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Joe_du

园龄：10年3个月粉丝：19关注：50

C#大数计算 .Net Framework4.0以下

  • 在.Net Framework4.0以下的框架中C#不支持大数计算.若是需要对大数进行计算就需要自己实现计算方法,本类借鉴网上开源的算法.重载了如下运算符.
  • +,++,-,--,*,<<,>>,~,-,==,!=,>,<,>=,<=,/,%,&,|,^
  • 实现了如下函数: Abs(),ToString(),ToHexString(),BitCount(),Sqrt()
  • 对于使用.Net Framework 4.0及以上版本的小伙伴可以使用微软提供的API来实现,听说效率高到爆.
/// <summary>
/// 求 BigInteger 的绝对值
/// </summary>
/// <returns>返回 BigInteger 的绝对值</returns>
public BigInteger Abs()
/// <summary>
///  返回一个字符串,表示符号和大小的 BigInteger 在10进制数格式.
/// </summary>
/// <returns>表示符号和大小的 BigInteger 在10进制数格式</returns>
public override string ToString()
/// <summary>
/// 返回一个字符串, 表示符号和大小的 BigInteger指定进制数的格式.
/// </summary>
/// <param name="radix">进制数2-36</param>
/// <returns>
///如果 BigInteger 的值在 10进制 中为-255, 则ToString (16) 返回 "-FF"
///</returns>
public string ToString(int radix)
/// <summary>
/// 返回BigInteger的十六进制字符串
/// </summary>
/// <returns>
/// 1) 如果 BigInteger 的值为255在 10进制 中, 则ToHexString () 返回 "FF"
/// 2) 如果 BigInteger 的值为-255 在 10进制 中, 则ToHexString () 返回 "..。FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01 ",           这是2的补语表示-255。
/// </returns>
public string ToHexString()
/// <summary>
/// 返回 BigInteger 中最重要位的位置。
/// 结果为 0, 如果 BigInteger 的值为 0... 0000 0000
/// 结果为 1, 如果 BigInteger 的值为 0... 0000 0001
/// 结果为 2, 如果 BigInteger 的值为 0... 0000 0010
/// 结果为 3, 如果 BigInteger 的值为 0... 0000 0011
/// </summary>
/// <returns></returns>
public int BitCount()   /// <summary>
/// 返回 BigInteger 中最重要位的位置。
/// 结果为 0, 如果 BigInteger 的值为 0... 0000 0000
/// 结果为 1, 如果 BigInteger 的值为 0... 0000 0001
/// 结果为 2, 如果 BigInteger 的值为 0... 0000 0010
/// 结果为 3, 如果 BigInteger 的值为 0... 0000 0011
/// </summary>
/// <returns></returns>
public int BitCount()
/// <summary>
/// 计算当前BigInteger的平方根
/// </summary>
/// <returns>返回一个等效于 BigInteger 的整数平方根的值。</returns>
public BigInteger Sqrt()

namespace BigInteger
{
    using System;
    /// <summary>
    /// 大数之间的常用数据运算
    /// </summary>
    public class BigInteger
    {
        private const int maxLength = 70;
        public static readonly int[] primesBelow2000 = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999 };
        private uint[] data = null;
        public int dataLength;
        /// <summary>
        /// 构造函数 (BigInteger 的默认值为 0)
        /// </summary>
        public BigInteger()
        {
            data = new uint[maxLength];
            dataLength = 1;
        }
        /// <summary>
        /// 构造函数 (由 long 提供的默认值)
        /// </summary>
        /// <param name="value"></param>
        public BigInteger(long value)
        {
            data = new uint[maxLength];
            long tempVal = value;
            dataLength = 0;
            while (value != 0 && dataLength < maxLength)
            {
                data[dataLength] = (uint)(value & 0xFFFFFFFF);
                value >>= 32;
                dataLength++;
            }
            if (tempVal > 0)
            {
                if (value != 0 || (data[maxLength - 1] & 0x80000000) != 0)
                    throw (new ArithmeticException("构造函数中的正溢出."));
            }
            else if (tempVal < 0)
            {
                if (value != -1 || (data[dataLength - 1] & 0x80000000) == 0)
                    throw (new ArithmeticException("构造函数中的负溢出."));
            }
            if (dataLength == 0)
                dataLength = 1;
        }
        /// <summary>
        /// 构造函数 (由 ulong 提供的默认值)
        /// </summary>
        /// <param name="value"></param>
        public BigInteger(ulong value)
        {
            data = new uint[maxLength];
            dataLength = 0;
            while (value != 0 && dataLength < maxLength)
            {
                data[dataLength] = (uint)(value & 0xFFFFFFFF);
                value >>= 32;
                dataLength++;
            }
            if (value != 0 || (data[maxLength - 1] & 0x80000000) != 0)
                throw (new ArithmeticException("构造函数中的正溢出."));
            if (dataLength == 0)
                dataLength = 1;
        }
