public void DivideSingleByte(BigInteger bi2)
{
int resultPos = 0;
ulong divisor = (ulong)bi2.Data[0];
int pos = Length - 1;
ulong dividend = (ulong)Data[pos];
var remainder = new BigInteger(this);
if (dividend >= divisor)
{
ulong quotient = dividend / divisor;
Data[resultPos++] = (uint)quotient;
remainder.Data[pos] = (uint)(dividend % divisor);
}
pos--;
while (pos >= 0)
{
//Console.WriteLine(pos);
dividend = ((ulong)remainder.Data[pos + 1] << 32) + (ulong)remainder.Data[pos];
ulong quotient = dividend / divisor;
Data[resultPos++] = (uint)quotient;
remainder.Data[pos + 1] = 0;
remainder.Data[pos--] = (uint)(dividend % divisor);
//Console.WriteLine(">>>> " + bi1);
}
Length = resultPos;
remainder.Recycle();
}
public void DivideMultiByte(BigInteger bi2)
{
int remainderLen = Length + 1;
uint mask = 0x80000000;
uint val = bi2.Data[bi2.Length - 1];
int shift = 0, resultPos = 0;
while (mask != 0 && (val & mask) == 0)
{
shift++; mask >>= 1;
}
var remainder = new BigInteger(this)
{
Length = remainderLen
};
shiftLeft(remainder.Data, shift);
bi2 = bi2 << shift;
int j = remainderLen - bi2.Length;
int pos = remainderLen - 1;
ulong firstDivisorByte = bi2.Data[bi2.Length - 1];
ulong secondDivisorByte = bi2.Data[bi2.Length - 2];
int divisorLen = bi2.Length + 1;
var kk = new BigInteger(0)
{
Length = divisorLen
};
var ss = new BigInteger(0);
while (j > 0)
{
ulong dividend = ((ulong)remainder.Data[pos] << 32) + (ulong)remainder.Data[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.Data[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
{
done = false;
}
}
}
kk.Length = divisorLen;
Array.Copy(remainder.Data, pos - divisorLen + 1, kk.Data, 0, divisorLen);
while (kk.Length > 1 && kk.Data[kk.Length - 1] == 0)
{
kk.Length--;
}
// BigInteger ss = bi2 * (long)q_hat;
Multiply(bi2, q_hat, ref ss);
while (ss > kk)
{
q_hat--;
ss.Subtract(bi2);
}
kk.Subtract(ss);
Array.Copy(kk.Data, 0, remainder.Data, pos - divisorLen + 1, divisorLen);
Data[resultPos++] = (uint)q_hat;
pos--;
j--;
}
Length = resultPos;
Array.Reverse(Data, 0, Length);
Array.Clear(Data, Length, maxLength - Length);
while (Length > 1 && Data[Length - 1] == 0)
{
Length--;
}
if (Length == 0)
{
Length = 1;
}
kk.Recycle();
ss.Recycle();
remainder.Recycle();
}
//***********************************************************************
// Fast calculation of modular reduction using Barrett's reduction.
// Requires x < b^(2k), where b is the base. In this case, base is
// 2^32 (uint).
