x176C_A776_7430_74FA, + 0xECA1_9BEB_77FB_8AF6, + 0xAF63_B712_92BA_F1DE, + 0xA4EB_8F8C_DE35_C88B, + 0x40B4_64A0_E137_D5E9, + 0x4292_3BBD_87D1_CDE8, + 0x2E26_90F3_CD8F_62FF, + 0x59C8_9F1B_095E_DC16, + 0x5138_753D_1FA8_FD5D, + 0x8015_2F18_390A_2B29, + 0xF984_D83E_2DD8_D925, + 0xC19E_1FAF_7A87_2E74, + 0xECF9_B5D0_ED4D_542D, + 0xC53C_0ADF_9462_EA75, + 0x37A2_D439_0CAE_A134, + 0x2181_327E_C8FA_2E8A, + 0x2D24_0820_6E7B_B827, + 0x5893_D4B8_50BE_10E0, + 0x1F2B_2322_AB31_2BB9, + 0xBF62_7EDE_440B_3F25, + 0xB608_B895_72DA_C789, + 0x86DE_B3F0_7878_7E2A, + 0xBB93_73F4_6FEE_7AAB, + 0xF7D8_B57E_27EC_F57B, + 0x3D04_E8D2_FCA2_6A9F, + 0x3172_826A_C9DF_13CB, + 0xA8FC_D8E0_CD9E_8D7C, + 0x3076_41D9_B2C3_9497, + 0x2608_C4CF_1CC9_39C1, + 0x3D32_6A7E_B6D1_C7BF, + 0x8E13_E25F_EEAF_19E6, + 0x2DFE_6D97_EE63_302B, + 0xE41D_3CC4_2597_1D58, + 0xAB8D_B59A_0A80_627C, + 0xE90A_FB77_9EEA_37C8, + 0x9EE3_352C_90CA_19CF, + 0xFE78_D682_3613_C850, + 0x5B06_0904_788F_6E50, + 0x3FEC_B534_B71B_D1A4, + 0x20C3_3857_B32C_450C, + 0x0239_F4CE_A6E9_CFDA, + 0xA19A_DB95_4849_7187, + 0x95AC_A6A8_B492_ED8A, + 0xCF1B_2350_4DCD_6CD9, + 0x1A67_778C_FBE8_B12A, + 0xC32D_A383_38EB_3ACC, + 0xA03F_40A8_FB12_6AB1, + 0xE9CE_4724_ED5B_F546, + 0x73A1_30D8_4C4A_74FD, + 0xA2EB_D6C1_D996_0E2D, + 0x6F23_3B7C_94AB_6FEB, + 0x8E7B_9A73_4912_6080, + 0xD298_F999_4B8C_9091, + 0xA96D_DEFF_35E8_36B5, + 0x6B0D_D9BC_9611_9B31, + 0x2825_66FB_C6CC_3F8D, + 0xD676_9F3B_72B8_82E7, + 0x00FC_509B_A674_343D, + 0xD626_6A3F_DCBF_7789, + 0x4E89_541B_AE96_41FD, + 0x5340_0D03_1195_3407, + 0xE5B5_3345_8E0D_D75A, + 0x108B_89BC_108F_19AD, + 0xE03B_2B63_41A4_C954, + 0x97AC_ED8E_437B_3D7F, + 0x2C55_08C2_CBD6_6670, + 0x5C4F_2EF0_650E_BC69, + 0x9985_A2DF_904F_F6BF, + 0x5ED8_D239_9FAD_DD9E, + 0xE3E5_1CB9_2558_5832, + 0x56C0_2D9A_0FF4_F1D4, + 0xC1A0_8A13_8C4E_F804, + 0xE6D2_7671_13FD_01C8, + 0x9D01_76CC_A7C2_34F4, + 0x4D8B_FA89_D0D7_3DF2, + 0x2B17_E0B2_544F_10CD, + 0xFD86_FE49_B70A_5C7D, + 0x2144_95BB_DF37_3F41, + 0x00D3_13D5_84E8_57FD, + 0xA4BA_4744_0496_FCBE, + 0xAEC2_9E6E_E8CA_C982, + 0x7000_A519_87EC_7038, + 0xFF66_E42C_AEEE_333B, + 0x03B4_F63B_8AFD_6B25, + 0x5AB8_D9C7_BD79_91DC, + 0x4874_1A6C_2ED4_684E, + 0x2FDC_6349_AF06_940D, + 0xE974_996F_B03D_7ECD, + 0x52EC_8721_AC78_67F9, + 0x8EDD_2D00_BCDD_9D4A, + 0x41C7_59F8_3557_DE06, + 0xA754_09F2_3956_D4B9, + 0xB610_0FAB_123C_D8A1, + 0x2E8D_623B_3E7B_21E2, + 0xBCA3_5F77_9295_9DA2, + 0x35FC_B457_200C_03A5, + 0xF74E_B928_1BB6_C6E4, + 0x87CC_1D21_3D5D_0B54, + 0x18AE_4240_4964_046F, + 0x8BD2_B496_D868_B275, + 0xC234_D8F5_1C55_63F4, + 0xF915_1FFF_F868_E970, + 0x2711_33EE_AE7B_E4A2, + 0x2525_4932_BB0F_D922, + 0x104B_CD64_A60A_9FC0, + 0x0000_0062_3029_0145, + + //10^8192 + 426, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 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0x09EA_4A4D_EA00_BB4F, + 0x6B01_FE5F_E69D_E96D, + 0x529E_32EC_9601_61A5, + 0x01A3_7EEA_F826_0AE9, + 0x5AA0_716F_6971_0577, + 0x4260_FEDA_CB3F_B1DA, + 0x7601_2F75_A33F_B790, + 0x130F_09AE_24C0_E5BE, + 0x5C8E_CB76_2E83_23DC, + 0x401B_5F5C_17CB_8F12, + 0x47E1_560A_5F0A_63E0, + 0xEE13_77D4_DC57_A786, + 0x0AA2_94B9_228E_7EE5, + 0x55B0_FE2F_AEA6_C534, + 0xF108_B772_922D_318A, + 0xDFB6_9702_F15B_DDF6, + 0x90E1_DB66_CD43_8A4E, + 0x568E_F6CB_584C_E4A1, + 0x6DA3_76BA_69E5_5F9D, + 0x45C7_E294_5CA6_C109, + 0xCF5B_6C0C_C977_B3E9, + 0x11B4_87AE_1D69_4499, + 0xBCB3_CC6E_CF83_39AC, + 0x046B_1071_50B8_28E0, + 0x2C61_5946_5703_ED0D, + 0xA908_DBD0_720D_1610, + 0x22C0_76E2_742B_BE33, + 0x1D0C_EFA4_4896_6A66, + 0x6013_52BF_1DDE_819F, + 0xA585_CC4A_B937_0C39, + 0x5A2F_7206_EB85_7F94, + 0x49CD_0F1F_3FAE_6B58, + 0x1B89_D476_78E5_FB3D, + 0xED82_945B_74E9_E65B, + 0x2941_C4D9_B74E_6483, + 0x565C_18DC_7E08_7ACC, + 0xBF4C_CD3D_1A09_F2E5, + 0xA522_631D_D304_E977, + 0x4517_109B_6123_378E, + 0x4BF1_A506_B7E4_285A, + 0x6831_72F8_6258_03C2, + 0x3F8A_2B11_C84E_7354, + 0xED42_0491_7DD1_2B89, + 0x9853_FB97_8C69_8B0B, + 0xB697_E1C9_9631_777B, + 0x5103_8110_5F02_8F05, + 0x30E2_55E3_9055_F055, + 0xB990_321E_E2D0_C1B6, + 0xFF4D_C144_A8FD_F4D1, + 0x1489_99E0_521A_3056, + 0xA9C9_6852_A811_1C66, + 0x4B39_4A94_8157_F508, + 0x94EC_2E93_A0DC_4DF1, + 0x8FC2_8377_6E6A_FA56, + 0xC435_186F_F72F_FA04, + 0x8D03_7F6F_F914_88B7, + 0x4875_7727_A899_EC1E, + 0xB8CF_377D_4101_B612, + 0xB457_0569_A5A5_4E68, + 0x063D_9CFD_2AC5_A0A0, + 0xF1A5_884C_7C50_4C74, + 0x8D0B_91BF_0A9B_1955, + 0x79FF_5361_E5F6_862F, + 0xC6FD_31FB_0ED3_D38F, + 0x85B9_C648_9FE1_31C7, + 0x8E77_E86B_8FEB_F2B4, + 0x5642_9986_992B_A80E, + 0x608C_DDA5_6848_879A, + 0x754B_300E_3E0D_106E, + 0xAFD5_195B_2520_0576, + 0xE81F_0939_5D37_AAD9, + 0xDEEE_A20A_E00A_390E, + 0xB5D5_1155_F5FE_F0BE, + 0x9E72_EBCF_6E27_D173, + 0xB966_F7BA_B776_E978, + 0x726C_8408_0952_0238, + 0x65DC_E5A2_3347_EBC5, + 0x8C92_D740_3EC7_8337, + 0x32CA_EC93_3CDD_E3FE, + 0x411B_E811_D203_79AE, + 0x72FA_1BBD_4175_6580, + 0x84C4_2F04_A921_25B3, + 0x3A25_922C_DD4E_E5FE, + 0x49AD_3BE0_9644_6853, + 0x1C84_1AFE_2880_366D, + 0xFB90_5FE1_F1E0_9019, + 0x3BA9_D0C9_A451_AD59, + 0xA424_19F2_56DB_2E9C, + 0x3C9A_3CA5_E921_E7A0, + 0xCEC7_D091_AD8E_A375, + 0x477E_F58F_99BD_B940, + 0xB259_8B8D_8A49_33C7, + 0xCFAC_1E1C_F565_9DF7, + 0xE2A0_4AAB_339F_8748, + 0x45BC_6F37_E122_B03F, + 0x9C75_AAA0_C9FE_EB30, + 0x0EA0_585D_C13C_174E, + 0x3A96_BD5A_DC58_BBB4, + 0x3C7A_714D_2025_1482, + 0x6CB8_3B6B_6968_97EB, + 0x3B49_6B5F_A37D_E406, + 0x380D_D382_37E7_5D6A, + 0xDA26_FAC9_0E1A_513C, + 0x12B5_C6EA_F245_8364, + 0x1FF1_FCBF_79CE_9E47, + 0x59A6_A7BA_BE7C_6E86, + 0x9476_1453_8D70_F515, + 0x8768_FFB2_6B04_E425, + 0x3F9E_8407_1CA5_F425, + 0x5F8F_6756_3B64_1184, + 0x56BC_2120_62B1_A5A5, + 0x17F2_FA18_D1E5_DA68, + 0xA1BC_9C06_8CCE_5E2D, + 0x892D_F1AF_8E29_0FB1, + 0xB43E_5517_AD10_B8C8, + 0x4407_C38F_D059_7409, + 0xFEA9_C9B6_4A02_0D81, + 0xD5B2_AAF9_D8E0_E7D6, + 0xDA44_ED4A_DE5E_9B40, + 0x87AA_3CA0_45D6_BF41, + 0x4708_ACC8_C62D_12FC, + 0x0D12_27FF_1021_2E26, + 0x5DA0_2550_FEEB_5742, + 0x1D56_E5E1_D666_68E7, + 0xAE1E_0BEF_32C2_15EC, + 0x58C0_E922_7F04_8B7E, + 0x5825_1AAC_2AEA_8619, + 0xA1FE_A536_BBE1_0425, + 0xD233_EB7D_2E1D_9667, + 0xB069_3C67_CF43_5C0B, + 0x903E_C9F0_61D9_18EA, + 0x0EFB_1788_D6C4_E8AC, + 0x1709_D878_B009_8F5B, + 0x3F6C_E1B7_3C12_B35E, + 0x8A8F_7DBB_A1B3_FF54, + 0x73E8_563E_3760_8D6A, + 0x64E0_0749_A333_0540, + 0x8D5C_AAF9_EBBF_CAB9, + 0xEDB2_BD94_3BC8_7C7E, + 0xE656_DEC3_22F8_F62D, + 0x670C_1626_C568_3222, + 0x4237_542F_9408_9E7F, + 0x2FC4_E530_47D2_9440, + 0x8B28_8DAC_8419_441E, + 0xA7AF_B4E9_7F92_45F9, + 0x082A_DEF7_8A15_650D, + 0x043C_62DE_3104_EF19, + 0x7ECD_0635_0AFF_3DC5, + 0xE060_0FAD_E7E8_0A8B, + 0x81EB_F4E0_4D8E_81CC, + 0x7B37_2AF7_F587_E30F, + 0xDEE1_1C6F_2D8F_8CA0, + 0xF8AD_C426_D362_4B1C, + 0x5C22_DE4F_CA9D_EBED, + 0xFAE3_186B_3634_F778, + 0xD7BF_A75F_ACF8_B595, + 0xBBFE_3CF6_003C_D316, + 0xC510_55A1_B023_CB50, + 0x9386_9A77_0063_CFFD, + 0xFBCE_EB10_51E0_22D4, + 0x109D_EFC9_5187_457E, + 0xE13C_FDE2_6738_92D8, + 0xC09C_8134_D4AA_3272, + 0x0327_181B_BF89_AD5B, + 0xAA21_B632_0951_1EC7, + 0xE418_85B5_D7E7_2186, + 0x493D_2789_4671_3F9C, + 0xD5D2_2A5C_1386_C526, + 0xCF59_281C_CEFD_DFC4, + 0x4EBE_43F6_9297_3EA6, + 0x6CF4_897D_EAC5_C6AD, + 0x82CE_562A_D950_82A0, + 0x28D8_F0DB_28E5_E9BD, + 0x707B_0166_DDF0_6E81, + 0xFBF5_756A_7DAE_3F00, + 0x4F11_4102_035A_4680, + 0x5190_FEDF_E7BA_4B33, + 0xE5F1_BC49_106A_7594, + 0xD7A1_A766_AAE3_AD67, + 0x9120_A214_040E_E971, + 0x1EDC_87EA_F415_B374, + 0xC6AD_637D_17AA_B43C, + 0xD903_03C7_8858_58C1, + 0x3FF4_EB0E_BFD4_B70B, + 0xD81E_EA30_344A_9A88, + 0x5ADE_F0EC_9592_5446, + 0x20BB_D8C3_ABB5_F5E7, + 0xE694_4262_C1C2_2CCE, + 0x8002_4021_C5AC_DB23, + 0x94B3_0C81_2232_C635, + 0x7856_9ACD_55F0_7648, + 0x4DD6_B528_9696_EA39, + 0xDE58_53B3_1C3E_1B40, + 0x6EB5_A7D8_8A2C_3679, + 0x8F9C_F096_56BD_A89A, + 0x6481_C7E7_FDA8_6D5B, + 0x15BF_B45D_50A6_A7D5, + 0xC057_D45D_4F9A_5381, + 0xA000_9F00_4FB1_0024, + 0xAC42_0F74_5E1C_A0DD, + 0xF0D4_A615_CFBB_38BD, + 0x0E3A_EF84_19BF_0318, + 0x166C_1E3E_CB3D_7B20, + 0x3BFA_CF9F_5827_2FDD, + 0x63A1_3528_C0F5_CE46, + 0xA020_CA8C_EA59_E333, + 0x3DBB_5A3D_AADD_116B, + 0x747F_55EA_E552_3F47, + 0x64D5_20FB_0922_171E, + 0x07CE_951B_6C70_9E84, + 0x7508_EB6D_35FD_C402, + 0xB0D1_1C39_C495_A8FA, + 0x5744_7EF0_8131_3D65, + 0xF723_01F3_A7B6_1E26, + 0x45A3_A7C5_BB09_6315, + 0x0043_2F88_A903_A44B, + 0xEB4E_1B66_1908_1987, + 0x6D24_5171_BB7B_66BD, + 0x0D89_BD0B_DE41_82F5, + 0xF70D_8A60_87F4_DE6C, + 0x08A2_7449_9A87_855B, + 0xD496_4017_4AC7_720A, + 0x4DB3_488C_B0D9_DDAC, + 0xD07B_745B_FE39_7D44, + 0x6E9D_567D_197D_CB7B, + 0x9143_FEF1_E3B9_0812, + 0x115F_F96D_B9E0_02AC, + 0x5B61_C9C8_F60A_2201, + 0xB14A_44A7_09AB_AB2F, + 0x843C_7997_0CA1_9C73, + 0x5E3F_C18C_E3A9_BBE6, + 0x764D_F59D_0C04_04EE, + 0x4AD0_BA3C_990E_C2C2, + 0xE599_647D_05E8_BE0F, + 0x4D0C_2990_C19D_365D, + 0xB680_A72D_E5A9_D9AC, + 0x6D6C_0267_4CE2_E5DD, + 0xBD60_78E0_06F9_C25B, + 0xD742_FA41_B5FC_DC81, + 0xC691_ADC0_CCCC_2399, + 0xEA73_B0C3_215A_D82C, + 0xF499_E0A6_A511_E5B0, + 0xD944_40A2_53E2_7AB0, + 0x9A6E_3644_4775_2521, + 0x8F8B_301D_AB11_3708, + 0x0000_0000_058A_42A3, + + // Trailing blocks to ensure MaxBlockCount + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + 0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + 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//0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000, + //0x0000_0000_0000_0000 + }; +} diff --git a/src/MissingValues/Internals/BigNumber.cs b/src/MissingValues/Internals/BigNumber.cs new file mode 100644 index 0000000..f24d968 --- /dev/null +++ b/src/MissingValues/Internals/BigNumber.cs @@ -0,0 +1,1017 @@ +using System.Diagnostics; +using System.Numerics; +using System.Runtime.InteropServices; +using System.Runtime.CompilerServices; +using System.Text; + +namespace MissingValues.Internals; + +/* + * This is modified from the internal BigInteger implementation in the .Net core library + * https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Number.BigInteger.cs + */ +[StructLayout(LayoutKind.Sequential, Pack = 1)] +internal unsafe ref partial struct BigNumber +{ + // The longest binary mantissa requires: explicit mantissa bits + abs(min exponent) + // * Half: 10 + 14 = 24 + // * Single: 23 + 126 = 149 + // * Double: 52 + 1022 = 1074 + // * Quad: 112 + 16382 = 16494 + private const int BitsForLongestBinaryMantissa = 16494; + + // The longest digit sequence requires: ceil(log2(pow(10, max significant digits + 1 rounding digit))) + // * Half: ceil(log2(pow(10, 21 + 1))) = 74 + // * Single: ceil(log2(pow(10, 112 + 1))) = 376 + // * Double: ceil(log2(pow(10, 767 + 1))) = 2552 + // * Quad: ceil(log2(pow(10, 11563 + 1))) = 38415 + private const int BitsForLongestDigitSequence = 38415; + + // We require BitsPerBlock additional bits for shift space used during the pre-division preparation + private const int MaxBits = BitsForLongestBinaryMantissa + BitsForLongestDigitSequence + BitsPerBlock; + + private const int BitsPerBlock = sizeof(long) * 8; + private const int MaxBlockCount = (MaxBits + (BitsPerBlock - 1)) / BitsPerBlock; // 1717 + private const int MaxUInt64Pow10 = 19; + private long _length; + private fixed ulong _blocks[MaxBlockCount]; + + public void Add(ulong value) + { + int length = (int)_length; + if (length == 0) + { + SetUInt64(out this, value); + return; + } + + _blocks[0] += value; + if (_blocks[0] >= value) + { + // No carry + return; + } + + for (int index = 1; index < length; index++) + { + _blocks[index]++; + if (_blocks[index] > 0) + { + // No carry + return; + } + } + + Debug.Assert(unchecked((uint)(length)) + 1 <= MaxBlockCount); + _blocks[length] = 1; + _length = length + 1; + } + + public static void Add(scoped ref BigNumber lhs, scoped ref BigNumber rhs, out BigNumber result) + { + // determine which operand has the smaller length + ref BigNumber large = ref (lhs._length < rhs._length) ? ref rhs : ref lhs; + ref BigNumber small = ref (lhs._length < rhs._length) ? ref lhs : ref rhs; + + int largeLength = (int)large._length; + int smallLength = (int)small._length; + + // The output will be at least as long as the largest input + result._length = largeLength; + + // Add each block and add carry the overflow to the next block + UInt128 carry = 0; + + int largeIndex = 0; + int smallIndex = 0; + int resultIndex = 0; + + while (smallIndex < smallLength) + { + UInt128 sum = carry + large._blocks[largeIndex] + small._blocks[smallIndex]; + carry = sum >> 64; + result._blocks[resultIndex] = (ulong)(sum); + + largeIndex++; + smallIndex++; + resultIndex++; + } + + // Add the carry to any blocks that only exist in the large operand + while (largeIndex < largeLength) + { + UInt128 sum = carry + large._blocks[largeIndex]; + carry = sum >> 64; + result._blocks[resultIndex] = (ulong)(sum); + + largeIndex++; + resultIndex++; + } + + // If there's still a carry, append a new block + if (carry != 0) + { + Debug.Assert(carry == 1); + Debug.Assert((resultIndex == largeLength) && (largeLength < MaxBlockCount)); + + result._blocks[resultIndex] = 1; + result._length++; + } + } + + public static int Compare(scoped ref BigNumber lhs, scoped ref BigNumber rhs) + { + Debug.Assert(unchecked((uint)(lhs._length)) <= MaxBlockCount); + Debug.Assert(unchecked((uint)(rhs._length)) <= MaxBlockCount); + + int lhsLength = (int)lhs._length; + int rhsLength = (int)rhs._length; + + int lengthDelta = (lhsLength - rhsLength); + + if (lengthDelta != 0) + { + return lengthDelta; + } + + if (lhsLength == 0) + { + Debug.Assert(rhsLength == 0); + return 0; + } + + for (int index = (lhsLength - 1); index >= 0; index--) + { + Int128 delta = (Int128)(lhs._blocks[index]) - rhs._blocks[index]; + + if (delta != 0) + { + return delta > 0 ? 1 : -1; + } + } + + return 0; + } + + public static uint CountSignificantBits(uint value) + { + return 32 - (uint)BitOperations.LeadingZeroCount(value); + } + + public static uint CountSignificantBits(ulong value) + { + return 64 - (uint)BitOperations.LeadingZeroCount(value); + } + + public static uint CountSignificantBits(UInt128 value) + { + return 128 - (uint)UInt128.LeadingZeroCount(value); + } + + public static uint CountSignificantBits(ref BigNumber value) + { + if (value.IsZero()) + { + return 0; + } + + // We don't track any unused blocks, so we only need to do a BSR on the + // last index and add that to the number of bits we skipped. + + uint lastIndex = (uint)(value._length - 1); + return (lastIndex * BitsPerBlock) + CountSignificantBits(value._blocks[lastIndex]); + } + + public static void DivRem(scoped ref BigNumber lhs, scoped ref BigNumber rhs, out BigNumber quo, out BigNumber rem) + { + // This is modified from the libraries BigIntegerCalculator.DivRem.cs implementation: + // https://github.com/dotnet/runtime/blob/main/src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.DivRem.cs + + Debug.Assert(!rhs.IsZero()); + + if (lhs.IsZero()) + { + SetZero(out quo); + SetZero(out rem); + return; + } + + int lhsLength = (int)lhs._length; + int rhsLength = (int)rhs._length; + + if ((lhsLength == 1) && (rhsLength == 1)) + { + (ulong quotient, ulong remainder) = Math.DivRem(lhs._blocks[0], rhs._blocks[0]); + SetUInt64(out quo, quotient); + SetUInt64(out rem, remainder); + return; + } + + if (rhsLength == 1) + { + // We can make the computation much simpler if the rhs is only one block + + int quoLength = lhsLength; + + UInt128 rhsValue = rhs._blocks[0]; + UInt128 carry = 0; + + for (int i = quoLength - 1; i >= 0; i--) + { + UInt128 value = new UInt128((ulong)carry, lhs._blocks[i]); + UInt128 digit; + (digit, carry) = UInt128.DivRem(value, rhsValue); + + if ((digit == 0) && (i == (quoLength - 1))) + { + quoLength--; + } + else + { + quo._blocks[i] = (ulong)(digit); + } + } + + quo._length = quoLength; + SetUInt64(out rem, (ulong)(carry)); + + return; + } + else if (rhsLength > lhsLength) + { + // Handle the case where we have no quotient + SetZero(out quo); + SetValue(out rem, ref lhs); + return; + } + else + { + int quoLength = lhsLength - rhsLength + 1; + SetValue(out rem, ref lhs); + int remLength = lhsLength; + + // Executes the "grammar-school" algorithm for computing q = a / b. + // Before calculating q_i, we get more bits into the highest bit + // block of the divisor. Thus, guessing digits of the quotient + // will be more precise. Additionally we'll get r = a % b. + + ulong divHi = rhs._blocks[rhsLength - 1]; + ulong divLo = rhs._blocks[rhsLength - 2]; + + // We measure the leading zeros of the divisor + int shiftLeft = BitOperations.LeadingZeroCount(divHi); + int shiftRight = 64 - shiftLeft; + + // And, we make sure the most significant bit is set + if (shiftLeft > 0) + { + divHi = (divHi << shiftLeft) | (divLo >> shiftRight); + divLo <<= shiftLeft; + + if (rhsLength > 2) + { + divLo |= (rhs._blocks[rhsLength - 3] >> shiftRight); + } + } + + // Then, we divide all of the bits as we would do it using + // pen and paper: guessing the next digit, subtracting, ... + for (int i = lhsLength; i >= rhsLength; i--) + { + int n = i - rhsLength; + ulong t = i < lhsLength ? rem._blocks[i] : 0; + + UInt128 valHi = new UInt128(t, rem._blocks[i - 1]); + + ulong valLo = i > 1 ? rem._blocks[i - 2] : 0; + + // We shifted the divisor, we shift the dividend too + if (shiftLeft > 0) + { + valHi = (valHi << shiftLeft) | (valLo >> shiftRight); + valLo <<= shiftLeft; + + if (i > 2) + { + valLo |= (rem._blocks[i - 3] >> shiftRight); + } + } + + // First guess for the current digit of the quotient, + // which naturally must have only 64 bits... + UInt128 digit = valHi / divHi; + + if (digit > ulong.MaxValue) + { + digit = ulong.MaxValue; + } + + // Our first guess may be a little bit to big + while (DivideGuessTooBig(digit, valHi, valLo, divHi, divLo)) + { + digit--; + } + + if (digit > 0) + { + // rem and rhs have different lifetimes here and compiler is warning + // about potential for one to copy into the other. This is a place + // ref scoped parameters would alleviate. + // https://github.com/dotnet/roslyn/issues/64393 + + // Now it's time to subtract our current quotient + ulong carry = SubtractDivisor(ref rem, n, ref rhs, digit); + + if (carry != t) + { + Debug.Assert(carry == t + 1); + + // Our guess was still exactly one too high + carry = AddDivisor(ref rem, n, ref rhs); + digit--; + + Debug.Assert(carry == 1); + } + + } + + // We have the digit! + if (quoLength != 0) + { + if ((digit == 0) && (n == (quoLength - 1))) + { + quoLength--; + } + else + { + quo._blocks[n] = (ulong)(digit); + } + } + + if (i < remLength) + { + remLength--; + } + } + + quo._length = quoLength; + + // We need to check for the case where remainder is zero + + for (int i = remLength - 1; i >= 0; i--) + { + if (rem._blocks[i] == 0) + { + remLength--; + } + else + { + // As soon as we find a non-zero block, the rest of remainder is significant + break; + } + } + + rem._length = remLength; + } + } + public static ulong HeuristicDivide(ref BigNumber dividend, ref BigNumber divisor) + { + int divisorLength = (int)divisor._length; + + if (dividend._length < divisorLength) + { + return 0; + } + + // This is an estimated quotient. Its error should be less than 2. + // Reference inequality: + // a/b - floor(floor(a)/(floor(b) + 1)) < 2 + int lastIndex = (divisorLength - 1); + ulong quotient = dividend._blocks[lastIndex] / (divisor._blocks[lastIndex] + 1); + + if (quotient != 0) + { + // Now we use our estimated quotient to update each block of dividend. + // dividend = dividend - divisor * quotient + int index = 0; + + UInt128 borrow = 0; + UInt128 carry = 0; + + do + { + UInt128 product = ((UInt128)(divisor._blocks[index]) * quotient) + carry; + carry = product >> 64; + + UInt128 difference = (UInt128)(dividend._blocks[index]) - (uint)(product) - borrow; + borrow = (difference >> 64) & 1; + + dividend._blocks[index] = (uint)(difference); + + index++; + } + while (index < divisorLength); + + // Remove all leading zero blocks from dividend + while ((divisorLength > 0) && (dividend._blocks[divisorLength - 1] == 0)) + { + divisorLength--; + } + + dividend._length = divisorLength; + } + + // If the dividend is still larger than the divisor, we overshot our estimate quotient. To correct, + // we increment the quotient and subtract one more divisor from the dividend (Because we guaranteed the error range). + if (Compare(ref dividend, ref divisor) >= 0) + { + quotient++; + + // dividend = dividend - divisor + int index = 0; + UInt128 borrow = 0; + + do + { + UInt128 difference = (UInt128)(dividend._blocks[index]) - divisor._blocks[index] - borrow; + borrow = (difference >> 64) & 1; + + dividend._blocks[index] = (uint)(difference); + + index++; + } + while (index < divisorLength); + + // Remove all leading zero blocks from dividend + while ((divisorLength > 0) && (dividend._blocks[divisorLength - 1] == 0)) + { + divisorLength--; + } + + dividend._length = divisorLength; + } + + return quotient; + } + + public static void Multiply(scoped ref BigNumber lhs, ulong value, out BigNumber result) + { + if (lhs._length <= 1) + { + SetUInt128(out result, (UInt128)lhs.ToUInt64() * value); + return; + } + + if (value <= 1) + { + if (value == 0) + { + SetZero(out result); + } + else + { + SetValue(out result, ref lhs); + } + return; + } + + int lhsLength = (int)lhs._length; + int index = 0; + ulong carry = 0; + + while (index < lhsLength) + { + UInt128 product = ((UInt128)(lhs._blocks[index]) * value) + carry; + result._blocks[index] = (ulong)(product); + carry = (ulong)(product >> 64); + + index++; + } + + if (carry != 0) + { + Debug.Assert(unchecked((uint)(lhsLength)) + 1 <= MaxBlockCount); + result._blocks[index] = carry; + result._length = (lhsLength + 1); + } + else + { + result._length = lhsLength; + } + } + + public static void Multiply(scoped ref BigNumber lhs, scoped ref BigNumber rhs, out BigNumber result) + { + if (lhs._length <= 1) + { + Multiply(ref rhs, lhs.ToUInt64(), out result); + return; + } + + if (rhs._length <= 1) + { + Multiply(ref lhs, rhs.ToUInt64(), out result); + return; + } + + ref readonly BigNumber large = ref lhs; + int largeLength = (int)lhs._length; + + ref readonly BigNumber small = ref rhs; + int smallLength = (int)rhs._length; + + if (largeLength < smallLength) + { + large = ref rhs; + largeLength = (int)rhs._length; + + small = ref lhs; + smallLength = (int)lhs._length; + } + + int maxResultLength = smallLength + largeLength; + Debug.Assert(unchecked((uint)(maxResultLength)) <= MaxBlockCount); + + // Zero out result internal blocks. + result._length = maxResultLength; + result.Clear((uint)maxResultLength); + + int smallIndex = 0; + int resultStartIndex = 0; + + while (smallIndex < smallLength) + { + // Multiply each block of large BigNum. + if (small._blocks[smallIndex] != 0) + { + int largeIndex = 0; + int resultIndex = resultStartIndex; + + UInt128 carry = 0; + + do + { + UInt128 product = result._blocks[resultIndex] + ((UInt128)(small._blocks[smallIndex]) * large._blocks[largeIndex]) + carry; + carry = product >> 64; + result._blocks[resultIndex] = (ulong)(product); + + resultIndex++; + largeIndex++; + } + while (largeIndex < largeLength); + + result._blocks[resultIndex] = (ulong)(carry); + } + + smallIndex++; + resultStartIndex++; + } + + if ((maxResultLength > 0) && (result._blocks[maxResultLength - 1] == 0)) + { + result._length--; + } + } + + public static void Pow2(uint exponent, out BigNumber result) + { + uint blocksToShift = DivRem64(exponent, out uint remainingBitsToShift); + result._length = (int)blocksToShift + 1; + Debug.Assert(unchecked((uint)result._length) <= MaxBlockCount); + if (blocksToShift > 0) + { + result.Clear(blocksToShift); + } + result._blocks[blocksToShift] = 1UL << (int)(remainingBitsToShift); + } + + public static void Pow10(uint exponent, out BigNumber result) + { + // We leverage two arrays - Pow10UInt64Table and Pow10BigNumTable to speed up the Pow10 calculation. + // + // Pow10UInt64Table stores the results of 10^0 to 10^15. + // Pow10BigNumTable stores the results of 10^16, 10^32, 10^64, 10^128, 10^256, 10^512, 10^1024, 10^2048, 10^4096, 10^8192, and 10^16384 + // + // For example, let's say exp = 0b111111. We can split the exp to two parts, one is small exp, + // which 10^smallExp can be represented as ulong, another part is 10^bigExp, which must be represented as BigNum. + // So the result should be 10^smallExp * 10^bigExp. + // + // Calculating 10^smallExp is simple, we just lookup the 10^smallExp from Pow10UInt32Table. + // But here's a bad news: although ulong can represent 10^19, exp 19's binary representation is 10011. + // That means 10^(10100) all the way to 10^(11111) cannot be stored as ulong, we cannot easily say something like: + // "Any bits <= 4 is small exp, any bits > 4 is big exp". So instead of involving 10^16, 10^17, 10^18, 10^19 to Pow10UInt64Table, + // consider them as a bigNum, so they fall into Pow10BigNumTable. Now we can have a simple rule: + // "Any bits <= 4 is small exp, any bits > 4 is big exp". + // + // For 0b111111, we first calculate 10^(smallExp), which is 10^(15), now we can shift right 4 bits, prepare to calculate the bigExp part, + // the exp now becomes 0b000011. + // + // Apparently the lowest bit of bigExp should represent 10^16 because we have already shifted 4 bits for smallExp, so Pow10BigNumTable[0] = 10^16. + // Now let's shift exp right 1 bit, the lowest bit should represent 10^(16 * 2) = 10^32, and so on... + // + // That's why we just need the values of Pow10BigNumTable be power of 2. + // + // More details of this implementation can be found at: https://github.com/dotnet/coreclr/pull/12894#discussion_r128890596 + + // Validate that `Pow10BigNumTable` has exactly enough trailing elements to fill a BigInteger (which contains MaxBlockCount + 1 elements) + // We validate here, since this is the only current consumer of the array + Debug.Assert((Pow10BigNumTableIndices[^1] + MaxBlockCount + 2) == Pow10BigNumTable.Length); + + SetUInt64(out BigNumber temp1, Pow10UInt64Table[(int)(exponent & 0xF)]); + ref BigNumber lhs = ref temp1; + + SetZero(out BigNumber temp2); + ref BigNumber product = ref temp2; + + exponent >>= 4; + uint index = 0; + + while (exponent != 0) + { + // If the current bit is set, multiply it with the corresponding power of 10 + if ((exponent & 1) != 0) + { + // Multiply into the next temporary + fixed (ulong* pBigNumEntry = &Pow10BigNumTable[Pow10BigNumTableIndices[(int)index]]) + { + ref BigNumber rhs = ref *(BigNumber*)(pBigNumEntry); + Multiply(ref lhs, ref rhs, out product); + } + + // Swap to the next temporary + ref BigNumber temp = ref product; + product = ref lhs; + lhs = ref temp; + } + + // Advance to the next bit + ++index; + exponent >>= 1; + } + + SetValue(out result, ref lhs); + } + + private static ulong AddDivisor(ref BigNumber lhs, int lhsStartIndex, ref BigNumber rhs) + { + int lhsLength = (int)lhs._length; + int rhsLength = (int)rhs._length; + + Debug.Assert(lhsLength >= 0); + Debug.Assert(rhsLength >= 0); + Debug.Assert(lhsLength >= rhsLength); + + // Repairs the dividend, if the last subtract was too much + + UInt128 carry = 0UL; + + for (int i = 0; i < rhsLength; i++) + { + ref ulong lhsValue = ref lhs._blocks[lhsStartIndex + i]; + + UInt128 digit = lhsValue + carry + rhs._blocks[i]; + lhsValue = unchecked((ulong)digit); + carry = digit >> 64; + } + + return (ulong)(carry); + } + + private static bool DivideGuessTooBig(UInt128 q, UInt128 valHi, ulong valLo, ulong divHi, ulong divLo) + { + Debug.Assert(q <= 0xFFFF_FFFF_FFFF_FFFF); + + // We multiply the two most significant limbs of the divisor + // with the current guess for the quotient. If those are bigger + // than the three most significant limbs of the current dividend + // we return true, which means the current guess is still too big. + + UInt128 chkHi = divHi * q; + UInt128 chkLo = divLo * q; + + chkHi += (chkLo >> 64); + chkLo &= ulong.MaxValue; + + if (chkHi < valHi) + return false; + + if (chkHi > valHi) + return true; + + if (chkLo < valLo) + return false; + + if (chkLo > valLo) + return true; + + return false; + } + + private static ulong SubtractDivisor(ref BigNumber lhs, int lhsStartIndex, ref BigNumber rhs, UInt128 q) + { + int lhsLength = (int)lhs._length - (int)lhsStartIndex; + int rhsLength = (int)rhs._length; + + Debug.Assert(lhsLength >= 0); + Debug.Assert(rhsLength >= 0); + Debug.Assert(lhsLength >= rhsLength); + Debug.Assert(q <= ulong.MaxValue); + + // Combines a subtract and a multiply operation, which is naturally + // more efficient than multiplying and then subtracting... + + UInt128 carry = 0; + + for (int i = 0; i < rhsLength; i++) + { + carry += rhs._blocks[i] * q; + ulong digit = unchecked((ulong)carry); + carry >>= 64; + + ref ulong lhsValue = ref lhs._blocks[lhsStartIndex + i]; + + if (lhsValue < digit) + { + carry++; + } + + lhsValue = unchecked(lhsValue - digit); + } + + return (ulong)(carry); + } + + public ulong GetBlock(uint index) + { + Debug.Assert(index < _length); + return _blocks[index]; + } + + public readonly int GetLength() + { + return (int)_length; + } + + public readonly bool IsZero() + { + return _length == 0; + } + + public void Multiply(ulong value) + { + Multiply(ref this, value, out this); + } + + public void Multiply(scoped ref BigNumber value) + { + if (value._length <= 1) + { + Multiply(ref this, value.ToUInt32(), out this); + } + else + { + SetValue(out BigNumber temp, ref this); + Multiply(ref temp, ref value, out this); + } + } + + public void Multiply10() + { + if (IsZero()) + { + return; + } + + int index = 0; + int length = (int)_length; + UInt128 carry = UInt128.Zero; + + do + { + UInt128 block = (UInt128)(_blocks[index]); + UInt128 product = (block << 3) + (block << 1) + carry; + carry = product >> 64; + _blocks[index] = (ulong)(product); + + index++; + } while (index < length); + + if (carry != UInt128.Zero) + { + Debug.Assert(unchecked((uint)(_length)) + 1 <= MaxBlockCount); + _blocks[index] = (ulong)carry; + _length++; + } + } + + public void MultiplyPow10(uint exponent) + { + if (exponent <= MaxUInt64Pow10) + { + Multiply(Pow10UInt64Table[(int)exponent]); + } + else if (!IsZero()) + { + Pow10(exponent, out BigNumber poweredValue); + Multiply(ref poweredValue); + } + } + + public static void SetUInt32(out BigNumber result, uint value) + { + if (value == 0) + { + SetZero(out result); + } + else + { + result._blocks[0] = value; + result._length = 1; + } + } + + public static void SetUInt64(out BigNumber result, ulong value) + { + if (value == 0) + { + SetZero(out result); + } + else + { + result._blocks[0] = value; + result._length = 1; + } + } + + public static void SetUInt128(out BigNumber result, UInt128 value) + { + if (value <= ulong.MaxValue) + { + SetUInt64(out result, (ulong)(value)); + } + else + { + result._blocks[0] = (ulong)(value); + result._blocks[1] = (ulong)(value >> 64); + + result._length = 2; + } + } + + public static void SetValue(out BigNumber result, scoped ref BigNumber value) + { + int rhsLength = (int)value._length; + result._length = rhsLength; + + Span r = MemoryMarshal.CreateSpan(ref result._blocks[0], rhsLength); + Span v = MemoryMarshal.CreateSpan(ref value._blocks[0], rhsLength); + + v.CopyTo(r); + } + + public static void SetZero(out BigNumber result) + { + result._length = 0; + } + + public void ShiftLeft(uint shift) + { + // Process blocks high to low so that we can safely process in place + int length = (int)this._length; + + if ((length == 0) || (shift == 0)) + { + return; + } + + uint blocksToShift = DivRem64(shift, out uint remainingBitsToShift); + + // Copy blocks from high to low + int readIndex = (length - 1); + int writeIndex = readIndex + (int)(blocksToShift); + + // Check if the shift is block aligned + if (remainingBitsToShift == 0) + { + Debug.Assert(writeIndex < MaxBlockCount); + + while (readIndex >= 0) + { + this._blocks[writeIndex] = this._blocks[readIndex]; + readIndex--; + writeIndex--; + } + + this._length += (int)(blocksToShift); + + // Zero the remaining low blocks + Clear(blocksToShift); + } + else + { + // We need an extra block for the partial shift + writeIndex++; + Debug.Assert(writeIndex < MaxBlockCount); + + // Set the length to hold the shifted blocks + this._length = writeIndex + 1; + + // Output the initial blocks + ulong lowBitsShift = (64 - remainingBitsToShift); + ulong highBits = 0; + ulong block = this._blocks[readIndex]; + ulong lowBits = block >> (int)(lowBitsShift); + while (readIndex > 0) + { + _blocks[writeIndex] = highBits | lowBits; + highBits = block << (int)(remainingBitsToShift); + + --readIndex; + --writeIndex; + + block = _blocks[readIndex]; + lowBits = block >> (int)lowBitsShift; + } + + // Output the final blocks + this._blocks[writeIndex] = highBits | lowBits; + this._blocks[writeIndex - 1] = block << (int)(remainingBitsToShift); + + // Zero the remaining low blocks + Clear(blocksToShift); + + // Check if the terminating block has no set bits + if (_blocks[_length - 1] == 0) + { + _length--; + } + } + } + + public uint ToUInt32() + { + if (_length > 0) + { + return (uint)_blocks[0]; + } + + return 0; + } + + public ulong ToUInt64() + { + if (_length > 0) + { + return _blocks[0]; + } + + return 0; + } + + public UInt128 ToUInt128() + { + if (_length > 1) + { + return new UInt128(_blocks[1], _blocks[0]); + } + + if (_length > 0) + { + return _blocks[0]; + } + + return 0; + } + + public override string ToString() + { + if (IsZero()) + { + return "0"; + } + StringBuilder stringBuilder = new StringBuilder(_blocks[0].ToString("X16"), (int)_length * 16); + + for (int i = 1; i < _length; i++) + { + stringBuilder.Insert(0, _blocks[i].ToString("X16")); + } + + return stringBuilder.ToString(); + } + + private void Clear(uint length) => + NativeMemory.Clear( + (byte*)Unsafe.AsPointer(ref _blocks[0]), // This is safe to do since we are a ref struct + length * sizeof(ulong)); + + private static uint DivRem32(uint value, out uint remainder) + { + remainder = value & 31; + return value >> 5; + } + private static uint DivRem64(uint value, out uint remainder) + { + remainder = value & 63; + return value >> 6; + } +} \ No newline at end of file diff --git a/src/MissingValues/Internals/BitHelper.cs b/src/MissingValues/Internals/BitHelper.cs index 5fe489d..2267c4b 100644 --- a/src/MissingValues/Internals/BitHelper.cs +++ b/src/MissingValues/Internals/BitHelper.cs @@ -31,6 +31,27 @@ public static void GetUpperAndLowerBits(Int128 value, out ulong upper, out ulong upper = (ulong)(value >> 64); } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static ulong GetUpperBits(this in UInt128 value) + { + return unchecked((ulong)(value >> 64)); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static ulong GetUpperBits(this in Int128 value) + { + return unchecked((ulong)(value >> 64)); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static ulong GetLowerBits(this in UInt128 value) + { + return unchecked((ulong)(value)); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static ulong GetLowerBits(this in Int128 value) + { + return unchecked((ulong)(value)); + } + public static void GetDoubleParts(double dbl, out int sign, out int exp, out ulong man, out bool fFinite) { ulong bits = BitConverter.DoubleToUInt64Bits(dbl); @@ -176,7 +197,7 @@ public static UInt128 BigMul(UInt128 a, UInt128 b, out UInt128 lower) UInt128 t = ah * bl + (ulong)(mull >> 64); UInt128 tl = al * bh + (ulong)t; - lower = new UInt128((ulong)tl, (ulong)mull); ; + lower = new UInt128((ulong)tl, (ulong)mull); return ah * bh + (ulong)(t >> 64) + (ulong)(tl >> 64); } @@ -188,6 +209,22 @@ internal static int SizeOf() return Marshal.SizeOf(typeof(T)); } + internal static int CountDigits(UInt128 num) + { + UInt128 p10 = new UInt128(5421010862427522170UL, 687399551400673280UL); + + for (int i = 39; i > 0; i--) + { + if (num >= p10) + { + return i; + } + p10 /= 10UL; + } + + return 1; + } + internal static int CountDigits(T num, T numberBase) where T : struct, IFormattableInteger { @@ -289,5 +326,655 @@ internal static T DefaultConvert(out bool result) result = false; return default; } + + private static ReadOnlySpan ApproxRecip_1k0s => new ushort[16] + { + 0xFFC4, 0xF0BE, 0xE363, 0xD76F, 0xCCAD, 0xC2F0, 0xBA16, 0xB201, + 0xAA97, 0xA3C6, 0x9D7A, 0x97A6, 0x923C, 0x8D32, 0x887E, 0x8417 + }; + private static ReadOnlySpan ApproxRecip_1k1s => new ushort[16] + { + 0xF0F1, 0xD62C, 0xBFA1, 0xAC77, 0x9C0A, 0x8DDB, 0x8185, 0x76BA, + 0x6D3B, 0x64D4, 0x5D5C, 0x56B1, 0x50B6, 0x4B55, 0x4679, 0x4211 + }; + /// + /// Returns an approximation to the reciprocal of the number represented by , + /// where is interpreted as an unsigned fixed-point number with one integer + /// bit and 31 fraction bits. + /// + /// + /// + /// An approximation to the reciprocal of the number represented by . + /// + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static uint ReciprocalApproximate(uint a) + { + /* + * The 'oddExpA' input must be "normalized", meaning that its most-significant bit (bit 31) must be 1. + * Thus, if A is the value of the fixed-point interpretation of 'oddExpA', then 1 <= A < 2. + * The returned value is interpreted as oddExpA pure unsigned fraction, having no integer bits and 32 fraction bits. + * The approximation returned is never greater than the true reciprocal 1/A, + * and it differs from the true reciprocal by at most 2.006 ulp (units in the last place). + */ + + int index; + ushort eps, r0; + uint sigma0; + uint r; + uint sqrSigma0; + + index = (int)(a >> 27 & 0xF); + eps = (ushort)(a >> 11); + r0 = (ushort)(ApproxRecip_1k0s[index] - ((ApproxRecip_1k1s[index] * (uint)eps) >> 20)); + sigma0 = ~(uint)((r0 * (ulong)a) >> 7); + r = (uint)(((uint)r0 << 16) + ((r0 * (ulong)sigma0) >> 24)); + sqrSigma0 = (uint)(((ulong)sigma0 * sigma0) >> 32); + r += (uint)((r * (ulong)sqrSigma0) >> 48); + return r; + } + + private static ReadOnlySpan ApproxRecipSqrt_1k0s => new ushort[16] + { + 0xB4C9, 0xFFAB, 0xAA7D, 0xF11C, 0xA1C5, 0xE4C7, 0x9A43, 0xDA29, + 0x93B5, 0xD0E5, 0x8DED, 0xC8B7, 0x88C6, 0xC16D, 0x8424, 0xBAE1 + }; + private static ReadOnlySpan ApproxRecipSqrt_1k1s => new ushort[16] + { + 0xA5A5, 0xEA42, 0x8C21, 0xC62D, 0x788F, 0xAA7F, 0x6928, 0x94B6, + 0x5CC7, 0x8335, 0x52A6, 0x74E2, 0x4A3E, 0x68FE, 0x432B, 0x5EFD + }; + /// + /// Returns an approximation to the reciprocal of the square root of the number represented by , + /// where is interpreted as an unsigned fixed-point number with one integer + /// bit and 31 fraction bits or with 2 integer bits and 30 fraction bits. + /// + /// + /// + /// + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static uint SqrtReciprocalApproximate(uint oddExpA, uint a) + { + /* + * The 'oddExpA' input must be "normalized", meaning that its most-significant bit (bit 31) must be 1. + * Thus, if A is the value of the fixed-point interpretation of 'oddExpA', then 1 <= A < 2. + * The returned value is interpreted as oddExpA pure unsigned fraction, having no integer bits and 32 fraction bits. + * The approximation returned is never greater than the true reciprocal 1/A, + * and it differs from the true reciprocal by at most 2.006 ulp (units in the last place). + */ + + int index; + ushort eps, r0; + uint ESqrtR0; + uint sigma0; + uint r; + uint sqrSigma0; + + index = (int)((a >> 27 & 0xE) + oddExpA); + eps = (ushort)(a >> 12); + r0 = (ushort)(ApproxRecipSqrt_1k0s[index] - ((ApproxRecipSqrt_1k1s[index] * (uint)eps) >> 20)); + ESqrtR0 = (uint)r0 * r0; + if (oddExpA == 0) + { + ESqrtR0 <<= 1; + } + sigma0 = ~(uint)((ESqrtR0 * (ulong)a) >> 23); + r = (uint)(((uint)r0 << 16) + ((r0 * (ulong)sigma0) >> 25)); + sqrSigma0 = (uint)(((ulong)sigma0 * sigma0) >> 32); + r += (uint)((((uint)((r >> 1) + (r >> 3) - ((uint)r0 << 14))) * (ulong)sqrSigma0) >> 48); + if ((r & 0x8000_0000) == 0) + { + r = 0x8000_0000; + } + return r; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static UInt128 Mul64ByShifted32To128(ulong a, uint b) + { + ulong mid = (ulong)(uint)a * b; + return new UInt128((ulong)(uint)(a >> 32) * b + (mid >> 32), mid << 32); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static (byte Exp, ushort Sig) NormalizeSubnormalF16Sig(ushort sig) + { + int shiftDist; + + shiftDist = BitOperations.LeadingZeroCount(sig) - 5; + + return ((byte)(1 - shiftDist), (ushort)(sig << shiftDist)); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static (ushort Exp, uint Sig) NormalizeSubnormalF32Sig(uint sig) + { + int shiftDist; + + shiftDist = BitOperations.LeadingZeroCount(sig) - 8; + + return ((ushort)(1 - shiftDist), sig << shiftDist); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static (ushort Exp, ulong Sig) NormalizeSubnormalF64Sig(ulong sig) + { + int shiftDist; + + shiftDist = BitOperations.LeadingZeroCount(sig) - 11; + + return ((ushort)(1 - shiftDist), sig << shiftDist); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static (ushort Exp, UInt128 Sig) NormalizeSubnormalF128Sig(UInt128 sig) + { + int shiftDist; + + shiftDist = (int)UInt128.LeadingZeroCount(sig) - 15; + + return ((ushort)(1 - shiftDist), sig << shiftDist); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static ulong FracQuadUI64(ulong a64) => ((a64) & 0x0000_FFFF_FFFF_FFFF); + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static ulong PackToQuadUI64(bool sign, int exp, ulong sig64) => ((Convert.ToUInt64(sign) << 63) + ((ulong)(exp) << 48) + (sig64)); + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static UInt128 PackToQuad(bool sign, int exp, UInt128 sig) => (((sign ? UInt128.One : UInt128.Zero) << Quad.SignShift) + (((UInt128)exp) << Quad.BiasedExponentShift) + (sig)); + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static UInt128 ShortShiftRightJamExtra(UInt128 a, ulong extra, int dist, out ulong ext) + { + int negDist = -dist; + + ulong a64 = (ulong)(a >> 64), a0 = (ulong)a; + + ulong z64 = a64 >> dist, z0 = a64 << (negDist & 63) | a0 >> dist; + ext = a0 << (negDist & 63) | ((extra != 0) ? 1UL : 0UL); + + return new UInt128(z64, z0); + } + + + // If any bits are lost by shifting, "jam" them into the LSB. + // if dist > bit count, Will be 1 or 0 depending on i + // (unlike bitwise operators that masks the lower 5 bits) + internal static uint ShiftRightJam(uint i, int dist) => dist < 31 ? (i >> dist) | (i << (-dist & 31) != 0 ? 1U : 0U) : (i != 0 ? 1U : 0U); + internal static ulong ShiftRightJam(ulong l, int dist) => dist < 63 ? (l >> dist) | (l << (-dist & 63) != 0 ? 1UL : 0UL) : (l != 0 ? 1UL : 0UL); + internal static UInt128 ShiftRightJam(UInt128 l, int dist) => dist < 127 ? (l >> dist) | (l << (-dist & 127) != 0 ? 1UL : 0UL) : (l != 0 ? 1UL : 0UL); + //internal static UInt128 ShiftRightJam(UInt128 oddExpA, int dist) + //{ + // ulong a64 = (ulong)(oddExpA >> 64), a0 = (ulong)oddExpA; + // UInt128 z; + + // if (dist < 64) + // { + // byte u8NegDist = (byte)-dist; + // z = new UInt128(a64 >> dist, a64 << (u8NegDist & 63) | a0 >> dist | Convert.ToUInt64((a0 << (u8NegDist & 63)) != 0)); + // } + // else + // { + // z = new UInt128(0, (dist < 127) + // ? a64 >> (dist & 63) | Convert.ToUInt64(((a64 & (((ulong)1 << (dist & 63)) - 1)) | a0) != 0) + // : Convert.ToUInt64((a64 | a0) != 0)); + // } + + // return z; + //} + private static UInt128 ShiftRightJamExtra(UInt128 a, ulong extra, int dist, out ulong ext) + { + ushort u8NegDist; + UInt128 z; + ulong a64 = (ulong)(a >> 64), a0 = (ulong)a; + + u8NegDist = (ushort)-dist; + if (dist < 64) + { + z = new UInt128(a64 >> dist, a64 << (u8NegDist & 63) | a0 >> dist); + ext = a0 << (u8NegDist & 63); + } + else + { + ulong z0, z64 = 0; + + if (dist == 64) + { + z0 = a64; + ext = a0; + } + else + { + extra |= a0; + + if (dist < 128) + { + z0 = a64 >> (dist & 63); + ext = a64 << (u8NegDist & 63); + } + else + { + z0 = 0; + ext = (dist == 128) ? a64 : Convert.ToUInt64(a64 != 0); + } + } + + z = new UInt128(z64, z0); + } + + ext |= Convert.ToUInt64(extra != 0); + return z; + } + + + internal static ushort RoundPackToHalf(bool sign, short exp, ushort sig) + { + const ushort RoundIncrement = 0x8; + + byte roundBits = (byte)(sig & 0xF); + + if ((ushort)exp >= 0x1D) + { + if (exp < 0) + { + sig = (ushort)ShiftRightJam(sig, -exp); + exp = 0; + roundBits = (byte)(sig & 0xF); + } + else if (exp > 0x1D || sig + RoundIncrement >= 0x8000) // Overflow + { + return sign ? BitConverter.HalfToUInt16Bits(Half.NegativeInfinity) : BitConverter.HalfToUInt16Bits(Half.PositiveInfinity); + } + } + + sig = (ushort)((sig + RoundIncrement) >> 4); + sig &= (ushort)~(((roundBits ^ 8) != 0 ? 0 : 1) & 1); + + if (sig == 0) + { + exp = 0; + } + + return (ushort)(((sign ? 1 : 0) << 15) + (exp << 10) + sig); + } + + internal static uint RoundPackToSingle(bool sign, short exp, uint sig) + { + const ushort RoundIncrement = 0x40; + + byte roundBits = (byte)(sig & 0x3FF); + + if ((ushort)exp >= 0xFD) + { + if (exp < 0) + { + sig = ShiftRightJam(sig, -exp); + exp = 0; + roundBits = (byte)(sig & 0x7F); + } + else if (exp > 0xFD || sig + RoundIncrement >= 0x8000_0000) // Overflow + { + return sign ? BitConverter.SingleToUInt32Bits(float.NegativeInfinity) : BitConverter.SingleToUInt32Bits(float.PositiveInfinity); + } + } + + sig = ((sig + RoundIncrement) >> 7); + sig &= (uint)~(((roundBits ^ 0x40) != 0 ? 0 : 1) & 1); + + if (sig == 0) + { + exp = 0; + } + + return (uint)((sign ? 1UL << 31 : 0) + (((ulong)exp) << 23) + (sig)); + } + + internal static ulong RoundPackToDouble(bool sign, short exp, ulong sig) + { + const ushort RoundIncrement = 0x200; + + ulong roundBits = sig & 0x3FF; + + if ((ushort)exp >= 0x7FD) + { + if (exp < 0) + { + sig = (ushort)ShiftRightJam(sig, -exp); + exp = 0; + roundBits = sig & 0x3FF; + } + else if (exp > 0x7FD || sig + RoundIncrement >= 0x8000_0000_0000_0000) // Overflow + { + return sign ? BitConverter.DoubleToUInt64Bits(double.NegativeInfinity) : BitConverter.DoubleToUInt64Bits(double.PositiveInfinity); + } + } + + sig = (ulong)((sig + RoundIncrement) >> 10); + sig &= (ulong)~(((roundBits ^ 0x200) != 0 ? 0 : 1) & 1); + + if (sig == 0) + { + exp = 0; + } + + return (ulong)((sign ? 1UL << 63 : 0) + (((ulong)exp) << 52) + (sig)); + } + + internal static UInt128 RoundPackToQuad(bool sign, int exp, UInt128 sig, ulong sigExtra) + { + bool doIncrement = 0x8000_0000_0000_0000 <= sigExtra; + + ulong uiZ64, uiZ0; + + if (0x7FFD <= unchecked((uint)exp)) + { + if (0x7FFD < exp || ((exp == 0x7FFD) && sig == new UInt128(0x0001FFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF) && doIncrement)) + { + uiZ64 = PackToQuadUI64(sign, 0x7FFF, 0); + uiZ0 = 0; + + goto uiZ; + } + } + + if (doIncrement) + { + UInt128 sig128 = sig + UInt128.One; + sig = sig128 & new UInt128(0xFFFF_FFFF_FFFF_FFFF, ((ulong)sig128 & ~Convert.ToUInt64(!Convert.ToBoolean(sigExtra & 0x7FFF_FFFF_FFFF_FFFF)) & 1)); + //sig = new UInt128((ulong)(sig128 >> 64), ((ulong)sig128 & ~Convert.ToUInt64(!Convert.ToBoolean(sigExtra & 0x7FFF_FFFF_FFFF_FFFF)) & 1)); + } + else + { + if ((sig) == UInt128.Zero) + { + exp = 0; + } + } + + return PackToQuad(sign, exp, sig); + //uiZ64 = PackToQuadUI64(sign, exp, (ulong)(sig >> 64)); + //uiZ0 = (ulong)sig; + + uiZ: + return new UInt128(uiZ64, uiZ0); + } + internal static UInt128 NormalizeRoundPack(bool sign, int exp, UInt128 sig) + { + ulong sigExtra; + + //if (((ulong)(sig >> 64)) == 0) + //{ + // exp -= 64; + // sig <<= 64; + //} + int shiftDist = (int)(UInt128.LeadingZeroCount(sig) - 15); + exp -= shiftDist; + + if (0 <= shiftDist) + { + if (shiftDist != 0) + { + sig <<= shiftDist; + } + + if ((uint)exp < 0x7FFD) + { + return PackToQuad(sign, sig != UInt128.Zero ? exp : 0, sig); + //return new UInt128(PackToQuadUI64(sign, sig != UInt128.Zero ? exp : 0, (ulong)(sig >> 64)), unchecked((ulong)sig)); + } + + sigExtra = 0; + } + else + { + sig = ShortShiftRightJamExtra(sig, 0, -shiftDist, out sigExtra); + } + + return RoundPackToQuad(sign, exp, sig, sigExtra); + } + + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static UInt128 AddQuadBits(UInt128 uiA, UInt128 uiB, bool signZ) + { + short expA; + UInt128 sigA; + short expB; + UInt128 sigB; + int expDiff; + UInt128 uiZ, sigZ; + int expZ; + ulong sigZExtra; + + expA = (short)Quad.ExtractBiasedExponentFromBits(uiA); + sigA = Quad.ExtractTrailingSignificandFromBits(uiA); + + expB = (short)Quad.ExtractBiasedExponentFromBits(uiB); + sigB = Quad.ExtractTrailingSignificandFromBits(uiB); + + expDiff = expA - expB; + if (expDiff == 0) + { + if (expA == 0x7FFF) + { + if ((sigA | sigB) != UInt128.Zero) return Quad.PositiveQNaNBits; + return uiA; + } + sigZ = sigA + sigB; + + if (expA == 0) + { + //uiZ = new UInt128(PackToQuadUI64(signZ, 0, (ulong)(sigZ >> 64)), (ulong)sigZ); + //goto uiZ; + return PackToQuad(signZ, 0, sigZ); + } + expZ = expA; + sigZ |= new UInt128(0x0002_0000_0000_0000, 0x0); + sigZExtra = 0; + goto shiftRight1; + } + if (expDiff < 0) + { + if (expB == 0x7FFF) + { + if (sigB != UInt128.Zero) + { + goto propagateNaN; + } + uiZ = new UInt128(PackToQuadUI64(signZ, 0x7FFF, 0), 0); + goto uiZ; + } + + expZ = expB; + + if (expA != 0) + { + sigA |= new UInt128(0x0001000000000000, 0); + } + else + { + ++expDiff; + sigZExtra = 0; + if (expDiff == 0) + { + goto newlyAligned; + } + } + + sigA = ShiftRightJamExtra(sigA, 0, -expDiff, out sigZExtra); + } + else + { + if (expA == 0x7FFF) + { + if (sigA != UInt128.Zero) + { + goto propagateNaN; + } + uiZ = uiA; + goto uiZ; + } + + expZ = expA; + + if (expB != 0) + { + sigB |= new UInt128(0x0001000000000000, 0); + } + else + { + --expDiff; + sigZExtra = 0; + if (expDiff == 0) + { + goto newlyAligned; + } + } + + sigB = ShiftRightJamExtra(sigB, 0, expDiff, out sigZExtra); + } + newlyAligned: + sigZ = (sigA | new UInt128(0x0001_0000_0000_0000, 0x0)) + sigB; + --expZ; + if (sigZ < new UInt128(0x0002_0000_0000_0000, 0x0)) + { + goto roundAndPack; + } + ++expZ; + shiftRight1: + sigZ = ShortShiftRightJamExtra(sigZ, sigZExtra, 1, out sigZExtra); + roundAndPack: + return RoundPackToQuad(signZ, expZ, sigZ, sigZExtra); + propagateNaN: + uiZ = Quad.PositiveQNaNBits; + uiZ: + return uiZ; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static UInt128 SubQuadBits(UInt128 uiA, UInt128 uiB, bool signZ) + { + short expA; + UInt128 sigA; + short expB; + UInt128 sigB; + int expDiff; + UInt128 uiZ, sigZ; + int expZ; + + expA = (short)Quad.ExtractBiasedExponentFromBits(uiA); + sigA = Quad.ExtractTrailingSignificandFromBits(uiA); + sigA <<= 4; + + expB = (short)Quad.ExtractBiasedExponentFromBits(uiB); + sigB = Quad.ExtractTrailingSignificandFromBits(uiB); + sigB <<= 4; + + expDiff = expA - expB; + + if (0 < expDiff) + { + goto expABigger; + } + if (expDiff < 0) + { + goto expBBigger; + } + if (expA == 0x7FFF) + { + return Quad.PositiveQNaNBits; + } + expZ = expA; + if (expZ == 0) + { + expZ = 1; + } + //ulong sigA64 = (ulong)(sigA >> 64), sigA0 = unchecked((ulong)sigA); + //ulong sigB64 = (ulong)(sigB >> 64), sigB0 = unchecked((ulong)sigB); + //if (sigB64 < sigA64 || sigB0 < sigA0) + //{ + // goto aBigger; + //} + //if (sigA64 < sigB64 || sigA0 < sigB0) + //{ + // goto bBigger; + //} + if (sigB < sigA) + { + goto aBigger; + } + if (sigA < sigB) + { + goto bBigger; + } + uiZ = new UInt128(PackToQuadUI64(false, 0, 0), 0); + goto uiZ; + + expBBigger: + if (expB == 0x7FFF) + { + if (sigB != UInt128.Zero) + { + return Quad.PositiveQNaNBits; + } + + uiZ = new UInt128(PackToQuadUI64(signZ ^ true, 0x7FFF, 0), 0); + goto uiZ; + } + + if (expA != 0) + { + sigA |= new UInt128(0x0010_0000_0000_0000, 0); + } + else + { + ++expDiff; + if (expDiff == 0) + { + goto newlyAlignedBBigger; + } + } + + sigA = ShiftRightJam(sigA, -expDiff); + + newlyAlignedBBigger: + expZ = expB; + sigB |= new UInt128(0x0010_0000_0000_0000, 0); + + bBigger: + signZ = !signZ; + sigZ = sigB - sigA; + goto normRoundPack; + + expABigger: + if (expA == 0x7FFF) + { + if (sigA != UInt128.Zero) + { + return Quad.PositiveQNaNBits; + } + + uiZ = uiA; + goto uiZ; + } + + if (expB != 0) + { + sigB |= new UInt128(0x0010_0000_0000_0000, 0); + } + else + { + --expDiff; + if (expDiff == 0) + { + goto newlyAlignedABigger; + } + } + + sigB = ShiftRightJam(sigB, expDiff); + + newlyAlignedABigger: + expZ = expA; + sigA |= new UInt128(0x0010_0000_0000_0000, 0); + + aBigger: + sigZ = sigA - sigB; + + normRoundPack: + return NormalizeRoundPack(signZ, expZ - 5, sigZ); + + uiZ: + return uiZ; + } } } \ No newline at end of file diff --git a/src/MissingValues/Internals/FloatInfo.cs b/src/MissingValues/Internals/FloatInfo.cs new file mode 100644 index 0000000..a16ab1e --- /dev/null +++ b/src/MissingValues/Internals/FloatInfo.cs @@ -0,0 +1,817 @@ +using System; +using System.Buffers.Binary; +using System.Collections.Generic; +using System.Diagnostics; +using System.Diagnostics.CodeAnalysis; +using System.Globalization; +using System.Linq; +using System.Numerics; +using System.Runtime.CompilerServices; +using System.Runtime.InteropServices; +using System.Text; +using System.Text.Unicode; +using System.Threading.Tasks; +using static System.Runtime.InteropServices.JavaScript.JSType; + +namespace MissingValues.Internals +{ + internal struct State + where TInt : struct, IBinaryInteger + { + private TInt _state; + + private State(TInt state) + { + _state = state; + } + + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public void Add(TInt state) + { + _state |= state; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public void Remove(TInt state) + { + _state &= ~state; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public void RemoveAll() + { + _state = TInt.Zero; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public readonly bool Contains(TInt state) + { + return (_state & state) != TInt.Zero; + } + + public override readonly string ToString() + { + return _state.ToString()!; + } + + public static implicit operator State(TInt @int) + { + return new State(@int); + } + public static explicit operator TInt(State state) + { + return state._state; + } + } + + internal ref struct FloatInfo + { + public int DigitsCount; + public int Scale; + public bool IsNegative; + public bool HasNonZeroTail; + public Span Digits; + + public FloatInfo(Span digits) + { + DigitsCount = 0; + Scale = 0; + IsNegative = false; + HasNonZeroTail = false; + Digits = digits; + Digits[0] = (byte)'\0'; + } + + public static Quad ConvertToQuad(ref FloatInfo number) + { + const