Int128.cs

Posted on July 31, 2020Tags ,   Leave a comment on Int128.cs

Int128 Bit Class

using System;
using System.ComponentModel;
using System.Diagnostics;
using System.Globalization;
using System.Runtime.InteropServices;
using System.Text;
[Serializable]
[StructLayout(LayoutKind.Sequential)]
[TypeConverter(typeof(Int128Converter))]
[DebuggerDisplay("{DDisplay}")]
public struct Int128 : IComparable<Int128>, IComparable, IEquatable<Int128>, IConvertible, IFormattable
{
    public        ulong _hi;
    public        ulong _lo;
    private const ulong HiNeg = 0x8000000000000000;
    [DebuggerBrowsable(DebuggerBrowsableState.Never)]
    private string DDisplay => "0x" + ToString("X1");
    public static Int128 Zero;
    public static Int128 Ten      = new Int128(10);
    public static Int128 One      = new Int128(1);
    public static Int128 MaxValue = GetMaxValue();
    public static Int128 MinValue = GetMinValue();
    private static Int128 GetMaxValue()
    {
        return new Int128(long.MaxValue, ulong.MaxValue);
    }
    private static Int128 GetMinValue()
    {
        return new Int128(0x8000000000000000, 0);
    }
    /// <summary>
    ///     Either base10 or base 16
    /// </summary>
    public Int128(string value)
    {
        TryParse(value, out var result);
        _hi = result._hi;
        _lo = result._lo;
    }
    public Int128(byte value)
    {
        _hi = 0;
        _lo = value;
    }
    public Int128(bool value)
    {
        _hi = 0;
        _lo = (ulong) (value ? 1 : 0);
    }
    public Int128(char value)
    {
        _hi = 0;
        _lo = value;
    }
    public Int128(decimal value)
    {
        if (value < 0)
        {
            var n = -new Int128(-value);
            _hi = n._hi;
            _lo = n._lo;
            return;
        }
        var bits = decimal.GetBits(value);
        _hi = (uint) bits[2];
        _lo = (uint) bits[0] | ((ulong) bits[1] << 32);
    }
    public Int128(double value)
        : this((decimal) value)
    {
    }
    public Int128(float value)
        : this((decimal) value)
    {
    }
    public Int128(short value)
    {
        if (value < 0)
        {
            var n = -new Int128(-(value + 1)) - 1;
            _hi = n._hi;
            _lo = n._lo;
            return;
        }
        _hi = 0;
        _lo = (ulong) value;
    }
    public Int128(int value)
    {
        if (value < 0)
        {
            var n = -new Int128(-(value + 1)) - 1;
            _hi = n._hi;
            _lo = n._lo;
            return;
        }
        _hi = 0;
        _lo = (ulong) value;
    }
    public Int128(long value)
    {
        if (value < 0)
        {
            var n = -new Int128(-(value + 1)) - 1;
            _hi = n._hi;
            _lo = n._lo;
            return;
        }
        _hi = 0;
        _lo = (ulong) value;
    }
    public Int128(sbyte value)
    {
        if (value < 0)
        {
            var n = -new Int128(-(value + 1)) - 1;
            _hi = n._hi;
            _lo = n._lo;
            return;
        }
        _hi = 0;
        _lo = (ulong) value;
    }
    public Int128(ushort value)
    {
        _hi = 0;
        _lo = value;
    }
    public Int128(uint value)
    {
        _hi = 0;
        _lo = value;
    }
    public Int128(ulong value)
    {
        _hi = 0;
        _lo = value;
    }
    public Int128(Guid value)
        : this(value.ToByteArray())
    {
    }
    public Int128(byte[] value)
    {
        if (value == null)
            throw new ArgumentNullException("value");
        if (value.Length != 16)
            throw new ArgumentException(null, "value");
        _hi = BitConverter.ToUInt64(value, 8);
        _lo = BitConverter.ToUInt64(value, 0);
    }
    public Int128(ulong hi, ulong lo)
    {
        _hi = hi;
        _lo = lo;
    }
    public Int128(int sign, uint[] ints)
    {
        if (ints == null)
            throw new ArgumentNullException("ints");
        var lo = new byte[8];
        var hi = new byte[8];
        if (ints.Length > 0)
        {
            Array.Copy(BitConverter.GetBytes(ints[0]), 0, lo, 0, 4);
            if (ints.Length > 1)
            {
                Array.Copy(BitConverter.GetBytes(ints[1]), 0, lo, 4, 4);
                if (ints.Length > 2)
                {
                    Array.Copy(BitConverter.GetBytes(ints[2]), 0, hi, 0, 4);
                    if (ints.Length > 3)
                        Array.Copy(BitConverter.GetBytes(ints[3]), 0, hi, 4, 4);