        /// <summary>
        /// 构造函数 (由 BigInteger 提供的默认值)
        /// </summary>
        /// <param name="bi"></param>
        public BigInteger(BigInteger bi)
        {
            data = new uint[maxLength];
            dataLength = bi.dataLength;
            for (int i = 0; i < dataLength; i++)
                data[i] = bi.data[i];
        }
        /// <summary>
        /// 构造函数 (由指定基的数字字符串提供的默认值)
        /// 示例 (10进制)
        /// 在 10进制 中初始化默认值为1234年的 "a"
        ///       BigInteger a = new BigInteger ("1234", 10)
        /// 初始化默认值为-1234 的 "a"
        ///       BigInteger a = new BigInteger ("-1234", 10)
        /// 示例 (16进制)
        /// 在 base 16 中初始化具有默认值0x1D4F 的 "a"
        ///       BigInteger a = new BigInteger ("1D4F", 16)
        /// 使用默认值0x1d4f 初始化 "a"
        ///       BigInteger a = new BigInteger ("-1D4F", 16)
        /// </summary>
        /// <param name="value">值</param>
        /// <param name="radix">进制</param>
        public BigInteger(string value, int radix)
        {
            BigInteger multiplier = new BigInteger(1);
            BigInteger result = new BigInteger();
            value = (value.ToUpper()).Trim();
            int limit = 0;
            if (value[0] == '-')
                limit = 1;
            for (int i = value.Length - 1; i >= limit; i--)
            {
                int posVal = (int)value[i];
                if (posVal >= '0' && posVal <= '9')
                    posVal -= '0';
                else if (posVal >= 'A' && posVal <= 'Z')
                    posVal = (posVal - 'A') + 10;
                else
                    posVal = 9999999;
                if (posVal >= radix)
                    throw (new ArithmeticException("构造函数中的字符串无效."));
                else
                {
                    if (value[0] == '-')
                        posVal = -posVal;
                    result = result + (multiplier * posVal);
                    if ((i - 1) >= limit)
                        multiplier = multiplier * radix;
                }
            }
            if (value[0] == '-')
            {
                if ((result.data[maxLength - 1] & 0x80000000) == 0)
                    throw (new ArithmeticException("构造函数中的负溢出."));
            }
            else
            {
                if ((result.data[maxLength - 1] & 0x80000000) != 0)
                    throw (new ArithmeticException("构造函数中的正溢出."));
            }
            data = new uint[maxLength];
            for (int i = 0; i < result.dataLength; i++)
                data[i] = result.data[i];
            dataLength = result.dataLength;
        }
        /// <summary>
        /// 构造函数 (由字节数组提供的默认值)
        /// 输入字节数组的最低索引 (i. e [0]) 应包含数字中最重要的字节, 最高索引应包含最不重要的字节。
        /// 例如:
        /// 在 16进制 中初始化具有默认值0x1D4F 的 "a"
        ///       byte[] temp = {0x1D, 0x4F};
        ///       BigInteger a = new BigInteger (temp);
        /// 请注意, 此初始化方法不允许指定符号.
        /// </summary>
        /// <param name="inData"></param>
        public BigInteger(byte[] inData)
        {
            dataLength = inData.Length >> 2;
            int leftOver = inData.Length & 0x3;
            if (leftOver != 0)
                dataLength++;
            if (dataLength > maxLength)
                throw (new ArithmeticException("构造函数中的字节溢出."));
            data = new uint[maxLength];
            for (int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++)
            {
                data[j] = (uint)((inData[i - 3] << 24) + (inData[i - 2] << 16) + (inData[i - 1] << 8) + inData[i]);
            }
            if (leftOver == 1)
                data[dataLength - 1] = (uint)inData[0];
            else if (leftOver == 2)
                data[dataLength - 1] = (uint)((inData[0] << 8) + inData[1]);
            else if (leftOver == 3)
                data[dataLength - 1] = (uint)((inData[0] << 16) + (inData[1] << 8) + inData[2]);
            while (dataLength > 1 && data[dataLength - 1] == 0)
                dataLength--;
        }
        /// <summary>
        /// 构造函数 (由指定长度的字节数组提供的默认值.)