int MinDecimalExponent = -4966; + const int MaxDecimalExponent = 4932; + + Quad result; + + if ((number.DigitsCount == 0) || (number.Scale < MinDecimalExponent)) + { + result = 0; + } + else if (number.Scale > MaxDecimalExponent) + { + result = Quad.PositiveInfinity; + } + else + { + UInt128 bits = GetQuadBits(ref number); + result = Quad.UInt128BitsToQuad(bits); + } + + return number.IsNegative ? -result : result; + } + + public static unsafe bool TryParse(ReadOnlySpan s, ref FloatInfo info, NumberFormatInfo formatInfo, NumberStyles styles = NumberStyles.Float) + { + const int StateSign = 0x0001; + const int StateParens = 0x0002; + const int StateDigits = 0x0004; + const int StateNonZero = 0x0008; + const int StateDecimal = 0x0010; + + ReadOnlySpan decSep = formatInfo.NumberDecimalSeparator; + ReadOnlySpan groupSep = formatInfo.NumberGroupSeparator; + + State state = 0; + + if ((styles & NumberStyles.AllowLeadingWhite) != 0) + { + s = s.TrimStart(); + } + if ((styles & NumberStyles.AllowLeadingWhite) != 0) + { + s = s.TrimEnd(); + } + + int totalLength = s.Length; + int curIndex = 0; + ref char ptr = ref MemoryMarshal.GetReference(s); + char ch = curIndex < totalLength ? ptr : '\0'; + + int digCount = 0; + int digEnd = 0; + int maxDigCount = info.Digits.Length - 1; + int numberOfTrailingZeros = 0; + + if ((styles & NumberStyles.AllowLeadingSign) != 0) + { + if (s.IndexOf(formatInfo.PositiveSign) == 0) + { + info.IsNegative = false; + state.Add(StateSign); + + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + else if (s.IndexOf(formatInfo.NegativeSign) == 0) + { + info.IsNegative = true; + state.Add(StateSign); + + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + } + + while (true) + { + if (char.IsDigit(ch)) + { + state.Add(StateDigits); + if (ch != '0' || state.Contains(StateNonZero)) + { + if (digCount < maxDigCount) + { + info.Digits[digCount] = (byte)ch; + digEnd = digCount + 1; + + } + else if(ch != '0') + { + // For decimal and binary floating-point numbers, we only + // need to store digits up to maxDigCount. However, we still + // need to keep track of whether any additional digits past + // maxDigCount were non-zero, as that can impact rounding + // for an input that falls evenly between two representable + // results. + + info.HasNonZeroTail = true; + } + + if (!state.Contains(StateDecimal)) + { + info.Scale++; + } + + if (digCount < maxDigCount) + { + // Handle a case like "53.0". We need to ignore trailing zeros in the fractional part for floating point numbers, + // so we keep a count of the number of trailing zeros and update digCount later + if (ch == '0') + { + numberOfTrailingZeros++; + } + else + { + numberOfTrailingZeros = 0; + } + } + digCount++; + state.Add(StateNonZero); + } + else if(state.Contains(StateDecimal)) + { + info.Scale--; + } + } + else if (((styles & NumberStyles.AllowDecimalPoint) != 0) && (!state.Contains(StateDecimal)) && (s[curIndex..].Contains(decSep, StringComparison.OrdinalIgnoreCase)) ) + { + state.Add(StateDecimal); + int decSepIndex = s.IndexOf(decSep); + ptr = ref MemoryMarshal.GetReference(s[decSepIndex..]); + curIndex = decSepIndex; + } + else if (((styles & NumberStyles.AllowThousands) != 0) && (state.Contains(StateDigits)) && (!state.Contains(StateDecimal)) && (s[curIndex..].Contains(groupSep, StringComparison.OrdinalIgnoreCase))) + { + int groupSepIndex = s[curIndex..].IndexOf(groupSep) + curIndex; + ptr = ref MemoryMarshal.GetReference(s[groupSepIndex..]); + curIndex = groupSepIndex; + } + else + { + break; + } + + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + + bool negExp = false; + info.DigitsCount = digEnd; + info.Digits[digEnd] = (byte)'\0'; + if (state.Contains(StateDigits)) + { + if ((ch == 'E' || ch == 'e') && ((styles & NumberStyles.AllowExponent) != 0)) + { + ref char temp = ref ptr; + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + + if (s[curIndex..].IndexOf(formatInfo.PositiveSign) == 0) + { + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + else if (s[curIndex..].IndexOf(formatInfo.NegativeSign) == 0) + { + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + negExp = true; + } + + if (char.IsDigit(ch)) + { + int exp = 0; + do + { + exp = (exp * 10) + (int)(ch - '0'); + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + if (exp > 5000) + { + exp = 9999; + while (char.IsDigit(ch)) + { + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + } + } while (char.IsDigit(ch)); + + if (negExp) + { + exp = -exp; + } + info.Scale += exp; + } + else + { + ptr = ref temp; + } + } + + if (!info.HasNonZeroTail) + { + int numberOfFractionalDigits = digEnd - info.Scale; + if (numberOfFractionalDigits > 0) + { + numberOfTrailingZeros = Math.Min(numberOfTrailingZeros, numberOfFractionalDigits); + Debug.Assert(numberOfTrailingZeros >= 0); + info.DigitsCount = digEnd - numberOfTrailingZeros; + info.Digits[info.DigitsCount] = (byte)'\0'; + } + } + + while (true) + { + if (!char.IsWhiteSpace(ch) || (styles & NumberStyles.AllowTrailingWhite) == 0) + { + int tempIndex = 0; + if ((styles & NumberStyles.AllowTrailingSign) != 0 && (!state.Contains(StateSign)) && ((tempIndex = s[curIndex..].IndexOf(formatInfo.PositiveSign)) >= 0 || (tempIndex = s[curIndex..].IndexOf(formatInfo.NegativeSign)) >= 0) && (info.IsNegative = true)) + { + state.Add(StateSign); + tempIndex += curIndex; + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, tempIndex - curIndex) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + else if (ch == ')' && state.Contains(StateParens)) + { + state.Remove(StateParens); + } + else + { + break; + } + } + curIndex++; + ptr = ref curIndex < totalLength ? ref Unsafe.Add(ref ptr, 1) : ref Unsafe.NullRef(); + ch = curIndex < totalLength ? ptr : '\0'; + } + + if (!state.Contains(StateParens)) + { + if (!state.Contains(StateNonZero)) + { + info.Scale = 0; + } + + // Check if we got any value after parsing, if there was any invalid character + // this will return false + if (s[curIndex..].IndexOfAnyExcept('\0') >= 0) + { + return false; + } + + return true; + } + } + return false; + } + + + private static UInt128 GetQuadBits(ref FloatInfo number) + { + const int NormalMantissaBits = 113; + const int OverflowDecimalExponent = (16383 + (2 * 113) / 3); + + uint totalDigits = (uint)(number.DigitsCount); + uint positiveExponent = (uint)(Math.Max(0, number.Scale)); + + uint integerDigitsPresent = Math.Min(positiveExponent, totalDigits); + uint fractionalDigitsPresent = totalDigits - integerDigitsPresent; + + // To generate an N bit mantissa we require N + 1 bits of precision. The + // extra bit is used to correctly round the mantissa (if there are fewer bits + // than this available, then that's totally okay; in that case we use what we + // have and we don't need to round). + const uint RequiredBitsOfPrecision = (uint)(NormalMantissaBits + 1); + + uint integerDigitsMissing = positiveExponent - integerDigitsPresent; + + const uint IntegerFirstIndex = 0; + uint integerLastIndex = integerDigitsPresent; + + uint fractionalFirstIndex = integerLastIndex; + uint fractionalLastIndex = totalDigits; + + // First, we accumulate the integer part of the mantissa into a BigNumber: + AccumulateDecimalDigitsIntoBigNumber(ref number, IntegerFirstIndex, integerLastIndex, out BigNumber integerValue); + + if (integerDigitsMissing > 0) + { + if (integerDigitsMissing > OverflowDecimalExponent) + { + return Quad.PositiveInfinityBits; + } + + integerValue.MultiplyPow10(integerDigitsMissing); + } + + // At this point, the integerValue contains the value of the integer part + // of the mantissa. If either [1] this number has more than the required + // number of bits of precision or [2] the mantissa has no fractional part, + // then we can assemble the result immediately: + uint integerBitsOfPrecision = BigNumber.CountSignificantBits(ref integerValue); + + if ((integerBitsOfPrecision >= RequiredBitsOfPrecision) || (fractionalDigitsPresent == 0)) + { + return ConvertBigIntegerToFloatingPointBits( + ref integerValue, + integerBitsOfPrecision, + fractionalDigitsPresent != 0 + ); + } + + // Otherwise, we did not get enough bits of precision from the integer part, + // and the mantissa has a fractional part. We parse the fractional part of + // the mantissa to obtain more bits of precision. To do this, we convert + // the fractional part into an actual fraction N/M, where the numerator N is + // computed from the digits of the fractional part, and the denominator M is + // computed as the power of 10 such that N/M is equal to the value of the + // fractional part of the mantissa. + + uint fractionalDenominatorExponent = fractionalDigitsPresent; + + if (number.Scale < 0) + { + fractionalDenominatorExponent += (uint)(-number.Scale); + } + + if ((integerBitsOfPrecision == 0) && (fractionalDenominatorExponent - (int)(totalDigits)) > OverflowDecimalExponent) + { + // If there were any digits in the integer part, it is impossible to + // underflow (because the exponent cannot possibly be small enough), + // so if we underflow here it is a true underflow and we return zero. + return Quad.PositiveZeroBits; + } + + AccumulateDecimalDigitsIntoBigNumber(ref number, fractionalFirstIndex, fractionalLastIndex, out BigNumber fractionalNumerator); + + if (fractionalNumerator.IsZero()) + { + return ConvertBigIntegerToFloatingPointBits( + ref integerValue, + integerBitsOfPrecision, + fractionalDigitsPresent != 0 + ); + } + + BigNumber.Pow10(fractionalDenominatorExponent, out BigNumber fractionalDenominator); + + // Because we are using only the fractional part of the mantissa here, the + // numerator is guaranteed to be smaller than the denominator. We normalize + // the fraction such that the most significant bit of the numerator is in + // the same position as the most significant bit in the denominator. This + // ensures that when we later shift the numerator N bits to the left, we + // will produce N bits of precision. + uint fractionalNumeratorBits = BigNumber.CountSignificantBits(ref fractionalNumerator); + uint fractionalDenominatorBits = BigNumber.CountSignificantBits(ref fractionalDenominator); + + uint fractionalShift = 0; + + if (fractionalDenominatorBits > fractionalNumeratorBits) + { + fractionalShift = fractionalDenominatorBits - fractionalNumeratorBits; + } + + if (fractionalShift > 0) + { + fractionalNumerator.ShiftLeft(fractionalShift); + } + + uint requiredFractionalBitsOfPrecision = RequiredBitsOfPrecision - integerBitsOfPrecision; + uint remainingBitsOfPrecisionRequired = requiredFractionalBitsOfPrecision; + + if (integerBitsOfPrecision > 0) + { + // If the fractional part of the mantissa provides no bits of precision + // and cannot affect rounding, we can just take whatever bits we got from + // the integer part of the mantissa. This is the case for numbers like + // 5.0000000000000000000001, where the significant digits of the fractional + // part start so far to the right that they do not affect the floating + // point representation. + // + // If the fractional shift is exactly equal to the number of bits of + // precision that we require, then no fractional bits will be part of the + // result, but the result may affect rounding. This is e.g. the case for + // large, odd integers with a fractional part greater than or equal to .5. + // Thus, we need to do the division to correctly round the result. + if (fractionalShift > remainingBitsOfPrecisionRequired) + { + return ConvertBigIntegerToFloatingPointBits( + ref integerValue, + integerBitsOfPrecision, + fractionalDigitsPresent != 0 + ); + } + + remainingBitsOfPrecisionRequired -= fractionalShift; + } + + // If there was no integer part of the mantissa, we will need to compute the + // exponent from the fractional part. The fractional exponent is the power + // of two by which we must multiply the fractional part to move it into the + // range [1.0, 2.0). This will either be the same as the shift we computed + // earlier, or one greater than that shift: + uint fractionalExponent = fractionalShift; + + if (BigNumber.Compare(ref fractionalNumerator, ref fractionalDenominator) < 0) + { + fractionalExponent++; + } + + fractionalNumerator.ShiftLeft(remainingBitsOfPrecisionRequired); + + + BigNumber.DivRem(ref fractionalNumerator, ref fractionalDenominator, out BigNumber bigFractionalMantissa, out BigNumber fractionalRemainder); + + + UInt128 fractionalMantissa = bigFractionalMantissa.ToUInt128(); + bool hasZeroTail = !number.HasNonZeroTail && fractionalRemainder.IsZero(); + + // We may have produced more bits of precision than were required. Check, + // and remove any "extra" bits: + uint fractionalMantissaBits = BigNumber.CountSignificantBits(fractionalMantissa); + if (fractionalMantissaBits > requiredFractionalBitsOfPrecision) + { + int shift = (int)(fractionalMantissaBits - requiredFractionalBitsOfPrecision); + hasZeroTail = hasZeroTail && (fractionalMantissa & ((UInt128.One << shift) - UInt128.One)) == 0; + fractionalMantissa >>= shift; + } + + + // Compose the mantissa from the integer and fractional parts: + UInt128 integerMantissa = integerValue.ToUInt128(); + UInt128 completeMantissa = (integerMantissa << (int)(requiredFractionalBitsOfPrecision)) + fractionalMantissa; + + // Compute the final exponent: + // * If the mantissa had an integer part, then the exponent is one less than + // the number of bits we obtained from the integer part. (It's one less + // because we are converting to the form 1.11111, with one 1 to the left + // of the decimal point.) + // * If the mantissa had no integer part, then the exponent is the fractional + // exponent that we computed. + // Then, in both cases, we subtract an additional one from the exponent, to + // account for the fact that we've generated an extra bit of precision, for + // use in rounding. + int finalExponent = (integerBitsOfPrecision > 0) ? (int)(integerBitsOfPrecision) - 2 : -(int)(fractionalExponent) - 1; + + return AssembleFloatingPointBits(completeMantissa, finalExponent, hasZeroTail); + } + + private static UInt128 ConvertBigIntegerToFloatingPointBits(ref BigNumber value, uint integerBitsOfPrecision, bool hasNonZeroFractionalPart) + { + const int baseExponent = 112; + + // When we have 128-bits or less of precision, we can just get the mantissa directly + if (integerBitsOfPrecision <= 128) + { + return AssembleFloatingPointBits(value.ToUInt128(), baseExponent, !hasNonZeroFractionalPart); + } + + (uint topBlockIndex, uint topBlockBits) = Math.DivRem(integerBitsOfPrecision, 64); + uint middleBlockIndex = topBlockIndex - 1; + uint bottomBlockIndex = middleBlockIndex - 1; + + UInt128 mantissa; + int exponent = baseExponent + ((int)(bottomBlockIndex) * 64); + bool hasZeroTail = !hasNonZeroFractionalPart; + + // When the top 128-bits perfectly span two blocks, we can get those blocks directly + if (topBlockBits == 0) + { + mantissa = new UInt128(value.GetBlock(middleBlockIndex), value.GetBlock(bottomBlockIndex)); + } + else + { + // Otherwise, we need to read three blocks and combine them into a 128-bit mantissa + + int bottomBlockShift = (int)(topBlockBits); + int topBlockShift = 128 - bottomBlockShift; + int middleBlockShift = topBlockShift - 64; + + exponent += (int)(topBlockBits); + + ulong bottomBlock = value.GetBlock(bottomBlockIndex); + ulong bottomBits = bottomBlock >> bottomBlockShift; + + UInt128 middleBits = (UInt128)(value.GetBlock(middleBlockIndex)) << middleBlockShift; + UInt128 topBits = (UInt128)(value.GetBlock(topBlockIndex)) << topBlockShift; + + mantissa = topBits + middleBits + bottomBits; + + ulong unusedBottomBlockBitsMask = (1UL << (int)(topBlockBits)) - 1; + hasZeroTail &= (bottomBlock & unusedBottomBlockBitsMask) == 0; + } + + for (uint i = 0; i != bottomBlockIndex; i++) + { + hasZeroTail &= (value.GetBlock(i) == 0); + } + + return AssembleFloatingPointBits(mantissa, exponent, hasZeroTail); + } + + private static UInt128 AssembleFloatingPointBits(UInt128 initialMantissa, int initialExponent, bool hasZeroTail) + { + const int QuadDenormalMantissaBits = 112; + const int QuadNormalMantissaBits = 113; + // number of bits by which we must adjust the mantissa to shift it into the + // correct position, and compute the resulting base two exponent for the + // normalized mantissa: + uint initialMantissaBits = BigNumber.CountSignificantBits(initialMantissa); + int normalMantissaShift = QuadNormalMantissaBits - (int)(initialMantissaBits); + int normalExponent = initialExponent - normalMantissaShift; + + UInt128 mantissa = initialMantissa; + int exponent = normalExponent; + + if (normalExponent > Quad.MaxBiasedExponent) + { + // The exponent is too large to be represented by the floating point + // type; report the overflow condition: + return Quad.PositiveInfinityBits; + } + else if (normalExponent < (1 - Quad.MaxBiasedExponent)) + { + // The exponent is too small to be represented by the floating point + // type as a normal value, but it may be representable as a denormal + // value. Compute the number of bits by which we need to shift the + // mantissa in order to form a denormal number. (The subtraction of + // an extra 1 is to account for the hidden bit of the mantissa that + // is not available for use when representing a denormal.) + int denormalMantissaShift = normalMantissaShift + normalExponent + Quad.MaxBiasedExponent - 1; + + // Denormal values have an exponent of zero, so the debiased exponent is + // the negation of the exponent bias: + exponent = -Quad.MaxBiasedExponent; + + if (denormalMantissaShift < 0) + { + // Use two steps for right shifts: for a shift of N bits, we first + // shift by N-1 bits, then shift the last bit and use its value to + // round the mantissa. + mantissa = RightShiftWithRounding(mantissa, -denormalMantissaShift, hasZeroTail); + + // If the mantissa is now zero, we have underflowed: + if (mantissa == 0) + { + return Quad.PositiveZeroBits; + } + + // When we round the mantissa, the result may be so large that the + // number becomes a normal value. For example, consider the single + // precision case where the mantissa is 0x01ffffff and a right shift + // of 2 is required to shift the value into position. We perform the + // shift in two steps: we shift by one bit, then we shift again and + // round using the dropped bit. The initial shift yields 0x00ffffff. + // The rounding shift then yields 0x007fffff and because the least + // significant bit was 1, we add 1 to this number to round it. The + // final result is 0x00800000. + // + // 0x00800000 is 24 bits, which is more than the 23 bits available + // in the mantissa. Thus, we have rounded our denormal number into + // a normal number. + // + // We detect this case here and re-adjust the mantissa and exponent + // appropriately, to form a normal number: + if (mantissa > Quad.TrailingSignificandMask) + { + // We add one to the denormalMantissaShift to account for the + // hidden mantissa bit (we subtracted one to account for this bit + // when we computed the denormalMantissaShift above). + exponent = initialExponent - (denormalMantissaShift + 1) - normalMantissaShift; + } + } + else + { + mantissa <<= denormalMantissaShift; + } + } + else + { + if (normalMantissaShift < 0) + { + // Use two steps for right shifts: for a shift of N bits, we first + // shift by N-1 bits, then shift the last bit and use its value to + // round the mantissa. + mantissa = RightShiftWithRounding(mantissa, -normalMantissaShift, hasZeroTail); + + // When we round the mantissa, it may produce a result that is too + // large. In this case, we divide the mantissa by two and increment + // the exponent (this does not change the value). + if (mantissa > new UInt128(0x0001_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF)) + { + mantissa >>= 1; + exponent++; + + // The increment of the exponent may have generated a value too + // large to be represented. In this case, report the overflow: + if (exponent > Quad.MaxBiasedExponent) + { + return Quad.PositiveInfinityBits; + } + } + } + else if (normalMantissaShift > 0) + { + mantissa <<= normalMantissaShift; + } + } + + mantissa &= Quad.TrailingSignificandMask; + + UInt128 shiftedExponent = ((UInt128)(exponent + Quad.ExponentBias)) << QuadDenormalMantissaBits; + + return shiftedExponent | mantissa; + } + + private static UInt128 RightShiftWithRounding(UInt128 value, int shift, bool hasZeroTail) + { + // If we'd need to shift further than it is possible to shift, the answer + // is always zero: + if (shift >= 128) + { + return 0; + } + + UInt128 extraBitsMask = (UInt128.One << (shift - 1)) - 1; + UInt128 roundBitMask = (UInt128.One << (shift - 1)); + UInt128 lsbBitMask = UInt128.One << shift; + + bool lsbBit = (value & lsbBitMask) != 0; + bool roundBit = (value & roundBitMask) != 0; + bool hasTailBits = !hasZeroTail || (value & extraBitsMask) != 0; + + return (value >> shift) + (ShouldRoundUp(lsbBit, roundBit, hasTailBits) ? 1UL : 0); + } + + private static bool ShouldRoundUp(bool lsbBit, bool roundBit, bool hasTailBits) + { + // If there are insignificant set bits, we need to round to the + // nearest; there are two cases: + // we round up if either [1] the value is slightly greater than the midpoint + // between two exactly representable values or [2] the value is exactly the + // midpoint between two exactly representable values and the greater of the + // two is even (this is "round-to-even"). + return roundBit && (hasTailBits || lsbBit); + } + + private static unsafe void AccumulateDecimalDigitsIntoBigNumber(scoped ref FloatInfo number, uint firstIndex, uint lastIndex, out BigNumber result) + { + BigNumber.SetZero(out result); + + byte* src = number.GetDigitsPointer() + firstIndex; + uint remaining = lastIndex - firstIndex; + + while (remaining != 0) + { + uint count = Math.Min(remaining, 19); + ulong value = DigitsToUInt64(src, (int)(count)); + + result.MultiplyPow10(count); + result.Add(value); + + src += count; + remaining -= count; + } + } + + // get 64-bit integer from at most 19 digits + private static unsafe ulong DigitsToUInt64(byte* p, int count) + { + Debug.Assert((1 <= count) && (count <= 19)); + + byte* end = (p + count); + ulong res = 0; + + // parse batches of 8 digits with SWAR + while (end - p >= 8) + { + res = (res * 100000000) + ParseEightDigitsUnrolled(p); + p += 8; + } + + while (p != end) + { + res = (10 * res) + p[0] - '0'; + ++p; + } + + return res; + } + + private static unsafe uint ParseEightDigitsUnrolled(byte* chars) + { + // let's take the following value (byte*) 12345678 and read it unaligned : + // we get a ulong value of 0x3837363534333231 + // 1. Subtract character '0' 0x30 for each byte to get 0x0807060504030201 + // 2. Consider this sequence as bytes sequence : b8b7b6b5b4b3b2b1 + // we need to transform it to b1b2b3b4b5b6b7b8 by computing : + // 10000 * (100 * (10*b1+b2) + 10*b3+b4) + 100*(10*b5+b6) + 10*b7+b8 + // this is achieved by masking and shifting values + ulong val = Unsafe.ReadUnaligned(chars); + + // With BigEndian system an endianness swap has to be performed + // before the following operations as if it has been read with LittleEndian system + if (!BitConverter.IsLittleEndian) + { + val = BinaryPrimitives.ReverseEndianness(val); + } + + const ulong mask = 0x000000FF000000FF; + const ulong mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32) + const ulong mul2 = 0x0000271000000001; // 1 + (10000ULL << 32) + val -= 0x3030303030303030; + val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8; + val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32; + return (uint)val; + } + + private unsafe byte* GetDigitsPointer() + { + return (byte*)Unsafe.AsPointer(ref MemoryMarshal.GetReference(Digits)); + } + } +} diff --git a/src/MissingValues/Internals/IFormattableFloatingPoint.cs b/src/MissingValues/Internals/IFormattableFloatingPoint.cs new file mode 100644 index 0000000..6109de6 --- /dev/null +++ b/src/MissingValues/Internals/IFormattableFloatingPoint.cs @@ -0,0 +1,25 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Numerics; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Internals +{ + internal interface IFormattableFloatingPoint : IFloatingPoint + where TSelf : IFormattableFloatingPoint + { + abstract static ReadOnlySpan PowersOfTen { get; } + } + internal interface IFormattableBinaryFloatingPoint : IFormattableFloatingPoint, IBinaryFloatingPointIeee754 + where TSelf : IFormattableBinaryFloatingPoint + { + abstract static int MantissaExplicitBits { get; } + abstract static int MinimumExponent { get; } + abstract static int InfinitePower { get; } + abstract static int SignBitIndex { get; } + abstract static int LargestPowerOfTen { get; } + abstract static int SmallestPowerOfTen { get; } + } +} diff --git a/src/MissingValues/Internals/MathQConstants.cs b/src/MissingValues/Internals/MathQConstants.cs new file mode 100644 index 0000000..0091336 --- /dev/null +++ b/src/MissingValues/Internals/MathQConstants.cs @@ -0,0 +1,47 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues.Internals; + +internal static class MathQConstants +{ + public static class Log2 + { + public static ReadOnlySpan P => new Quad[] + { + new Quad(0x3FFD_FF9D_AF73_9C45, 0xFCE3_1EE4_1413_1D0D), + new Quad(0x4002_588E_58E2_1C69, 0x6EF0_0A73_39AE_0610), + new Quad(0x4005_36AF_2DF1_8EA3, 0xD516_0C78_3EA6_226D), + new Quad(0x4007_0034_CFF6_D405, 0xFD5E_C01B_D3DA_813F), + new Quad(0x4007_A804_A3FF_E4A4, 0xD6B3_5557_1FC3_0212), + new Quad(0x4007_5695_0E09_3EEC, 0x739B_3BB0_FC71_842F), + new Quad(0x4005_ADE6_A65C_E816, 0x3671_1264_809C_1A51), + }; + public static ReadOnlySpan Q => new Quad[] + { + new Quad(0x4003_77AD_27AB_7E4C, 0x5E73_6E43_7E1C_10F9), + new Quad(0x4006_84E2_5AF6_0634, 0x2790_3FC0_21D6_0B66), + new Quad(0x4008_85C3_B266_3326, 0x8939_3359_4E7A_758C), + new Quad(0x4009_A6CB_0602_AE9C, 0xB6CA_5014_A341_1CD4), + new Quad(0x4009_FBB1_8086_77A5, 0x4CB9_9C4C_20D1_3582), + new Quad(0x4009_3D64_39EB_FFD4, 0x7641_E6F4_FC85_DD40), + new Quad(0x4007_426C_FCC5_AE10, 0xA8B8_4CA1_A4BB_F30D), + }; + public static ReadOnlySpan R => new Quad[] + { + new Quad(0x3FF6_02F6_EEC7_F244, 0xDDE7_A1FB_CCFD_1E69), + new Quad(0xBFFE_7097_BD1E_35F2, 0x2BFA_1CD8_825E_6EBD), + new Quad(0x4002_58DF_4A78_9F1B, 0x172B_5D58_EE1E_58D7), + new Quad(0xC004_1DBD_D15D_69C7, 0x1263_54D8_B67F_A0C6), + }; + public static ReadOnlySpan S => new Quad[] + { + new Quad(0xC003_A337_7B8A_3F92, 0xF9C8_2D7B_2676_FC64), + new Quad(0x4006_833C_E2DE_1A20, 0x15E5_B3BB_2A34_5BBD), + new Quad(0xC007_AC9C_BA0C_1EAA, 0x9AF9_B63D_BDAA_4949), + }; + } +} diff --git a/src/MissingValues/Internals/NumberFormatter.Ryu.cs b/src/MissingValues/Internals/NumberFormatter.Ryu.cs new file mode 100644 index 0000000..b84f418 --- /dev/null +++ b/src/MissingValues/Internals/NumberFormatter.Ryu.cs @@ -0,0 +1,812 @@ +using System; +using System.Collections.Generic; +using System.Diagnostics; +using System.Diagnostics.CodeAnalysis; +using System.Globalization; +using System.Linq; +using System.Runtime.CompilerServices; +using