                }
            }
        }
        _lo = BitConverter.ToUInt64(lo, 0);
        _hi = BitConverter.ToUInt64(hi, 0);
        if (sign < 0)
            _hi |= HiNeg;
        else
            _hi &= ~HiNeg;
    }
    public int BitWidth
    {
        get
        {
            Int128 bitWidth = 1;
            var    v        = this;
            while ((v >>= 1) > 0)
                bitWidth++;
            if (bitWidth < 8)
                bitWidth = 8;
            while (bitWidth % 8 != 0)
                bitWidth++;
            return (int) bitWidth;
        }
    }
    public int Sign
    {
        get
        {
            if (_hi == 0 && _lo == 0)
                return 0;
            return (_hi & HiNeg) == 0 ? 1 : -1;
        }
    }
    public override int GetHashCode()
    {
        return _hi.GetHashCode() ^ _lo.GetHashCode();
    }
    public override bool Equals(object obj)
    {
        return base.Equals(obj);
    }
    public bool Equals(Int128 obj)
    {
        return _hi == obj._hi && _lo == obj._lo;
    }
    public override string ToString()
    {
        return ToString(null, null);
    }
    public string ToString(string format)
    {
        return ToString(format, null);
    }
    public string ToString(string format, IFormatProvider formatProvider)
    {
        if (formatProvider == null)
            formatProvider = CultureInfo.CurrentCulture;
        if (!string.IsNullOrEmpty(format))
        {
            var ch = format[0];
            if (ch == 'x' || ch == 'X')
            {
                int min;
                int.TryParse(format.Substring(1).Trim(), out min);
                return ToHexString(ch == 'X', min);
            }
            if (ch != 'G' && ch != 'g' && ch != 'D' && ch != 'd')
                throw new NotSupportedException("Not supported format: " + format);
        }
        return ToString((NumberFormatInfo) formatProvider.GetFormat(typeof(NumberFormatInfo)));
    }
    private string ToHexString(bool caps, int min)
    {
        var sb = new StringBuilder();
        var x  = caps ? "X" : "x";
        if (min < 0 || min > 16 || _hi != 0)
        {
            sb.Append(min > 16 ? _hi.ToString(x + (min - 16)) : _hi.ToString(x));
            sb.Append(_lo.ToString(x + "16"));
        }
        else
        {
            sb.Append(_lo.ToString(x + min));
        }
        return sb.ToString();
    }
    private string ToString(NumberFormatInfo info)
    {
        if (Sign == 0)
            return "0";
        var sb      = new StringBuilder();
        var current = this;
        current._hi &= ~HiNeg;
        Int128 r;
        while (true)
        {
            current = DivRem(current, Ten, out r);
            if (r._lo > 0 || current.Sign != 0 || sb.Length == 0)
                sb.Insert(0, (char) ('0' + r._lo));
            if (current.Sign == 0)
                break;
        }
        var s = sb.ToString();
        if (Sign < 0 && s != "0")
            return info.NegativeSign + s;
        return s;
    }
    TypeCode IConvertible.GetTypeCode()
    {
        return TypeCode.Object;
    }
    bool IConvertible.ToBoolean(IFormatProvider provider)
    {
        return (bool) this;
    }
    byte IConvertible.ToByte(IFormatProvider provider)
    {
        return (byte) this;
    }
    char IConvertible.ToChar(IFormatProvider provider)
    {
        return (char) this;
    }
    DateTime IConvertible.ToDateTime(IFormatProvider provider)
    {
        throw new InvalidCastException();
    }
    decimal IConvertible.ToDecimal(IFormatProvider provider)
    {
        return (decimal) this;
    }
    double IConvertible.ToDouble(IFormatProvider provider)
    {
        return (double) this;
    }
    short IConvertible.ToInt16(IFormatProvider provider)
    {
        return (short) this;
    }
    int IConvertible.ToInt32(IFormatProvider provider)
    {
        return (int) this;
    }
    long IConvertible.ToInt64(IFormatProvider provider)
    {
        return (int) this;
    }
    sbyte IConvertible.ToSByte(IFormatProvider provider)
    {
        return (sbyte) this;
    }
    float IConvertible.ToSingle(IFormatProvider provider)
    {
        return (float) this;
    }
    string IConvertible.ToString(IFormatProvider provider)
    {
        return ToString(null, provider);
    }
    public bool TryConvert(Type conversionType, IFormatProvider provider, out object value)
    {
        if (conversionType == typeof(bool))