        /// </summary>
        /// <param name="inData">字节数组</param>
        /// <param name="inLen">长度</param>
        public BigInteger(byte[] inData, int inLen)
        {
            dataLength = inLen >> 2;
            int leftOver = inLen & 0x3;
            if (leftOver != 0)
                dataLength++;
            if (dataLength > maxLength || inLen > inData.Length)
                throw (new ArithmeticException("构造函数中的字节溢出."));
            data = new uint[maxLength];
            for (int i = inLen - 1, j = 0; i >= 3; i -= 4, j++)
            {
                data[j] = (uint)((inData[i - 3] << 24) + (inData[i - 2] << 16) + (inData[i - 1] << 8) + inData[i]);
            }
            if (leftOver == 1)
                data[dataLength - 1] = (uint)inData[0];
            else if (leftOver == 2)
                data[dataLength - 1] = (uint)((inData[0] << 8) + inData[1]);
            else if (leftOver == 3)
                data[dataLength - 1] = (uint)((inData[0] << 16) + (inData[1] << 8) + inData[2]);
            if (dataLength == 0)
                dataLength = 1;
            while (dataLength > 1 && data[dataLength - 1] == 0)
                dataLength--;
        }
        /// <summary>
        /// 构造函数 (由无符号整数数组提供的默认值)
        /// </summary>
        /// <param name="inData"></param>
        public BigInteger(uint[] inData)
        {
            dataLength = inData.Length;
            if (dataLength > maxLength)
                throw (new ArithmeticException("构造函数中的字节溢出."));
            data = new uint[maxLength];
            for (int i = dataLength - 1, j = 0; i >= 0; i--, j++)
                data[j] = inData[i];
            while (dataLength > 1 && data[dataLength - 1] == 0)
                dataLength--;
        }
        public static implicit operator BigInteger(long value)
        {
            return (new BigInteger(value));
        }
        public static implicit operator BigInteger(ulong value)
        {
            return (new BigInteger(value));
        }
        public static implicit operator BigInteger(int value)
        {
            return (new BigInteger((long)value));
        }
        public static implicit operator BigInteger(uint value)
        {
            return (new BigInteger((ulong)value));
        }
        /// <summary>
        /// 加法运算符的重载
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>bi1与bi2的加法运算结果</returns>
        public static BigInteger operator +(BigInteger bi1, BigInteger bi2)
        {
            BigInteger result = new BigInteger();
            result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            long carry = 0;
            for (int i = 0; i < result.dataLength; i++)
            {
                long sum = (long)bi1.data[i] + (long)bi2.data[i] + carry;
                carry = sum >> 32;
                result.data[i] = (uint)(sum & 0xFFFFFFFF);
            }
            if (carry != 0 && result.dataLength < maxLength)
            {
                result.data[result.dataLength] = (uint)(carry);
                result.dataLength++;
            }
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            int lastPos = maxLength - 1;
            if ((bi1.data[lastPos] & 0x80000000) == (bi2.data[lastPos] & 0x80000000) && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
            {
                throw (new ArithmeticException("加法运算溢出."));
            }
            return result;
        }
        /// <summary>
        /// 一元 ++ 运算符的重载
        /// </summary>
        /// <param name="bi1"></param>
        /// <returns></returns>
        public static BigInteger operator ++(BigInteger bi1)
        {
            BigInteger result = new BigInteger(bi1);
            long val, carry = 1;
            int index = 0;
            while (carry != 0 && index < maxLength)
            {
                val = (long)(result.data[index]);
                val++;
                result.data[index] = (uint)(val & 0xFFFFFFFF);
                carry = val >> 32;
                index++;
            }
            if (index > result.dataLength)
                result.dataLength = index;
            else
            {
                while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                    result.dataLength--;
            }
            int lastPos = maxLength - 1;
            if ((bi1.data[lastPos] & 0x80000000) == 0 && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
            {
                throw (new ArithmeticException("++运算溢出."));
            }
            return result;
        }
        /// <summary>
        /// 减法运算符的重载
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>bi1与bi2的减法运算结果</returns>
        public static BigInteger operator -(BigInteger bi1, BigInteger bi2)
        {
            BigInteger result = new BigInteger();
            result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            long carryIn = 0;
            for (int i = 0; i < result.dataLength; i++)
            {
                long diff;
                diff = (long)bi1.data[i] - (long)bi2.data[i] - carryIn;
                result.data[i] = (uint)(diff & 0xFFFFFFFF);
                if (diff < 0)
                    carryIn = 1;
                else
                    carryIn = 0;
            }
            if (carryIn != 0)
            {
                for (int i = result.dataLength; i < maxLength; i++)
                    result.data[i] = 0xFFFFFFFF;
                result.dataLength = maxLength;
            }
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            int lastPos = maxLength - 1;
            if ((bi1.data[lastPos] & 0x80000000) != (bi2.data[lastPos] & 0x80000000) && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
            {