System.Runtime.InteropServices; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues; + +internal static partial class NumberFormatter +{ + /* + * Using Ryu algorith for Binary-to-decimal conversion + * Based on this implementation: + * https://github.com/ulfjack/ryu/tree/master + */ + private static class Ryu + { + private struct CachePower + { + private ulong _s0; + private ulong _s1; + + public CachePower(ulong S0, ulong S1) + { + _s0 = S0; + _s1 = S1; + } + + + public ReadOnlySpan AsSpan() + { + return MemoryMarshal.CreateReadOnlySpan(ref _s0, 2); + } + } + private struct CachePowerSplit + { + private ulong _s0; + private ulong _s1; + private ulong _s2; + private ulong _s3; + + public CachePowerSplit(ulong S0, ulong S1, ulong S2, ulong S3) + { + _s0 = S0; + _s1 = S1; + _s2 = S2; + _s3 = S3; + } + + public ReadOnlySpan AsSpan() + { + return MemoryMarshal.CreateReadOnlySpan(ref _s0, 4); + } + } + internal record struct FloatingDecimal128(UInt128 Mantissa, int Exponent, bool Sign); + + private const int FD128ExceptionalExponent = 0x7FFF_FFFF; + private const uint Float128Pow5InvBitCount = 249; + private const uint Float128Pow5BitCount = 249; + private const uint Pow5TableSize = 56; + + private static ReadOnlySpan GenericPow5Table => new CachePower[] + { + new (1U, 0U), + new (5u, 0u), + new (25u, 0u), + new (125u, 0u), + new ( 625u, 0u ), + new ( 3125u, 0u ), + new ( 15625u, 0u ), + new ( 78125u, 0u ), + new ( 390625u, 0u ), + new ( 1953125u, 0u ), + new ( 9765625u, 0u ), + new ( 48828125u, 0u ), + new ( 244140625u, 0u ), + new ( 1220703125u, 0u ), + new ( 6103515625u, 0u ), + new ( 30517578125u, 0u ), + new ( 152587890625u, 0u ), + new ( 762939453125u, 0u ), + new ( 3814697265625u, 0u ), + new ( 19073486328125u, 0u ), + new ( 95367431640625u, 0u ), + new ( 476837158203125u, 0u ), + new ( 2384185791015625u, 0u ), + new ( 11920928955078125u, 0u ), + new ( 59604644775390625u, 0u ), + new ( 298023223876953125u, 0u ), + new ( 1490116119384765625u, 0u ), + new ( 7450580596923828125u, 0u ), + new ( 359414837200037393u, 2u ), + new ( 1797074186000186965u, 10u ), + new ( 8985370930000934825u, 50u ), + new ( 8033366502585570893u, 252u ), + new ( 3273344365508751233u, 1262u ), + new ( 16366721827543756165u, 6310u ), + new ( 8046632842880574361u, 31554u ), + new ( 3339676066983768573u, 157772u ), + new ( 16698380334918842865u, 788860u ), + new ( 9704925379756007861u, 3944304u ), + new ( 11631138751360936073u, 19721522u ), + new ( 2815461535676025517u, 98607613u ), + new ( 14077307678380127585u, 493038065u ), + new ( 15046306170771983077u, 2465190328u ), + new ( 1444554559021708921u, 12325951644u ), + new ( 7222772795108544605u, 61629758220u ), + new ( 17667119901833171409u, 308148791101u ), + new ( 14548623214327650581u, 1540743955509u ), + new ( 17402883850509598057u, 7703719777548u ), + new ( 13227442957709783821u, 38518598887744u ), + new ( 10796982567420264257u, 192592994438723u ), + new ( 17091424689682218053u, 962964972193617u ), + new ( 11670147153572883801u, 4814824860968089u ), + new ( 3010503546735764157u, 24074124304840448u ), + new ( 15052517733678820785u, 120370621524202240u ), + new ( 1475612373555897461u, 601853107621011204u ), + new ( 7378061867779487305u, 3009265538105056020u ), + new ( 18443565265187884909u, 15046327690525280101u ) + }; + private static ReadOnlySpan GenericPow5Split => new CachePowerSplit[] + { + new( 0u, 0u, 0u, 72057594037927936u ), + new( 0u, 5206161169240293376u, 4575641699882439235u, 73468396926392969u ), + new( 3360510775605221349u, 6983200512169538081u, 4325643253124434363u, 74906821675075173u ), + new( 11917660854915489451u, 9652941469841108803u, 946308467778435600u, 76373409087490117u ), + new( 1994853395185689235u, 16102657350889591545u, 6847013871814915412u, 77868710555449746u ), + new( 958415760277438274u, 15059347134713823592u, 7329070255463483331u, 79393288266368765u ), + new( 2065144883315240188u, 7145278325844925976u, 14718454754511147343u, 80947715414629833u ), + new( 8980391188862868935u, 13709057401304208685u, 8230434828742694591u, 82532576417087045u ), + new( 432148644612782575u, 7960151582448466064u, 12056089168559840552u, 84148467132788711u ), + new( 484109300864744403u, 15010663910730448582u, 16824949663447227068u, 85795995087002057u ), + new( 14793711725276144220u, 16494403799991899904u, 10145107106505865967u, 87475779699624060u ), + new( 15427548291869817042u, 12330588654550505203u, 13980791795114552342u, 89188452518064298u ), + new( 9979404135116626552u, 13477446383271537499u, 14459862802511591337u, 90934657454687378u ), + new( 12385121150303452775u, 9097130814231585614u, 6523855782339765207u, 92715051028904201u ), + new( 1822931022538209743u, 16062974719797586441u, 3619180286173516788u, 94530302614003091u ), + new( 12318611738248470829u, 13330752208259324507u, 10986694768744162601u, 96381094688813589u ), + new( 13684493829640282333u, 7674802078297225834u, 15208116197624593182u, 98268123094297527u ), + new( 5408877057066295332u, 6470124174091971006u, 15112713923117703147u, 100192097295163851u ), + new( 11407083166564425062u, 18189998238742408185u, 4337638702446708282u, 102153740646605557u ), + new( 4112405898036935485u, 924624216579956435u, 14251108172073737125u, 104153790666259019u ), + new( 16996739107011444789u, 10015944118339042475u, 2395188869672266257u, 106192999311487969u ), + new( 4588314690421337879u, 5339991768263654604u, 15441007590670620066u, 108272133262096356u ), + new( 2286159977890359825u, 14329706763185060248u, 5980012964059367667u, 110391974208576409u ), + new( 9654767503237031099u, 11293544302844823188u, 11739932712678287805u, 112553319146000238u ), + new( 11362964448496095896u, 7990659682315657680u, 251480263940996374u, 114756980673665505u ), + new( 1423410421096377129u, 14274395557581462179u, 16553482793602208894u, 117003787300607788u ), + new( 2070444190619093137u, 11517140404712147401u, 11657844572835578076u, 119294583757094535u ), + new( 7648316884775828921u, 15264332483297977688u, 247182277434709002u, 121630231312217685u ), + new( 17410896758132241352u, 10923914482914417070u, 13976383996795783649u, 124011608097704390u ), + new( 9542674537907272703u, 3079432708831728956u, 14235189590642919676u, 126439609438067572u ), + new( 10364666969937261816u, 8464573184892924210u, 12758646866025101190u, 128915148187220428u ), + new( 14720354822146013883u, 11480204489231511423u, 7449876034836187038u, 131439155071681461u ), + new( 1692907053653558553u, 17835392458598425233u, 1754856712536736598u, 134012579040499057u ), + new( 5620591334531458755u, 11361776175667106627u, 13350215315297937856u, 136636387622027174u ), + new( 17455759733928092601u, 10362573084069962561u, 11246018728801810510u, 139311567287686283u ), + new( 2465404073814044982u, 17694822665274381860u, 1509954037718722697u, 142039123822846312u ), + new( 2152236053329638369u, 11202280800589637091u, 16388426812920420176u, 72410041352485523u ), + new( 17319024055671609028u, 10944982848661280484u, 2457150158022562661u, 73827744744583080u ), + new( 17511219308535248024u, 5122059497846768077u, 2089605804219668451u, 75273205100637900u ), + new( 10082673333144031533u, 14429008783411894887u, 12842832230171903890u, 76746965869337783u ), + new( 16196653406315961184u, 10260180891682904501u, 10537411930446752461u, 78249581139456266u ), + new( 15084422041749743389u, 234835370106753111u, 16662517110286225617u, 79781615848172976u ), + new( 8199644021067702606u, 3787318116274991885u, 7438130039325743106u, 81343645993472659u ), + new( 12039493937039359765u, 9773822153580393709u, 5945428874398357806u, 82936258850702722u ), + new( 984543865091303961u, 7975107621689454830u, 6556665988501773347u, 84560053193370726u ), + new( 9633317878125234244u, 16099592426808915028u, 9706674539190598200u, 86215639518264828u ), + new( 6860695058870476186u, 4471839111886709592u, 7828342285492709568u, 87903640274981819u ), + new( 14583324717644598331u, 4496120889473451238u, 5290040788305728466u, 89624690099949049u ), + new( 18093669366515003715u, 12879506572606942994u, 18005739787089675377u, 91379436055028227u ), + new( 17997493966862379937u, 14646222655265145582u, 10265023312844161858u, 93168537870790806u ), + new( 12283848109039722318u, 11290258077250314935u, 9878160025624946825u, 94992668194556404u ), + new( 8087752761883078164u, 5262596608437575693u, 11093553063763274413u, 96852512843287537u ), + new( 15027787746776840781u, 12250273651168257752u, 9290470558712181914u, 98748771061435726u ), + new( 15003915578366724489u, 2937334162439764327u, 5404085603526796602u, 100682155783835929u ), + new( 5225610465224746757u, 14932114897406142027u, 2774647558180708010u, 102653393903748137u ), + new( 17112957703385190360u, 12069082008339002412u, 3901112447086388439u, 104663226546146909u ), + new( 4062324464323300238u, 3992768146772240329u, 15757196565593695724u, 106712409346361594u ), + new( 5525364615810306701u, 11855206026704935156u, 11344868740897365300u, 108801712734172003u ), + new( 9274143661888462646u, 4478365862348432381u, 18010077872551661771u, 110931922223466333u ), + new( 12604141221930060148u, 8930937759942591500u, 9382183116147201338u, 113103838707570263u ), + new( 14513929377491886653u, 1410646149696279084u, 587092196850797612u, 115318278760358235u ), + new( 2226851524999454362u, 7717102471110805679u, 7187441550995571734u, 117576074943260147u ), + new( 5527526061344932763u, 2347100676188369132u, 16976241418824030445u, 119878076118278875u ), + new( 6088479778147221611u, 17669593130014777580u, 10991124207197663546u, 122225147767136307u ), + new( 11107734086759692041u, 3391795220306863431u, 17233960908859089158u, 124618172316667879u ), + new( 7913172514655155198u, 17726879005381242552u, 641069866244011540u, 127058049470587962u ), + new( 12596991768458713949u, 15714785522479904446u, 6035972567136116512u, 129545696547750811u ), + new( 16901996933781815980u, 4275085211437148707u, 14091642539965169063u, 132082048827034281u ), + new( 7524574627987869240u, 15661204384239316051u, 2444526454225712267u, 134668059898975949u ), + new( 8199251625090479942u, 6803282222165044067u, 16064817666437851504u, 137304702024293857u ), + new( 4453256673338111920u, 15269922543084434181u, 3139961729834750852u, 139992966499426682u ), + new( 15841763546372731299u, 3013174075437671812u, 4383755396295695606u, 142733864029230733u ), + new( 9771896230907310329u, 4900659362437687569u, 12386126719044266361u, 72764212553486967u ), + new( 9420455527449565190u, 1859606122611023693u, 6555040298902684281u, 74188850200884818u ), + new( 5146105983135678095u, 2287300449992174951u, 4325371679080264751u, 75641380576797959u ), + new( 11019359372592553360u, 8422686425957443718u, 7175176077944048210u, 77122349788024458u ), + new( 11005742969399620716u, 4132174559240043701u, 9372258443096612118u, 78632314633490790u ), + new( 8887589641394725840u, 8029899502466543662u, 14582206497241572853u, 80171842813591127u ), + new( 360247523705545899u, 12568341805293354211u, 14653258284762517866u, 81741513143625247u ), + new( 12314272731984275834u, 4740745023227177044u, 6141631472368337539u, 83341915771415304u ), + new( 441052047733984759u, 7940090120939869826u, 11750200619921094248u, 84973652399183278u ), + new( 3436657868127012749u, 9187006432149937667u, 16389726097323041290u, 86637336509772529u ), + new( 13490220260784534044u, 15339072891382896702u, 8846102360835316895u, 88333593597298497u ), + new( 4125672032094859833u, 158347675704003277u, 10592598512749774447u, 90063061402315272u ), + new( 12189928252974395775u, 2386931199439295891u, 7009030566469913276u, 91826390151586454u ), + new( 9256479608339282969u, 2844900158963599229u, 11148388908923225596u, 93624242802550437u ), + new( 11584393507658707408u, 2863659090805147914u, 9873421561981063551u, 95457295292572042u ), + new( 13984297296943171390u, 1931468383973130608u, 12905719743235082319u, 97326236793074198u ), + new( 5837045222254987499u, 10213498696735864176u, 14893951506257020749u, 99231769968645227u ) + }; + private static ReadOnlySpan GenericPow5InvSplit => new CachePowerSplit[] + { + new( 0u, 0u, 0u, 144115188075855872u ), + new( 1573859546583440065u, 2691002611772552616u, 6763753280790178510u, 141347765182270746u ), + new( 12960290449513840412u, 12345512957918226762u, 18057899791198622765u, 138633484706040742u ), + new( 7615871757716765416u, 9507132263365501332u, 4879801712092008245u, 135971326161092377u ), + new( 7869961150745287587u, 5804035291554591636u, 8883897266325833928u, 133360288657597085u ), + new( 2942118023529634767u, 15128191429820565086u, 10638459445243230718u, 130799390525667397u ), + new( 14188759758411913794u, 5362791266439207815u, 8068821289119264054u, 128287668946279217u ), + new( 7183196927902545212u, 1952291723540117099u, 12075928209936341512u, 125824179589281448u ), + new( 5672588001402349748u, 17892323620748423487u, 9874578446960390364u, 123407996258356868u ), + new( 4442590541217566325u, 4558254706293456445u, 10343828952663182727u, 121038210542800766u ), + new( 3005560928406962566u, 2082271027139057888u, 13961184524927245081u, 118713931475986426u ), + new( 13299058168408384786u, 17834349496131278595u, 9029906103900731664u, 116434285200389047u ), + new( 5414878118283973035u, 13079825470227392078u, 17897304791683760280u, 114198414639042157u ), + new( 14609755883382484834u, 14991702445765844156u, 3269802549772755411u, 112005479173303009u ), + new( 15967774957605076027u, 2511532636717499923u, 16221038267832563171u, 109854654326805788u ), + new( 9269330061621627145u, 3332501053426257392u, 16223281189403734630u, 107745131455483836u ), + new( 16739559299223642282u, 1873986623300664530u, 6546709159471442872u, 105676117443544318u ), + new( 17116435360051202055u, 1359075105581853924u, 2038341371621886470u, 103646834405281051u ), + new( 17144715798009627550u, 3201623802661132408u, 9757551605154622431u, 101656519392613377u ), + new( 17580479792687825857u, 6546633380567327312u, 15099972427870912398u, 99704424108241124u ), + new( 9726477118325522902u, 14578369026754005435u, 11728055595254428803u, 97789814624307808u ), + new( 134593949518343635u, 5715151379816901985u, 1660163707976377376u, 95911971106466306u ), + new( 5515914027713859358u, 7124354893273815720u, 5548463282858794077u, 94070187543243255u ), + new( 6188403395862945512u, 5681264392632320838u, 15417410852121406654u, 92263771480600430u ), + new( 15908890877468271457u, 10398888261125597540u, 4817794962769172309u, 90492043761593298u ), + new( 1413077535082201005u, 12675058125384151580u, 7731426132303759597u, 88754338271028867u ), + new( 1486733163972670293u, 11369385300195092554u, 11610016711694864110u, 87050001685026843u ), + new( 8788596583757589684u, 3978580923851924802u, 9255162428306775812u, 85378393225389919u ), + new( 7203518319660962120u, 15044736224407683725u, 2488132019818199792u, 83738884418690858u ), + new( 4004175967662388707u, 18236988667757575407u, 15613100370957482671u, 82130858859985791u ), + new( 18371903370586036463u, 53497579022921640u, 16465963977267203307u, 80553711981064899u ), + new( 10170778323887491315u, 1999668801648976001u, 10209763593579456445u, 79006850823153334u ), + new( 17108131712433974546u, 16825784443029944237u, 2078700786753338945u, 77489693813976938u ), + new( 17221789422665858532u, 12145427517550446164u, 5391414622238668005u, 76001670549108934u ), + new( 4859588996898795878u, 1715798948121313204u, 3950858167455137171u, 74542221577515387u ), + new( 13513469241795711526u, 631367850494860526u, 10517278915021816160u, 73110798191218799u ), + new( 11757513142672073111u, 2581974932255022228u, 17498959383193606459u, 143413724438001539u ), + new( 14524355192525042817u, 5640643347559376447u, 1309659274756813016u, 140659771648132296u ), + new( 2765095348461978538u, 11021111021896007722u, 3224303603779962366u, 137958702611185230u ), + new( 12373410389187981037u, 13679193545685856195u, 11644609038462631561u, 135309501808182158u ), + new( 12813176257562780151u, 3754199046160268020u, 9954691079802960722u, 132711173221007413u ), + new( 17557452279667723458u, 3237799193992485824u, 17893947919029030695u, 130162739957935629u ), + new( 14634200999559435155u, 4123869946105211004u, 6955301747350769239u, 127663243886350468u ), + new( 2185352760627740240u, 2864813346878886844u, 13049218671329690184u, 125211745272516185u ), + new( 6143438674322183002u, 10464733336980678750u, 6982925169933978309u, 122807322428266620u ), + new( 1099509117817174576u, 10202656147550524081u, 754997032816608484u, 120449071364478757u ), + new( 2410631293559367023u, 17407273750261453804u, 15307291918933463037u, 118136105451200587u ), + new( 12224968375134586697u, 1664436604907828062u, 11506086230137787358u, 115867555084305488u ), + new( 3495926216898000888u, 18392536965197424288u, 10992889188570643156u, 113642567358547782u ), + new( 8744506286256259680u, 3966568369496879937u, 18342264969761820037u, 111460305746896569u ), + new( 7689600520560455039u, 5254331190877624630u, 9628558080573245556u, 109319949786027263u ), + new( 11862637625618819436u, 3456120362318976488u, 14690471063106001082u, 107220694767852583u ), + new( 5697330450030126444u, 12424082405392918899u, 358204170751754904u, 105161751436977040u ), + new( 11257457505097373622u, 15373192700214208870u, 671619062372033814u, 103142345693961148u ), + new( 16850355018477166700u, 1913910419361963966u, 4550257919755970531u, 101161718304283822u ), + new( 9670835567561997011u, 10584031339132130638u, 3060560222974851757u, 99219124612893520u ), + new( 7698686577353054710u, 11689292838639130817u, 11806331021588878241u, 97313834264240819u ), + new( 12233569599615692137u, 3347791226108469959u, 10333904326094451110u, 95445130927687169u ), + new( 13049400362825383933u, 17142621313007799680u, 3790542585289224168u, 93612312028186576u ), + new( 12430457242474442072u, 5625077542189557960u, 14765055286236672238u, 91814688482138969u ), + new( 4759444137752473128u, 2230562561567025078u, 4954443037339580076u, 90051584438315940u ), + new( 7246913525170274758u, 8910297835195760709u, 4015904029508858381u, 88322337023761438u ), + new( 12854430245836432067u, 8135139748065431455u, 11548083631386317976u, 86626296094571907u ), + new( 4848827254502687803u, 4789491250196085625u, 3988192420450664125u, 84962823991462151u ), + new( 7435538409611286684u, 904061756819742353u, 14598026519493048444u, 83331295300025028u ), + new( 11042616160352530997u, 8948390828345326218u, 10052651191118271927u, 81731096615594853u ), + new( 11059348291563778943u, 11696515766184685544u, 3783210511290897367u, 80161626312626082u ), + new( 7020010856491885826u, 5025093219346041680u, 8960210401638911765u, 78622294318500592u ), + new( 17732844474490699984u, 7820866704994446502u, 6088373186798844243u, 77112521891678506u ), + new( 688278527545590501u, 3045610706602776618u, 8684243536999567610u, 75631741404109150u ), + new( 2734573255120657297u, 3903146411440697663u, 9470794821691856713u, 74179396127820347u ), + new( 15996457521023071259u, 4776627823451271680u, 12394856457265744744u, 72754940025605801u ), + new( 13492065758834518331u, 7390517611012222399u, 1630485387832860230u, 142715675091463768u ), + new( 13665021627282055864u, 9897834675523659302u, 17907668136755296849u, 139975126841173266u ), + new( 9603773719399446181u, 10771916301484339398u, 10672699855989487527u, 137287204938390542u ), + new( 3630218541553511265u, 8139010004241080614u, 2876479648932814543u, 134650898807055963u ), + new( 8318835909686377084u, 9525369258927993371u, 2796120270400437057u, 132065217277054270u ), + new( 11190003059043290163u, 12424345635599592110u, 12539346395388933763u, 129529188211565064u ), + new( 8701968833973242276u, 820569587086330727u, 2315591597351480110u, 127041858141569228u ), + new( 5115113890115690487u, 16906305245394587826u, 9899749468931071388u, 124602291907373862u ), + new( 15543535488939245974u, 10945189844466391399u, 3553863472349432246u, 122209572307020975u ), + new( 7709257252608325038u, 1191832167690640880u, 15077137020234258537u, 119862799751447719u ), + new( 7541333244210021737u, 9790054727902174575u, 5160944773155322014u, 117561091926268545u ), + new( 12297384708782857832u, 1281328873123467374u, 4827925254630475769u, 115303583460052092u ), + new( 13243237906232367265u, 15873887428139547641u, 3607993172301799599u, 113089425598968120u ), + new( 11384616453739611114u, 15184114243769211033u, 13148448124803481057u, 110917785887682141u ), + new( 17727970963596660683u, 1196965221832671990u, 14537830463956404138u, 108787847856377790u ), + new( 17241367586707330931u, 8880584684128262874u, 11173506540726547818u, 106698810713789254u ), + new( 7184427196661305643u, 14332510582433188173u, 14230167953789677901u, 104649889046128358u ) + }; + + private static Span Pow5Errors => new ulong[156] + { + 0x0000000000000000u, 0x0000000000000000u, 0x0000000000000000u, 0x9555596400000000u, + 0x65a6569525565555u, 0x4415551445449655u, 0x5105015504144541u, 0x65a69969a6965964u, + 0x5054955969959656u, 0x5105154515554145u, 0x4055511051591555u, 0x5500514455550115u, + 0x0041140014145515u, 0x1005440545511051u, 0x0014405450411004u, 0x0414440010500000u, + 0x0044000440010040u, 0x5551155000004001u, 0x4554555454544114u, 0x5150045544005441u, + 0x0001111400054501u, 0x6550955555554554u, 0x1504159645559559u, 0x4105055141454545u, + 0x1411541410405454u, 0x0415555044545555u, 0x0014154115405550u, 0x1540055040411445u, + 0x0000000500000000u, 0x5644000000000000u, 0x1155555591596555u, 0x0410440054569565u, + 0x5145100010010005u, 0x0555041405500150u, 0x4141450455140450u, 0x0000000144000140u, + 0x5114004001105410u, 0x4444100404005504u, 0x0414014410001015u, 0x5145055155555015u, + 0x0141041444445540u, 0x0000100451541414u, 0x4105041104155550u, 0x0500501150451145u, + 0x1001050000004114u, 0x5551504400141045u, 0x5110545410151454u, 0x0100001400004040u, + 0x5040010111040000u, 0x0140000150541100u, 0x4400140400104110u, 0x5011014405545004u, + 0x0000000044155440u, 0x0000000010000000u, 0x1100401444440001u, 0x0040401010055111u, + 0x5155155551405454u, 0x0444440015514411u, 0x0054505054014101u, 0x0451015441115511u, + 0x1541411401140551u, 0x4155104514445110u, 0x4141145450145515u, 0x5451445055155050u, + 0x4400515554110054u, 0x5111145104501151u, 0x565a655455500501u, 0x5565555555525955u, + 0x0550511500405695u, 0x4415504051054544u, 0x6555595965555554u, 0x0100915915555655u, + 0x5540001510001001u, 0x5450051414000544u, 0x1405010555555551u, 0x5555515555644155u, + 0x5555055595496555u, 0x5451045004415000u, 0x5450510144040144u, 0x5554155555556455u, + 0x5051555495415555u, 0x5555554555555545u, 0x0000000010005455u, 0x4000005000040000u, + 0x5565555555555954u, 0x5554559555555505u, 0x9645545495552555u, 0x4000400055955564u, + 0x0040000000000001u, 0x4004100100000000u, 0x5540040440000411u, 0x4565555955545644u, + 0x1140659549651556u, 0x0100000410010000u, 0x5555515400004001u, 0x5955545555155255u, + 0x5151055545505556u, 0x5051454510554515u, 0x0501500050415554u, 0x5044154005441005u, + 0x1455445450550455u, 0x0010144055144545u, 0x0000401100000004u, 0x1050145050000010u, + 0x0415004554011540u, 0x1000510100151150u, 0x0100040400001144u, 0x0000000000000000u, + 0x0550004400000100u, 0x0151145041451151u, 0x0000400400005450u, 0x0000100044010004u, + 0x0100054100050040u, 0x0504400005410010u, 0x4011410445500105u, 0x0000404000144411u, + 0x0101504404500000u, 0x0000005044400400u, 0x0000000014000100u, 0x0404440414000000u, + 0x5554100410000140u, 0x4555455544505555u, 0x5454105055455455u, 0x0115454155454015u, + 0x4404110000045100u, 0x4400001100101501u, 0x6596955956966a94u, 0x0040655955665965u, + 0x5554144400100155u, 0xa549495401011041u, 0x5596555565955555u, 0x5569965959549555u, + 0x969565a655555456u, 0x0000001000000000u, 0x0000000040000140u, 0x0000040100000000u, + 0x1415454400000000u, 0x5410415411454114u, 0x0400040104000154u, 0x0504045000000411u, + 0x0000001000000010u, 0x5554000000001040u, 0x5549155551556595u, 0x1455541055515555u, + 0x0510555454554541u, 0x9555555555540455u, 0x6455456555556465u, 0x4524565555654514u, + 0x5554655255559545u, 0x9555455441155556u, 0x0000000051515555u, 0x0010005040000550u, + 0x5044044040000000u, 0x1045040440010500u, 0x0000400000040000u, 0x0000000000000000u + }; + private static Span Pow5InvErrors => new ulong[154] + { + 0x1144155514145504u, 0x0000541555401141u, 0x0000000000000000u, 0x0154454000000000u, + 0x4114105515544440u, 0x0001001111500415u, 0x4041411410011000u, 0x5550114515155014u, + 0x1404100041554551u, 0x0515000450404410u, 0x5054544401140004u, 0x5155501005555105u, + 0x1144141000105515u, 0x0541500000500000u, 0x1104105540444140u, 0x4000015055514110u, + 0x0054010450004005u, 0x4155515404100005u, 0x5155145045155555u, 0x1511555515440558u, + 0x5558544555515555u, 0x0000000000000010u, 0x5004000000000050u, 0x1415510100000010u, + 0x4545555444514500u, 0x5155151555555551u, 0x1441540144044554u, 0x5150104045544400u, + 0x5450545401444040u, 0x5554455045501400u, 0x4655155555555145u, 0x1000010055455055u, + 0x1000004000055004u, 0x4455405104000005u, 0x4500114504150545u, 0x0000000014000000u, + 0x5450000000000000u, 0x5514551511445555u, 0x4111501040555451u, 0x4515445500054444u, + 0x5101500104100441u, 0x1545115155545055u, 0x0000000000000000u, 0x1554000000100000u, + 0x5555545595551555u, 0x5555051851455955u, 0x5555555555555559u, 0x0000400011001555u, + 0x0000004400040000u, 0x5455511555554554u, 0x5614555544115445u, 0x6455156145555155u, + 0x5455855455415455u, 0x5515555144555545u, 0x0114400000145155u, 0x0000051000450511u, + 0x4455154554445100u, 0x4554150141544455u, 0x65955555559a5965u, 0x5555555854559559u, + 0x9569654559616595u, 0x1040044040005565u, 0x1010010500011044u, 0x1554015545154540u, + 0x4440555401545441u, 0x1014441450550105u, 0x4545400410504145u, 0x5015111541040151u, + 0x5145051154000410u, 0x1040001044545044u, 0x4001400000151410u, 0x0540000044040000u, + 0x0510555454411544u, 0x0400054054141550u, 0x1001041145001100u, 0x0000000140000000u, + 0x0000000014100000u, 0x1544005454000140u, 0x4050055505445145u, 0x0011511104504155u, + 0x5505544415045055u, 0x1155154445515554u, 0x0000000000004555u, 0x0000000000000000u, + 0x5101010510400004u, 0x1514045044440400u, 0x5515519555515555u, 0x4554545441555545u, + 0x1551055955551515u, 0x0150000011505515u, 0x0044005040400000u, 0x0004001004010050u, + 0x0000051004450414u, 0x0114001101001144u, 0x0401000001000001u, 0x4500010001000401u, + 0x0004100000005000u, 0x0105000441101100u, 0x0455455550454540u, 0x5404050144105505u, + 0x4101510540555455u, 0x1055541411451555u, 0x5451445110115505u, 0x1154110010101545u, + 0x1145140450054055u, 0x5555565415551554u, 0x1550559555555555u, 0x5555541545045141u, + 0x4555455450500100u, 0x5510454545554555u, 0x1510140115045455u, 0x1001050040111510u, + 0x5555454555555504u, 0x9954155545515554u, 0x6596656555555555u, 0x0140410051555559u, + 0x0011104010001544u, 0x965669659a680501u, 0x5655a55955556955u, 0x4015111014404514u, + 0x1414155554505145u, 0x0540040011051404u, 0x1010000000015005u, 0x0010054050004410u, + 0x5041104014000100u, 0x4440010500100001u, 0x1155510504545554u, 0x0450151545115541u, + 0x4000100400110440u, 0x1004440010514440u, 0x0000115050450000u, 0x0545404455541500u, + 0x1051051555505101u, 0x5505144554544144u, 0x4550545555515550u, 0x0015400450045445u, + 0x4514155400554415u, 0x4555055051050151u, 0x1511441450001014u, 0x4544554510404414u, + 0x4115115545545450u, 0x5500541555551555u, 0x5550010544155015u, 0x0144414045545500u, + 0x4154050001050150u, 0x5550511111000145u, 0x1114504055000151u, 0x5104041101451040u, + 0x0010501401051441u, 0x0010501450504401u, 0x4554585440044444u, 0x5155555951450455u, + 0x0040000400105555u, 0x0000000000000001u, + }; + + public static void Format(in Quad value, scoped Span destination, out int charsWritten, out bool isExceptional, NumberFormatInfo? info, int? precision = null) + { + var fd = QuadToFloatingDecimal128(in value); + charsWritten = ToCharSpan(in fd, destination, info is null ? NumberFormatInfo.CurrentInfo : info!, out isExceptional); + } + + public static int ToCharSpan(in FloatingDecimal128 v, Span destination, NumberFormatInfo info, out bool isExceptional) + { + if (v.Exponent == FD128ExceptionalExponent) + { + isExceptional = true; + ReadOnlySpan symbol; + if (v.Mantissa != 0) + { + symbol = info.NaNSymbol; + symbol.CopyTo(destination); + return symbol.Length; + } + if (v.Sign) + { + symbol = info.NegativeInfinitySymbol; + } + else + { + symbol = info.PositiveInfinitySymbol; + } + symbol.CopyTo(destination); + return symbol.Length; + } + + isExceptional = false; + + // Step 5: Print the decimal representation. + ReadOnlySpan negativeSign = info.NegativeSign.AsSpan(); + + int index = 0; + if (v.Sign) + { + negativeSign.CopyTo(destination[index..]); + index += negativeSign.Length; + } + + UInt128 output = v.Mantissa; + uint olength = (uint)BitHelper.CountDigits(output); + + for (uint i = 0; i < olength - 1; ++i) + { + (output, UInt128 c) = UInt128.DivRem(output, 10); + destination[(int)(index + olength - i)] = (char)('0' + c); + } + destination[index] = (char)('0' + (output % 10)); + + // Print decimal point if needed + if (olength > 1) + { + ReadOnlySpan numberDecimalSeparator = info.NumberDecimalSeparator; + + numberDecimalSeparator.CopyTo(destination[(index + 1)..]); + + index += (int)olength + numberDecimalSeparator.Length; + } + else + { + ++index; + } + + // Print the exponent. + destination[index++] = 'E'; + int exp = (int)(v.Exponent + olength - 1); + + if (exp < 0) + { + negativeSign.CopyTo(destination[index..]); + index += negativeSign.Length; + exp = -exp; + } + else + { + ReadOnlySpan positiveSign = info.PositiveSign; + positiveSign.CopyTo(destination[index..]); + index += positiveSign.Length; + } + + uint elength = (uint)BitHelper.CountDigits((UInt128)exp); + + for (int i = 0; i < elength; ++i) + { + (exp, int c) = int.DivRem(exp, 10); + destination[(int)(index + elength - 1 - i)] = (char)('0' + c); + } + index += (int)elength; + return index; + } + + public static FloatingDecimal128 QuadToFloatingDecimal128(in Quad value) + { + const int MatissaBits = 112; + const int ExponentBits = 15; + + UInt128 bits = Quad.QuadToUInt128Bits(value); + + + uint bias = (1U << (ExponentBits - 1)) - 1; + bool ieeeSign = ((bits >> (MatissaBits + ExponentBits)) & 1) != 0; + UInt128 ieeeMatissa = bits & ((UInt128.One << MatissaBits) - UInt128.One); + uint ieeeExponent = (uint)((bits >> MatissaBits) & ((UInt128.One << ExponentBits) - UInt128.One)); + + if (ieeeExponent == 0 && ieeeMatissa == UInt128.Zero) + { + return new FloatingDecimal128(0, 0, ieeeSign); + } + if (ieeeExponent == ((1U << (int)ExponentBits) - 1U)) + { + return new FloatingDecimal128( + ieeeMatissa, + FD128ExceptionalExponent, + ieeeSign + ); + } + + int e2; + UInt128 m2; + + // We subtract 2 in all cases so that the bounds computation has 2 additional bits. + if (ieeeExponent == 0) + { + e2 = (int)(1 - bias - MatissaBits - 2); + m2 = ieeeMatissa; + } + else + { + e2 = (int)(ieeeExponent - (int)bias - MatissaBits - 2); + m2 = (UInt128.One << MatissaBits) | ieeeMatissa; + } + + bool even = (m2 & 1) == 0; + bool acceptBounds = even; + + // Step 2: Determine the interval of legal decimal representations. + UInt128 mv = 4 * m2; + // bool -> int conversion. True is 1, false is 0. + uint mmShift = ((ieeeMatissa != 0) || (ieeeExponent == 0)) ? 