        {
            value = (bool) this;
            return true;
        }
        if (conversionType == typeof(byte))
        {
            value = (byte) this;
            return true;
        }
        if (conversionType == typeof(char))
        {
            value = (char) this;
            return true;
        }
        if (conversionType == typeof(decimal))
        {
            value = (decimal) this;
            return true;
        }
        if (conversionType == typeof(double))
        {
            value = (double) this;
            return true;
        }
        if (conversionType == typeof(short))
        {
            value = (short) this;
            return true;
        }
        if (conversionType == typeof(int))
        {
            value = (int) this;
            return true;
        }
        if (conversionType == typeof(long))
        {
            value = (long) this;
            return true;
        }
        if (conversionType == typeof(sbyte))
        {
            value = (sbyte) this;
            return true;
        }
        if (conversionType == typeof(float))
        {
            value = (float) this;
            return true;
        }
        if (conversionType == typeof(string))
        {
            value = ToString(null, provider);
            return true;
        }
        if (conversionType == typeof(ushort))
        {
            value = (ushort) this;
            return true;
        }
        if (conversionType == typeof(uint))
        {
            value = (uint) this;
            return true;
        }
        if (conversionType == typeof(ulong))
        {
            value = (ulong) this;
            return true;
        }
        if (conversionType == typeof(byte[]))
        {
            value = ToByteArray();
            return true;
        }
        if (conversionType == typeof(Guid))
        {
            value = new Guid(ToByteArray());
            return true;
        }
        value = null;
        return false;
    }
    public static Int128 Parse(string value)
    {
        return Parse(value, NumberStyles.Integer, NumberFormatInfo.CurrentInfo);
    }
    public static Int128 Parse(string value, NumberStyles style)
    {
        return Parse(value, style, NumberFormatInfo.CurrentInfo);
    }
    public static Int128 Parse(string value, IFormatProvider provider)
    {
        return Parse(value, NumberStyles.Integer, NumberFormatInfo.GetInstance(provider));
    }
    public static Int128 Parse(string value, NumberStyles style, IFormatProvider provider)
    {
        Int128 result;
        if (!TryParse(value, style, provider, out result))
            throw new ArgumentException(null, "value");
        return result;
    }
    public static bool TryParse(string value, out Int128 result)
    {
        return TryParse(value, NumberStyles.Integer, NumberFormatInfo.CurrentInfo, out result);
    }
    public static bool TryParse(string value, NumberStyles style, IFormatProvider provider, out Int128 result)
    {
        result = Zero;
        if (string.IsNullOrEmpty(value))
            return false;
        if (value.StartsWith("x", StringComparison.OrdinalIgnoreCase))
        {
            style |= NumberStyles.AllowHexSpecifier;
            value =  value.Substring(1);
        }
        else
        {
            if (value.StartsWith("0x", StringComparison.OrdinalIgnoreCase))
            {
                style |= NumberStyles.AllowHexSpecifier;
                value =  value.Substring(2);
            }
        }
        if ((style & NumberStyles.AllowHexSpecifier) == NumberStyles.AllowHexSpecifier)
            return TryParseHex(value, out result);
        return TryParseNum(value, out result);
    }
    private static bool TryParseHex(string value, out Int128 result)
    {
        if (value.Length > 32)
            throw new OverflowException();
        result = Zero;
        var hi  = false;
        var pos = 0;
        for (var i = value.Length - 1; i >= 0; i--)
        {
            var   ch = value[i];
            ulong b;
            if (ch >= '0' && ch <= '9')
                b = (ulong) (ch - '0');
            else if (ch >= 'A' && ch <= 'F')
                b = (ulong) (ch - 'A' + 10);
            else if (ch >= 'a' && ch <= 'f')
                b = (ulong) (ch - 'a' + 10);
            else
                return false;
            if (hi)
            {
                result._hi |= b << pos;