                throw (new ArithmeticException("减法运算溢出."));
            }
            return result;
        }
        /// <summary>
        /// 一元--运算符的重载
        /// </summary>
        /// <param name="bi1"></param>
        /// <returns></returns>
        public static BigInteger operator --(BigInteger bi1)
        {
            BigInteger result = new BigInteger(bi1);
            long val;
            bool carryIn = true;
            int index = 0;
            while (carryIn && index < maxLength)
            {
                val = (long)(result.data[index]);
                val--;
                result.data[index] = (uint)(val & 0xFFFFFFFF);
                if (val >= 0)
                    carryIn = false;
                index++;
            }
            if (index > result.dataLength)
                result.dataLength = index;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            int lastPos = maxLength - 1;
            if ((bi1.data[lastPos] & 0x80000000) != 0 && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
            {
                throw (new ArithmeticException("--运算溢出."));
            }
            return result;
        }
        /// <summary>
        /// 乘法运算符的重载
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>bi1与bi2的乘法运算结果</returns>
        public static BigInteger operator *(BigInteger bi1, BigInteger bi2)
        {
            int lastPos = maxLength - 1;
            bool bi1Neg = false, bi2Neg = false;
            try
            {
                if ((bi1.data[lastPos] & 0x80000000) != 0)
                {
                    bi1Neg = true;
                    bi1 = -bi1;
                }
                if ((bi2.data[lastPos] & 0x80000000) != 0)
                {
                    bi2Neg = true;
                    bi2 = -bi2;
                }
            }
            catch (Exception) { }
            BigInteger result = new BigInteger();
            try
            {
                for (int i = 0; i < bi1.dataLength; i++)
                {
                    if (bi1.data[i] == 0)
                        continue;
                    ulong mcarry = 0;
                    for (int j = 0, k = i; j < bi2.dataLength; j++, k++)
                    {
                        ulong val = ((ulong)bi1.data[i] * (ulong)bi2.data[j]) + (ulong)result.data[k] + mcarry;
                        result.data[k] = (uint)(val & 0xFFFFFFFF);
                        mcarry = (val >> 32);
                    }
                    if (mcarry != 0)
                        result.data[i + bi2.dataLength] = (uint)mcarry;
                }
            }
            catch (Exception)
            {
                throw (new ArithmeticException("乘法溢出."));
            }
            result.dataLength = bi1.dataLength + bi2.dataLength;
            if (result.dataLength > maxLength)
                result.dataLength = maxLength;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            if ((result.data[lastPos] & 0x80000000) != 0)
            {
                if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000)
                {
                    if (result.dataLength == 1)
                        return result;
                    else
                    {
                        bool isMaxNeg = true;
                        for (int i = 0; i < result.dataLength - 1 && isMaxNeg; i++)
                        {
                            if (result.data[i] != 0)
                                isMaxNeg = false;
                        }
                        if (isMaxNeg)
                            return result;
                    }
                }
                throw (new ArithmeticException("乘法溢出."));
            }
            if (bi1Neg != bi2Neg)
                return -result;
            return result;
        }
        /// <summary>
        ///  一元 << 运算符的重载(左移位运算)
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="shiftVal">移动位数</param>
        /// <returns></returns>
        public static BigInteger operator <<(BigInteger bi1, int shiftVal)
        {
            BigInteger result = new BigInteger(bi1);
            result.dataLength = ShiftLeft(result.data, shiftVal);
            return result;
        }
        private static int ShiftLeft(uint[] buffer, int shiftVal)
        {
            int shiftAmount = 32;
            int bufLen = buffer.Length;
            while (bufLen > 1 && buffer[bufLen - 1] == 0)
                bufLen--;
            for (int count = shiftVal; count > 0; )
            {
                if (count < shiftAmount)
                    shiftAmount = count;
                ulong carry = 0;
                for (int i = 0; i < bufLen; i++)
                {
                    ulong val = ((ulong)buffer[i]) << shiftAmount;
                    val |= carry;
                    buffer[i] = (uint)(val & 0xFFFFFFFF);
                    carry = val >> 32;
                }
                if (carry != 0)
                {
                    if (bufLen + 1 <= buffer.Length)
                    {
                        buffer[bufLen] = (uint)carry;
                        bufLen++;
                    }
                }
                count -= shiftAmount;
            }
            return bufLen;
        }
        /// <summary>
        /// 一元 >> 运算符的重载(右移位运算)
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="shiftVal">移动位数</param>
        /// <returns></returns>
        public static BigInteger operator >>(BigInteger bi1, int shiftVal)
        {
            BigInteger result = new BigInteger(bi1);
            result.dataLength = ShiftRight(result.data, shiftVal);
            if ((bi1.data[maxLength - 1] & 0x80000000) != 0)
            {
                for (int i = maxLength - 1; i >= result.dataLength; i--)
