static BigInteger GetNextFactorial(BigInteger thisFactorial, ref BigInteger lastFactorial) { BigInteger tmp = thisFactorial; BigInteger result = thisFactorial + lastFactorial; lastFactorial = tmp; return result; }
public static BigInteger Factorial(int num) { BigInteger bi = new BigInteger(1); for(int i=1;i<=num;i++) bi *= i; return bi; }
public static BigInteger CombinatoricsShortFactorial(int numerator, int highestDenom) { if (highestDenom > numerator) throw new ArgumentException("'highestDenom' has to be less than or equal to 'numerator' "); BigInteger bi = new BigInteger(1); for (int i = numerator; i > highestDenom; i--) bi *= i; return bi; }
public static string GetSequence(int num, int denom) { int decimalsOfPrecision = denom * 2; decimalsOfPrecision = Math.Max(5, decimalsOfPrecision); BigInteger offset = new BigInteger("1" + Repeat('0', decimalsOfPrecision),10); // use offset to get n decimals of precision BigInteger fraction = offset * num / denom; string unitFraction = fraction.ToString(); unitFraction = Repeat('0', decimalsOfPrecision - unitFraction.Length) + unitFraction; string sequence = GetRepeatingElement(unitFraction); return (sequence == "0") ? "" : sequence; }
static void GetIteration(int numIters, ref BigInteger numer, ref BigInteger denom) { // if numIterations == 1 then, send back what they sent! BigInteger swap = 0; for(int a = 1; a < numIters; a++) { numer = 2 * denom + numer; //denom = denom; swap = denom; denom = numer; numer = swap; } //MyMath.ReduceFraction(ref numer, ref denom); }
public static void OldSolve(int numZeros) { BigInteger notBouncy = 0; BigInteger max = BigInteger.Pow(10, numZeros); for (BigInteger num = 1; num < max; ) { int bouncedAtIdx = 0; char lastChar, thisChar; string numStr = num.ToString(); if (MiscFunctions.IsBouncy(numStr, out bouncedAtIdx, out thisChar, out lastChar)) { // go ahead and fastforward to next possible non-bouncy number int len = numStr.Length; string topSide, repeater; if (thisChar > lastChar) { // was supposed to be going down, so next char needs to be smaller // num=9624 // AtIdx = 3, lastChar = 2, thisChar = 4 // increment the top part to 963 and put 0's the rest of the way out // giving 9630 BigInteger topSideBi = new BigInteger(numStr.Substring(0, bouncedAtIdx), 10); topSideBi++; topSide = topSideBi.ToString(); repeater = new string('0', len - bouncedAtIdx); } else { //if (bouncedAtIdx + 1 == len) continue; // it's at the 1s digit // was supposed to be going up. So next set of chars need to be the lowest value going up // num = 1240 // AtIdx = 3, lastChar = 4, thisChar = 0 // next char will be all 4's starting after position 3. // giving 124 + 4 being 1244 topSide = numStr.Substring(0, bouncedAtIdx); repeater = new string(lastChar, len - bouncedAtIdx); } num = new BigInteger(topSide + repeater, 10); } else { notBouncy++; num++; } } Console.WriteLine("For {0} {1}", max, notBouncy); }
private static bool WellBalanced(BigInteger bi) { char[] digits = bi.ToString().ToCharArray(); int midIdx = (int)Math.Ceiling(digits.Length/(double) 2) - 1; int maxIdx = digits.Length - 1; int left = 0; int right = 0; //int idxLeft = midIdx; //int idxRight = digits.Length - midIdx - 1; for (int i = 0; i <= midIdx ;i++ ) { left += (int)digits[i]; right += (int)digits[maxIdx - i]; } return left==right; }
public static bool IsPrime(BigInteger number) { if (number <= 1) return false; if (number <= 3) return true; BigInteger max = 1 + number.sqrt(); for (BigInteger den = 2; den <= max; den++) { if ((number % den) == 0) { return false; } } return true; }
private void BuildTriangle() { values = new BigInteger[_numRows + 1][]; values[0] = new BigInteger[] { 1 }; values[1] = new BigInteger[] { 1, 1 }; //row num is rowIdx + 1 for (int rowIdx = 2; rowIdx <= _numRows; rowIdx++) { // build the new row values[rowIdx] = new BigInteger[rowIdx+1]; values[rowIdx][0] = 1; values[rowIdx][rowIdx] = 1; int midPoint = rowIdx/2; for (int col = 1; col <= midPoint; col++) { values[rowIdx][col] = values[rowIdx-1][col - 1] + values[rowIdx-1][col]; values[rowIdx][rowIdx - col] = values[rowIdx][col]; } } }