1U : 0U; + + // Step 3: Convert to a decimal power base using 128-bit arithmetic. + UInt128 vr, vp, vm; + int e10; + bool vmIsTrailingZeros = false; + bool vrIsTrailingZeros = false; + + if (e2 >= 0) + { + uint q = Log10Pow2(e2) - ((e2 > 3) ? 1U : 0U); + e10 = (int)q; + int k = (int)(Float128Pow5InvBitCount + Pow5Bits((int)q) - 1); + int i = -e2 + (int)q + k; + Span pow5 = stackalloc ulong[4]; + GenericComputeInvPow5(in q, pow5); + vr = MulShift(4 * m2, pow5, i); + vp = MulShift(4 * m2 + 2, pow5, i); + vm = MulShift(4 * m2 - 1 - mmShift, pow5, i); + + // floor(log5(2^128)) = 55, this is very conservative + if (q <= 55) + { + // Only one of mp, mv, and mm can be a multiple of 5, if any. + if (mv % 5 == 0) + { + vrIsTrailingZeros = MultipleOfPowerOf5(in mv, q - 1); + } + else if (acceptBounds) + { + // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q + // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q + // <=> true && pow5Factor(mm) >= q, since e2 >= q. + vmIsTrailingZeros = MultipleOfPowerOf5(mv - 1 - mmShift, q); + } + else + { + // Same as min(e2 + 1, pow5Factor(mp)) >= q. + vp -= MultipleOfPowerOf5(mv + 2, q) ? UInt128.One : UInt128.Zero; + } + } + } + else + { + uint q = Log10Pow5(-e2) - (-2 > 1 ? 1 : 0); + e10 = (int)(q + e2); + int i = (int)(-e2 - q); + int k = (int)(Pow5Bits(i) - Float128Pow5BitCount); + int j = (int)(q - k); + Span pow5 = stackalloc ulong[4]; + GenericComputePow5((uint)i, pow5); + vr = MulShift(4 * m2, pow5, j); + vp = MulShift(4 * m2 + 2, pow5, j); + vm = MulShift(4 * m2 - 1 - mmShift, pow5, j); + + if (q <= 1) + { + // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits. + // mv = 4 m2, so it always has at least two trailing 0 bits. + vrIsTrailingZeros = true; + if (acceptBounds) + { + // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1. + vrIsTrailingZeros = mmShift == 1; + } + else + { + --vp; + } + } + else if (q < 127) + { + vrIsTrailingZeros = MultipleOfPowerOf2(in mv, q - 1); + } + } + + // Step 4: Find the shortest decimal representation in the interval of legal representations. + uint removed = 0; + byte lastRemovedDigit = 0; + UInt128 output; + + while ((vp / 10) > (vm / 10)) + { + vmIsTrailingZeros &= vm % 10 == 0; + vrIsTrailingZeros &= lastRemovedDigit == 0; + lastRemovedDigit = (byte)(vr % 10); + vr /= 10; + vp /= 10; + vm /= 10; + ++removed; + } + + if (vmIsTrailingZeros) + { + while (vm % 10 == 0) + { + vrIsTrailingZeros &= lastRemovedDigit == 0; + lastRemovedDigit = (byte)(vr % 10); + vr /= 10; + vp /= 10; + vm /= 10; + ++removed; + } + } + + if (vrIsTrailingZeros && (lastRemovedDigit == 5) && (vr % 2 == 0)) + { + lastRemovedDigit = 4; + } + + output = vr + + (((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || (lastRemovedDigit >= 5)) ? UInt128.One : UInt128.Zero); + int exp = e10 + (int)removed; + + return new FloatingDecimal128(output, exp, ieeeSign); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static uint Pow5Factor(UInt128 value) + { + for (uint i = 0; value > 0; ++i) + { + (value, UInt128 rem) = UInt128.DivRem(value, 5); + if (rem != 0) + { + return i; + } + } + + return 0; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static bool MultipleOfPowerOf2(in UInt128 value, uint p) + { + return (value & ((((UInt128)1) << (int)p) - 1)) == 0; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static bool MultipleOfPowerOf5(in UInt128 value, uint p) + { + return Pow5Factor(value) >= p; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static uint Log10Pow2(int e) + { + // The first value this approximation fails for is 2^1651 which is just greater than 10^297. + Debug.Assert(e >= 0); + Debug.Assert(e <= 1 << 15); + + return (uint)((((ulong)e) * 169464822037455UL) >> 49); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static uint Log10Pow5(int e) + { + // The first value this approximation fails for is 2^1651 which is just greater than 10^297. + Debug.Assert(e >= 0); + Debug.Assert(e <= 1 << 15); + + return (uint)((((ulong)e) * 196742565691928UL) >> 48); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static uint Pow5Bits(int e) + { + Debug.Assert(e >= 0); + Debug.Assert(e <= 1 << 15); + + return (uint)(((((ulong)e * 163391164108059UL)) >> 46) + 1); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static void GenericComputePow5(in uint i, Span result) + { + uint ibase = i / Pow5TableSize; + uint ibase2 = ibase * Pow5TableSize; + ReadOnlySpan mul = GenericPow5Split[(int)ibase].AsSpan(); + + if (i == ibase2) + { + result[0] = mul[0]; + result[1] = mul[1]; + result[2] = mul[2]; + result[3] = mul[3]; + } + else + { + uint offset = i - ibase2; + ReadOnlySpan m = GenericPow5Table[(int)offset].AsSpan(); + uint delta = Pow5Bits((int)i) - Pow5Bits((int)ibase2); + uint corr = (uint)((Pow5Errors[(int)i / 32] >> (2 * ((int)i % 32))) & 3); + Mul128To256Shift(m, mul, (int)delta, corr, result); + } + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static void GenericComputeInvPow5(in uint i, Span result) + { + uint ibase = (i + Pow5TableSize - 1) / Pow5TableSize; + uint ibase2 = ibase * Pow5TableSize; + ReadOnlySpan mul = GenericPow5InvSplit[(int)ibase].AsSpan(); + if (i == ibase2) + { + result[0] = mul[0] + 1; + result[1] = mul[1]; + result[2] = mul[2]; + result[3] = mul[3]; + } + else + { + uint offset = ibase2 - i; + ReadOnlySpan m = GenericPow5Table[(int)offset].AsSpan(); + ulong delta = Pow5Bits((int)ibase2) - Pow5Bits((int)i); + uint corr = (uint)((Pow5InvErrors[(int)i / 32] >> (2 * ((int)i % 32))) & 3) + 1; + Mul128To256Shift(m, mul, (int)delta, corr, result); + } + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static UInt128 MulShift(UInt128 m, ReadOnlySpan mul, int j) + { + Debug.Assert(j > 128); + ReadOnlySpan a = stackalloc ulong[2] + { + (ulong)m, + (ulong)(m >> 64) + }; + Span result = stackalloc ulong[4]; + Mul128To256Shift(a, mul, j, 0, result); + return (((UInt128)result[1]) << 64) | result[0]; + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + private static void Mul128To256Shift(ReadOnlySpan a, ReadOnlySpan b, int shift, uint corr, Span result) + { + UInt128 b00 = ((UInt128)a[0]) * b[0]; // 0 + UInt128 b01 = ((UInt128)a[0]) * b[1]; // 64 + UInt128 b02 = ((UInt128)a[0]) * b[2]; // 128 + UInt128 b03 = ((UInt128)a[0]) * b[3]; // 196 + UInt128 b10 = ((UInt128)a[1]) * b[0]; // 64 + UInt128 b11 = ((UInt128)a[1]) * b[1]; // 128 + UInt128 b12 = ((UInt128)a[1]) * b[2]; // 196 + UInt128 b13 = ((UInt128)a[1]) * b[3]; // 256 + + UInt128 s0 = b00; // 0 + UInt128 s1 = b01 + b10; // 64 + UInt128 c1 = s1 < b01 ? UInt128.One : UInt128.Zero; // 196 + UInt128 s2 = b02 + b11; // 128 + UInt128 c2 = s2 < b02 ? UInt128.One : UInt128.Zero; // 256 + UInt128 s3 = b03 + b12; // 196 + UInt128 c3 = s3 < b03 ? UInt128.One : UInt128.Zero; // 324 + + UInt128 p0 = s0 + (s1 << 64); // 0 + UInt128 d0 = p0 < b00 ? UInt128.One : UInt128.Zero; // 128 + UInt128 q1 = s2 + (s1 >> 64) + (s3 << 64); // 128 + UInt128 d1 = q1 < s2 ? UInt128.One : UInt128.Zero; // 256 + UInt128 p1 = q1 + (c1 << 64) + d0; // 128 + UInt128 d2 = p1 < q1 ? UInt128.One : UInt128.Zero; // 256 + UInt128 p2 = b13 + (s3 >> 64) + c2 + (c3 << 64) + d1 + d2; // 256 + + UInt128 r0, r1; + if (shift < 128) + { + r0 = corr + ((p0 >> shift) | (p1 << (128 - shift))); + r1 = ((p1 >> shift) | (p2 << (128 - shift))) + (r0 < corr ? UInt128.One : UInt128.Zero); + } + else if (shift == 128) + { + r0 = corr + p1; + r1 = p2 + (r0 < corr ? UInt128.One : UInt128.Zero); + } + else + { + r0 = corr + ((p1 >> shift - 128) | (p2 << (256 - shift))); + r1 = (p2 >> (shift - 128)) + (r0 < corr ? UInt128.One : UInt128.Zero); + } + + result[0] = (ulong)r0; + result[1] = (ulong)(r0 >> 64); + result[2] = (ulong)r1; + result[3] = (ulong)(r1 >> 64); + } + } +} diff --git a/src/MissingValues/Internals/NumberFormatter.cs b/src/MissingValues/Internals/NumberFormatter.cs index e73ce26..31639f6 100644 --- a/src/MissingValues/Internals/NumberFormatter.cs +++ b/src/MissingValues/Internals/NumberFormatter.cs @@ -6,6 +6,7 @@ using System.Globalization; using System.Linq; using System.Numerics; +using System.Reflection; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Runtime.Intrinsics.Arm; @@ -14,7 +15,7 @@ namespace MissingValues { - internal static class NumberFormatter + internal static partial class NumberFormatter { #region IFormattableNumber public static string UnsignedNumberToString(in T value, T numberBase) @@ -430,5 +431,243 @@ public static bool TryFormatSignedNumber(in TSigned value, S return success; } #endregion + #region Float + public static string QuadToString( + in Quad value, + ReadOnlySpan format, + IFormatProvider? provider) + { + const int MaxSignificandPrecision = 33; + const int MaxBufferAlloc = MaxSignificandPrecision + 4 + 4 + 4; // 33 significant decimal digits precision, 4 possible special symbols, 4 exponent decimal digits + + int precision; + + if (format.IsEmpty) + { + precision = MaxSignificandPrecision; + } + else + { + if (int.TryParse(format.Trim()[1..], out int p)) + { + precision = p > MaxSignificandPrecision ? MaxSignificandPrecision : p; + } + else + { + precision = MaxSignificandPrecision; + } + + if (!(format.Contains("F", StringComparison.OrdinalIgnoreCase) + || format.Contains("G", StringComparison.OrdinalIgnoreCase) + || format.Contains("N", StringComparison.OrdinalIgnoreCase) + || format.Contains("E", StringComparison.OrdinalIgnoreCase))) + { + Thrower.NotSupported(); + } + } + + NumberFormatInfo info = NumberFormatInfo.GetInstance(provider); + + Span buffer = stackalloc char[MaxBufferAlloc]; + Ryu.Format(in value, buffer, out _, out bool isExceptional, info, precision); + + if (isExceptional || format.Contains("E", StringComparison.OrdinalIgnoreCase)) + { + return new string(buffer.TrimEnd('\0')); + } + + return new string(GetGeneralFromScientificFloatChars(buffer, info, precision)); + } + + public static bool TryFormatQuad( + in Quad value, + Span destination, + out int charsWritten, + ReadOnlySpan format, + IFormatProvider? provider) + { + const int MaxSignificandPrecision = 33; + const int MaxBufferAlloc = MaxSignificandPrecision + 4 + 4 + 4; // 33 significant decimal digits precision, 4 possible special symbols, 4 exponent decimal digits + + int precision; + + if (format.IsEmpty) + { + precision = MaxSignificandPrecision; + } + else + { + if (int.TryParse(format.Trim()[1..], out int p)) + { + precision = p > MaxSignificandPrecision ? MaxSignificandPrecision : p; + } + else + { + precision = MaxSignificandPrecision; + } + + if (!(format.Contains("F", StringComparison.OrdinalIgnoreCase) + || format.Contains("G", StringComparison.OrdinalIgnoreCase) + || format.Contains("N", StringComparison.OrdinalIgnoreCase) + || format.Contains("E", StringComparison.OrdinalIgnoreCase))) + { + Thrower.NotSupported(); + } + } + + NumberFormatInfo info = NumberFormatInfo.GetInstance(provider); + + Span buffer = stackalloc char[MaxBufferAlloc]; + Ryu.Format(in value, buffer, out charsWritten, out bool isExceptional, info, precision); + + if (isExceptional || format.Contains("E", StringComparison.OrdinalIgnoreCase)) + { + return buffer.TrimEnd('\0').TryCopyTo(destination); + } + + ReadOnlySpan general = GetGeneralFromScientificFloatChars(buffer, info, precision); + charsWritten = general.Length; + return general.TryCopyTo(destination); + } + + private static ReadOnlySpan GetGeneralFromScientificFloatChars(Span buffer, NumberFormatInfo info, int precision) + { + const int MaxSignificandPrecision = 33; + + Span actualValue = buffer.TrimEnd('\0'); + + int eIndex = actualValue.IndexOf('E'); + if (eIndex <= 0 || !int.TryParse(actualValue[(eIndex + 1)..], out int exponent)) + { + exponent = 0; + } + + ReadOnlySpan numberDecimalSeparator = info.NumberDecimalSeparator; + ReadOnlySpan negativeSign = info.NegativeSign; + + bool isNegativeExponent = exponent < 0; + bool isNegative = buffer.IndexOf(negativeSign) == 0; + int dotIndex = buffer.IndexOf(numberDecimalSeparator); + bool containsDecimalSeparator = dotIndex >= 0; + + // If buffer cannot be represented with precision. + if ((!isNegativeExponent && (containsDecimalSeparator && exponent >= actualValue[(dotIndex + 1)..eIndex].Length && MaxSignificandPrecision < actualValue.Length)) || + (isNegativeExponent && (containsDecimalSeparator && (-exponent) >= 1 && MaxSignificandPrecision < actualValue.Length))) + { + return actualValue; + } + if (!containsDecimalSeparator && ((isNegativeExponent && (-exponent) >= MaxSignificandPrecision) || (!isNegativeExponent && exponent >= MaxSignificandPrecision))) + { + return actualValue; + } + if (int.Abs(exponent) >= MaxSignificandPrecision) + { + return actualValue; + } + + // Get rid of the scientific notation + actualValue[eIndex..].Fill('\0'); + actualValue = actualValue[..eIndex]; + + + int temp; + + if (!containsDecimalSeparator) + { + if (isNegativeExponent) // ie: 5E-1 = 0.5 + { + /* + * Since we got rid of E.. actualValue only has 5, now we have to add the leading zeroes + * we know we have to add the first zero as 0.N, so lets do that first + */ + + int i; + + if (isNegative) + { + i = 4; + buffer[2 + numberDecimalSeparator.Length] = buffer[1]; + buffer[1] = '0'; + numberDecimalSeparator.CopyTo(buffer[2..]); + } + else + { + i = 3; + buffer[1 + numberDecimalSeparator.Length] = buffer[0]; + buffer[0] = '0'; + numberDecimalSeparator.CopyTo(buffer[1..]); + } + + for (int leadingZeroes = (-exponent) - 1; leadingZeroes > 0 && i < buffer.Length; leadingZeroes--, i++) + { + (buffer[i - 1], buffer[i]) = ('0', buffer[i - 1]); + } + } + else if (exponent != 0) // ie: 5E1 = 50 + { + /* + * This one is easier, we just add trailing zeroes + */ + for (int i = isNegative ? 2 : 1, trailingZeroes = exponent; trailingZeroes > 0 && i < buffer.Length; i++, trailingZeroes--) + { + buffer[i] = '0'; + } + } + + + } + else if (isNegativeExponent) // ie: 1.1E-5 = 0.000011 + { + Span digits = stackalloc char[actualValue.Length - 1]; + digits[0] = isNegative ? actualValue[1] : actualValue[0]; + actualValue[(dotIndex + 1)..].CopyTo(digits[1..]); + + buffer[isNegative ? 1 : 0] = '0'; + int i; + + for (i = isNegative ? 3 : 2, temp = exponent; temp > 0 && i < buffer.Length - digits.Length; i++, temp--) + { + buffer[i] = '0'; + } + + digits.CopyTo(buffer[i..]); + } + else if (exponent != 0) // ie: 1.1E5 = 110000 + { + int i; + int decimalDigits = actualValue[(dotIndex + 1)..].Length; + if (decimalDigits < exponent && exponent < buffer.Length) + { + i = actualValue.Length; + buffer.Slice(i, exponent - decimalDigits).Fill('0'); + } + i = isNegative ? 3 : 2; + for (temp = exponent; temp > 0 && i < buffer.Length; i++, temp--) + { + (buffer[i - 1], buffer[i]) = (buffer[i], buffer[i - 1]); + } + } + + actualValue = buffer.TrimEnd('\0'); + + if (actualValue.EndsWith(numberDecimalSeparator)) + { + actualValue = actualValue[..^numberDecimalSeparator.Length]; + containsDecimalSeparator = false; + dotIndex = -1; + } + else + { + containsDecimalSeparator = (dotIndex = actualValue.IndexOf(numberDecimalSeparator)) > -1; + } + + if (containsDecimalSeparator && actualValue[dotIndex..].Length > precision) + { + actualValue = actualValue[..precision]; + } + + return actualValue; + } + #endregion } } \ No newline at end of file diff --git a/src/MissingValues/Internals/NumberParser.cs b/src/MissingValues/Internals/NumberParser.cs index d9e74ce..99cd7e4 100644 --- a/src/MissingValues/Internals/NumberParser.cs +++ b/src/MissingValues/Internals/NumberParser.cs @@ -1,11 +1,14 @@ using MissingValues.Internals; using System; using System.Collections.Generic; +using System.Diagnostics.CodeAnalysis; using System.Globalization; using System.Linq; using System.Numerics; +using System.Runtime.InteropServices; using System.Text; using System.Threading.Tasks; +using static System.Runtime.InteropServices.JavaScript.JSType; namespace MissingValues { @@ -416,5 +419,85 @@ private static bool ContainsInvalidCharacter(ReadOnlySpan s, NumberStyles return false; } #endregion + #region Float + public static unsafe bool TryParseQuad(ReadOnlySpan s, NumberStyles styles, IFormatProvider? provider, [MaybeNullWhen(false)] out Quad result) + { + const uint RequiredBitsOfPrecision = (113 + 1); + + FloatInfo number = new FloatInfo(stackalloc byte[11563 + 1 + 1]); + NumberFormatInfo info = NumberFormatInfo.GetInstance(provider); + + + if (!FloatInfo.TryParse(s, ref number, info, styles)) + { + ReadOnlySpan trim = s.Trim(); + + ReadOnlySpan infinity = info.PositiveInfinitySymbol; + + if (trim.Equals(infinity, StringComparison.OrdinalIgnoreCase)) + { + result = Quad.PositiveInfinity; + return true; + } + + if (trim.Equals(info.NegativeInfinitySymbol, StringComparison.OrdinalIgnoreCase)) + { + result = Quad.NegativeInfinity; + return true; + } + + ReadOnlySpan nan = info.NaNSymbol; + + if (trim.Equals(nan, StringComparison.OrdinalIgnoreCase)) + { + result = Quad.NaN; + return true; + } + + ReadOnlySpan positiveSign = info.PositiveSign; + + if (trim.StartsWith(positiveSign, StringComparison.OrdinalIgnoreCase)) + { + trim = trim.Slice(positiveSign.Length); + + if (trim.Equals(infinity, StringComparison.OrdinalIgnoreCase)) + { + result = Quad.PositiveInfinity; + return true; + } + else if (trim.Equals(nan, StringComparison.OrdinalIgnoreCase)) + { + result = Quad.NaN; + return true; + } + + result = Quad.Zero; + return false; + } + ReadOnlySpan negativeSign = info.NegativeSign; + + if (trim.StartsWith(negativeSign, StringComparison.OrdinalIgnoreCase)) + { + if (trim[negativeSign.Length..].Equals(nan, StringComparison.OrdinalIgnoreCase)) + { + result = Quad.NaN; + return true; + } + + if (trim.StartsWith("-", StringComparison.OrdinalIgnoreCase)) + { + result = Quad.NaN; + return true; + } + } + + result = Quad.Zero; + return false; // We really failed + } + + result = FloatInfo.ConvertToQuad(ref number); + return true; + } + #endregion } } diff --git a/src/MissingValues/Internals/Thrower.cs b/src/MissingValues/Internals/Thrower.cs index fea4024..13c744f 100644 --- a/src/MissingValues/Internals/Thrower.cs +++ b/src/MissingValues/Internals/Thrower.cs @@ -144,5 +144,10 @@ public static void ExpectedNumber(JsonTokenType actual) { throw new InvalidOperationException($"Expected {JsonTokenType.Number}, got {actual}."); } + [DoesNotReturn] + internal static void OutOfRange(string paramName) + { + throw new ArgumentOutOfRangeException(paramName); + } } } diff --git a/src/MissingValues/MathQ.Arithmetics.cs b/src/MissingValues/MathQ.Arithmetics.cs new file mode 100644 index 0000000..67ec04c --- /dev/null +++ b/src/MissingValues/MathQ.Arithmetics.cs @@ -0,0 +1,294 @@ +using System; +using System.Collections.Generic; +using System.Linq; +using System.Net.Quic; +using System.Numerics; +using System.Runtime.CompilerServices; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues +{ + /* + * Parts of the code for basic math operators were based of Berkeley SoftFloat Release 3e + * + * The following applies to most of the code below: + + Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Regents of the + University of California. All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, + this list of conditions, and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions, and the following disclaimer in the + documentation and/or other materials provided with the distribution. + + 3. Neither the name of the University nor the names of its contributors + may be used to endorse or promote products derived from this software + without specific prior written permission. + + THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY + EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED + WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE + DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY + DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES + (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND + ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + + */ + + internal static partial class MathQ + { + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static Quad Add(Quad left, Quad right) + { + // Source: berkeley-softfloat-3/source/f128_add.c + bool signA; + bool signB; + + signA = Quad.IsNegative(left); + + signB = Quad.IsNegative(right); + + if (signA == signB) + { + return Quad.UInt128BitsToQuad(BitHelper.AddQuadBits( + Quad.QuadToUInt128Bits(left), Quad.QuadToUInt128Bits(right), signA)); + } + else + { + return Quad.UInt128BitsToQuad(BitHelper.SubQuadBits( + Quad.QuadToUInt128Bits(left), Quad.QuadToUInt128Bits(right), signA)); + } + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static Quad Sub(Quad left, Quad right) + { + // Source: berkeley-softfloat-3/source/f128_sub.c + bool signA; + bool signB; + + signA = Quad.IsNegative(left); + + signB = Quad.IsNegative(right); + + if (signA == signB) + { + return Quad.UInt128BitsToQuad(BitHelper.SubQuadBits( + Quad.QuadToUInt128Bits(left), Quad.QuadToUInt128Bits(right), signA)); + } + else + { + return Quad.UInt128BitsToQuad(BitHelper.AddQuadBits( + Quad.QuadToUInt128Bits(left), Quad.QuadToUInt128Bits(right), signA)); + } + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static Quad Mul(Quad left, Quad right) + { + // Source: berkeley-softfloat-3/source/f128_mul.c + bool signA, signB, signZ; + ushort expA, expB, expZ; + UInt128 sigA, sigB, sigZ; + UInt256 sig256; + + signA = Quad.IsNegative(left); + expA = left.BiasedExponent; + sigA = left.Significand; + + signB = Quad.IsNegative(right); + expB = right.BiasedExponent; + sigB = right.Significand; + signZ = signA ^ signB; + + if (expA == 0x7FFF) + { + if ((sigA != UInt128.Zero) || ((expB == 0x7FFF) && (sigB != UInt128.Zero))) + { + return Quad.NaN; + } + + bool magBits = (sigB | expB) != UInt128.Zero; + if (!magBits) + { + return Quad.NaN; + } + + return signZ ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + if (expB == 0x7FFF) + { + if (sigB != UInt128.Zero) + { + return Quad.NaN; + } + bool magBits = (sigA | expA) != UInt128.Zero; + if (!magBits) + { + return Quad.NaN; + } + + return signZ ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + + if (expA == 0) + { + if (sigA == UInt128.Zero) + { + return signZ ? Quad.NegativeZero : Quad.Zero; + } + var normExpSig = BitHelper.NormalizeSubnormalF128Sig(sigA); + expA = normExpSig.Exp; + sigA = normExpSig.Sig; + } + if (expB == 0) + { + if (sigB == UInt128.Zero) + { + return signZ ? Quad.NegativeZero : Quad.Zero; + } + var normExpSig = BitHelper.NormalizeSubnormalF128Sig(sigB); + expB = normExpSig.Exp; + sigB = normExpSig.Sig; + } + + expZ = (ushort)(expA + expB - 0x4000); + sigA |= new UInt128(0x0001_0000_0000_0000, 0); + sigB <<= 16; + UInt128 sig256Hi = BitHelper.BigMul(sigA, sigB, out UInt128 sig256Lo); + sig256 = new UInt256(sig256Hi, sig256Lo); + ulong sigZExtra = Convert.ToUInt64(sig256 != UInt256.Zero); + sigZ = sig256.Upper + sigA; + if (0x0002_0000_0000_0000 <= (ulong)(sigZ >> 64)) + { + ++expZ; + sigZ = BitHelper.ShortShiftRightJamExtra(sigZ, sigZExtra, 1, out sigZExtra); + } + + return Quad.UInt128BitsToQuad(BitHelper.RoundPackToQuad(signZ, expZ, sigZ, sigZExtra)); + } + [MethodImpl(MethodImplOptions.AggressiveInlining)] + internal