                    result.data[i] = 0xFFFFFFFF;
                uint mask = 0x80000000;
                for (int i = 0; i < 32; i++)
                {
                    if ((result.data[result.dataLength - 1] & mask) != 0)
                        break;
                    result.data[result.dataLength - 1] |= mask;
                    mask >>= 1;
                }
                result.dataLength = maxLength;
            }
            return result;
        }
        private static int ShiftRight(uint[] buffer, int shiftVal)
        {
            int shiftAmount = 32;
            int invShift = 0;
            int bufLen = buffer.Length;
            while (bufLen > 1 && buffer[bufLen - 1] == 0)
                bufLen--;
            for (int count = shiftVal; count > 0; )
            {
                if (count < shiftAmount)
                {
                    shiftAmount = count;
                    invShift = 32 - shiftAmount;
                }
                ulong carry = 0;
                for (int i = bufLen - 1; i >= 0; i--)
                {
                    ulong val = ((ulong)buffer[i]) >> shiftAmount;
                    val |= carry;
                    carry = ((ulong)buffer[i]) << invShift;
                    buffer[i] = (uint)(val);
                }
                count -= shiftAmount;
            }
            while (bufLen > 1 && buffer[bufLen - 1] == 0)
                bufLen--;
            return bufLen;
        }
        /// <summary>
        /// 非运算符重载 (1 的补数)
        /// </summary>
        /// <param name="bi1">需要取非的 BigInteger</param>
        /// <returns>返回1的补数</returns>
        public static BigInteger operator ~(BigInteger bi1)
        {
            BigInteger result = new BigInteger(bi1);
            for (int i = 0; i < maxLength; i++)
                result.data[i] = (uint)(~(bi1.data[i]));
            result.dataLength = maxLength;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            return result;
        }
        /// <summary>
        /// 否定运算符的重载 (2 的补数)
        /// </summary>
        /// <param name="bi1">需要取否的 BigInteger</param>
        /// <returns>返回2的补数</returns>
        public static BigInteger operator -(BigInteger bi1)
        {
            if (bi1.dataLength == 1 && bi1.data[0] == 0)
                return (new BigInteger());
            BigInteger result = new BigInteger(bi1);
            for (int i = 0; i < maxLength; i++)
                result.data[i] = (uint)(~(bi1.data[i]));
            long val, carry = 1;
            int index = 0;
            while (carry != 0 && index < maxLength)
            {
                val = (long)(result.data[index]);
                val++;
                result.data[index] = (uint)(val & 0xFFFFFFFF);
                carry = val >> 32;
                index++;
            }
            if ((bi1.data[maxLength - 1] & 0x80000000) == (result.data[maxLength - 1] & 0x80000000))
                throw (new ArithmeticException("在否定运算中溢出."));
            result.dataLength = maxLength;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            return result;
        }
        #region 相等运算符的重载
        public static bool operator ==(BigInteger bi1, BigInteger bi2)
        {
            return bi1.Equals(bi2);
        }
        public static bool operator !=(BigInteger bi1, BigInteger bi2)
        {
            return !(bi1.Equals(bi2));
        }
        public override bool Equals(object o)
        {
            BigInteger bi = (BigInteger)o;
            if (this.dataLength != bi.dataLength)
                return false;
            for (int i = 0; i < this.dataLength; i++)
            {
                if (this.data[i] != bi.data[i])
                    return false;
            }
            return true;
        }
        #endregion
        /// <summary>
        /// 获取当前 BigInteger 在10进制数格式字符串的哈希代码
        /// </summary>
        /// <returns></returns>
        public override int GetHashCode()
        {
            return this.ToString().GetHashCode();
        }
        #region 不等式运算符的重载
        public static bool operator >(BigInteger bi1, BigInteger bi2)
        {
            int pos = maxLength - 1;
            if ((bi1.data[pos] & 0x80000000) != 0 && (bi2.data[pos] & 0x80000000) == 0)
                return false;
            else if ((bi1.data[pos] & 0x80000000) == 0 && (bi2.data[pos] & 0x80000000) != 0)
                return true;
            int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            for (pos = len - 1; pos >= 0 && bi1.data[pos] == bi2.data[pos]; pos--) ;
            if (pos >= 0)
            {
                if (bi1.data[pos] > bi2.data[pos])
                    return true;
                return false;
            }
            return false;
        }
        public static bool operator <(BigInteger bi1, BigInteger bi2)
        {
            int pos = maxLength - 1;
            if ((bi1.data[pos] & 0x80000000) != 0 && (bi2.data[pos] & 0x80000000) == 0)
                return true;
            else if ((bi1.data[pos] & 0x80000000) == 0 && (bi2.data[pos] & 0x80000000) != 0)
                return false;
            int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            for (pos = len - 1; pos >= 0 && bi1.data[pos] == bi2.data[pos]; pos--) ;
            if (pos >= 0)
            {
                if (bi1.data[pos] < bi2.data[pos])
                    return true;
                return false;
            }
            return false;
        }
        public static bool operator >=(BigInteger bi1, BigInteger bi2)
        {
            return (bi1 == bi2 || bi1 > bi2);
        }
        public static bool operator <=(BigInteger bi1, BigInteger bi2)
        {
