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.
https://msdn.microsoft.com/zh-cn/library/system.numerics.biginteger(v=vs.110).aspx
/// <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; } } }