                pos        += 4;
            }
            else
            {
                result._lo |= b << pos;
                pos        += 4;
                if (pos == 64)
                {
                    pos = 0;
                    hi  = true;
                }
            }
        }
        return true;
    }
    private static bool TryParseNum(string value, out Int128 result)
    {
        result = Zero;
        foreach (var ch in value)
        {
            byte b;
            if (ch >= '0' && ch <= '9')
                b = (byte) (ch - '0');
            else
                return false;
            result =  Ten * result;
            result += b;
        }
        return true;
    }
    public object ToType(Type conversionType, IFormatProvider provider)
    {
        object value;
        if (TryConvert(conversionType, provider, out value))
            return value;
        throw new InvalidCastException();
    }
    ushort IConvertible.ToUInt16(IFormatProvider provider)
    {
        if (_hi != 0)
            throw new OverflowException();
        return Convert.ToUInt16(_lo);
    }
    uint IConvertible.ToUInt32(IFormatProvider provider)
    {
        if (_hi != 0)
            throw new OverflowException();
        return Convert.ToUInt32(_lo);
    }
    ulong IConvertible.ToUInt64(IFormatProvider provider)
    {
        if (_hi != 0)
            throw new OverflowException();
        return _lo;
    }
    int IComparable.CompareTo(object obj)
    {
        return Compare(this, obj);
    }
    public static int Compare(Int128 left, object right)
    {
        if (right is Int128)
            return Compare(left, (Int128) right);
        if (right is bool)
            return Compare(left, new Int128((bool) right));
        if (right is byte)
            return Compare(left, new Int128((byte) right));
        if (right is char)
            return Compare(left, new Int128((char) right));
        if (right is decimal)
            return Compare(left, new Int128((decimal) right));
        if (right is double)
            return Compare(left, new Int128((double) right));
        if (right is short)
            return Compare(left, new Int128((short) right));
        if (right is int)
            return Compare(left, new Int128((int) right));
        if (right is long)
            return Compare(left, new Int128((long) right));
        if (right is sbyte)
            return Compare(left, new Int128((sbyte) right));
        if (right is float)
            return Compare(left, new Int128((float) right));
        if (right is ushort)
            return Compare(left, new Int128((ushort) right));
        if (right is uint)
            return Compare(left, new Int128((uint) right));
        if (right is ulong)
            return Compare(left, new Int128((ulong) right));
        var bytes = right as byte[];
        if (bytes != null && bytes.Length != 16)
            return Compare(left, new Int128(bytes));
        if (right is Guid)
            return Compare(left, new Int128((Guid) right));
        throw new ArgumentException();
    }
    public byte[] ToByteArray()
    {
        var bytes = new byte[16];
        Buffer.BlockCopy(BitConverter.GetBytes(_lo), 0, bytes, 0, 8);
        Buffer.BlockCopy(BitConverter.GetBytes(_hi), 0, bytes, 8, 8);
        return bytes;
    }
    public static int Compare(Int128 left, Int128 right)
    {
        if (left.Sign < 0)
        {
            if (right.Sign >= 0)
                return -1;
            var xhi = left._hi  & ~HiNeg;
            var yhi = right._hi & ~HiNeg;
            if (xhi != yhi)
                return -xhi.CompareTo(yhi);
            return -left._lo.CompareTo(right._lo);
        }
        if (right.Sign < 0)
            return 1;
        if (left._hi != right._hi)
            return left._hi.CompareTo(right._hi);
        return left._lo.CompareTo(right._lo);
    }
    public int CompareTo(Int128 value)
    {
        return Compare(this, value);
    }
    public static implicit operator Int128(bool value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(byte value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(char value)
    {
        return new Int128(value);
    }
    public static explicit operator Int128(decimal value)
    {
        return new Int128(value);
    }