            return (bi1 == bi2 || bi1 < bi2);
        }
        #endregion
        /// <summary>
        /// 私有函数, 它支持两个数的除法, 除数超过1位。
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <param name="outQuotient">出商</param>
        /// <param name="outRemainder">出余数</param>
        private static void MultiByteDivide(BigInteger bi1, BigInteger bi2, BigInteger outQuotient, BigInteger outRemainder)
        {
            uint[] result = new uint[maxLength];
            int remainderLen = bi1.dataLength + 1;
            uint[] remainder = new uint[remainderLen];
            uint mask = 0x80000000;
            uint val = bi2.data[bi2.dataLength - 1];
            int shift = 0, resultPos = 0;
            while (mask != 0 && (val & mask) == 0)
            {
                shift++; mask >>= 1;
            }
            for (int i = 0; i < bi1.dataLength; i++)
                remainder[i] = bi1.data[i];
            ShiftLeft(remainder, shift);
            bi2 = bi2 << shift;
            int j = remainderLen - bi2.dataLength;
            int pos = remainderLen - 1;
            ulong firstDivisorByte = bi2.data[bi2.dataLength - 1];
            ulong secondDivisorByte = bi2.data[bi2.dataLength - 2];
            int divisorLen = bi2.dataLength + 1;
            uint[] dividendPart = new uint[divisorLen];
            while (j > 0)
            {
                ulong dividend = ((ulong)remainder[pos] << 32) + (ulong)remainder[pos - 1];
                ulong q_hat = dividend / firstDivisorByte;
                ulong r_hat = dividend % firstDivisorByte;
                bool done = false;
                while (!done)
                {
                    done = true;
                    if (q_hat == 0x100000000 || (q_hat * secondDivisorByte) > ((r_hat << 32) + remainder[pos - 2]))
                    {
                        q_hat--;
                        r_hat += firstDivisorByte;
                        if (r_hat < 0x100000000)
                            done = false;
                    }
                }
                for (int h = 0; h < divisorLen; h++)
                    dividendPart[h] = remainder[pos - h];
                BigInteger kk = new BigInteger(dividendPart);
                BigInteger ss = bi2 * (long)q_hat;
                while (ss > kk)
                {
                    q_hat--;
                    ss -= bi2;
                }
                BigInteger yy = kk - ss;
                for (int h = 0; h < divisorLen; h++)
                    remainder[pos - h] = yy.data[bi2.dataLength - h];
                result[resultPos++] = (uint)q_hat;
                pos--;
                j--;
            }
            outQuotient.dataLength = resultPos;
            int y = 0;
            for (int x = outQuotient.dataLength - 1; x >= 0; x--, y++)
                outQuotient.data[y] = result[x];
            for (; y < maxLength; y++)
                outQuotient.data[y] = 0;
            while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0)
                outQuotient.dataLength--;
            if (outQuotient.dataLength == 0)
                outQuotient.dataLength = 1;
            outRemainder.dataLength = ShiftRight(remainder, shift);
            for (y = 0; y < outRemainder.dataLength; y++)
                outRemainder.data[y] = remainder[y];
            for (; y < maxLength; y++)
                outRemainder.data[y] = 0;
        }
        /// <summary>
        /// 私有函数, 它支持两个数的除法, 除数只有1位。
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <param name="outQuotient">出商</param>
        /// <param name="outRemainder">出余数</param>
        private static void SingleByteDivide(BigInteger bi1, BigInteger bi2, BigInteger outQuotient, BigInteger outRemainder)
        {
            uint[] result = new uint[maxLength];
            int resultPos = 0;
            for (int i = 0; i < maxLength; i++)
                outRemainder.data[i] = bi1.data[i];
            outRemainder.dataLength = bi1.dataLength;
            while (outRemainder.dataLength > 1 && outRemainder.data[outRemainder.dataLength - 1] == 0)
                outRemainder.dataLength--;
            ulong divisor = (ulong)bi2.data[0];
            int pos = outRemainder.dataLength - 1;
            ulong dividend = (ulong)outRemainder.data[pos];
            if (dividend >= divisor)
            {
                ulong quotient = dividend / divisor;
                result[resultPos++] = (uint)quotient;
                outRemainder.data[pos] = (uint)(dividend % divisor);
            }
            pos--;
            while (pos >= 0)
            {
                dividend = ((ulong)outRemainder.data[pos + 1] << 32) + (ulong)outRemainder.data[pos];
                ulong quotient = dividend / divisor;
                result[resultPos++] = (uint)quotient;
                outRemainder.data[pos + 1] = 0;
                outRemainder.data[pos--] = (uint)(dividend % divisor);
            }
            outQuotient.dataLength = resultPos;
            int j = 0;
            for (int i = outQuotient.dataLength - 1; i >= 0; i--, j++)
                outQuotient.data[j] = result[i];
            for (; j < maxLength; j++)
                outQuotient.data[j] = 0;
            while (outQuotient.dataLength > 1 && outQuotient.data[outQuotient.dataLength - 1] == 0)
                outQuotient.dataLength--;
            if (outQuotient.dataLength == 0)
                outQuotient.dataLength = 1;
            while (outRemainder.dataLength > 1 && outRemainder.data[outRemainder.dataLength - 1] == 0)
                outRemainder.dataLength--;
        }
        /// <summary>
        /// 除法运算符的重载
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>返回bi1与bi2进行除法运算的结果</returns>
        public static BigInteger operator /(BigInteger bi1, BigInteger bi2)