public static string GetSequence(BigInteger num, BigInteger denom) { Console.WriteLine("\tBEFORE {0} {1}", num,denom); MyMath.ReduceFraction(ref num, ref denom); Console.WriteLine("\tAFTER {0} {1}", num, denom); return ""; int decimalsOfPrecision = 0; Int32.TryParse(denom.ToString(),out decimalsOfPrecision); decimalsOfPrecision *= 2; decimalsOfPrecision = Math.Max(5, decimalsOfPrecision); //BigInteger offset = BigInteger.Parse("1" + Repeat('0', decimalsOfPrecision)); // use offset to get n decimals of precision BigInteger offset = BigInteger.Pow(10, decimalsOfPrecision); Console.WriteLine("decimalsOfPrecision={0}", decimalsOfPrecision); BigInteger fraction = offset * num / denom; string unitFraction = fraction.ToString(); unitFraction = Repeat('0', decimalsOfPrecision - unitFraction.Length) + unitFraction; string sequence = GetRepeatingElement(unitFraction); return (sequence=="0")?"":sequence; }
/// <summary> /// Tests the correct implementation of the /, %, * and + operators /// </summary> /// <param name="rounds">The rounds.</param> public static void MulDivTest(int rounds) { Random rand = new Random(); byte[] val = new byte[64]; byte[] val2 = new byte[64]; for (int count = 0; count < rounds; count++) { // generate 2 numbers of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 65); int t2 = 0; while (t2 == 0) t2 = (int)(rand.NextDouble() * 65); bool done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t1) val[i] = (byte)(rand.NextDouble() * 256); else val[i] = 0; if (val[i] != 0) done = true; } } done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t2) val2[i] = (byte)(rand.NextDouble() * 256); else val2[i] = 0; if (val2[i] != 0) done = true; } } while (val[0] == 0) val[0] = (byte)(rand.NextDouble() * 256); while (val2[0] == 0) val2[0] = (byte)(rand.NextDouble() * 256); Console.WriteLine(count); BigInteger bn1 = new BigInteger(val, t1); BigInteger bn2 = new BigInteger(val2, t2); // Determine the quotient and remainder by dividing // the first number by the second. BigInteger bn3 = bn1 / bn2; BigInteger bn4 = bn1 % bn2; // Recalculate the number BigInteger bn5 = (bn3 * bn2) + bn4; // Make sure they're the same if (bn5 != bn1) { Console.WriteLine("Error at " + count); Console.WriteLine(bn1 + "\n"); Console.WriteLine(bn2 + "\n"); Console.WriteLine(bn3 + "\n"); Console.WriteLine(bn4 + "\n"); Console.WriteLine(bn5 + "\n"); return; } } }
/// <summary> /// Tests the correct implementation of the modulo exponential function /// using RSA encryption and decryption (using pre-computed encryption and /// decryption keys). /// </summary> /// <param name="rounds">The rounds.</param> public static void RSATest(int rounds) { Random rand = new Random(1); byte[] val = new byte[64]; // private and public key BigInteger bi_e = new BigInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", 16); BigInteger bi_d = new BigInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", 16); BigInteger bi_n = new BigInteger("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f", 16); Console.WriteLine("e =\n" + bi_e.ToString(10)); Console.WriteLine("\nd =\n" + bi_d.ToString(10)); Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n"); for (int count = 0; count < rounds; count++) { // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 65); bool done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t1) val[i] = (byte)(rand.NextDouble() * 256); else val[i] = 0; if (val[i] != 0) done = true; } } while (val[0] == 0) val[0] = (byte)(rand.NextDouble() * 256); Console.Write("Round = " + count); // encrypt and decrypt data BigInteger bi_data = new BigInteger(val, t1); BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n); BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n); // compare if (bi_decrypted != bi_data) { Console.WriteLine("\nError at round " + count); Console.WriteLine(bi_data + "\n"); return; } Console.WriteLine(" <PASSED>."); } }
//root function public BigInteger root(int order) { uint numBits = (uint)this.bitCount(); if ((numBits & 0x1) != 0) // odd number of bits 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) { // guess result.data[i] ^= mask; // undo the guess if its square is larger than this if ((result.Pow(order)) > this) result.data[i] ^= mask; mask >>= 1; } mask = 0x80000000; } return result; }
/// <summary> /// Overloading of the NOT operator (1's complement) /// </summary> /// <param name="bi1">The bi1.</param> /// <returns>The result of the operator.</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> /// Overloading of unary << operators /// </summary> /// <param name="bi1">The bi1.</param> /// <param name="shiftVal">The shift val.</param> /// <returns>The result of the operator.</returns> public static BigInteger operator <<(BigInteger bi1, int shiftVal) { BigInteger result = new BigInteger(bi1); result.dataLength = shiftLeft(result.data, shiftVal); return result; }
