From 6b656b90e306db152fa6fd28b32b9a085b0799c2 Mon Sep 17 00:00:00 2001
From: Thorsten Sommer <thorsten.sommer@dlr.de>
Date: Fri, 7 Jul 2023 10:06:07 +0200
Subject: [PATCH] Attempt to implement factorial calculation for generic math

---
 FastRng/HugeInteger.cs      | 555 ++++++++++++++++++++++++++++++++++++
 FastRng/IntegerMathTools.cs |  29 ++
 2 files changed, 584 insertions(+)
 create mode 100644 FastRng/HugeInteger.cs
 create mode 100644 FastRng/IntegerMathTools.cs

diff --git a/FastRng/HugeInteger.cs b/FastRng/HugeInteger.cs
new file mode 100644
index 0000000..561a20a
--- /dev/null
+++ b/FastRng/HugeInteger.cs
@@ -0,0 +1,555 @@
+using System;
+using System.Globalization;
+using System.Linq;
+using System.Numerics;
+
+namespace FastRng;
+
+public struct HugeInteger<TOtherNum> :
+    IBinaryInteger<HugeInteger<TOtherNum>>,
+    IComparisonOperators<HugeInteger<TOtherNum>, TOtherNum, HugeInteger<TOtherNum>>,
+    IMultiplyOperators<HugeInteger<TOtherNum>, TOtherNum, HugeInteger<TOtherNum>>
+    where TOtherNum : IBinaryInteger<TOtherNum>
+{
+    private ulong value = default;
+
+    public HugeInteger(ulong value) => this.value = value;
+
+    #region IBinaryInteger
+    
+    #region Implementation of IComparable
+
+    /// <inheritdoc />
+    public int CompareTo(object obj) => this.value.CompareTo(obj);
+
+    #endregion
+
+    #region Implementation of IComparable<in HugeInteger>
+
+    /// <inheritdoc />
+    public int CompareTo(HugeInteger<TOtherNum> other) => this.value.CompareTo(other.value);
+
+    #endregion
+
+    #region Implementation of IEquatable<HugeInteger>
+
+    /// <inheritdoc />
+    public bool Equals(HugeInteger<TOtherNum> other) => this.value.Equals(other.value);
+
+    #endregion
+
+    #region Implementation of IFormattable
+
+    /// <inheritdoc />
+    public string ToString(string format, IFormatProvider formatProvider) => this.value.ToString(format, formatProvider);
+
+    #endregion
+
+    #region Implementation of IParsable<HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Parse(string s, IFormatProvider provider) => new(ulong.Parse(s, provider));
+
+    /// <inheritdoc />
+    public static bool TryParse(string s, IFormatProvider provider, out HugeInteger<TOtherNum> result)
+    {
+        if (ulong.TryParse(s, NumberStyles.Integer, provider, out var value))
+        {
+            result = new HugeInteger<TOtherNum>(value);
+            return true;
+        }
+
+        result = default;
+        return false;
+    }
+
+    #endregion
+
+    #region Implementation of ISpanFormattable
+
+    /// <inheritdoc />
+    public bool TryFormat(Span<char> destination, out int charsWritten, ReadOnlySpan<char> format, IFormatProvider provider) => this.value.TryFormat(destination, out charsWritten, format, provider);
+
+    #endregion
+
+    #region Implementation of ISpanParsable<HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Parse(ReadOnlySpan<char> s, IFormatProvider provider) => new(ulong.Parse(s, provider));
+
+    /// <inheritdoc />
+    public static bool TryParse(ReadOnlySpan<char> s, IFormatProvider provider, out HugeInteger<TOtherNum> result)
+    {
+        if (ulong.TryParse(s, NumberStyles.Integer, provider, out var value))
+        {
+            result = new HugeInteger<TOtherNum>(value);
+            return true;
+        }
+
+        result = default;
+        return false;
+    }
+
+    #endregion
+
+    #region Implementation of IAdditionOperators<HugeInteger,HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator +(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value + right.value);
+
+    #endregion
+
+    #region Implementation of IAdditiveIdentity<HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> AdditiveIdentity => new(0);
+
+    #endregion
+
+    #region Implementation of IBitwiseOperators<HugeInteger,HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator &(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value & right.value);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator |(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value | right.value);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator ^(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value ^ right.value);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator ~(HugeInteger<TOtherNum> value) => new(~value.value);
+
+    #endregion
+
+    #region Implementation of IEqualityOperators<HugeInteger,HugeInteger,bool>
+
+    /// <inheritdoc />
+    public static bool operator ==(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => left.value == right.value;
+
+    /// <inheritdoc />
+    public static bool operator !=(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => left.value != right.value;
+
+    #endregion
+
+    #region Implementation of IComparisonOperators<HugeInteger,HugeInteger,bool>
+
+    /// <inheritdoc />