//
// Reference [4]
//***********************************************************************
private void BarrettReduction(ref BigInteger x1, BigInteger x2, BigInteger n, BigInteger constant, ref BigInteger temp)
{
Multiply(x1, x2, ref temp);
int k = n.Length,
kPlusOne = k + 1,
kMinusOne = k - 1;
//var q1 = new BigInteger(0);
//// q1 = x / b^(k-1)
//for (int i = kMinusOne, j = 0; i < x.Length; i++, j++)
// q1.Data[j] = x.Data[i];
//q1.Length = x.Length - kMinusOne;
//if(q1.Length <= 0)
// q1.Length = 1;
//var q2 = q1 * constant;
//q1.Recycle();
//q1 = q2;
var q1 = new BigIntegerShell(temp, kMinusOne, temp.Length - kMinusOne) * constant;
// r1 = x mod b^(k+1)
// i.e. keep the lowest (k+1) words
//var r1 = new BigInteger(0);
//int lengthToCopy = (x.Length > kPlusOne) ? kPlusOne : x.Length;
temp.Length = (temp.Length > kPlusOne) ? kPlusOne : temp.Length;
//for(int i = 0; i < lengthToCopy; i++)
// r1.Data[i] = x.Data[i];
//r1.Length = lengthToCopy;
// r2 = (q3 * n) mod b^(k+1)
// partial multiplication of q3 and n
var r2 = new BigInteger(0);
for (int i = kPlusOne; i < q1.Length; i++)
{
if (q1.Data[i] == 0)
{
continue;
}
ulong mcarry = 0;
int t = i - kPlusOne;
for (int j = 0; j < n.Length && t < kPlusOne; j++, t++)
{
// t = i + j
ulong val = (q1.Data[i] * (ulong)n.Data[j]) +
r2.Data[t] + mcarry;
r2.Data[t] = (uint)val;
mcarry = (val >> 32);
}
if (t < kPlusOne)
{
r2.Data[t] = (uint)mcarry;
}
}
r2.Length = kPlusOne;
while (r2.Length > 1 && r2.Data[r2.Length - 1] == 0)
{
r2.Length--;
}
temp.Subtract(r2);
r2.Recycle();
if ((temp.Data[maxLength - 1] & 0x80000000) != 0) // negative
{
ulong carry = 1;
for (var i = kPlusOne; carry != 0 && i < maxLength; i++)
{
var sum = temp.Data[i] + carry;
carry = sum >> 32;
temp.Data[i] = (uint)sum;
}
}
while (temp >= n)
{
temp.Subtract(n);
}
q1.Recycle();
q1 = temp;
temp = x1;
x1 = q1;
}
//***********************************************************************
// Modulo Exponentiation
//***********************************************************************
public BigInteger ModPow(BigInteger exp, BigInteger n)
{
if ((exp.Data[maxLength - 1] & 0x80000000) != 0)
{
throw (new ArithmeticException("Positive exponents only."));
}
BigInteger resultNum = 1;
BigInteger tempNum;
bool thisNegative = false;
if ((this.Data[maxLength - 1] & 0x80000000) != 0) // negative this
{
tempNum = -this % n;
thisNegative = true;
}
else
{
tempNum = this % n; // ensures (tempNum * tempNum) < b^(2k)
}
if ((n.Data[maxLength - 1] & 0x80000000) != 0) // negative n
{
n = -n;
}
// calculate constant = b^(2k) / m
var constant = new BigInteger(0);
int i = n.Length << 1;
constant.Data[i] = 0x00000001;
constant.Length = i + 1;
constant.Divide(n);
//constant /= n;
int totalBits = exp.bitCount();
int count = 0;
var temp = new BigInteger(0);
// perform squaring and multiply exponentiation
for (var pos = 0; pos < exp.Length; pos++)
{
uint mask = 0x01;
//Console.WriteLine("pos = " + pos);
for (var index = 0; index < 32; index++)
{
if ((exp.Data[pos] & mask) != 0)
{
BarrettReduction(ref resultNum, tempNum, n, constant, ref temp);
}
mask <<= 1;
BarrettReduction(ref tempNum, tempNum, n, constant, ref temp);
if (tempNum.Length == 1 && tempNum.Data[0] == 1)
{
if (thisNegative && (exp.Data[0] & 0x1) != 0) //odd exp
{
resultNum.Negative();
}
return(resultNum);
}
count++;
if (count == totalBits)
{
break;
}
}
}
constant.Recycle();
temp.Recycle();
if (thisNegative && (exp.Data[0] & 0x1) != 0) //odd exp
{
resultNum.Negative();
}
return(resultNum);
}
public BigInteger GetRemainderMultiByte(BigInteger bi2)
{
var remainder = new BigInteger(this);
remainder.Length++;
uint mask = 0x80000000;
uint val = bi2.Data[bi2.Length - 1];
int shift = 0;
while (mask != 0 && (val & mask) == 0)