    public static explicit operator Int128(double value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(short value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(int value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(long value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(sbyte value)
    {
        return new Int128(value);
    }
    public static explicit operator Int128(float value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(ushort value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(uint value)
    {
        return new Int128(value);
    }
    public static implicit operator Int128(ulong value)
    {
        return new Int128(value);
    }
    public static explicit operator bool(Int128 value)
    {
        return value.Sign != 0;
    }
    public static explicit operator byte(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        if (value.Sign < 0 || value._lo > 0xFF)
            throw new OverflowException();
        return (byte) value._lo;
    }
    public static explicit operator char(Int128 value)
    {
        if (value.Sign == 0)
            return (char) 0;
        if (value.Sign < 0 || value._lo > 0xFFFF)
            throw new OverflowException();
        return (char) (ushort) value._lo;
    }
    public static explicit operator decimal(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        return new decimal((int) (value._lo & 0xFFFFFFFF), (int) (value._lo >> 32), (int) (value._hi & 0xFFFFFFFF),
            value.Sign < 0, 0);
    }
    public static explicit operator double(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        double d;
        var    nfi = CultureInfo.InvariantCulture.NumberFormat;
        if (!double.TryParse(value.ToString(nfi), NumberStyles.Number, nfi, out d))
            throw new OverflowException();
        return d;
    }
    public static explicit operator float(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        float f;
        var   nfi = CultureInfo.InvariantCulture.NumberFormat;
        if (!float.TryParse(value.ToString(nfi), NumberStyles.Number, nfi, out f))
            throw new OverflowException();
        return f;
    }
    public static explicit operator short(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        if (value._lo > 0x8000)
            throw new OverflowException();
        if (value._lo == 0x8000 && value.Sign > 0)
            throw new OverflowException();
        return (short) ((int) value._lo * value.Sign);
    }
    public static explicit operator int(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        if (value._lo > 0x80000000)
            throw new OverflowException();
        if (value._lo == 0x80000000 && value.Sign > 0)
            throw new OverflowException();
        return (int) value._lo * value.Sign;
    }
    public static explicit operator long(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        if (value._lo > long.MaxValue)
            throw new OverflowException();
        return (long) value._lo * value.Sign;
    }
    public static explicit operator uint(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        if (value.Sign < 0 || value._lo > uint.MaxValue)
            throw new OverflowException();
        return (uint) value._lo;
    }
    public static explicit operator ushort(Int128 value)
    {
        if (value.Sign == 0)
            return 0;
        if (value.Sign < 0 || value._lo > ushort.MaxValue)
            throw new OverflowException();
        return (ushort) value._lo;
    }
    public static explicit operator ulong(Int128 value)
    {
        if (value.Sign < 0 || value._hi != 0)
            throw new OverflowException();
        return value._lo;
    }
    public static bool operator >(Int128 left, Int128 right)
    {
        return Compare(left, right) > 0;
    }
    public static bool operator <(Int128 left, Int128 right)
    {
        return Compare(left, right) < 0;
    }
    public static bool operator >=(Int128 left, Int128 right)
    {
        return Compare(left, right) >= 0;
    }
    public static bool operator <=(Int128 left, Int128 right)
    {
        return Compare(left, right) <= 0;
    }
    public static bool operator !=(Int128 left, Int128 right)
    {
        return Compare(left, right) != 0;
    }
    public static bool operator ==(Int128 left, Int128 right)
    {
        return Compare(left, right) == 0;
    }
    public static Int128 operator +(Int128 value)
    {
        return value;
    }
    public static Int128 operator -(Int128 value)
    {
        return Negate(value);
    }