/// <summary> /// Implements the operator --. /// </summary> /// <param name="bi1">The bi1.</param> /// <returns>The result of the operator.</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--; // overflow check int lastPos = maxLength - 1; // overflow if initial value was -ve but -- caused a sign // change to positive. if ((bi1.data[lastPos] & 0x80000000) != 0 && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException("Underflow in --.")); } return result; }
/// <summary> /// Implements the operator ++. /// </summary> /// <param name="bi1">The bi1.</param> /// <returns>The result of the operator.</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--; } // overflow check int lastPos = maxLength - 1; // overflow if initial value was +ve but ++ caused a sign // change to negative. if ((bi1.data[lastPos] & 0x80000000) == 0 && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException("Overflow in ++.")); } return result; }
/// <summary> /// Tests the correct implementation of sqrt() method. /// </summary> /// <param name="rounds">The rounds.</param> public static void SqrtTest(int rounds) { Random rand = new Random(); for (int count = 0; count < rounds; count++) { // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 1024); Console.Write("Round = " + count); BigInteger a = new BigInteger(); a.genRandomBits(t1, rand); BigInteger b = a.sqrt(); BigInteger c = (b + 1) * (b + 1); // check that b is the largest integer such that b*b <= a if (c <= a) { Console.WriteLine("\nError at round " + count); Console.WriteLine(a + "\n"); return; } Console.WriteLine(" <PASSED>."); } }
/// <summary> /// Tests the correct implementation of the modulo exponential and /// inverse modulo functions using RSA encryption and decryption. The two /// pseudoprimes p and q are fixed, but the two RSA keys are generated /// for each round of testing. /// </summary> /// <param name="rounds">The rounds.</param> public static void RSATest2(int rounds) { Random rand = new Random(); byte[] val = new byte[64]; byte[] pseudoPrime1 = { (byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A, (byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C, (byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3, (byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41, (byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56, (byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE, (byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41, (byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA, (byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF, (byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D, (byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3, }; byte[] pseudoPrime2 = { (byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7, (byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E, (byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3, (byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93, (byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF, (byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20, (byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8, (byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F, (byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C, (byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80, (byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB, }; BigInteger bi_p = new BigInteger(pseudoPrime1); BigInteger bi_q = new BigInteger(pseudoPrime2); BigInteger bi_pq = (bi_p - 1) * (bi_q - 1); BigInteger bi_n = bi_p * bi_q; for (int count = 0; count < rounds; count++) { // generate private and public key BigInteger bi_e = bi_pq.genCoPrime(512, rand); BigInteger bi_d = bi_e.modInverse(bi_pq); Console.WriteLine("\ne =\n" + bi_e.ToString(10)); Console.WriteLine("\nd =\n" + bi_d.ToString(10)); Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n"); // generate data of random length int t1 = 0; while (t1 == 0) t1 = (int)(rand.NextDouble() * 65); bool done = false; while (!done) { for (int i = 0; i < 64; i++) { if (i < t1) val[i] = (byte)(rand.NextDouble() * 256); else val[i] = 0; if (val[i] != 0) done = true; } } while (val[0] == 0) val[0] = (byte)(rand.NextDouble() * 256); Console.Write("Round = " + count); // encrypt and decrypt data BigInteger bi_data = new BigInteger(val, t1); BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n); BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n); // compare if (bi_decrypted != bi_data) { Console.WriteLine("\nError at round " + count); Console.WriteLine(bi_data + "\n"); return; } Console.WriteLine(" <PASSED>."); } }