{
shift++; mask >>= 1;
}
shiftLeft(remainder.Data, shift);
bi2 = bi2 << shift;
int j = remainder.Length - bi2.Length;
int pos = remainder.Length - 1;
ulong firstDivisorByte = bi2.Data[bi2.Length - 1];
ulong secondDivisorByte = bi2.Data[bi2.Length - 2];
int divisorLen = bi2.Length + 1;
var kk = new BigInteger(0)
{
Length = divisorLen
};
var ss = new BigInteger(0);
while (j > 0)
{
ulong dividend = ((ulong)remainder.Data[pos] << 32) + (ulong)remainder.Data[pos - 1];
//Console.WriteLine("dividend = {0}", dividend);
ulong q_hat = dividend / firstDivisorByte;
ulong r_hat = dividend % firstDivisorByte;
//Console.WriteLine("q_hat = {0:X}, r_hat = {1:X}", q_hat, r_hat);
bool done = false;
while (!done)
{
done = true;
if (q_hat == 0x100000000 ||
(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder.Data[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
{
done = false;
}
}
}
kk.Length = divisorLen;
Array.Copy(remainder.Data, pos - divisorLen + 1, kk.Data, 0, divisorLen);
while (kk.Length > 1 && kk.Data[kk.Length - 1] == 0)
{
kk.Length--;
}
//var ss = bi2 * (long)q_hat;
Multiply(bi2, q_hat, ref ss);
while (ss > kk)
{
q_hat--;
ss.Subtract(bi2);
}
kk.Subtract(ss);
Array.Copy(kk.Data, 0, remainder.Data, pos - divisorLen + 1, divisorLen);
pos--;
j--;
}
ss.Recycle();
kk.Recycle();
remainder.Length = shiftRight(remainder.Data, shift);
return(remainder);
}
public void DivideSingleByte(BigInteger bi2)
{
int resultPos = 0;
ulong divisor = (ulong)bi2.Data[0];
int pos = Length - 1;
ulong dividend = (ulong)Data[pos];
var remainder = new BigInteger(this);
if (dividend >= divisor)
{
ulong quotient = dividend / divisor;
Data[resultPos++] = (uint)quotient;
remainder.Data[pos] = (uint)(dividend % divisor);
}
pos--;
while (pos >= 0)
{
//Console.WriteLine(pos);
dividend = ((ulong)remainder.Data[pos + 1] << 32) + (ulong)remainder.Data[pos];
ulong quotient = dividend / divisor;
Data[resultPos++] = (uint)quotient;
remainder.Data[pos + 1] = 0;
remainder.Data[pos--] = (uint)(dividend % divisor);
//Console.WriteLine(">>>> " + bi1);
}
Length = resultPos;
remainder.Recycle();
}
public BigInteger GetRemainderMultiByte(BigInteger bi2)
{
var remainder = new BigInteger(this);
remainder.Length++;
uint mask = 0x80000000;
uint val = bi2.Data[bi2.Length - 1];
int shift = 0;
while (mask != 0 && (val & mask) == 0)
{
shift++; mask >>= 1;
}
shiftLeft(remainder.Data, shift);
bi2 = bi2 << shift;
int j = remainder.Length - bi2.Length;
int pos = remainder.Length - 1;
ulong firstDivisorByte = bi2.Data[bi2.Length - 1];
ulong secondDivisorByte = bi2.Data[bi2.Length - 2];
int divisorLen = bi2.Length + 1;
var kk = new BigInteger(0) { Length = divisorLen };
var ss = new BigInteger(0);
while (j > 0)
{
ulong dividend = ((ulong)remainder.Data[pos] << 32) + (ulong)remainder.Data[pos - 1];
//Console.WriteLine("dividend = {0}", dividend);
ulong q_hat = dividend / firstDivisorByte;
ulong r_hat = dividend % firstDivisorByte;
//Console.WriteLine("q_hat = {0:X}, r_hat = {1:X}", q_hat, r_hat);
bool done = false;
while (!done)
{
done = true;
if (q_hat == 0x100000000 ||
(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder.Data[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
done = false;
}
}
kk.Length = divisorLen;
Array.Copy(remainder.Data, pos - divisorLen + 1, kk.Data, 0, divisorLen);
while (kk.Length > 1 && kk.Data[kk.Length - 1] == 0)kk.Length--;
//var ss = bi2 * (long)q_hat;
Multiply(bi2, q_hat, ref ss);
while (ss > kk)
{
q_hat--;
ss.Subtract(bi2);
}
kk.Subtract(ss);
Array.Copy(kk.Data, 0, remainder.Data, pos - divisorLen + 1, divisorLen);
pos--;
j--;
}
ss.Recycle();
kk.Recycle();
remainder.Length = shiftRight(remainder.Data, shift);
return remainder;
}
public void DivideMultiByte(BigInteger bi2)