    public static Int128 operator ~(Int128 value)
    {
        return -(value + One);
    }
    public static Int128 operator ++(Int128 value)
    {
        return value + 1;
    }
    public static Int128 operator --(Int128 value)
    {
        return value - 1;
    }
    public static Int128 Negate(Int128 value)
    {
        return new Int128(~value._hi, ~value._lo) + 1;
    }
    public Int128 ToAbs()
    {
        return Abs(this);
    }
    public static Int128 Abs(Int128 value)
    {
        if (value.Sign < 0)
            return -value;
        return value;
    }
    public static Int128 operator +(Int128 left, Int128 right)
    {
        var add = left;
        add._hi += right._hi;
        add._lo += right._lo;
        if (add._lo < left._lo)
            add._hi++;
        return add;
    }
    public static Int128 operator -(Int128 left, Int128 right)
    {
        return left + -right;
    }
    public static Int128 Add(Int128 left, Int128 right)
    {
        return left + right;
    }
    public static Int128 Subtract(Int128 left, Int128 right)
    {
        return left - right;
    }
    public static Int128 Divide(Int128 dividend, Int128 divisor)
    {
        Int128 integer;
        return DivRem(dividend, divisor, out integer);
    }
    public static Int128 DivRem(Int128 dividend, Int128 divisor, out Int128 remainder)
    {
        if (divisor == 0)
            throw new DivideByZeroException();
        uint[] quotient;
        uint[] rem;
        DivRem(dividend.ToUIn32Array(), divisor.ToUIn32Array(), out quotient, out rem);
        remainder = new Int128(1, rem);
        return new Int128(dividend.Sign * divisor.Sign, quotient);
    }
    private static void DivRem(uint[] dividend, uint[] divisor, out uint[] quotient, out uint[] remainder)
    {
        const ulong hiBit       = 0x100000000;
        var         divisorLen  = GetLength(divisor);
        var         dividendLen = GetLength(dividend);
        if (divisorLen <= 1)
        {
            ulong rem = 0;
            var   div = divisor[0];
            quotient  = new uint[dividendLen];
            remainder = new uint[1];
            for (var i = dividendLen - 1; i >= 0; i--)
            {
                rem *= hiBit;
                rem += dividend[i];
                var q = rem / div;
                rem         -= q * div;
                quotient[i] =  (uint) q;
            }
            remainder[0] = (uint) rem;
            return;
        }
        if (dividendLen >= divisorLen)
        {
            var shift        = GetNormalizeShift(divisor[divisorLen - 1]);
            var normDividend = new uint[dividendLen + 1];
            var normDivisor  = new uint[divisorLen];
            Normalize(dividend, dividendLen, normDividend, shift);
            Normalize(divisor,  divisorLen,  normDivisor,  shift);
            quotient = new uint[dividendLen - divisorLen + 1];
            for (var j = dividendLen - divisorLen; j >= 0; j--)
            {
                var dx = hiBit * normDividend[j + divisorLen] + normDividend[j + divisorLen - 1];
                var qj = dx / normDivisor[divisorLen                                        - 1];
                dx -= qj * normDivisor[divisorLen - 1];
                do
                {
                    if (qj < hiBit && qj * normDivisor[divisorLen - 2] <= dx * hiBit + normDividend[j + divisorLen - 2])
                        break;
                    qj -= 1L;
                    dx += normDivisor[divisorLen - 1];
                } while (dx < hiBit);
                long di = 0;
                long dj;
                var  index = 0;
                while (index < divisorLen)
                {
                    var dqj = normDivisor[index] * qj;
                    dj                      = normDividend[index + j] - (uint) dqj - di;
                    normDividend[index + j] = (uint) dj;
                    dqj                     = dqj >> 32;
                    dj                      = dj  >> 32;
                    di                      = (long) dqj - dj;
                    index++;
                }
                dj                           = normDividend[j + divisorLen] - di;
                normDividend[j + divisorLen] = (uint) dj;
                quotient[j]                  = (uint) qj;
                if (dj < 0)
                {
                    quotient[j]--;
                    ulong sum = 0;
                    for (index = 0; index < divisorLen; index++)