        {
            BigInteger quotient = new BigInteger();
            BigInteger remainder = new BigInteger();
            int lastPos = maxLength - 1;
            bool divisorNeg = false, dividendNeg = false;
            if ((bi1.data[lastPos] & 0x80000000) != 0)
            {
                bi1 = -bi1;
                dividendNeg = true;
            }
            if ((bi2.data[lastPos] & 0x80000000) != 0)
            {
                bi2 = -bi2;
                divisorNeg = true;
            }
            if (bi1 < bi2)
                return quotient;
            else
            {
                if (bi2.dataLength == 1)
                    SingleByteDivide(bi1, bi2, quotient, remainder);
                else
                    MultiByteDivide(bi1, bi2, quotient, remainder);
                if (dividendNeg != divisorNeg)
                    return -quotient;
                return quotient;
            }
        }
        /// <summary>
        /// 模数运算符的重载(取余)
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>返回bi1与bi2取余运算后的结果</returns>
        public static BigInteger operator %(BigInteger bi1, BigInteger bi2)
        {
            BigInteger quotient = new BigInteger();
            BigInteger remainder = new BigInteger(bi1);
            int lastPos = maxLength - 1;
            bool dividendNeg = false;
            if ((bi1.data[lastPos] & 0x80000000) != 0)
            {
                bi1 = -bi1;
                dividendNeg = true;
            }
            if ((bi2.data[lastPos] & 0x80000000) != 0)
                bi2 = -bi2;
            if (bi1 < bi2)
                return remainder;
            else
            {
                if (bi2.dataLength == 1)
                    SingleByteDivide(bi1, bi2, quotient, remainder);
                else
                    MultiByteDivide(bi1, bi2, quotient, remainder);
                if (dividendNeg)
                    return -remainder;
                return remainder;
            }
        }
        /// <summary>
        /// 按位 AND 运算符重载(与运算)
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>返回bi1与bi2进行与运算的结果</returns>
        public static BigInteger operator &(BigInteger bi1, BigInteger bi2)
        {
            BigInteger result = new BigInteger();
            int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            for (int i = 0; i < len; i++)
            {
                uint sum = (uint)(bi1.data[i] & bi2.data[i]);
                result.data[i] = sum;
            }
            result.dataLength = maxLength;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            return result;
        }
        /// <summary>
        /// 按位 OR 运算符重载(或)
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>返回bi1与bi2进行或运算的结果</returns>
        public static BigInteger operator |(BigInteger bi1, BigInteger bi2)
        {
            BigInteger result = new BigInteger();
            int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            for (int i = 0; i < len; i++)
            {
                uint sum = (uint)(bi1.data[i] | bi2.data[i]);
                result.data[i] = sum;
            }
            result.dataLength = maxLength;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            return result;
        }
        /// <summary>
        /// 按位 XOR 运算符的重载(异或运算)
        /// </summary>
        /// <param name="bi1"></param>
        /// <param name="bi2"></param>
        /// <returns>返回bi1与bi2进行异或逻辑运算的结果</returns>
        public static BigInteger operator ^(BigInteger bi1, BigInteger bi2)
        {
            BigInteger result = new BigInteger();
            int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
            for (int i = 0; i < len; i++)
            {
                uint sum = (uint)(bi1.data[i] ^ bi2.data[i]);
                result.data[i] = sum;
            }
            result.dataLength = maxLength;
            while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0)
                result.dataLength--;
            return result;
        }
        /// <summary>
        /// 求 BigInteger 的绝对值
        /// </summary>
        /// <returns>返回 BigInteger 的绝对值</returns>
        public BigInteger Abs()
        {
            if ((this.data[maxLength - 1] & 0x80000000) != 0)
                return (-this);
            else
                return (new BigInteger(this));
        }
        /// <summary>
        ///  返回一个字符串,表示符号和大小的 BigInteger 在10进制数格式.
        /// </summary>
        /// <returns>表示符号和大小的 BigInteger 在10进制数格式</returns>
        public override string ToString()
        {
            return ToString(10);
        }
        /// <summary>
        /// 返回一个字符串, 表示符号和大小的 BigInteger指定进制数的格式.
        /// </summary>
        /// <param name="radix">进制数2-36</param>
        /// <returns>
        ///如果 BigInteger 的值在 10进制 中为-255, 则ToString (16) 返回 "-FF"
        ///</returns>
        public string ToString(int radix)
        {
            if (radix < 2 || radix > 36)
                throw (new ArgumentException("进制数需 >= 2 和 <= 36"));
            string charSet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
            string result = "";
            BigInteger a = this;
            bool negative = false;
            if ((a.data[maxLength - 1] & 0x80000000) != 0)
            {
                negative = true;
                try
                {
                    a = -a;
                }
                catch (Exception) { }
            }
            BigInteger quotient = new BigInteger();
            BigInteger remainder = new BigInteger();
            BigInteger biRadix = new BigInteger(radix);
            if (a.dataLength == 1 && a.data[0] == 0)
                result = "0";
            else
            {