/// <summary> ///Returns the k_th number in the Lucas Sequence reduced modulo n. /// /// Uses index doubling to speed up the process. For example, to calculate V(k), /// we maintain two numbers in the sequence V(n) and V(n+1). /// /// To obtain V(2n), we use the identity /// V(2n) = (V(n) * V(n)) - (2 * Q^n) /// To obtain V(2n+1), we first write it as /// V(2n+1) = V((n+1) + n) /// and use the identity /// V(m+n) = V(m) * V(n) - Q * V(m-n) /// Hence, /// V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n) /// = V(n+1) * V(n) - Q^n * V(1) /// = V(n+1) * V(n) - Q^n * P /// /// We use k in its binary expansion and perform index doubling for each /// bit position. For each bit position that is set, we perform an /// index doubling followed by an index addition. This means that for V(n), /// we need to update it to V(2n+1). For V(n+1), we need to update it to /// V((2n+1)+1) = V(2*(n+1)) /// /// This function returns /// [0] = U(k) /// [1] = V(k) /// [2] = Q^n /// /// Where U(0) = 0 % n, U(1) = 1 % n /// V(0) = 2 % n, V(1) = P % n /// </summary> /// <param name="P">The P.</param> /// <param name="Q">The Q.</param> /// <param name="k">The k.</param> /// <param name="n">The n.</param> /// <returns></returns> public static BigInteger[] LucasSequence(BigInteger P, BigInteger Q, BigInteger k, BigInteger n) { if (k.dataLength == 1 && k.data[0] == 0) { BigInteger[] result = new BigInteger[3]; result[0] = 0; result[1] = 2 % n; result[2] = 1 % n; return result; } // calculate constant = b^(2k) / m // for Barrett Reduction BigInteger constant = new BigInteger(); int nLen = n.dataLength << 1; constant.data[nLen] = 0x00000001; constant.dataLength = nLen + 1; constant = constant / n; // calculate values of s and t int s = 0; for (int index = 0; index < k.dataLength; index++) { uint mask = 0x01; for (int i = 0; i < 32; i++) { if ((k.data[index] & mask) != 0) { index = k.dataLength; // to break the outer loop break; } mask <<= 1; s++; } } BigInteger t = k >> s; //Console.WriteLine("s = " + s + " t = " + t); return LucasSequenceHelper(P, Q, t, n, constant, s); }
/// <summary> /// Implements the operator +. /// </summary> /// <param name="bi1">The bi1.</param> /// <param name="bi2">The bi2.</param> /// <returns>The result of the operator.</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--; // overflow check int lastPos = maxLength - 1; if ((bi1.data[lastPos] & 0x80000000) == (bi2.data[lastPos] & 0x80000000) && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException()); } return result; }
/// <summary> /// Performs the calculation of the kth term in the Lucas Sequence. /// For details of the algorithm, see reference [9]. /// k must be odd. i.e LSB == 1 /// </summary> /// <param name="P">The P.</param> /// <param name="Q">The Q.</param> /// <param name="k">The k.</param> /// <param name="n">The n.</param> /// <param name="constant">The constant.</param> /// <param name="s">The s.</param> /// <returns></returns> private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q, BigInteger k, BigInteger n, BigInteger constant, int s) { BigInteger[] result = new BigInteger[3]; if ((k.data[0] & 0x00000001) == 0) throw (new ArgumentException("Argument k must be odd.")); int numbits = k.bitCount(); uint mask = (uint)0x1 << ((numbits & 0x1F) - 1); // v = v0, v1 = v1, u1 = u1, Q_k = Q^0 BigInteger v = 2 % n, Q_k = 1 % n, v1 = P % n, u1 = Q_k; bool flag = true; for (int i = k.dataLength - 1; i >= 0; i--) // iterate on the binary expansion of k { //Console.WriteLine("round"); while (mask != 0) { if (i == 0 && mask == 0x00000001) // last bit break; if ((k.data[i] & mask) != 0) // bit is set { // index doubling with addition u1 = (u1 * v1) % n; v = ((v * v1) - (P * Q_k)) % n; v1 = n.BarrettReduction(v1 * v1, n, constant); v1 = (v1 - ((Q_k * Q) << 1)) % n; if (flag) flag = false; else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); Q_k = (Q_k * Q) % n; } else { // index doubling u1 = ((u1 * v) - Q_k) % n; v1 = ((v * v1) - (P * Q_k)) % n; v = n.BarrettReduction(v * v, n, constant); v = (v - (Q_k << 1)) % n; if (flag) { Q_k = Q % n; flag = false; } else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); } mask >>= 1; } mask = 0x80000000; } // at this point u1 = u(n+1) and v = v(n) // since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1) u1 = ((u1 * v) - Q_k) % n; v = ((v * v1) - (P * Q_k)) % n; if (flag) flag = false; else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); Q_k = (Q_k * Q) % n; for (int i = 0; i < s; i++) { // index doubling u1 = (u1 * v) % n; v = ((v * v) - (Q_k << 1)) % n; if (flag) { Q_k = Q % n; flag = false; } else Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); } result[0] = u1; result[1] = v; result[2] = Q_k; return result; }