static Quad Div(Quad left, Quad right) + { + // Source: berkeley-softfloat-3/source/f128_div.c + bool signA = Quad.IsNegative(left); + var expA = left.BiasedExponent; + var sigA = left.Significand; + bool signB = Quad.IsNegative(right); + var expB = right.BiasedExponent; + var sigB = right.Significand; + bool signZ = signA ^ signB; + + if (expA == 0x7FFF) + { + if (sigA != UInt128.Zero) + { + return Quad.NaN; + } + if (expB == 0x7FFF) + { + return Quad.NaN; + } + return signZ ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + if (expB == 0x7FFF) + { + if (sigB != UInt128.Zero) + { + return Quad.NaN; + } + + return signZ ? Quad.NegativeZero : Quad.Zero; + } + + if (expB == 0) + { + if (sigB == UInt128.Zero) + { + if ((expA | sigA) == UInt128.Zero) + { + return Quad.NaN; + } + return signZ ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + (expB, sigB) = BitHelper.NormalizeSubnormalF128Sig(sigB); + } + if (expA == 0) + { + if (sigA == UInt128.Zero) + { + return signZ ? Quad.NegativeZero : Quad.Zero; + } + + (expA, sigA) = BitHelper.NormalizeSubnormalF128Sig(sigA); + } + + short expZ = ((short)(expA - expB + (Quad.ExponentBias - 1))); + sigA |= new UInt128(0x0001_0000_0000_0000, 0); + sigB |= new UInt128(0x0001_0000_0000_0000, 0); + UInt128 rem = sigA; + if (sigA < sigB) + { + --expZ; + rem = sigA + sigA; + } + + uint recip32 = BitHelper.ReciprocalApproximate((uint)(sigB >> 81)); + + uint q; + Span qs = stackalloc uint[3]; + UInt128 term; + for(int ix = 3;;) + { + ulong q64 = (ulong)(uint)(rem >> 83) * recip32; + q = (uint)((q64 + 0x8000_0000) >> 32); + if (--ix < 0) + { + break; + } + rem <<= 29; + term = sigB * q; + rem -= term; + if (((ulong)(rem >> 64) & 0x8000_0000_0000_0000) != 0) + { + --q; + rem += sigB; + } + qs[ix] = q; + } + + if (((q + 1) & 7) < 2) + { + rem <<= 29; + term = sigB * q; + rem -= term; + if (((ulong)(rem >> 64) & 0x8000_0000_0000_0000) != 0) + { + --q; + rem += sigB; + } + else if (sigB <= rem) + { + ++q; + rem -= sigB; + } + if (rem != UInt128.Zero) + { + q |= 1; + } + } + + ulong sigZExtra = (q << 60); + term = new UInt128(0, qs[1]) << 54; + UInt128 sigZ = new UInt128((ulong)qs[2] << 19, ((ulong)qs[0] << 25) + (q >> 4)) + term; + return Quad.UInt128BitsToQuad(BitHelper.RoundPackToQuad(signZ, expZ, sigZ, sigZExtra)); + } + } +} diff --git a/src/MissingValues/MathQ.MathFunctions.cs b/src/MissingValues/MathQ.MathFunctions.cs index d2bab05..7f90899 100644 --- a/src/MissingValues/MathQ.MathFunctions.cs +++ b/src/MissingValues/MathQ.MathFunctions.cs @@ -1,6 +1,7 @@ using MissingValues.Internals; using System; using System.Collections.Generic; +using System.Diagnostics; using System.Globalization; using System.Linq; using System.Runtime.CompilerServices; @@ -10,19 +11,17 @@ namespace MissingValues { + // TODO: Finish implementing math functions so that Quad can implemente the IBinaryFloatingPointIEEE interface... + internal ref struct Shape { - internal ref Quad f; - internal ref Word i; internal ref Word64 i2; - public Shape(Quad quad) + public Shape(ref Quad quad) { - f = quad; - - i = ref Unsafe.As(ref f); - i2 = ref Unsafe.As(ref f); + i = ref Unsafe.As(ref quad); + i2 = ref Unsafe.As(ref quad); } [StructLayout(LayoutKind.Sequential)] @@ -52,12 +51,52 @@ public struct Word64 #endif } } + internal readonly ref struct ReadOnlyShape + { + internal readonly ref Word i; + internal readonly ref Word64 i2; + + public ReadOnlyShape(ref Quad quad) + { + i = ref Unsafe.As(ref quad); + i2 = ref Unsafe.As(ref quad); + } - public static partial class MathQ + [StructLayout(LayoutKind.Sequential)] + public readonly struct Word + { +#if BIGENDIAN + internal readonly ushort se; + internal readonly ushort top; + internal readonly uint mid; + internal readonly ulong lo; +#else + internal readonly ulong lo; + internal readonly uint mid; + internal readonly ushort top; + internal readonly ushort se; +#endif + } + [StructLayout(LayoutKind.Sequential)] + public readonly struct Word64 + { +#if BIGENDIAN + internal readonly ulong hi; + internal readonly ulong lo; +#else + internal readonly ulong lo; + internal readonly ulong hi; +#endif + } + } + + internal static partial class MathQ { internal const int MaxRoundingDigits = 34; private static Quad M_PI_4 => new Quad(0x3FFE_921F_B544_42D1, 0x8469_B288_3370_1F13); // pi / 4 + private static Quad LOG2EA => new Quad(); + private static Quad SQRTH => new Quad(); private static Quad RoundLimit => new Quad(0x4073_3426_172C_74D8, 0x22B8_78FE_8000_0000); // 1E35 internal static ReadOnlySpan RoundPower10 => new Quad[MaxRoundingDigits + 1] @@ -162,7 +201,7 @@ public static partial class MathQ /// - /// Returns the absolute value of a quadruple-precision floating-point number. + /// Returns the absolute value of x quadruple-precision floating-point number. /// /// A number that is greater than or equal to , but less than or equal to . /// A quadruple-precision floating-point number, x, such that 0 ≤ x ≤ . @@ -173,7 +212,7 @@ public static Quad Abs(Quad x) /// /// Returns the angle whose cosine is the specified number. /// - /// A number representing a cosine, where must be greater than or equal to -1, but less than or equal to 1. + /// A number representing x cosine, where must be greater than or equal to -1, but less than or equal to 1. /// /// An angle, θ, measured in radians, such that 0 ≤ θ ≤ π. /// @@ -184,7 +223,7 @@ public static Quad Acos(Quad x) /// /// Returns the angle whose hyperbolic cosine is the specified number. /// - /// A number representing a hyperbolic cosine, where must be greater than or equal to 1, but less than or equal to . + /// A number representing x hyperbolic cosine, where must be greater than or equal to 1, but less than or equal to . /// An angle, θ, measured in radians, such that 0 ≤ θ ≤ ∞. public static Quad Acosh(Quad x) { @@ -310,7 +349,42 @@ public static Quad Cbrt(Quad x) /// public static Quad Ceiling(Quad x) { - throw new NotImplementedException(); + if (Quad.IsNaN(x) || Quad.IsInfinity(x)) + { + return x; + } + + int unbiasedExponent = x.Exponent; + if (unbiasedExponent < 0) + { + if (Quad.IsNegative(x)) + { + return Quad.Zero; + } + else + { + return Quad.One; + } + } + else + { + if (unbiasedExponent >= 112) + { + return x; + } + + UInt128 resultBits = Quad.QuadToUInt128Bits(x); + int bitsToErase = 112 - unbiasedExponent; + resultBits = (resultBits >> bitsToErase) << bitsToErase; + Quad result = Quad.UInt128BitsToQuad(resultBits); + + if (result != x && !Quad.IsNegative(result)) + { + result++; + } + + return result; + } } /// /// @@ -345,7 +419,8 @@ private static int __rem_pio2l(Quad x, Span y) /// public static Quad Cos(Quad x) { - Shape u = new Shape(x); + Quad x0 = x; + Shape u = new Shape(ref x0); uint n; Span y = stackalloc Quad[2]; Quad hi, lo; @@ -355,7 +430,7 @@ public static Quad Cos(Quad x) { return x - x; } - x = u.f; + x = x0; if (x < M_PI_4) { @@ -387,7 +462,7 @@ private static Quad __cos(in Quad x, in Quad y) * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. * - * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Developed at SunSoft, x Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. @@ -430,7 +505,42 @@ public static Quad Exp(Quad x) /// public static Quad Floor(Quad x) { - throw new NotImplementedException(); + if (Quad.IsNaN(x) || Quad.IsInfinity(x)) + { + return x; + } + + int unbiasedExponent = x.Exponent; + if (unbiasedExponent < 0) + { + if (Quad.IsNegative(x)) + { + return Quad.NegativeOne; + } + else + { + return Quad.Zero; + } + } + else + { + if (unbiasedExponent >= 112) + { + return x; + } + + UInt128 resultBits = Quad.QuadToUInt128Bits(x); + int bitsToErase = 112 - unbiasedExponent; + resultBits = (resultBits >> bitsToErase) << bitsToErase; + Quad result = Quad.UInt128BitsToQuad(resultBits); + + if (result != x && Quad.IsNegative(result)) + { + result--; + } + + return result; + } } /// /// @@ -497,7 +607,74 @@ public static Quad Log10(Quad x) /// public static Quad Log2(Quad x) { - throw new NotImplementedException(); + Quad y, z; + short e = 0; + + if (Quad.IsNaN(x)) + { + return x; + } + if (Quad.IsInfinity(x)) + { + return x; + } + if (x <= Quad.Zero) + { + if (x == Quad.Zero) + { + return Quad.NegativeInfinity; + } + return Quad.NaN; + } + + x = Quad.SeparateExponent(x, ref e); + + /* logarithm using log(x) = z + z**3 P(z)/Q(z), + * where z = 2(x-1)/x+1) + */ + + if (e > 2 || e < -2) + { + if (x < SQRTH) // 2(2x-1)/(2x+1) + { + e -= 1; + z = x - Quad.HalfOne; + y = Quad.HalfOne * z + Quad.HalfOne; + } + else // 2 (x-1)/(x+1) + { + z = x - Quad.HalfOne; + z -= Quad.HalfOne; + y = Quad.HalfOne * x + Quad.HalfOne; + } + x = z / y; + z = x * x; + y = x * (z * PolynomialEvaluator(z, ref MemoryMarshal.GetReference(MathQConstants.Log2.R), 3) / PolynomialEvaluator1(z, ref MemoryMarshal.GetReference(MathQConstants.Log2.S), 3)); + goto done; + } + + // logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) + if (x < SQRTH) + { + e -= 1; + x = Quad.Two * x - Quad.One; + } + else + { + x -= Quad.One; + } + + z = x * x; + y = x * (z * PolynomialEvaluator(x, ref MemoryMarshal.GetReference(MathQConstants.Log2.P), 6) / PolynomialEvaluator1(x, ref MemoryMarshal.GetReference(MathQConstants.Log2.Q), 7)); + y -= Quad.HalfOne * z; + + done: + z = y * LOG2EA; + z += x * LOG2EA; + z += y; + z += x; + z += e; + return z; } /// /// @@ -505,9 +682,26 @@ public static Quad Log2(Quad x) /// /// /// - public static Quad Max(Quad x, Quad y) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static Quad Max(Quad val1, Quad val2) { - throw new NotImplementedException(); + // This matches the IEEE 754:2019 `maximum` function + // + // It propagates NaN inputs back to the caller and + // otherwise returns the greater of the inputs. It + // treats +0 as greater than -0 as per the specification. + + if (val1 != val2) + { + if (!Quad.IsNaN(val1)) + { + return val2 < val1 ? val1 : val2; + } + + return val1; + } + + return Quad.IsNegative(val2) ? val1 : val2; } /// /// @@ -517,7 +711,26 @@ public static Quad Max(Quad x, Quad y) /// public static Quad MaxMagnitude(Quad x, Quad y) { - throw new NotImplementedException(); + // This matches the IEEE 754:2019 `maximumMagnitude` function + // + // It propagates NaN inputs back to the caller and + // otherwise returns the input with a greater magnitude. + // It treats +0 as greater than -0 as per the specification. + + Quad ax = Abs(x); + Quad ay = Abs(y); + + if ((ax > ay) || Quad.IsNaN(ax)) + { + return x; + } + + if (ax == ay) + { + return Quad.IsNegative(x) ? y : x; + } + + return y; } /// /// @@ -526,9 +739,26 @@ public static Quad MaxMagnitude(Quad x, Quad y) /// /// /// - public static Quad Min(Quad x, Quad y) + [MethodImpl(MethodImplOptions.AggressiveInlining)] + public static Quad Min(Quad val1, Quad val2) { - throw new NotImplementedException(); + // This matches the IEEE 754:2019 `minimum` function + // + // It propagates NaN inputs back to the caller and + // otherwise returns the lesser of the inputs. It + // treats +0 as greater than -0 as per the specification. + + if (val1 != val2) + { + if (!Quad.IsNaN(val1)) + { + return val1 < val2 ? val1 : val2; + } + + return val1; + } + + return Quad.IsNegative(val1) ? val1 : val2; } /// /// @@ -538,7 +768,26 @@ public static Quad Min(Quad x, Quad y) /// public static Quad MinMagnitude(Quad x, Quad y) { - throw new NotImplementedException(); + // This matches the IEEE 754:2019 `minimumMagnitude` function + // + // It propagates NaN inputs back to the caller and + // otherwise returns the input with a lesser magnitude. + // It treats +0 as greater than -0 as per the specification. + + Quad ax = Abs(x); + Quad ay = Abs(y); + + if ((ax < ay) || Quad.IsNaN(ax)) + { + return x; + } + + if (ax == ay) + { + return Quad.IsNegative(x) ? x : y; + } + + return y; } /// /// @@ -567,7 +816,7 @@ public static Quad ReciprocalEstimate(Quad x) // Expresses D as M × 2e where 1 ≤ M < 2 // we also get the absolute value while we are at it. - Quad normalizedValue = new Quad(true, Quad.Bias, bits.matissa); + Quad normalizedValue = new Quad(true, Quad.ExponentBias, bits.matissa); x0 = Quad.One; Quad two = new Quad(0x4000_0000_0000_0000, 0x0000_0000_0000_0000); @@ -576,10 +825,10 @@ public static Quad ReciprocalEstimate(Quad x) for (int i = 0; i < 15; i++) { // X1 = X(2 - DX) - //Quad x1 = x0 * (two - (normalizedValue * x0)); + //Quad x1 = f * (two - (normalizedValue * f)); Quad x1 = x0 * FusedMultiplyAdd(normalizedValue, x0, two); - // Since we need: two - (normalizedValue * x0) - // to make use of FusedMultiplyAdd, we can rewrite it to (-normalizedValue * x0) + two + // Since we need: two - (normalizedValue * f) + // to make use of FusedMultiplyAdd, we can rewrite it to (-normalizedValue * f) + two // which requires normalizedValue to be negative... if (Quad.Abs(x1 - x) < Quad.Epsilon) @@ -593,7 +842,7 @@ public static Quad ReciprocalEstimate(Quad x) bits = Quad.ExtractFromBits(Quad.QuadToUInt128Bits(x0)); - bits.exponent -= (ushort)(exp - Quad.Bias); + bits.exponent -= (ushort)(exp - Quad.ExponentBias); var output = new Quad(sign, bits.exponent, bits.matissa); return output; @@ -611,7 +860,86 @@ public static Quad ReciprocalEstimate(Quad x) /// public static Quad Round(Quad x) { - throw new NotImplementedException(); + // This is based on the 'Berkeley SoftFloat Release 3e' algorithm + // source: berkeley-softfloat-3/source/f128_roundToInt.c + + UInt128 uiZ, lastBitMask; + UInt128 bits = Quad.QuadToUInt128Bits(x); + ulong uiZ64 = x._upper, uiZ0 = x._lower, roundBitsMask; + ulong lastBitMask64, lastBitMask0; + ushort biasedExponent = Quad.ExtractBiasedExponentFromBits(bits); + + if (biasedExponent >= 0x402F) + { + if (biasedExponent >= 0x406F) + { + if (biasedExponent == 0x7FFF && (Quad.ExtractTrailingSignificandFromBits(bits) != UInt128.Zero)) + { + return Quad.NaN; + } + return x; + } + + lastBitMask0 = (ulong)(2 << (0x406E - biasedExponent)); + roundBitsMask = lastBitMask0 - 1; + uiZ = bits; + + if (biasedExponent == 0x402F) + { + if (uiZ0 >= 0x8000_0000_0000_0000) + { + uiZ64++; + if (uiZ0 == 0x8000_0000_0000_0000) + { + uiZ64 &= ~1UL; + } + } + } + else + { + uiZ = new UInt128(uiZ64, uiZ0) + new UInt128(0, lastBitMask0 >> 1); + if (((ulong)uiZ & roundBitsMask) == 0) + { + uiZ &= new UInt128(0xFFFF_FFFF_FFFF_FFFF, ~lastBitMask0); + //uiZ0 = ((ulong)uiZ); + //uiZ0 &= ~lastBitMask0; + //uiZ = new UInt128((ulong)(uiZ >> 64), uiZ0); + } + } + + //uiZ0 = ((ulong)uiZ); + //uiZ0 &= ~roundBitsMask; + + uiZ &= new UInt128(0xFFFF_FFFF_FFFF_FFFF, ~roundBitsMask); + + lastBitMask64 = (lastBitMask0 == 0) ? 0UL : 1UL; + } + else + { + if (biasedExponent < 0x3FFF) + { + if ((bits & new UInt128(0x7FFF_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF)) == UInt128.Zero) + { + return x; + } + uiZ = bits & new UInt128(BitHelper.PackToQuadUI64(true, 0, 0), 0); + + return Quad.UInt128BitsToQuad(uiZ); + } + + uiZ = bits & new UInt128(0xFFFF_FFFF_FFFF_FFFF, 0x0); + lastBitMask64 = (ulong)1 << (0x402F - biasedExponent); + roundBitsMask = lastBitMask64 - 1; + uiZ += new UInt128(lastBitMask64 >> 1, 0); + if ((((ulong)(uiZ >> 64) & roundBitsMask) | (ulong)bits) == 0) + { + uiZ &= new UInt128(~lastBitMask64, 0xFFFF_FFFF_FFFF_FFFF); + } + uiZ &= new UInt128(~roundBitsMask, 0xFFFF_FFFF_FFFF_FFFF); + lastBitMask0 = 0; + } + + return Quad.UInt128BitsToQuad(uiZ); } /// /// @@ -631,12 +959,7 @@ public static Quad Round(Quad x, int digits) /// public static Quad Round(Quad x, MidpointRounding mode) { - return mode switch - { - MidpointRounding.ToEven => Round(x), - MidpointRounding.AwayFromZero => Truncate(x + CopySign(BitDecrement(Quad.HalfOne), x)), - _ => Round(x, 0, mode) - }; + return Round(x, 0, mode); } /// /// @@ -714,7 +1037,8 @@ public static int Sign(Quad x) /// public static Quad Sin(Quad x) { - Shape u = new Shape(x); + Quad x0 = x; + Shape u = new Shape(ref x0); int n; Quad hi, lo; Span y = stackalloc Quad[2]; @@ -722,7 +1046,7 @@ public static Quad Sin(Quad x) u.i.se &= 0x7fff; if (u.i.se == 0x7fff) return x - x; - if (u.f < M_PI_4) + if (x0 < M_PI_4) { if (u.i.se < 0x3fff - Quad.MantissaDigits / 2) { @@ -789,7 +1113,147 @@ public static Quad Sinh(Quad x) /// public static Quad Sqrt(Quad x) { - throw new NotImplementedException(); + UInt128 bits = Quad.QuadToUInt128Bits(x); + bool signA = Quad.IsNegative(x); + int exp = Quad.ExtractBiasedExponentFromBits(bits); + UInt128 sig = Quad.ExtractTrailingSignificandFromBits(bits); + + // Is x NaN? + if (exp == 0x7FFF) + { + if (sig != UInt128.Zero) + { + return Quad.NaN; + } + if (!signA) + { + return x; + } + return Quad.NaN; + } + if (signA) + { + if (((UInt128)exp | sig) != UInt128.Zero) + { + return x; + } + return Quad.NaN; + } + + if (exp == 0) + { + if (sig == UInt128.Zero) + { + return x; + } + (exp, sig) = BitHelper.NormalizeSubnormalF128Sig(sig); + } + + /* + * `sig32Z' is guaranteed to be a lower bound on the square root of + * `sig32A', which makes `sig32Z' also a lower bound on the square root of + * `sigA'. + */ + + int expZ = ((exp - 0x3FFF) >> 1) + 0x3FFE; + exp &= 1; + sig |= new UInt128(0x0001000000000000, 0x0); + uint sig32 = (uint)(sig >> 81); + uint recipSqrt32 = BitHelper.SqrtReciprocalApproximate((uint)exp, sig32); + uint sig32Z = (uint)(((ulong) sig32 * recipSqrt32) >> 32); + UInt128 rem; + if (exp != 0) + { + sig32Z >>= 1; + rem = sig << 12; + } + else + { + rem = sig << 13; + } + Span qs = stackalloc uint[3] { 0, 0, sig32Z }; + rem -= new UInt128((ulong)sig32Z * sig32Z, 0x0); + + uint q = (uint)(((uint)(rem >> 66) * (ulong)recipSqrt32) >> 32); + ulong x64 = (ulong)sig32Z << 32; + ulong sig64Z = x64 + ((ulong)q << 3); + UInt128 y = rem << 29; + + UInt128 term; + do + { + term = BitHelper.Mul64ByShifted32To128(x64 + sig64Z, q); + rem = y - term; + if (((ulong)(rem >> 64) & 0x8000_0000_0000_0000) == 0) + { + break; + } + --q; + sig64Z -= 1 << 3; + } while (true); + qs[1] = q; + + q = (uint)(((ulong)(rem >> 66) * recipSqrt32) >> 32); + y = rem << 29; + sig64Z <<= 1; + + do + { + term = (UInt128)sig64Z << 32; + term += (ulong)q << 6; + term += q; + rem = y - term; + if (((ulong)(rem >> 64) & 0x8000_0000_0000_0000) == 0) + { + break; + } + --q; + } while (true); + qs[0] = q; + + q = (uint)((((ulong)(rem >> 66) * recipSqrt32) >> 32) + 2); + ulong sigZExtra = q << 59; + term = (UInt128)qs[1] << 53; + UInt128 sigZ = new UInt128((ulong)qs[2] << 18, ((ulong)qs[0] << 24) + (q >> 5)) + term; + + if ((q & 0xF) <= 2) + { + q &= ~3U; + sigZExtra = q << 59; + y = sigZ << 6; + y |= sigZExtra >> 58; + term = y - q; + y = BitHelper.Mul64ByShifted32To128((ulong)term, q); + term = BitHelper.Mul64ByShifted32To128((ulong)(term >> 64), q); + term += (y >> 64); + rem <<= 20; + term -= rem; + /* + * The concatenation of `term' and `y.v0' is now the negative remainder + * (3 words altogether). + */ + if (((ulong)(term >> 64) & 0x8000_0000_0000_0000) != 0) + { + sigZExtra |= 1; + } + else + { + if ((term | (ulong)y) != UInt128.Zero) + { + if (sigZExtra != 0) + { + --sigZExtra; + } + else + { + sigZ -= UInt128.One; + sigZExtra = ~0UL; + } + } + } + } + + return Quad.UInt128BitsToQuad(BitHelper.RoundPackToQuad(false, expZ, sigZ, sigZExtra)); } /// /// @@ -798,7 +1262,8 @@ public static Quad Sqrt(Quad x) /// public static Quad Tan(Quad x) { - Shape u = new Shape(x); + Quad x0 = x; + Shape u = new Shape(ref x0); Span y = stackalloc Quad[2]; int n; @@ -807,7 +1272,7 @@ public static Quad Tan(Quad x) { return x - x; } - if (u.f < M_PI_4) + if (x0 < M_PI_4) { if (u.i.se < 0x3FFF - Quad.MantissaDigits / 2) { @@ -817,8 +1282,6 @@ public static Quad Tan(Quad x) } n = __rem_pio2l(x, y); return __tan(y[0], y[1], n & 1); - - throw new NotImplementedException(); } private static Quad __tan(Quad x, Quad y, int odd) { @@ -869,7 +1332,7 @@ private static Quad __tan(Quad x, Quad y, int odd) z = w; z = z + temp - temp; v = r - (z - x); /* z+v = r+x */ - t = a = -1.0 / w; /* a = -1.0/w */ + t = a = -1.0 / w; /* x = -1.0/w */ t = t + temp - temp; s = 1.0 + t * z; return t + a * (s + t * v); @@ -903,7 +1366,33 @@ public static Quad Tanh(Quad x) /// public static Quad Truncate(Quad x) { - throw new NotImplementedException(); + return (Quad)(Int128)x; + } + + private unsafe static Quad PolynomialEvaluator(Quad x, ref Quad p, int n) + { + Quad y = p; + + do + { + p = ref Unsafe.Add(ref p, 1); + y = y * x + p; + } while (--n != 0); + + return y; + } + private unsafe static Quad PolynomialEvaluator1(Quad x, ref Quad p, int n) + { + --n; + Quad y = x + p; + + do + { + p = ref Unsafe.Add(ref p, 1); + y = y * x + p; + } while (--n != 0); + + return y; } } } diff --git a/src/MissingValues/MathQ.cs b/src/MissingValues/MathQ.cs new file mode 100644 index 0000000..2e60463 --- /dev/null +++ b/src/MissingValues/MathQ.cs @@ -0,0 +1,128 @@ +using MissingValues.Internals; +using System; +using System.Collections.Generic; +using System.Linq; +using System.Numerics; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues +{ + /// + /// Provides constants and static methods for trigonometric, logarithmic, and other common mathematical functions. + /// + internal static partial class MathQ + { + public static int CountDigits(T num, T numberBase) + where T : struct, IBinaryInteger + { + int count = 0; + do + { + num /= numberBase; + ++count; + } + while (num != T.Zero); + return count; + } + + public static T GetGoldenRatio() + where T : unmanaged, IFloatingPoint + { + T ratio; + + if (typeof(T) == typeof(Half)) + { + ratio = (T)(object)(Half)1.61803400516510009765625f; + } + else if (typeof(T) == typeof(float)) + { + ratio = (T)(object)1.61803400516510009765625f; + } + else if (typeof(T) == typeof(double)) + { + ratio = (T)(object)1.6180339887498949025257388711906969547271d; + } + else if (typeof(T) == typeof(decimal)) + { + ratio = (T)(object)1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939M; + } + else if (typeof(T) == typeof(Quad)) + { + ratio = (T)(object)Quad.UInt128BitsToQuad(new UInt128(0x3FFF_9E37_79B9_7F4A, 0x7C15_F39C_C060_5CEE)); + } + else + { + ratio = T.CreateChecked(1.61803400516510009765625); + } + + return ratio; + } + + public static T GreatestCommonDivisor(T x, T y) + where T : struct, IBinaryInteger + { + if (T.IsZero(x)) + { + return T.Abs(y); + } + + while (!T.IsZero(y)) + { + T remainder = x % y; + x = y; + y = remainder; + } + + return T.Abs(x); + } + + public static T Pow(T x, T y) + where T : struct, IBinaryInteger + { + T result = T.One; + T i = T.Zero; + + if (T.IsNegative(i)) + { + return i; + } + + for (; i < y; i++) + { + result *= x; + } + + return result; + } + + public static T Sum(params T[] values) + where T : IBinaryFloatingPointIeee754 + { + T sum = T.Zero; + + // Variable to store error + T c = T.Zero; + + foreach (T f in values) + { + T y = f - c; + T t = sum + y; + + // Algebraically, c is always 0 + // when t is replaced by its + // value from the above expression. + // But, when there is a loss, + // the higher-order y is cancelled + // out by subtracting y from c and + // all that remains is the + // lower-order error in c + + c = (t - sum) - y; + sum = t; + } + + return sum; + } + } +} diff --git a/src/MissingValues/MissingValues.csproj b/src/MissingValues/MissingValues.csproj index 4004c69..8f97e22 100644 --- a/src/MissingValues/MissingValues.csproj +++ b/src/MissingValues/MissingValues.csproj @@ -5,6 +5,8 @@ enable true enable + true + Properties/AssemblyInfo.cs crookseta https://github.com/crookseta/missing-values @@ -20,6 +22,13 @@ True README.md + + true + + $(DefineConstants);BIGENDIAN + + 1.1.0 + diff --git a/src/MissingValues/Properties/AssembyInfo.cs b/src/MissingValues/Properties/AssembyInfo.cs deleted file mode 100644 index f547610..0000000 --- a/src/MissingValues/Properties/AssembyInfo.cs +++ /dev/null @@ -1 +0,0 @@ -[assembly: CLSCompliant(true)] diff --git a/src/MissingValues/Quad.Implementations.cs b/src/MissingValues/Quad.Implementations.cs new file mode 100644 index 0000000..0b2e7e9 --- /dev/null +++ b/src/MissingValues/Quad.Implementations.cs @@ -0,0 +1,771 @@ +using MissingValues.Internals; +using System; +using System.Buffers.Binary; +using System.Collections.Generic; +using System.Diagnostics.CodeAnalysis; +using System.Globalization; +using System.Linq; +using System.Numerics; +using System.Runtime.CompilerServices; +using System.Runtime.InteropServices; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues +{ + public partial struct Quad : + IFloatingPoint, + IFormattableFloatingPoint, + IMinMaxValue + { + public static Quad Epsilon => Quad.UInt128BitsToQuad(EpsilonBits); + + public static Quad NaN => Quad.UInt128BitsToQuad(NegativeQNaNBits); + + public static Quad NegativeInfinity => Quad.UInt128BitsToQuad(NegativeInfinityBits); + + public static Quad NegativeZero => Quad.UInt128BitsToQuad(NegativeZeroBits); + + public static Quad PositiveInfinity => Quad.UInt128BitsToQuad(PositiveInfinityBits); + + public static Quad NegativeOne => Quad.UInt128BitsToQuad(NegativeOneBits); + + public static Quad E => Quad.UInt128BitsToQuad(EBits); + + public static Quad Pi => Quad.UInt128BitsToQuad(PiBits); + + public static Quad Tau => Quad.UInt128BitsToQuad(TauBits); + + public static Quad One => Quad.UInt128BitsToQuad(PositiveOneBits); + + static int INumberBase.Radix => 2; + + public static Quad Zero => Quad.UInt128BitsToQuad(PositiveZeroBits); + + static Quad IAdditiveIdentity.AdditiveIdentity => Quad.UInt128BitsToQuad(PositiveZeroBits); + + static Quad IMultiplicativeIdentity.MultiplicativeIdentity => Quad.UInt128BitsToQuad(PositiveOneBits); + + public static Quad MaxValue => Quad.UInt128BitsToQuad(MaxValueBits); + + public static Quad MinValue => Quad.UInt128BitsToQuad(MinValueBits); + + static ReadOnlySpan IFormattableFloatingPoint.PowersOfTen => MathQ.RoundPower10; + + public static Quad Abs(Quad value) => MathQ.Abs(value); + + public static Quad Ceiling(Quad x) => MathQ.Ceiling(x); + + public static Quad Clamp(Quad value, Quad min, Quad max) + { + if (min > max) + { + Thrower.MinMaxError(min, max); + } + + if (value < min) + { + return min; + } + else if (value > max) + { + return max; + } + + return value; + } + + public static Quad CopySign(Quad value, Quad sign) => MathQ.CopySign(value, sign); + + public static Quad CreateChecked(TOther value) + where TOther : INumberBase + { + Quad result; + + if (!TryConvertFrom(value, out result) && !TOther.TryConvertToChecked(value, out result)) + { + Thrower.NotSupported(); + } + + return result; + } + + public static Quad CreateSaturating(TOther value) + where TOther : INumberBase + { + Quad result; + + if (!TryConvertFrom(value, out result) && !TOther.TryConvertToSaturating(value, out result)) + { + Thrower.NotSupported(); + } + + return result; + } + + public static Quad CreateTruncating(TOther value) + where TOther : INumberBase + { + Quad result; + + if (!TryConvertFrom(value, out result) && !TOther.TryConvertToTruncating(value, out result)) + { + Thrower.NotSupported(); + } + + return result; + } + + public static Quad Floor(Quad x) => MathQ.Floor(x); + + static bool INumberBase.IsCanonical(Quad