                    {
                        sum                     = normDivisor[index] + normDividend[j + index] + sum;
                        normDividend[j + index] = (uint) sum;
                        sum                     = sum >> 32;
                    }
                    sum += normDividend[j + divisorLen];
                    normDividend[j        + divisorLen] = (uint) sum;
                }
            }
            remainder = Unnormalize(normDividend, shift);
            return;
        }
        quotient  = new uint[0];
        remainder = dividend;
    }
    private static int GetLength(uint[] uints)
    {
        var index = uints.Length - 1;
        while (index >= 0 && uints[index] == 0)
            index--;
        return index + 1;
    }
    private static int GetNormalizeShift(uint ui)
    {
        var shift = 0;
        if ((ui & 0xffff0000) == 0)
        {
            ui    =  ui << 16;
            shift += 16;
        }
        if ((ui & 0xff000000) == 0)
        {
            ui    =  ui << 8;
            shift += 8;
        }
        if ((ui & 0xf0000000) == 0)
        {
            ui    =  ui << 4;
            shift += 4;
        }
        if ((ui & 0xc0000000) == 0)
        {
            ui    =  ui << 2;
            shift += 2;
        }
        if ((ui & 0x80000000) == 0)
            shift++;
        return shift;
    }
    private static uint[] Unnormalize(uint[] normalized, int shift)
    {
        var len         = GetLength(normalized);
        var unormalized = new uint[len];
        if (shift > 0)
        {
            var  rshift = 32 - shift;
            uint r      = 0;
            for (var i = len - 1; i >= 0; i--)
            {
                unormalized[i] = (normalized[i] >> shift) | r;
                r              = normalized[i] << rshift;
            }
        }
        else
        {
            for (var j = 0; j < len; j++)
                unormalized[j] = normalized[j];
        }
        return unormalized;
    }
    private static void Normalize(uint[] unormalized, int len, uint[] normalized, int shift)
    {
        int  i;
        uint n = 0;
        if (shift > 0)
        {
            var rshift = 32 - shift;
            for (i = 0; i < len; i++)
            {
                normalized[i] = (unormalized[i] << shift) | n;
                n             = unormalized[i] >> rshift;
            }
        }
        else
        {
            i = 0;
            while (i < len)
            {
                normalized[i] = unormalized[i];
                i++;
            }
        }
        while (i < normalized.Length)
            normalized[i++] = 0;
        if (n != 0)
            normalized[len] = n;
    }
    public static Int128 Remainder(Int128 dividend, Int128 divisor)
    {
        Int128 remainder;
        DivRem(dividend, divisor, out remainder);
        return remainder;
    }
    public static Int128 operator %(Int128 dividend, Int128 divisor)
    {
        return Remainder(dividend, divisor);
    }
    public static Int128 operator /(Int128 dividend, Int128 divisor)
    {
        return Divide(dividend, divisor);
    }
    public ulong[] ToUIn64Array()
    {
        return new[] {_hi, _lo};
    }
    public uint[] ToUIn32Array()
    {
        var ints = new uint[4];
        var lob  = BitConverter.GetBytes(_lo);
        var hib  = BitConverter.GetBytes(_hi);
        Buffer.BlockCopy(lob, 0, ints, 0,  4);
        Buffer.BlockCopy(lob, 4, ints, 4,  4);
        Buffer.BlockCopy(hib, 0, ints, 8,  4);
        Buffer.BlockCopy(hib, 4, ints, 12, 4);
        return ints;
    }
    public static Int128 Multiply(Int128 left, Int128 right)
    {
        var xInts   = left.ToUIn32Array();
        var yInts   = right.ToUIn32Array();
        var mulInts = new uint[8];
        for (var i = 0; i < xInts.Length; i++)
        {
            var   index     = i;
            ulong remainder = 0;
            foreach (var yi in yInts)
            {
                remainder        = remainder + (ulong) xInts[i] * yi + mulInts[index];
                mulInts[index++] = (uint) remainder;
                remainder        = remainder >> 32;
            }
            while (remainder != 0)
            {
                remainder        += mulInts[index];
                mulInts[index++] =  (uint) remainder;
                remainder        =  remainder >> 32;
            }
        }
        return new Int128(left.Sign * right.Sign, mulInts);