/// <summary> /// Implements the operator -. /// </summary> /// <param name="bi1">The bi1.</param> /// <param name="bi2">The bi2.</param> /// <returns>The result of the operator.</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; } // roll over to negative if (carryIn != 0) { for (int i = result.dataLength; i < maxLength; i++) result.data[i] = 0xFFFFFFFF; result.dataLength = maxLength; } // fixed in v1.03 to give correct datalength for a - (-b) while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; // overflow check int lastPos = maxLength - 1; if ((bi1.data[lastPos] & 0x80000000) != (bi2.data[lastPos] & 0x80000000) && (result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000)) { throw (new ArithmeticException()); } return result; }
/// <summary> /// Raises the current number to the power specified. /// </summary> /// <param name="number">The number to be raised.</param> /// <param name="raisedTo">The power to be raised to.</param> /// <returns> /// A BigInteger representing this raised to a power /// </returns> public static BigInteger Pow(BigInteger number, BigInteger raisedTo) { return number.Pow(raisedTo); }
/// <summary> /// Implements the operator *. /// </summary> /// <param name="bi1">The bi1.</param> /// <param name="bi2">The bi2.</param> /// <returns>The result of the operator.</returns> public static BigInteger operator *(BigInteger bi1, BigInteger bi2) { int lastPos = maxLength - 1; bool bi1Neg = false, bi2Neg = false; // take the absolute value of the inputs try { if ((bi1.data[lastPos] & 0x80000000) != 0) // bi1 negative { bi1Neg = true; bi1 = -bi1; } if ((bi2.data[lastPos] & 0x80000000) != 0) // bi2 negative { bi2Neg = true; bi2 = -bi2; } } catch (Exception) { } BigInteger result = new BigInteger(); // multiply the absolute values 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++) { // k = i + j 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("Multiplication overflow.")); } 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--; // overflow check (result is -ve) if ((result.data[lastPos] & 0x80000000) != 0) { if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000) // different sign { // handle the special case where multiplication produces // a max negative number in 2's complement. 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("Multiplication overflow.")); } // if input has different signs, then result is -ve if (bi1Neg != bi2Neg) return -result; return result; }
public BigInteger Pow(BigInteger exp) { return power(this, exp); }
/// <summary> /// Overloading of unary >> operators /// </summary> /// <param name="bi1">The bi1.</param> /// <param name="shiftVal">The shift val.</param> /// <returns>The result of the operator.</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) // negative { 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 BigInteger power(BigInteger number, BigInteger exponent) { if (exponent == 0) return 1; if (exponent == 1) return number; if (exponent % 2 == 0) return square(power(number, exponent / 2)); else return number * square(power(number, (exponent - 1) / 2)); }
/// <summary> /// Implements the operator -. /// </summary> /// <param name="bi1">The bi1.</param> /// <returns>The result of the operator.</returns> public static BigInteger operator -(BigInteger bi1) { // handle neg of zero separately since it'll cause an overflow // if we proceed. if (bi1.dataLength == 1 && bi1.data[0] == 0) return (new BigInteger()); BigInteger result = new BigInteger(bi1); // 1's complement for (int i = 0; i < maxLength; i++) result.data[i] = (uint)(~(bi1.data[i])); // add one to result of 1's complement 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("Overflow in negation.\n")); result.dataLength = maxLength; while (result.dataLength > 1 && result.data[result.dataLength - 1] == 0) result.dataLength--; return result; }
private static BigInteger square(BigInteger num) { return num * num; }