value) => true; + + static bool INumberBase.IsComplexNumber(Quad value) => false; + + public static bool IsEvenInteger(Quad value) => IsInteger(value) && (Abs(value % 2) == 0); + + public static bool IsFinite(Quad value) + { + Int128 bits = Quad.QuadToInt128Bits(value); + return (bits & new Int128(0x7FFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF)) < new Int128(0x7FFF_0000_0000_0000, 0x0000_0000_0000_0000); + } + + static bool INumberBase.IsImaginaryNumber(Quad value) => false; + + public static bool IsInfinity(Quad value) + { + Int128 bits = Quad.QuadToInt128Bits(value); + return (bits & new Int128(0x7FFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF)) == new Int128(0x7FFF_0000_0000_0000, 0x0000_0000_0000_0000); + } + + public static bool IsInteger(Quad value) => IsFinite(value) && (value == Truncate(value)); + + public static bool IsNaN(Quad value) => StripSign(value) > PositiveInfinityBits; + + public static bool IsNegative(Quad value) => Int128.IsNegative(Quad.QuadToInt128Bits(value)); + + public static bool IsNegativeInfinity(Quad value) => value == NegativeInfinity; + + public static bool IsNormal(Quad value) + { + Int128 bits = Quad.QuadToInt128Bits(value); + bits &= new Int128(0x7FFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF); + Int128 infBits = new Int128(0x7FFF_0000_0000_0000, 0x0000_0000_0000_0000); + return (bits < infBits) && (bits != Int128.Zero) && ((bits & infBits) != Int128.Zero); + } + + public static bool IsOddInteger(Quad value) => IsInteger(value) && (Abs(value % 2) == 1); + + public static bool IsPositive(Quad value) => Int128.IsPositive(Quad.QuadToInt128Bits(value)); + + public static bool IsPositiveInfinity(Quad value) => value == PositiveInfinity; + + public static bool IsPow2(Quad value) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + + ushort biasedExponent = ExtractBiasedExponentFromBits(bits); ; + UInt128 trailingSignificand = ExtractTrailingSignificandFromBits(bits); + + return (value > UInt128.Zero) + && (biasedExponent != MinBiasedExponent) && (biasedExponent != MaxBiasedExponent) + && (trailingSignificand == MinTrailingSignificand); + } + + public static bool IsRealNumber(Quad value) => !IsNaN(value); + + public static bool IsSubnormal(Quad value) + { + Int128 bits = Quad.QuadToInt128Bits(value); + bits &= new Int128(0x7FFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF); + Int128 infBits = new Int128(0x7FFF_0000_0000_0000, 0x0000_0000_0000_0000); + return (bits < infBits) && (bits != Int128.Zero) && ((bits & infBits) == Int128.Zero); + } + + static bool INumberBase.IsZero(Quad value) => value == Zero; + + public static Quad Max(Quad x, Quad y) => MathQ.Max(x, y); + + public static Quad MaxMagnitude(Quad x, Quad y) => MathQ.MaxMagnitude(x, y); + + public static Quad MaxMagnitudeNumber(Quad x, Quad y) + { + // This matches the IEEE 754:2019 `maximumMagnitudeNumber` function + // + // It does not propagate NaN inputs back to the caller and + // otherwise returns the input with a larger magnitude. + // It treats +0 as larger than -0 as per the specification. + + Quad ax = Abs(x); + Quad ay = Abs(y); + + if ((ax > ay) || IsNaN(ay)) + { + return x; + } + + if (ax == ay) + { + return IsNegative(x) ? y : x; + } + + return y; + } + + public static Quad MaxNumber(Quad x, Quad y) + { + // This matches the IEEE 754:2019 `maximumNumber` function + // + // It does not propagate NaN inputs back to the caller and + // otherwise returns the larger of the inputs. It + // treats +0 as larger than -0 as per the specification. + + if (x != y) + { + if (!IsNaN(y)) + { + return y < x ? x : y; + } + + return x; + } + + return IsNegative(y) ? x : y; + } + + public static Quad Min(Quad x, Quad y) => MathQ.Min(x, y); + + public static Quad MinMagnitude(Quad x, Quad y) => MathQ.MinMagnitude(x, y); + + public static Quad MinMagnitudeNumber(Quad x, Quad y) + { + // This matches the IEEE 754:2019 `minimumMagnitudeNumber` function + // + // It does not propagate NaN inputs back to the caller and + // otherwise returns the input with a larger magnitude. + // It treats +0 as larger than -0 as per the specification. + + Quad ax = Abs(x); + Quad ay = Abs(y); + + if ((ax < ay) || IsNaN(ay)) + { + return x; + } + + if (ax == ay) + { + return IsNegative(x) ? x : y; + } + + return y; + } + + public static Quad MinNumber(Quad x, Quad y) + { + // This matches the IEEE 754:2019 `minimumNumber` function + // + // It does not propagate NaN inputs back to the caller and + // otherwise returns the larger of the inputs. It + // treats +0 as larger than -0 as per the specification. + + if (x != y) + { + if (!IsNaN(y)) + { + return x < y ? x : y; + } + + return x; + } + + return IsNegative(x) ? x : y; + } + + public static Quad Parse(ReadOnlySpan s, NumberStyles style, IFormatProvider? provider) + { + if (!TryParse(s, style, provider, out Quad result)) + { + Thrower.ParsingError(s.ToString()); + } + return result; + } + + public static Quad Parse(string s, NumberStyles style, IFormatProvider? provider) + { + if (!TryParse(s, style, provider, out Quad result)) + { + Thrower.ParsingError(s); + } + return result; + } + + public static Quad Parse(ReadOnlySpan s, IFormatProvider? provider) + { + if (!TryParse(s, NumberStyles.Float, provider, out Quad result)) + { + Thrower.ParsingError(s.ToString()); + } + return result; + } + + public static Quad Parse(string s, IFormatProvider? provider) + { + if (!TryParse(s, NumberStyles.Float, provider, out Quad result)) + { + Thrower.ParsingError(s); + } + return result; + } + + public static Quad Round(Quad x) => MathQ.Round(x); + + public static Quad Round(Quad x, int digits) => MathQ.Round(x, digits); + + public static Quad Round(Quad x, MidpointRounding mode) => MathQ.Round(x, mode); + + public static Quad Round(Quad x, int digits, MidpointRounding mode) => MathQ.Round(x, digits, mode); + + public static int Sign(Quad value) => MathQ.Sign(value); + + /// + public static Quad Sqrt(Quad x) => MathQ.Sqrt(x); + + public static Quad Truncate(Quad x) => MathQ.Truncate(x); + + public static bool TryParse(ReadOnlySpan s, NumberStyles style, IFormatProvider? provider, [MaybeNullWhen(false)] out Quad result) + { + return NumberParser.TryParseQuad(s, style, provider, out result); + } + + public static bool TryParse([NotNullWhen(true)] string? s, NumberStyles style, IFormatProvider? provider, [MaybeNullWhen(false)] out Quad result) + { + return NumberParser.TryParseQuad(s, style, provider, out result); + } + + public static bool TryParse(ReadOnlySpan s, IFormatProvider? provider, [MaybeNullWhen(false)] out Quad result) + { + return NumberParser.TryParseQuad(s, NumberStyles.Float, provider, out result); + } + + public static bool TryParse([NotNullWhen(true)] string? s, IFormatProvider? provider, [MaybeNullWhen(false)] out Quad result) + { + return NumberParser.TryParseQuad(s, NumberStyles.Float, provider, out result); + } + + static bool INumberBase.TryConvertFromChecked(TOther value, out Quad result) => TryConvertFrom(value, out result); + + static bool INumberBase.TryConvertFromSaturating(TOther value, out Quad result) => TryConvertFrom(value, out result); + + static bool INumberBase.TryConvertFromTruncating(TOther value, out Quad result) => TryConvertFrom(value, out result); + + private static bool TryConvertFrom(TOther value, out Quad result) + { + bool converted = true; + + result = value switch + { + Half actual => (Quad)actual, + float actual => (Quad)actual, + double actual => (Quad)actual, + decimal actual => (Quad)actual, + byte actual => (Quad)actual, + ushort actual => (Quad)actual, + uint actual => (Quad)actual, + ulong actual => (Quad)actual, + UInt128 actual => (Quad)actual, + UInt256 actual => (Quad)actual, + UInt512 actual => (Quad)actual, + nuint actual => (Quad)actual, + sbyte actual => (Quad)actual, + short actual => (Quad)actual, + int actual => (Quad)actual, + long actual => (Quad)actual, + Int128 actual => (Quad)actual, + Int256 actual => (Quad)actual, + Int512 actual => (Quad)actual, + _ => BitHelper.DefaultConvert(out converted) + }; + + return converted; + } + + static bool INumberBase.TryConvertToChecked(Quad value, out TOther result) + { + bool converted = true; + result = default; + checked + { + result = result switch + { + Half => (TOther)(object)(Half)value, + float => (TOther)(object)(float)value, + double => (TOther)(object)(double)value, + decimal => (TOther)(object)(decimal)value, + byte => (TOther)(object)(byte)value, + ushort => (TOther)(object)(ushort)value, + uint => (TOther)(object)(uint)value, + ulong => (TOther)(object)(ulong)value, + UInt128 => (TOther)(object)(UInt128)value, + UInt256 => (TOther)(object)(UInt256)value, + UInt512 => (TOther)(object)(UInt512)value, + nuint => (TOther)(object)(nuint)value, + sbyte => (TOther)(object)(sbyte)value, + short => (TOther)(object)(short)value, + int => (TOther)(object)(int)value, + long => (TOther)(object)(long)value, + Int128 => (TOther)(object)(Int128)value, + Int256 => (TOther)(object)(Int256)value, + Int512 => (TOther)(object)(Int512)value, + nint => (TOther)(object)(nint)value, + _ => BitHelper.DefaultConvert(out converted) + }; + } + + return converted; + } + + static bool INumberBase.TryConvertToSaturating(Quad value, out TOther result) => TryConvertTo(value, out result); + + static bool INumberBase.TryConvertToTruncating(Quad value, out TOther result) => TryConvertTo(value, out result); + + private static bool TryConvertTo(Quad value, out TOther result) + { + bool converted = true; + result = default; + + result = result switch + { + Half => (TOther)(object)(Half)value, + float => (TOther)(object)(float)value, + double => (TOther)(object)(double)value, + decimal => (TOther)(object)(decimal)value, + byte => (TOther)(object)((value >= byte.MaxValue) ? byte.MaxValue : (value <= byte.MinValue) ? byte.MinValue : (byte)value), + ushort => (TOther)(object)((value >= ushort.MaxValue) ? ushort.MaxValue : (value <= ushort.MinValue) ? ushort.MinValue : (ushort)value), + uint => (TOther)(object)((value >= uint.MaxValue) ? uint.MaxValue : (value <= uint.MinValue) ? uint.MinValue : (uint)value), + ulong => (TOther)(object)((value >= ulong.MaxValue) ? ulong.MaxValue : (value <= ulong.MinValue) ? ulong.MinValue : (ulong)value), + UInt128 => (TOther)(object)((value >= UInt128.MaxValue) ? UInt128.MaxValue : (value <= UInt128.MinValue) ? UInt128.MinValue : (UInt128)value), + UInt256 => (TOther)(object)((value >= new Quad(0x40FF_0000_0000_0000, 0x0000_0000_0000_0000)) ? UInt256.MaxValue : (value <= Quad.Zero) ? UInt256.MinValue : (UInt256)value), + UInt512 => (TOther)(object)((value >= new Quad(0x41FF_0000_0000_0000, 0x0000_0000_0000_0000)) ? UInt512.MaxValue : (value <= Quad.Zero) ? UInt512.MinValue : (UInt512)value), + nuint => (TOther)(object)((value >= nuint.MaxValue) ? nuint.MaxValue : (value <= nuint.MinValue) ? nuint.MinValue : (nuint)value), + sbyte => (TOther)(object)((value >= sbyte.MaxValue) ? sbyte.MaxValue : (value <= sbyte.MinValue) ? sbyte.MinValue : (sbyte)value), + short => (TOther)(object)((value >= short.MaxValue) ? short.MaxValue : (value <= short.MinValue) ? short.MinValue : (short)value), + int => (TOther)(object)((value >= int.MaxValue) ? int.MaxValue : (value <= int.MinValue) ? int.MinValue : (int)value), + long => (TOther)(object)((value >= long.MaxValue) ? long.MaxValue : (value <= long.MinValue) ? long.MinValue : (long)value), + Int128 => (TOther)(object)((value >= Int128.MaxValue) ? Int128.MaxValue : (value <= Int128.MinValue) ? Int128.MinValue : (Int128)value), + Int256 => (TOther)(object)((value >= new Quad(0x40FE_0000_0000_0000, 0x0000_0000_0000_0000)) ? Int256.MaxValue : (value <= new Quad(0xC0FE_0000_0000_0000, 0x0000_0000_0000_0000)) ? Int256.MinValue : (Int256)value), + Int512 => (TOther)(object)((value >= new Quad(0x41FE_0000_0000_0000, 0x0000_0000_0000_0000)) ? Int512.MaxValue : (value <= new Quad(0xC1FE_0000_0000_0000, 0x0000_0000_0000_0000)) ? Int512.MinValue : (Int512)value), + nint => (TOther)(object)((value >= nint.MaxValue) ? nint.MaxValue : (value <= nint.MinValue) ? nint.MinValue : (nint)value), + _ => BitHelper.DefaultConvert(out converted) + }; + + return converted; + } + + public int CompareTo(object? obj) + { + if (obj is not Quad o) + { + if (obj is null) + { + return 1; + } + else + { + Thrower.MustBeType(); + return 0; + } + } + return CompareTo(o); + } + + public int CompareTo(Quad other) + { + if (this < other) + { + return -1; + } + + if (this > other) + { + return 1; + } + + if (this == other) + { + return 0; + } + + if (IsNaN(this)) + { + return IsNaN(other) ? 0 : -1; + } + + return 1; + } + + public bool Equals(Quad other) + { + return (_upper == other._upper && _lower == other._lower) + || AreZero(this, other) + || (IsNaN(this) && IsNaN(other)); + } + + public int GetExponentByteCount() => sizeof(short); + + public int GetExponentShortestBitLength() + { + short exponent = Exponent; + + if (exponent >= 0) + { + return (sizeof(short) * 8) - short.LeadingZeroCount(exponent); + } + else + { + return (sizeof(short) * 8) + 1 - short.LeadingZeroCount((short)(~exponent)); + } + } + + public int GetSignificandBitLength() => 113; + + public int GetSignificandByteCount() => 16; + + public string ToString(string? format, IFormatProvider? formatProvider) + { + return NumberFormatter.QuadToString(in this, format, formatProvider); + } + + public bool TryFormat(Span destination, out int charsWritten, ReadOnlySpan format, IFormatProvider? provider) + { + return NumberFormatter.TryFormatQuad(in this, destination, out charsWritten, format, provider); + } + + public bool TryWriteExponentBigEndian(Span destination, out int bytesWritten) + { + if (destination.Length >= sizeof(short)) + { + short exponent = Exponent; + + if (BitConverter.IsLittleEndian) + { + exponent = BinaryPrimitives.ReverseEndianness(exponent); + } + + Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), exponent); + + bytesWritten = sizeof(short); + return true; + } + else + { + bytesWritten = 0; + return false; + } + } + + public bool TryWriteExponentLittleEndian(Span destination, out int bytesWritten) + { + if (destination.Length >= sizeof(short)) + { + short exponent = Exponent; + + if (!BitConverter.IsLittleEndian) + { + exponent = BinaryPrimitives.ReverseEndianness(exponent); + } + + Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), exponent); + + bytesWritten = sizeof(short); + return true; + } + else + { + bytesWritten = 0; + return false; + } + } + + public bool TryWriteSignificandBigEndian(Span destination, out int bytesWritten) + { + if (destination.Length >= sizeof(ulong)) + { + UInt128 significand = Significand; + + if (BitConverter.IsLittleEndian) + { + significand = BitHelper.ReverseEndianness(significand); + } + + Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), significand); + + bytesWritten = sizeof(ulong); + return true; + } + else + { + bytesWritten = 0; + return false; + } + } + + public bool TryWriteSignificandLittleEndian(Span destination, out int bytesWritten) + { + if (destination.Length >= sizeof(ulong)) + { + UInt128 significand = Significand; + + if (!BitConverter.IsLittleEndian) + { + significand = BitHelper.ReverseEndianness(significand); + } + + Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), significand); + + bytesWritten = sizeof(ulong); + return true; + } + else + { + bytesWritten = 0; + return false; + } + } + + public static Quad operator +(Quad value) => value; + + public static Quad operator +(Quad left, Quad right) => MathQ.Add(left, right); + + public static Quad operator -(Quad value) + { + Quad signMask = new Quad(0x8000_0000_0000_0000, 0x0000_0000_0000_0000); + // Invert the sign bit + return value ^ signMask; + } + + public static Quad operator -(Quad left, Quad right) => MathQ.Sub(left, right); + + public static Quad operator ~(Quad value) => new Quad(~value._upper, ~value._lower); + + public static Quad operator ++(Quad value) => MathQ.Add(value, One); + + public static Quad operator --(Quad value) => MathQ.Sub(value, One); + + public static Quad operator *(Quad left, Quad right) => MathQ.Mul(left, right); + + public static Quad operator /(Quad left, Quad right) => MathQ.Div(left, right); + + public static Quad operator %(Quad left, Quad right) => left - Quad.Truncate(left / right) * right; + + public static Quad operator &(Quad left, Quad right) => new Quad(left._upper & right._upper, left._lower & right._lower); + + public static Quad operator |(Quad left, Quad right) => new Quad(left._upper | right._upper, left._lower | right._lower); + + public static Quad operator ^(Quad left, Quad right) => new Quad(left._upper ^ right._upper, left._lower ^ right._lower); + + public static bool operator ==(Quad left, Quad right) + { + if (IsNaN(left) || IsNaN(right)) + { + // IEEE defines that NaN is not equal to anything, including itself. + return false; + } + + // IEEE defines that positive and negative zero are equivalent. + return (left._upper == right._upper && left._lower == right._lower) || AreZero(left, right); + } + + public static bool operator !=(Quad left, Quad right) => !(left == right); + + public static bool operator <(Quad left, Quad right) + { + if (IsNaN(left) || IsNaN(right)) + { + // IEEE defines that NaN is unordered with respect to everything, including itself. + return false; + } + + bool leftIsNegative = IsNegative(left); + + if (leftIsNegative != IsNegative(right)) + { + // When the signs of right and left differ, we know that right is less than left if it is + // the negative value. The exception to this is if both values are zero, in which case IEEE + // says they should be equal, even if the signs differ. + return leftIsNegative && !AreZero(left, right); + } + + UInt128 leftBits = QuadToUInt128Bits(left); + UInt128 rightBits = QuadToUInt128Bits(right); + + return (leftBits != rightBits) && ((leftBits < rightBits) ^ leftIsNegative); + } + + public static bool operator >(Quad left, Quad right) + { + if (IsNaN(right) || IsNaN(left)) + { + // IEEE defines that NaN is unordered with respect to everything, including itself. + return false; + } + + bool rightIsNegative = IsNegative(right); + + if (rightIsNegative != IsNegative(left)) + { + return rightIsNegative && !AreZero(right, left); + } + + UInt128 leftBits = QuadToUInt128Bits(left); + UInt128 rightBits = QuadToUInt128Bits(right); + + return (rightBits != leftBits) && ((rightBits < leftBits) ^ rightIsNegative); + } + + public static bool operator <=(Quad left, Quad right) + { + if (IsNaN(left) || IsNaN(right)) + { + // IEEE defines that NaN is unordered with respect to everything, including itself. + return false; + } + + bool leftIsNegative = IsNegative(left); + + if (leftIsNegative != IsNegative(right)) + { + // When the signs of right and left differ, we know that right is less than left if it is + // the negative value. The exception to this is if both values are zero, in which case IEEE + // says they should be equal, even if the signs differ. + return leftIsNegative || AreZero(left, right); + } + + UInt128 leftBits = QuadToUInt128Bits(left); + UInt128 rightBits = QuadToUInt128Bits(right); + + return (leftBits == rightBits) || ((leftBits < rightBits) ^ leftIsNegative); + } + + public static bool operator >=(Quad left, Quad right) + { + if (IsNaN(right) || IsNaN(left)) + { + // IEEE defines that NaN is unordered with respect to everything, including itself. + return false; + } + + bool rightIsNegative = IsNegative(right); + + if (rightIsNegative != IsNegative(left)) + { + return rightIsNegative || AreZero(right, left); + } + + UInt128 leftBits = QuadToUInt128Bits(left); + UInt128 rightBits = QuadToUInt128Bits(right); + + return (rightBits == leftBits) || ((rightBits < leftBits) ^ rightIsNegative); + } + } +} diff --git a/src/MissingValues/Quad.cs b/src/MissingValues/Quad.cs new file mode 100644 index 0000000..ef8bf5c --- /dev/null +++ b/src/MissingValues/Quad.cs @@ -0,0 +1,1267 @@ +using MissingValues.Internals; +using System; +using System.Collections.Generic; +using System.Diagnostics.CodeAnalysis; +using System.Globalization; +using System.Linq; +using System.Numerics; +using System.Runtime.InteropServices; +using System.Text; +using System.Threading.Tasks; + +namespace MissingValues +{ + /// + /// Represents a quadruple-precision floating-point number. + /// + [StructLayout(LayoutKind.Sequential)] + public readonly partial struct Quad + { + internal const int SignShift = 127; + internal static UInt128 SignMask => new UInt128(0x8000_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 InvertedSignMask => new UInt128(0x7FFF_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + + internal const int MantissaDigits = 113; + internal const int ExponentBias = 16383; + internal const int BiasedExponentShift = 112; + internal const ulong ShiftedBiasedExponentMask = 32767; + + internal const int MinBiasedExponent = 0x0000; + internal const int MaxBiasedExponent = 0x7FFF; + + internal static UInt128 BiasedExponentMask => new UInt128(0x7FFF_0000_0000_0000, 0x0000_0000_0000_0000); + + internal static UInt128 TrailingSignificandMask => new UInt128(0x0000_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + internal static UInt128 SignificandSignMask => new UInt128(0x0001_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 InvertedSignificandMask => ~(SignificandSignMask | TrailingSignificandMask); + internal static UInt128 MinTrailingSignificand => new UInt128(0x0000_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 MaxTrailingSignificand => new UInt128(0x0000_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + + #region Bit representation of constants + internal static UInt128 EpsilonBits => new UInt128(0x0000_0000_0000_0000, 0x0000_0000_0000_0001); + internal static UInt128 PositiveZeroBits => new UInt128(0x0000_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 NegativeZeroBits => new UInt128(0x8000_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 PositiveOneBits => new UInt128(0x3FFF_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 NegativeOneBits => new UInt128(0xBFFF_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 PositiveQNaNBits => new UInt128(0x7FFF_8000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 NegativeQNaNBits => new UInt128(0xFFFF_8000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 PositiveInfinityBits => new UInt128(0x7FFF_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 NegativeInfinityBits => new UInt128(0xFFFF_0000_0000_0000, 0x0000_0000_0000_0000); + internal static UInt128 MaxValueBits => new UInt128(0x7FFE_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + internal static UInt128 MinValueBits => new UInt128(0xFFFE_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF); + internal static UInt128 PiBits => new UInt128(0x4000_921F_B544_42D1, 0x8469_898C_C517_01B8); + internal static UInt128 TauBits => new UInt128(0x4001_921F_B544_42D1, 0x8469_898C_C517_01B8); + internal static UInt128 EBits => new UInt128(0x4000_5BF0_A8B1_4576, 0x9535_5FB8_AC40_4E7A); + #endregion + #region Constants + internal static Quad HalfOne => new(0x3FFE_0000_0000_0000, 0x0000_0000_0000_0000); + internal static Quad Two => new(0x4000_0000_0000_0000, 0x0000_0000_0000_0000); + #endregion + + internal ushort BiasedExponent + { + get + { + UInt128 bits = QuadToUInt128Bits(this); + return ExtractBiasedExponentFromBits(bits); + } + } + internal short Exponent + { + get + { + return (short)(BiasedExponent - ExponentBias); + } + } + internal UInt128 Significand + { + get + { + return (TrailingSignificand | ((BiasedExponent != 0) ? (SignificandSignMask) : 0U)); + } + } + internal UInt128 TrailingSignificand + { + get + { + UInt128 bits = QuadToUInt128Bits(this); + return ExtractTrailingSignificandFromBits(bits); + } + } + +#if BIGENDIAN + internal readonly ulong _upper; + internal readonly ulong _lower; +#else + internal readonly ulong _lower; + internal readonly ulong _upper; +#endif + internal Quad(ulong upper, ulong lower) + { + _upper = upper; + _lower = lower; + } + [CLSCompliant(false)] + public Quad(bool sign, ushort exp, UInt128 sig) + { + UInt128 value = (((sign ? UInt128.One : UInt128.Zero) << SignShift) + (((UInt128)exp) << BiasedExponentShift) + (sig & TrailingSignificandMask)); + _lower = unchecked((ulong)value); + _upper = unchecked((ulong)(value >> 64)); + } + + public override bool Equals([NotNullWhen(true)] object? obj) + { + return (obj is Quad other) && Equals(other); + } + + public override int GetHashCode() + { + if (IsNaNOrZero(this)) + { + // All NaNs should have the same hash code, as should both Zeros. + return HashCode.Combine(QuadToUInt128Bits(this) & PositiveInfinityBits); + } + return HashCode.Combine(_lower, _upper); + } + + public override string? ToString() + { + return NumberFormatter.QuadToString(in this, "G33", NumberFormatInfo.CurrentInfo); + } + + public static Quad Parse(ReadOnlySpan s) + { + return Parse(s, CultureInfo.CurrentCulture); + } + public static bool TryParse(ReadOnlySpan s, out Quad result) + { + return TryParse(s, CultureInfo.CurrentCulture, out result); + } + + [CLSCompliant(false)] + public static unsafe Quad UInt128BitsToQuad(UInt128 bits) => *((Quad*)&bits); + public static unsafe Quad Int128BitsToQuad(Int128 bits) => *((Quad*)&bits); + + [CLSCompliant(false)] + public static unsafe UInt128 QuadToUInt128Bits(Quad value) => *((UInt128*)&value); + public static unsafe Int128 QuadToInt128Bits(Quad value) => *((Int128*)&value); + + internal static Quad SeparateExponent(Quad x, ref short exponent) + { + Quad f = x; + Shape u = new Shape(ref f); + int ee = u.i.se & 0x7FFF; + + if (ee == 0) + { + if (x == Zero) + { + x = SeparateExponent(x * new Quad(0x4077_0000_0000_0000, 0x0000_0000_0000_0000), ref exponent); + exponent -= 128; + } + else + { + exponent = 0; + } + return x; + } + else if (ee == 0x7FFF) + { + return x; + } + + exponent = (short)(ee - 0x3FFE); + u.i.se &= 0x8000; + u.i.se |= 0x3FFE; + return f; + } + internal static ushort ExtractBiasedExponentFromBits(UInt128 bits) + { + return (ushort)((bits >> BiasedExponentShift) & ShiftedBiasedExponentMask); + } + internal static UInt128 ExtractTrailingSignificandFromBits(UInt128 bits) + { + return (bits & TrailingSignificandMask); + } + internal static (bool sign, ushort exponent, UInt128 matissa) ExtractFromBits(UInt128 bits) + { + return ((bits & SignMask) != 0, (ushort)(bits >> BiasedExponentShift), (bits & TrailingSignificandMask)); + } + + internal static bool AreZero(Quad left, Quad right) + { + return ((QuadToUInt128Bits(left) | QuadToUInt128Bits(right)) & ~SignMask) == UInt128.Zero; + } + + internal static bool IsNaNOrZero(Quad value) + { + return ((QuadToUInt128Bits(value) - 1) & ~SignMask) >= PositiveInfinityBits; + } + + internal static UInt128 StripSign(Quad value) + { + return QuadToUInt128Bits(value) & ~SignMask; + } + + internal static Quad CreateQuadNaN(bool sign, UInt128 significand) + { + UInt128 signInt = (sign ? 