    }
    public static Int128 operator *(Int128 left, Int128 right)
    {
        return Multiply(left, right);
    }
    public static Int128 operator >>(Int128 value, int shift)
    {
        if (shift == 0)
            return value;
        if (shift < 0)
            return value << -shift;
        shift = shift % 128;
        var shifted = new Int128();
        if (shift > 63)
        {
            shifted._lo = value._hi >> (shift - 64);
            shifted._hi = 0;
        }
        else
        {
            shifted._hi = value._hi >> shift;
            shifted._lo = (value._hi << (64 - shift)) | (value._lo >> shift);
        }
        return shifted;
    }
    public static Int128 operator <<(Int128 value, int shift)
    {
        if (shift == 0)
            return value;
        if (shift < 0)
            return value >> -shift;
        shift = shift % 128;
        var shifted = new Int128();
        if (shift > 63)
        {
            shifted._hi = value._lo << (shift - 64);
            shifted._lo = 0;
        }
        else
        {
            var ul = value._lo            >> (64 - shift);
            shifted._hi = ul | (value._hi << shift);
            shifted._lo = value._lo << shift;
        }
        return shifted;
    }
    public static Int128 operator |(Int128 left, Int128 right)
    {
        if (left == 0)
            return right;
        if (right == 0)
            return left;
        var x       = left.ToUIn32Array();
        var y       = right.ToUIn32Array();
        var z       = new uint[Math.Max(x.Length, y.Length)];
        var xExtend = left.Sign  < 0 ? uint.MaxValue : 0;
        var yExtend = right.Sign < 0 ? uint.MaxValue : 0;
        for (var i = 0; i < z.Length; i++)
        {
            var xu = i < x.Length ? x[i] : xExtend;
            var yu = i < y.Length ? y[i] : yExtend;
            z[i] = xu | yu;
        }
        return new Int128(left.Sign * right.Sign, z);
    }
    public static Int128 operator ^(Int128 left, Int128 right)
    {
        var x       = left.ToUIn32Array();
        var y       = right.ToUIn32Array();
        var z       = new uint[Math.Max(x.Length, y.Length)];
        var xExtend = left.Sign  < 0 ? uint.MaxValue : 0;
        var yExtend = right.Sign < 0 ? uint.MaxValue : 0;
        for (var i = 0; i < z.Length; i++)
        {
            var xu = i < x.Length ? x[i] : xExtend;
            var yu = i < y.Length ? y[i] : yExtend;
            z[i] = xu ^ yu;
        }
        return new Int128(left.Sign * right.Sign, z);
    }
    public static Int128 operator &(Int128 left, Int128 right)
    {
        if (left == 0 || right == 0)
            return Zero;
        var x       = left.ToUIn32Array();
        var y       = right.ToUIn32Array();
        var z       = new uint[Math.Max(x.Length, y.Length)];
        var xExtend = left.Sign  < 0 ? uint.MaxValue : 0;
        var yExtend = right.Sign < 0 ? uint.MaxValue : 0;
        for (var i = 0; i < z.Length; i++)
        {
            var xu = i < x.Length ? x[i] : xExtend;
            var yu = i < y.Length ? y[i] : yExtend;
            z[i] = xu & yu;
        }
        return new Int128(left.Sign * right.Sign, z);
    }
    public class Int128Converter : TypeConverter
    {
        public override bool CanConvertFrom(ITypeDescriptorContext context, Type sourceType)
        {
            if (sourceType == typeof(string))
                return true;
            return base.CanConvertFrom(context, sourceType);
        }
        public override object ConvertFrom(ITypeDescriptorContext context, CultureInfo culture, object value)
        {
            if (value != null)
            {
                Int128 i;
                if (TryParse($"{value}", out i))
                    return i;
            }
            return new Int128();
        }
        public override bool CanConvertTo(ITypeDescriptorContext context, Type destinationType)
        {
            if (destinationType == typeof(string))
                return true;
            return base.CanConvertTo(context, destinationType);
        }
        public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value,
            Type                                                destinationType)
        {
            if (destinationType == typeof(string))
                return $"{value}";
            return base.ConvertTo(context, culture, value, destinationType);
        }
        
    }
}