+    public static bool operator >(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => left.value > right.value;
+
+    /// <inheritdoc />
+    public static bool operator >=(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => left.value >= right.value;
+
+    /// <inheritdoc />
+    public static bool operator <(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => left.value < right.value;
+
+    /// <inheritdoc />
+    public static bool operator <=(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => left.value <= right.value;
+
+    #endregion
+
+    #region Implementation of IDecrementOperators<HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator --(HugeInteger<TOtherNum> value)
+    {
+        value.value--;
+        return value;
+    }
+
+    #endregion
+
+    #region Implementation of IDivisionOperators<HugeInteger,HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator /(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value / right.value);
+
+    #endregion
+
+    #region Implementation of IIncrementOperators<HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator ++(HugeInteger<TOtherNum> value)
+    {
+        value.value++;
+        return value;
+    }
+
+    #endregion
+
+    #region Implementation of IModulusOperators<HugeInteger,HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator %(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value % right.value);
+
+    #endregion
+
+    #region Implementation of IMultiplicativeIdentity<HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> MultiplicativeIdentity => new(1);
+
+    #endregion
+
+    #region Implementation of IMultiplyOperators<HugeInteger,HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator *(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value * right.value);
+
+    #endregion
+
+    #region Implementation of ISubtractionOperators<HugeInteger,HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator -(HugeInteger<TOtherNum> left, HugeInteger<TOtherNum> right) => new(left.value - right.value);
+
+    #endregion
+
+    #region Implementation of IUnaryNegationOperators<HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator -(HugeInteger<TOtherNum> value) => throw new NotImplementedException();
+
+    #endregion
+
+    #region Implementation of IUnaryPlusOperators<HugeInteger,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator +(HugeInteger<TOtherNum> value) => throw new NotImplementedException();
+
+    #endregion
+
+    #region Implementation of INumberBase<HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Abs(HugeInteger<TOtherNum> value) => value;
+
+    /// <inheritdoc />
+    public static bool IsCanonical(HugeInteger<TOtherNum> value) => true;
+
+    /// <inheritdoc />
+    public static bool IsComplexNumber(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsEvenInteger(HugeInteger<TOtherNum> value) => ulong.IsEvenInteger(value.value);
+
+    /// <inheritdoc />
+    public static bool IsFinite(HugeInteger<TOtherNum> value) => true;
+
+    /// <inheritdoc />
+    public static bool IsImaginaryNumber(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsInfinity(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsInteger(HugeInteger<TOtherNum> value) => true;
+
+    /// <inheritdoc />
+    public static bool IsNaN(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsNegative(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsNegativeInfinity(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsNormal(HugeInteger<TOtherNum> value) => true;
+
+    /// <inheritdoc />
+    public static bool IsOddInteger(HugeInteger<TOtherNum> value) => ulong.IsOddInteger(value.value);
+
+    /// <inheritdoc />
+    public static bool IsPositive(HugeInteger<TOtherNum> value) => true;
+
+    /// <inheritdoc />
+    public static bool IsPositiveInfinity(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsRealNumber(HugeInteger<TOtherNum> value) => true;
+
+    /// <inheritdoc />
+    public static bool IsSubnormal(HugeInteger<TOtherNum> value) => false;
+
+    /// <inheritdoc />
+    public static bool IsZero(HugeInteger<TOtherNum> value) => value.value == 0;
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> MaxMagnitude(HugeInteger<TOtherNum> x, HugeInteger<TOtherNum> y) => x.value > y.value ? x : y;
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> MaxMagnitudeNumber(HugeInteger<TOtherNum> x, HugeInteger<TOtherNum> y) => x.value > y.value ? x : y;
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> MinMagnitude(HugeInteger<TOtherNum> x, HugeInteger<TOtherNum> y) => x.value < y.value ? x : y;
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> MinMagnitudeNumber(HugeInteger<TOtherNum> x, HugeInteger<TOtherNum> y) => x.value < y.value ? x : y;
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Parse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider provider) => new(ulong.Parse(s, style, provider));