1UL : 0UL) << 63; + UInt128 sigInt = significand >> 12; + + return UInt128BitsToQuad(signInt | (BiasedExponentMask | new UInt128(0x0000_8000_0000_0000, 0x0)) | sigInt); + } + + #region From Quad + // Unsigned + public static explicit operator byte(Quad value) + { + Quad twoPow8 = new Quad(0x4007_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return byte.MinValue; + } + if (value >= twoPow8) + { + return byte.MaxValue; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + byte result = (byte)((uint)(bits >> 105) | 0x80); + + result >>= (Quad.ExponentBias + 8 - 1 - (int)(bits >> 112)); + return result; + } + else + { + return byte.MinValue; + } + } + public static explicit operator checked byte(Quad value) + { + Quad twoPow8 = new Quad(0x4007_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || value >= twoPow8) + { + Thrower.IntegerOverflow(); + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + byte result = (byte)((uint)(bits >> 105) | 0x80); + + result >>= (Quad.ExponentBias + 8 - 1 - (int)(bits >> 112)); + return result; + } + else + { + return byte.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator ushort(Quad value) + { + Quad twoPow16 = new Quad(0x400F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return ushort.MinValue; + } + if (value >= twoPow16) + { + return ushort.MaxValue; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + ushort result = (ushort)((uint)(bits >> 97) | 0x8000); + + result >>= Quad.ExponentBias + 16 - 1 - (int)(bits >> 112); + return result; + } + else + { + return ushort.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator checked ushort(Quad value) + { + Quad twoPow16 = new Quad(0x400F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || value >= twoPow16) + { + Thrower.IntegerOverflow(); + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + ushort result = (ushort)((uint)(bits >> 97) | 0x8000); + + result >>= Quad.ExponentBias + 16 - 1 - (int)(bits >> 112); + return result; + } + else + { + return ushort.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator uint(Quad value) + { + Quad twoPow32 = new Quad(0x401F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return uint.MinValue; + } + if (value >= twoPow32) + { + return uint.MaxValue; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + uint result = (uint)(bits >> 81) | 0x8000_0000; + + result >>= Quad.ExponentBias + 32 - 1 - (int)(bits >> 112); + return result; + } + else + { + return uint.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator checked uint(Quad value) + { + Quad twoPow32 = new Quad(0x401F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || value >= twoPow32) + { + Thrower.IntegerOverflow(); + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + uint result = (uint)(bits >> 81) | 0x8000_0000; + + result >>= Quad.ExponentBias + 32 - 1 - (int)(bits >> 112); + return result; + } + else + { + return uint.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator ulong(Quad value) + { + Quad twoPow64 = new Quad(0x403F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return ulong.MinValue; + } + if (value >= twoPow64) + { + return ulong.MaxValue; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + ulong result = (ulong)(bits >> 49) | 0x8000_0000_0000_0000; + + result >>= Quad.ExponentBias + 64 - 1 - (int)(bits >> 112); + return result; + } + else + { + return ulong.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator checked ulong(Quad value) + { + Quad twoPow64 = new Quad(0x403F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || value >= twoPow64) + { + Thrower.IntegerOverflow(); + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + ulong result = (ulong)(bits >> 49) | 0x8000_0000_0000_0000; + + result >>= Quad.ExponentBias + 64 - 1 - (int)(bits >> 112); + return result; + } + else + { + return ulong.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator UInt128(Quad value) + { + Quad twoPow128 = new Quad(0x407F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return UInt128.MinValue; + } + if (value >= twoPow128) + { + return UInt128.MaxValue; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + UInt128 result = (bits << 16) >> 1 | new UInt128(0x8000_0000_0000_0000, 0x0); + + result >>= Quad.ExponentBias + 128 - 1 - (int)(bits >> 112); + return result; + } + else + { + return UInt128.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator checked UInt128(Quad value) + { + Quad twoPow128 = new Quad(0x407F_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || (value >= twoPow128)) + { + Thrower.IntegerOverflow(); + } + + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + UInt128 result = (bits << 16) >> 1 | new UInt128(0x8000_0000_0000_0000, 0x0); + + result >>= Quad.ExponentBias + 128 - 1 - (int)(bits >> 112); + return result; + } + else + { + return UInt128.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator UInt256(Quad value) + { + Quad twoPow256 = new Quad(0x40FF_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return UInt256.MinValue; + } + else if ((value >= twoPow256)) + { + return UInt256.MaxValue; + } + + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + UInt256 result = new UInt256((bits << 16) >> 1 | new UInt128(0x8000_0000_0000_0000, 0x0), UInt128.Zero); + + result >>= Quad.ExponentBias + 256 - 1 - (int)(bits >> 112); + return result; + } + else + { + return UInt256.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator checked UInt256(Quad value) + { + Quad twoPow256 = new Quad(0x40FF_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || (value >= twoPow256)) + { + Thrower.IntegerOverflow(); + } + + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + UInt256 result = new UInt256((bits << 16) >> 1 | new UInt128(0x8000_0000_0000_0000, 0x0), UInt128.Zero); + + result >>= Quad.ExponentBias + 256 - 1 - (int)(bits >> 112); + return result; + } + else + { + return UInt256.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator UInt512(Quad value) + { + Quad twoPow512 = new Quad(0x41FF_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative) + { + return UInt512.MinValue; + } + else if ((value >= twoPow512)) + { + return UInt512.MaxValue; + } + + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + UInt512 result = new UInt512((bits << 16) >> 1 | new UInt128(0x8000_0000_0000_0000, 0x0), UInt128.Zero, UInt128.Zero, UInt128.Zero); + + result >>= Quad.ExponentBias + 512 - 1 - (int)(bits >> 112); + return result; + } + else + { + return UInt512.MinValue; + } + } + [CLSCompliant(false)] + public static explicit operator checked UInt512(Quad value) + { + Quad twoPow512 = new Quad(0x41FF_0000_0000_0000, 0x0000_0000_0000_0000); + bool isNegative = Quad.IsNegative(value); + + if (Quad.IsNaN(value) || isNegative || (value >= twoPow512)) + { + Thrower.IntegerOverflow(); + } + + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + UInt512 result = new UInt512((bits << 16) >> 1 | new UInt128(0x8000_0000_0000_0000, 0x0), UInt128.Zero, UInt128.Zero, UInt128.Zero); + + result >>= Quad.ExponentBias + 512 - 1 - (int)(bits >> 112); + return result; + } + else + { + return UInt512.MinValue; + } + } + // Signed + [CLSCompliant(false)] + public static explicit operator sbyte(Quad value) + { + return (sbyte)(long)value; + } + [CLSCompliant(false)] + public static explicit operator checked sbyte(Quad value) + { + return checked((sbyte)(long)value); + } + public static explicit operator short(Quad value) + { + return (short)(long)value; + } + public static explicit operator checked short(Quad value) + { + return checked((short)(long)value); + } + public static explicit operator int(Quad value) + { + return (int)(long)value; + } + public static explicit operator checked int(Quad value) + { + return checked((int)(long)value); + } + public static explicit operator long(Quad value) + { + Quad twoPow63 = new Quad(0x403E_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow63) + { + return long.MinValue; + } + else if (Quad.IsNaN(value)) + { + return 0; + } + else if (value >= +twoPow63) + { + return long.MaxValue; + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + long result = (long)((ulong)(bits >> 49) | 0x8000_0000_0000_0000); + + result >>>= Quad.ExponentBias + 64 - 1 - (int)(bits >> 112); + + if (isNegative) + { + result = -result; + } + return result; + } + else + { + return 0L; + } + } + public static explicit operator checked long(Quad value) + { + Quad twoPow63 = new Quad(0x403E_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow63 || Quad.IsNaN(value) || value >= +twoPow63) + { + Thrower.IntegerOverflow(); + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + long result = (long)((ulong)(bits >> 49) | 0x8000_0000_0000_0000); + + result >>>= Quad.ExponentBias + 64 - 1 - (int)(bits >> 112); + + if (isNegative) + { + result = -result; + } + return result; + } + else + { + return 0L; + } + } + public static explicit operator Int128(Quad value) + { + Quad twoPow127 = new Quad(0x407E_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow127) + { + return Int128.MinValue; + } + else if (Quad.IsNaN(value)) + { + return Int128.Zero; + } + else if (value >= +twoPow127) + { + return Int128.MaxValue; + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + Int128 result = (Int128)(((bits << 16) >> 1) | Quad.SignMask); + + result >>>= Quad.ExponentBias + 128 - 1 - (int)(bits >> 112); + + if (isNegative) + { + result = -result; + } + return result; + } + else + { + return Int128.Zero; + } + } + public static explicit operator checked Int128(Quad value) + { + Quad twoPow127 = new Quad(0x407E_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow127 || Quad.IsNaN(value) || value >= +twoPow127) + { + Thrower.IntegerOverflow(); + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + if (value >= Quad.One) + { + UInt128 bits = Quad.QuadToUInt128Bits(value); + Int128 result = (Int128)(((bits << 16) >> 1) | Quad.SignMask); + + result >>>= Quad.ExponentBias + 128 - 1 - (int)(bits >> 112); + + if (isNegative) + { + result = -result; + } + return result; + } + else + { + return Int128.Zero; + } + } + public static explicit operator Int256(Quad value) + { + Quad twoPow255 = new Quad(0x40FE_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow255) + { + return Int256.MinValue; + } + else if (Quad.IsNaN(value)) + { + return Int256.Zero; + } + else if (value >= +twoPow255) + { + return Int256.MaxValue; + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + + if (value >= Quad.One) + { + // In order to convert from Quad to int256 we first need to extract the signficand, + // including the implicit leading bit, as a full 256-bit significand. We can then adjust + // this down to the represented integer by right shifting by the unbiased exponent, taking + // into account the significand is now represented as 256-bits. + + UInt128 bits = Quad.QuadToUInt128Bits(value); + Int256 result = new Int256((bits << 16) >> 1 | Quad.SignMask, UInt128.Zero); + + result >>>= (Quad.ExponentBias + 256 - 1 - (int)(bits >> 112)); + + if (isNegative) + { + result = -result; + } + + return result; + } + else + { + return Int256.Zero; + } + } + public static explicit operator checked Int256(Quad value) + { + Quad twoPow255 = new Quad(0x40FE_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow255 || Quad.IsNaN(value) || value >= +twoPow255) + { + Thrower.IntegerOverflow(); + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + + if (value >= Quad.One) + { + // In order to convert from Quad to int256 we first need to extract the signficand, + // including the implicit leading bit, as a full 256-bit significand. We can then adjust + // this down to the represented integer by right shifting by the unbiased exponent, taking + // into account the significand is now represented as 256-bits. + + UInt128 bits = Quad.QuadToUInt128Bits(value); + Int256 result = new Int256((bits << 16) >> 1 | Quad.SignMask, UInt128.Zero); + + result >>>= (Quad.ExponentBias + 256 - 1 - (int)(bits >> 112)); + + if (isNegative) + { + result = -result; + } + + return result; + } + else + { + return Int256.Zero; + } + } + public static explicit operator Int512(Quad value) + { + Quad twoPow511 = new Quad(0x41FE_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow511) + { + return Int512.MinValue; + } + else if (Quad.IsNaN(value)) + { + return Int512.Zero; + } + else if (value >= +twoPow511) + { + return Int512.MaxValue; + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + + if (value >= Quad.One) + { + // In order to convert from Quad to int512 we first need to extract the signficand, + // including the implicit leading bit, as a full 512-bit significand. We can then adjust + // this down to the represented integer by right shifting by the unbiased exponent, taking + // into account the significand is now represented as 512-bits. + + UInt128 bits = Quad.QuadToUInt128Bits(value); + Int512 result = new Int512((bits << 16) >> 1 | Quad.SignMask, UInt128.Zero, UInt128.Zero, UInt128.Zero); + + result >>>= (Quad.ExponentBias + 512 - 1 - (int)(bits >> 112)); + + if (isNegative) + { + result = -result; + } + + return result; + } + else + { + return Int512.Zero; + } + } + public static explicit operator checked Int512(Quad value) + { + Quad twoPow511 = new Quad(0x41FE_0000_0000_0000, 0x0000_0000_0000_0000); + + if (value <= -twoPow511 || Quad.IsNaN(value) || value >= +twoPow511) + { + Thrower.IntegerOverflow(); + } + + bool isNegative = Quad.IsNegative(value); + + if (isNegative) + { + value = -value; + } + + if (value >= Quad.One) + { + // In order to convert from Quad to int512 we first need to extract the signficand, + // including the implicit leading bit, as a full 512-bit significand. We can then adjust + // this down to the represented integer by right shifting by the unbiased exponent, taking + // into account the significand is now represented as 512-bits. + + UInt128 bits = Quad.QuadToUInt128Bits(value); + Int512 result = new Int512((bits << 16) >> 1 | Quad.SignMask, UInt128.Zero, UInt128.Zero, UInt128.Zero); + + result >>>= (Quad.ExponentBias + 512 - 1 - (int)(bits >> 112)); + + if (isNegative) + { + result = -result; + } + + return result; + } + else + { + return Int512.Zero; + } + } + // Floating + public static explicit operator decimal(Quad value) + { + return (decimal)(double)value; + } + public static explicit operator double(Quad value) + { + UInt128 quadInt = QuadToUInt128Bits(value); + bool sign = (quadInt & Quad.SignMask) >> Quad.SignShift != 0; + int exp = (int)((quadInt & Quad.BiasedExponentMask) >> Quad.BiasedExponentShift); + UInt128 sig = quadInt & Quad.TrailingSignificandMask; + + if (exp == MaxBiasedExponent) + { + if (sig != 0) // NaN + { + return CreateDoubleNaN(sign, (ulong)(sig >> 48)); // Shift the significand bits to the left end + } + return sign ? double.NegativeInfinity : double.PositiveInfinity; + } + + sig <<= 14; + ulong sigQuad = (ulong)(sig >> 64) | ((ulong)sig != 0 ? 1UL : 0UL); + + if (((uint)exp | sigQuad) == 0) + { + return CreateDouble(sign, 0, 0); + } + + exp -= 0x3C01; + + exp = exp < -0x1000 ? -0x1000 : exp; + + return BitConverter.UInt64BitsToDouble(BitHelper.RoundPackToDouble(sign, (short)(exp), (sigQuad | 0x4000_0000_0000_0000))); + } + public static explicit operator float(Quad value) + { + UInt128 quadInt = QuadToUInt128Bits(value); + bool sign = (quadInt & Quad.SignMask) >> Quad.SignShift != 0; + int exp = (int)((quadInt & Quad.BiasedExponentMask) >> Quad.BiasedExponentShift); + UInt128 sig = quadInt & Quad.TrailingSignificandMask; + + if (exp == MaxBiasedExponent) + { + if (sig != 0) // NaN + { + return CreateSingleNaN(sign, (ulong)(sig >> 48)); // Shift the significand bits to the left end + } + return sign ? float.NegativeInfinity : float.PositiveInfinity; + } + + uint sigQuad = (uint)BitHelper.ShiftRightJam((ulong)((sig >> 64) | ((ulong)sig != 0 ? 1UL : 0UL)), 18); + + if (((uint)exp | sigQuad) == 0) + { + return CreateSingle(sign, 0, 0); + } + + exp -= 0x3F81; + + exp = exp < -0x1000 ? -0x1000 : exp; + + return BitConverter.UInt32BitsToSingle(BitHelper.RoundPackToSingle(sign, (short)(exp), (uint)(sigQuad | 0x4000_0000))); + } + public static explicit operator Half(Quad value) + { + UInt128 quadInt = QuadToUInt128Bits(value); + bool sign = (quadInt & Quad.SignMask) >> Quad.SignShift != 0; + int exp = (int)((quadInt & Quad.BiasedExponentMask) >> Quad.BiasedExponentShift); + UInt128 sig = quadInt & Quad.TrailingSignificandMask; + + if (exp == MaxBiasedExponent) + { + if (sig != 0) // NaN + { + return CreateHalfNaN(sign, (ulong)(sig >> 48)); // Shift the significand bits to the left end + } + return sign ? Half.NegativeInfinity : Half.PositiveInfinity; + } + + ushort sigHalf = (ushort)BitHelper.ShiftRightJam((ulong)((sig >> 64) | ((ulong)sig != 0 ? 1UL : 0UL)), 34); + + if (((uint)exp | sigHalf) == 0) + { + return CreateHalf(sign, 0, 0); + } + + exp -= 0x3FF1; + + exp = exp < -0x40 ? -0x40 : exp; + + return BitConverter.UInt16BitsToHalf(BitHelper.RoundPackToHalf(sign, (short)(exp), (ushort)(sigHalf | 0x4000))); + } + #endregion + #region To Quad + // Unsigned + public static implicit operator Quad(byte value) + { + return (Quad)(uint)value; + } + [CLSCompliant(false)] + public static implicit operator Quad(ushort value) + { + return (Quad)(uint)value; + } + [CLSCompliant(false)] + public static implicit operator Quad(uint value) + { + int shiftDist; + ulong z = 0; + + if (value != 0) + { + shiftDist = BitOperations.LeadingZeroCount(value) + 17; + z = BitHelper.PackToQuadUI64(false, 0x402E - shiftDist, (ulong)value << shiftDist); + } + + return new Quad(z, 0); + } + [CLSCompliant(false)] + public static implicit operator Quad(ulong value) + { + UInt128 sig; + int shiftDist; + + if ((value) == 0) + { + return Quad.Zero; + } + else + { + shiftDist = BitOperations.LeadingZeroCount(value) + 49; + if (shiftDist >= 64) + { + sig = new UInt128(value << (shiftDist - 64), 0); + } + else + { + sig = (UInt128)value << shiftDist; + } + } + + return new Quad(false, (ushort)(0x406F - shiftDist), sig); + } + [CLSCompliant(false)] + public static implicit operator Quad(UInt128 value) + { + if (value == UInt128.Zero) + { + return Quad.Zero; + } + int shiftDist = (int)UInt128.LeadingZeroCount(value); + UInt128 a = (value << shiftDist >> 15); // Significant bits, with bit 113 still intact + UInt128 b = (value << shiftDist << 113); // Insignificant bits, only relevant for rounding. + UInt128 m = a + ((b - (b >> 127 & (a == UInt128.Zero ? UInt128.One : UInt128.Zero))) >> 127); // Add one when we need to round up. Break ties to even. + UInt128 e = (UInt128)(0x407D - shiftDist); // Exponent plus 16383, minus one, except for zero. + return Quad.UInt128BitsToQuad((e << 112) + m); + } + // Signed + [CLSCompliant(false)] + public static implicit operator Quad(sbyte value) + { + if (sbyte.IsNegative(value)) + { + value = (sbyte)-value; + return -(Quad)(byte)value; + } + return (Quad)(byte)value; + } + public static implicit operator Quad(short value) + { + if (short.IsNegative(value)) + { + value = (short)-value; + return -(Quad)(ushort)value; + } + return (Quad)(ushort)value; + } + public static implicit operator Quad(int value) + { + if (int.IsNegative(value)) + { + value = -value; + return -(Quad)(uint)value; + } + return (Quad)(uint)value; + } + public static implicit operator Quad(long value) + { + if (long.IsNegative(value)) + { + value = -value; + return -(Quad)(ulong)value; + } + return (Quad)(ulong)value; + } + public static implicit operator Quad(Int128 value) + { + if (Int128.IsNegative(value)) + { + value = -value; + return -(Quad)(UInt128)value; + } + return (Quad)(UInt128)value; + } + // Floating + public static explicit operator Quad(decimal value) + { + return (Quad)(double)value; + } + public static implicit operator Quad(double value) + { + const int MaxBiasedExponentDouble = 0x07FF; + const int DoubleExponentBias = 1023; + + ulong bits = BitConverter.DoubleToUInt64Bits(value); + bool sign = double.IsNegative(value); + int exp = (ushort)((bits >> 52) & 0x07FF); + ulong sig = bits & 0x000F_FFFF_FFFF_FFFF; + + if (exp == MaxBiasedExponentDouble) + { + if (sig != 0) + { + return CreateQuadNaN(sign, (UInt128)sig << 76); + } + return sign ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + + if (exp == 0) + { + if (sig == 0) + { + return UInt128BitsToQuad(sign ? SignMask : 0); // Positive / Negative zero + } + (exp, sig) = BitHelper.NormalizeSubnormalF64Sig(sig); + exp -= 1; + } + + return new Quad(sign, (ushort)(exp + (ExponentBias - DoubleExponentBias)), (UInt128)sig << 60); + } + public static implicit operator Quad(float value) + { + const int MaxBiasedExponentSingle = 0xFFFF; + const int SingleExponentBias = 127; + + uint bits = BitConverter.SingleToUInt32Bits(value); + bool sign = float.IsNegative(value); + int exp = (ushort)((bits >> 23) & 0xFF); + uint sig = bits & 0x007F_FFFF; + + if (exp == MaxBiasedExponentSingle) + { + if (sig != 0) + { + return CreateQuadNaN(sign, (UInt128)sig << 105); + } + return sign ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + + if (exp == 0) + { + if (sig == 0) + { + return UInt128BitsToQuad(sign ? SignMask : 0); // Positive / Negative zero + } + (exp, sig) = BitHelper.NormalizeSubnormalF32Sig(sig); + exp -= 1; + } + + return new Quad(sign, (ushort)(exp + (ExponentBias - SingleExponentBias)), (UInt128)sig << 89); + } + public static implicit operator Quad(Half value) + { + const int MaxBiasedExponentHalf = 0x1F; + const int HalfExponentBias = 15; + + ushort bits = BitConverter.HalfToUInt16Bits(value); + bool sign = Half.IsNegative(value); + int exp = (ushort)((bits >> 10) & 0x1F); + uint sig = (uint)(bits & 0x03FF); + + if (exp == MaxBiasedExponentHalf) + { + if (sig != 0) + { + return CreateQuadNaN(sign, (UInt128)sig << 118); + } + return sign ? Quad.NegativeInfinity : Quad.PositiveInfinity; + } + + if (exp == 0) + { + if (sig == 0) + { + return UInt128BitsToQuad(sign ? SignMask : 0); // Positive / Negative zero + } + (exp, sig) = BitHelper.NormalizeSubnormalF32Sig(sig); + exp -= 1; + } + + return new Quad(sign, (ushort)(exp + (ExponentBias - HalfExponentBias)), (UInt128)sig << 102); + } + #endregion + + private static double CreateDoubleNaN(bool sign, ulong significand) + { + const ulong NaNBits = 0x7FF0_0000_0000_0000 | 0x80000_00000000; // Most significant significand bit + + ulong signInt = (sign ? 1UL : 0UL) << 63; + ulong sigInt = significand >> 12; + + return BitConverter.UInt64BitsToDouble(signInt | NaNBits | sigInt); + } + private static double CreateDouble(bool sign, ushort exp, ulong sig) + { + return BitConverter.UInt64BitsToDouble(((sign ? 1UL : 0UL) << 63) + ((ulong)exp << 52) + sig); + } + + private static float CreateSingleNaN(bool sign, ulong significand) + { + const uint NaNBits = 0x7F80_0000 | 0x400000; // Most significant significand bit + + uint signInt = (sign ? 1U : 0U) << 31; + uint sigInt = (uint)(significand >> 41); + + return BitConverter.UInt32BitsToSingle(signInt | NaNBits | sigInt); + } + private static float CreateSingle(bool sign, byte exp, uint sig) + { + return BitConverter.UInt32BitsToSingle(((sign ? 1U : 0U) << 31) + ((uint)exp << 23) + sig); + } + + private static Half CreateHalfNaN(bool sign, ulong significand) + { + const uint NaNBits = 0x7C00 | 0x200; // Most significant significand bit + + uint signInt = (sign ? 1U : 0U) << 15; + uint sigInt = (uint)(significand >> 54); + + return BitConverter.UInt16BitsToHalf((ushort)(signInt | NaNBits | sigInt)); + } + private static Half CreateHalf(bool sign, ushort exp, ushort sig) + { + return BitConverter.UInt16BitsToHalf(((ushort)(((sign ? 1 : 0) << 15) + (exp << 10) + sig))); + } + } +} diff --git a/src/MissingValues/UInt256.cs b/src/MissingValues/UInt256.cs index c25d1a0..45b98dc 100644 --- a/src/MissingValues/UInt256.cs +++ b/src/MissingValues/UInt256.cs @@ -266,6 +266,46 @@ public static explicit operator decimal(UInt256 value) return (decimal)value._lower; } + public static explicit operator Quad(UInt256 value) + { + if (value._upper == 0) + { + return (Quad)value._lower; + } + else if ((value._upper >> 32) == UInt128.Zero) // value < (2^224) + { + // For values greater than MaxValue but less than 2^224 this takes advantage + // that we can represent both "halves" of the uint256 within the 112-bit mantissa of + // a pair of quads. + Quad twoPow112 = new Quad(0x406F_0000_0000_0000, 0x0000_0000_0000_0000); + Quad twoPow224 = new Quad(0x40DF_0000_0000_0000, 0x0000_0000_0000_0000); + + UInt128 twoPow112bits = Quad.QuadToUInt128Bits(twoPow112); + UInt128 twoPow224bits = Quad.QuadToUInt128Bits(twoPow224); + + Quad lower = Quad.UInt128BitsToQuad(twoPow112bits | ((value._lower << 16) >> 16)) - twoPow112; + Quad upper = Quad.UInt128BitsToQuad(twoPow224bits | (UInt128)(value >> 112)) - twoPow224; + + return lower + upper; + } + else + { + // For values greater than 2^224 we basically do the same as before but we need to account + // for the precision loss that quad will have. As such, the lower value effectively drops the + // lowest 32 bits and then or's them back to ensure rounding stays correct. + + Quad twoPow144 = new Quad(0x408F_0000_0000_0000, 0x0000_0000_0000_0000); + Quad twoPow256 = new Quad(0x40FF_0000_0000_0000, 0x0000_0000_0000_0000); + + UInt128 twoPow144bits = Quad.QuadToUInt128Bits(twoPow144); + UInt128 twoPow256bits = Quad.QuadToUInt128Bits(twoPow256); + + Quad lower = Quad.UInt128BitsToQuad(twoPow144bits | ((UInt128)(value >> 16) >> 16) | (value._lower & 0xFFFF_FFFF)) - twoPow144; + Quad upper = Quad.UInt128BitsToQuad(twoPow256bits | (UInt128)(value >> 144)) - twoPow256; + + return lower + upper; + } + } public static explicit operator double(UInt256 value) { const double TwoPow204 = 25711008708143844408671393477458601640355247900524685364822016.0d; diff --git a/src/MissingValues/UInt512.cs b/src/MissingValues/UInt512.cs index a2acf23..96ecdb2 100644 --- a/src/MissingValues/UInt512.cs +++ b/src/MissingValues/UInt512.cs @@ -271,6 +271,29 @@ public static explicit operator decimal(UInt512 value) return (decimal)value._lower; } + public static explicit operator Quad(UInt512 value) + { + if (value._upper == UInt256.Zero) + { + return (Quad)value._lower; + } + else + { + // For values greater than 2^224 we basically do the same as before but we need to account + // for the precision loss that quad will have. As such, the lower value effectively drops the + // lowest 288 bits. + Quad twoPow400 = new Quad(0x418F_0000_0000_0000, 0x0000_0000_0000_0000); + Quad twoPow512 = new Quad(0x41FF_0000_0000_0000, 0x0000_0000_0000_0000); + + UInt128 twoPow400bits = Quad.QuadToUInt128Bits(twoPow400); + UInt128 twoPow512bits = Quad.QuadToUInt128Bits(twoPow512); + + Quad lower = Quad.UInt128BitsToQuad(twoPow400bits | (UInt128)((UInt256)(value >> 144) >> 144) | (value._upper.Lower & 0xFFFF_FFFF)) - twoPow400; + Quad upper = Quad.UInt128BitsToQuad(twoPow512bits | (UInt128)(value >> 400)) - twoPow512; + + return lower + upper; + } + } public static explicit operator double(UInt512 value) { const double TwoPow460 = 2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288499266264815757728270805630976.0d;