                while (a.dataLength > 1 || (a.dataLength == 1 && a.data[0] != 0))
                {
                    SingleByteDivide(a, biRadix, quotient, remainder);
                    if (remainder.data[0] < 10)
                        result = remainder.data[0] + result;
                    else
                        result = charSet[(int)remainder.data[0] - 10] + result;
                    a = quotient;
                }
                if (negative)
                    result = "-" + result;
            }
            return result;
        }
        /// <summary>
        /// 返回BigInteger的十六进制字符串
        /// </summary>
        /// <returns>
        /// 1) 如果 BigInteger 的值为255在 10进制 中, 则ToHexString () 返回 "FF"
        /// 2) 如果 BigInteger 的值为-255 在 10进制 中, 则ToHexString () 返回 "..。FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01 ",这是2的补语表示-255。
        /// </returns>
        public string ToHexString()
        {
            string result = data[dataLength - 1].ToString("X");
            for (int i = dataLength - 2; i >= 0; i--)
            {
                result += data[i].ToString("X8");
            }
            return result;
        }
        /// <summary>
        /// 利用Barrett's还原法快速计算模块化复位。需要 x 小于b ^ (2 k), 其中 b 是基数。 在这种情况下, 基是2 ^ 32 (uint)。
        /// </summary>
        /// <param name="x"></param>
        /// <param name="n"></param>
        /// <param name="constant"></param>
        /// <returns></returns>
        private BigInteger BarrettReduction(BigInteger x, BigInteger n, BigInteger constant)
        {
            int k = n.dataLength, kPlusOne = k + 1, kMinusOne = k - 1;
            BigInteger q1 = new BigInteger();
            for (int i = kMinusOne, j = 0; i < x.dataLength; i++, j++)
                q1.data[j] = x.data[i];
            q1.dataLength = x.dataLength - kMinusOne;
            if (q1.dataLength <= 0)
                q1.dataLength = 1;
            BigInteger q2 = q1 * constant;
            BigInteger q3 = new BigInteger();
            for (int i = kPlusOne, j = 0; i < q2.dataLength; i++, j++)
                q3.data[j] = q2.data[i];
            q3.dataLength = q2.dataLength - kPlusOne;
            if (q3.dataLength <= 0)
                q3.dataLength = 1;
            BigInteger r1 = new BigInteger();
            int lengthToCopy = (x.dataLength > kPlusOne) ? kPlusOne : x.dataLength;
            for (int i = 0; i < lengthToCopy; i++)
                r1.data[i] = x.data[i];
            r1.dataLength = lengthToCopy;
            BigInteger r2 = new BigInteger();
            for (int i = 0; i < q3.dataLength; i++)
            {
                if (q3.data[i] == 0)
                    continue;
                ulong mcarry = 0;
                int t = i;
                for (int j = 0; j < n.dataLength && t < kPlusOne; j++, t++)
                {
                    ulong val = ((ulong)q3.data[i] * (ulong)n.data[j]) + (ulong)r2.data[t] + mcarry;
                    r2.data[t] = (uint)(val & 0xFFFFFFFF);
                    mcarry = (val >> 32);
                }
                if (t < kPlusOne)
                    r2.data[t] = (uint)mcarry;
            }
            r2.dataLength = kPlusOne;
            while (r2.dataLength > 1 && r2.data[r2.dataLength - 1] == 0)
                r2.dataLength--;
            r1 -= r2;
            if ((r1.data[maxLength - 1] & 0x80000000) != 0)
            {
                BigInteger val = new BigInteger();
                val.data[kPlusOne] = 0x00000001;
                val.dataLength = kPlusOne + 1;
                r1 += val;
            }
            while (r1 >= n)
                r1 -= n;
            return r1;
        }
        /// <summary>
        /// 返回 BigInteger 中最重要位的位置。
        /// 结果为 0, 如果 BigInteger 的值为 0... 0000 0000
        /// 结果为 1, 如果 BigInteger 的值为 0... 0000 0001
        /// 结果为 2, 如果 BigInteger 的值为 0... 0000 0010
        /// 结果为 3, 如果 BigInteger 的值为 0... 0000 0011
        /// </summary>
        /// <returns></returns>
        public int BitCount()
        {
            while (dataLength > 1 && data[dataLength - 1] == 0)
                dataLength--;
            uint value = data[dataLength - 1];
            uint mask = 0x80000000;
            int bits = 32;
            while (bits > 0 && (value & mask) == 0)
            {
                bits--;
                mask >>= 1;
            }
            bits += ((dataLength - 1) << 5);
            return bits;
        }
        /// <summary>
        /// 计算当前BigInteger的平方根
        /// </summary>
        /// <returns>返回一个等效于 BigInteger 的整数平方根的值。</returns>
        public BigInteger Sqrt()
        {
            uint numBits = (uint)this.BitCount();
            if ((numBits & 0x1) != 0)
                numBits = (numBits >> 1) + 1;
            else
                numBits = (numBits >> 1);
            uint bytePos = numBits >> 5;
            byte bitPos = (byte)(numBits & 0x1F);
            uint mask;
            BigInteger result = new BigInteger();
            if (bitPos == 0)
                mask = 0x80000000;
            else
            {
                mask = (uint)1 << bitPos;
                bytePos++;
            }
            result.dataLength = (int)bytePos;
            for (int i = (int)bytePos - 1; i >= 0; i--)
            {
                while (mask != 0)
                {
                    result.data[i] ^= mask;
                    if ((result * result) > this)
                        result.data[i] ^= mask;
                    mask >>= 1;
                }
                mask = 0x80000000;
            }
            return result;
        }
    }
}

本文作者：Joe_du

本文链接：https://www.cnblogs.com/dygood/p/12937689.html

版权声明：本作品采用 MIT License 许可协议进行许可。

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