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Parse(string s, NumberStyles style, IFormatProvider provider) => new(ulong.Parse(s, style, provider));
+
+    /// <inheritdoc />
+    public static bool TryConvertFromChecked<TOther>(TOther value, out HugeInteger<TOtherNum> result) where TOther : INumberBase<TOther>
+    {
+        result = new HugeInteger<TOtherNum>(ulong.CreateChecked(value));
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryConvertFromSaturating<TOther>(TOther value, out HugeInteger<TOtherNum> result) where TOther : INumberBase<TOther>
+    {
+        result = new HugeInteger<TOtherNum>(ulong.CreateSaturating(value));
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryConvertFromTruncating<TOther>(TOther value, out HugeInteger<TOtherNum> result) where TOther : INumberBase<TOther>
+    {
+        result = new HugeInteger<TOtherNum>(ulong.CreateTruncating(value));
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryConvertToChecked<TOther>(HugeInteger<TOtherNum> value, out TOther result) where TOther : INumberBase<TOther>
+    {
+        result = TOther.CreateChecked(value.value);
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryConvertToSaturating<TOther>(HugeInteger<TOtherNum> value, out TOther result) where TOther : INumberBase<TOther>
+    {
+        result = TOther.CreateSaturating(value.value);
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryConvertToTruncating<TOther>(HugeInteger<TOtherNum> value, out TOther result) where TOther : INumberBase<TOther>
+    {
+        result = TOther.CreateTruncating(value.value);
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryParse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider provider, out HugeInteger<TOtherNum> result)
+    {
+        var state = ulong.TryParse(s, style, provider, out var value);
+        if(state)
+            result = new HugeInteger<TOtherNum>(value);
+        else
+            result = default;
+        
+        return state;
+    }
+
+    /// <inheritdoc />
+    public static bool TryParse(string s, NumberStyles style, IFormatProvider provider, out HugeInteger<TOtherNum> result)
+    {
+        var state = ulong.TryParse(s, style, provider, out var value);
+        if(state)
+            result = new HugeInteger<TOtherNum>(value);
+        else
+            result = default;
+        
+        return state;
+    }
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> One => new(1);
+
+    /// <inheritdoc />
+    public static int Radix => 2;
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Zero => new(0);
+
+    #endregion
+
+    #region Implementation of IBinaryNumber<HugeInteger>
+
+    /// <inheritdoc />
+    public static bool IsPow2(HugeInteger<TOtherNum> value) => ulong.IsPow2(value.value);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> Log2(HugeInteger<TOtherNum> value) => new(ulong.Log2(value.value));
+
+    #endregion
+
+    #region Implementation of IShiftOperators<HugeInteger,int,HugeInteger>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator <<(HugeInteger<TOtherNum> value, int shiftAmount) => new(value.value << shiftAmount);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator >> (HugeInteger<TOtherNum> value, int shiftAmount) => new(value.value >> shiftAmount);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator >>> (HugeInteger<TOtherNum> value, int shiftAmount) => new(value.value >>> shiftAmount);
+
+    #endregion
+
+    #region Implementation of IBinaryInteger<HugeInteger>
+
+    /// <inheritdoc />
+    public int GetByteCount() => sizeof(ulong);
+
+    /// <inheritdoc />
+    public int GetShortestBitLength() => (sizeof(ulong) * 8) - BitOperations.LeadingZeroCount(this.value);
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> PopCount(HugeInteger<TOtherNum> value) => new((ulong)BitOperations.PopCount(value.value));
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> TrailingZeroCount(HugeInteger<TOtherNum> value) => new((ulong)BitOperations.TrailingZeroCount(value.value));
+
+    /// <inheritdoc />
+    public static bool TryReadBigEndian(ReadOnlySpan<byte> source, bool isUnsigned, out HugeInteger<TOtherNum> value)
+    {
+        if (!isUnsigned)
+        {
+            value = default;
+            return false;
+        }
+
+        if(source.Length != sizeof(ulong))
+        {
+            value = default;
+            return false;
+        }
+        
+        var sourceBytes = source.ToArray();
+        if (BitConverter.IsLittleEndian)
+            sourceBytes = sourceBytes.Reverse().ToArray();
+        
+        value = new HugeInteger<TOtherNum>(BitConverter.ToUInt64(sourceBytes));
+        return true;
+    }
+
+    /// <inheritdoc />
+    public static bool TryReadLittleEndian(ReadOnlySpan<byte> source, bool isUnsigned, out HugeInteger<TOtherNum> value)
+    {
+        if (!isUnsigned)
+        {
+            value = default;
+            return false;
+        }
+
+        if(source.Length != sizeof(ulong))
+        {
+            value = default;
+            return false;
+        }
+        
+        var sourceBytes = source.ToArray();
+        if (!BitConverter.IsLittleEndian)
+            sourceBytes = sourceBytes.Reverse().ToArray();
+        
+        value = new HugeInteger<TOtherNum>(BitConverter.ToUInt64(sourceBytes));
+        return true;
+    }
+
+    /// <inheritdoc />
+    public bool TryWriteBigEndian(Span<byte> destination, out int bytesWritten)
+    {
+        var bytes = BitConverter.GetBytes(this.value);
+        if (BitConverter.IsLittleEndian)
+            bytes = bytes.Reverse().ToArray();
+        
+        bytes.CopyTo(destination);
+        bytesWritten = bytes.Length;
+        return true;
+    }
+
+    /// <inheritdoc />
+    public bool TryWriteLittleEndian(Span<byte> destination, out int bytesWritten)
+    {
+        var bytes = BitConverter.GetBytes(this.value);
+        if (!BitConverter.IsLittleEndian)
+            bytes = bytes.Reverse().ToArray();
+        
+        bytes.CopyTo(destination);
+        bytesWritten = bytes.Length;
+        return true;
+    }
+
+    #endregion
+    
+    #endregion
+
+    #region Necessary extra operators
+    
+    #region Implementation of IEqualityOperators<HugeInteger<TOtherNum>,TOtherNum,HugeInteger<TOtherNum>>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator ==(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        return left == right;
+    }
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator !=(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        return left != right;
+    }
+
+    #endregion
+
+    #region Implementation of IComparisonOperators<HugeInteger<TOtherNum>,TOtherNum,HugeInteger<TOtherNum>>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator >(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        return left > right;
+    }
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator >=(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        return left >= right;
+    }
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator <(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        return left < right;
+    }
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator <=(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        return left <= right;
+    }
+
+    #endregion
+
+    #region Implementation of IMultiplyOperators<HugeInteger<TOtherNum>,TOtherNum,HugeInteger<TOtherNum>>
+
+    /// <inheritdoc />
+    public static HugeInteger<TOtherNum> operator *(HugeInteger<TOtherNum> left, TOtherNum right)
+    {
+        // Would work, but TOtherNum might not be able to hold the result! Thus, we cannot convert
+        // left to TOtherNum, and we cannot convert right to HugeInteger<TOtherNum>.
+        // return new HugeInteger<TOtherNum>(ulong.CreateSaturating(TOtherNum.CreateSaturating(left.value) * right));
+
+        return left * right;
+    }
+
+    #endregion
+    
+    #endregion
+    
+    /// <summary>
+    /// Converts a ulong to a HugeInteger.
+    /// </summary>
+    public static implicit operator HugeInteger<TOtherNum>(ulong value) => new(value);
+    
+    /// <summary>
+    /// Converts a HugeInteger to a ulong.
+    /// </summary>
+    public static implicit operator ulong(HugeInteger<TOtherNum> value) => value.value;
+}
\ No newline at end of file
diff --git a/FastRng/IntegerMathTools.cs b/FastRng/IntegerMathTools.cs
new file mode 100644
index 0000000..d023729
--- /dev/null
+++ b/FastRng/IntegerMathTools.cs
@@ -0,0 +1,29 @@
+using System;
+using System.Numerics;
+
+namespace FastRng;
+
+/// <summary>
+/// Provides some mathematical function, which are not available within in .NET itself.
+/// </summary>
+public static class IntegerMathTools<TNum> where TNum : IBinaryInteger<TNum>, IComparisonOperators<HugeInteger<TNum>, TNum, HugeInteger<TNum>>, IMultiplyOperators<HugeInteger<TNum>, TNum, HugeInteger<TNum>>
+{
+    private static readonly TNum CONST20 = TNum.CreateChecked(20);
+    
+    /// <summary>
+    /// The mathematical factorial function for integer numbers.
+    /// </summary>
+    /// <param name="x">The value, for which you want to know the factorial.</param>
+    /// <exception cref="ArgumentOutOfRangeException">Throws, when x is greater than 20. Due to limitations of 64bit ulong type.</exception>
+    public static ulong Factorial(TNum x)
+    {
+        if (x > CONST20)
+            throw new ArgumentOutOfRangeException(nameof(x), $"Cannot compute {x}!, since ulong.max is 18_446_744_073_709_551_615.");
+            
+        var accumulator = new HugeInteger<TNum>(1);
+        for (var factor = TNum.One; factor <= x; factor++)
+            accumulator *= factor;
+
+        return accumulator;
+    }
+}
\ No newline at end of file