{
int remainderLen = Length + 1;
uint mask = 0x80000000;
uint val = bi2.Data[bi2.Length - 1];
int shift = 0, resultPos = 0;
while (mask != 0 && (val & mask) == 0)
{
shift++; mask >>= 1;
}
var remainder = new BigInteger(this) {Length = remainderLen};
shiftLeft(remainder.Data, shift);
bi2 = bi2 << shift;
int j = remainderLen - bi2.Length;
int pos = remainderLen - 1;
ulong firstDivisorByte = bi2.Data[bi2.Length - 1];
ulong secondDivisorByte = bi2.Data[bi2.Length - 2];
int divisorLen = bi2.Length + 1;
var kk = new BigInteger(0) {Length = divisorLen};
var ss = new BigInteger(0);
while (j > 0)
{
ulong dividend = ((ulong)remainder.Data[pos] << 32) + (ulong)remainder.Data[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.Data[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
done = false;
}
}
kk.Length = divisorLen;
Array.Copy(remainder.Data, pos - divisorLen + 1 ,kk.Data, 0, divisorLen);
while (kk.Length > 1 && kk.Data[kk.Length - 1] == 0)
kk.Length--;
// BigInteger ss = bi2 * (long)q_hat;
Multiply(bi2,q_hat,ref ss);
while (ss > kk)
{
q_hat--;
ss.Subtract(bi2);
}
kk.Subtract(ss);
Array.Copy(kk.Data,0, remainder.Data, pos - divisorLen + 1, divisorLen);
Data[resultPos++] = (uint)q_hat;
pos--;
j--;
}
Length = resultPos;
Array.Reverse(Data,0,Length);
Array.Clear(Data,Length,maxLength-Length);
while (Length > 1 && Data[Length - 1] == 0)
Length--;
if (Length == 0)
Length = 1;
kk.Recycle();
ss.Recycle();
remainder.Recycle();
}
//***********************************************************************
// Fast calculation of modular reduction using Barrett's reduction.
// Requires x < b^(2k), where b is the base. In this case, base is
// 2^32 (uint).
//
// Reference [4]
//***********************************************************************
private void BarrettReduction(ref BigInteger x1,BigInteger x2, BigInteger n, BigInteger constant,ref BigInteger temp)
{
Multiply(x1, x2, ref temp);
int k = n.Length,
kPlusOne = k+1,
kMinusOne = k-1;
//var q1 = new BigInteger(0);
//// q1 = x / b^(k-1)
//for (int i = kMinusOne, j = 0; i < x.Length; i++, j++)
// q1.Data[j] = x.Data[i];
//q1.Length = x.Length - kMinusOne;
//if(q1.Length <= 0)
// q1.Length = 1;
//var q2 = q1 * constant;
//q1.Recycle();
//q1 = q2;
var q1 = new BigIntegerShell(temp, kMinusOne, temp.Length - kMinusOne) * constant;
// r1 = x mod b^(k+1)
// i.e. keep the lowest (k+1) words
//var r1 = new BigInteger(0);
//int lengthToCopy = (x.Length > kPlusOne) ? kPlusOne : x.Length;
temp.Length = (temp.Length > kPlusOne) ? kPlusOne : temp.Length;
//for(int i = 0; i < lengthToCopy; i++)
// r1.Data[i] = x.Data[i];
//r1.Length = lengthToCopy;
// r2 = (q3 * n) mod b^(k+1)
// partial multiplication of q3 and n
var r2 = new BigInteger(0);
for (int i = kPlusOne; i < q1.Length; i++)
{
if(q1.Data[i] == 0) continue;
ulong mcarry = 0;
int t = i - kPlusOne;
for(int j = 0; j < n.Length && t < kPlusOne; j++, t++)
{
// t = i + j
ulong val = (q1.Data[i] * (ulong)n.Data[j]) +
r2.Data[t] + mcarry;
r2.Data[t] = (uint)val;
mcarry = (val >> 32);
}
if(t < kPlusOne)
r2.Data[t] = (uint)mcarry;
}
r2.Length = kPlusOne;
while(r2.Length > 1 && r2.Data[r2.Length-1] == 0)
r2.Length--;
temp.Subtract(r2);
r2.Recycle();
if ((temp.Data[maxLength - 1] & 0x80000000) != 0) // negative
{
ulong carry = 1;
for (var i = kPlusOne; carry != 0 && i<maxLength; i++)
{
var sum = temp.Data[i] + carry;
carry = sum >> 32;
temp.Data[i] = (uint)sum;
}
}
while (temp >= n)
temp.Subtract(n);
q1.Recycle();
q1 = temp;
temp = x1;
x1 = q1;
}
//***********************************************************************
// Modulo Exponentiation
//***********************************************************************
public BigInteger ModPow(BigInteger exp, BigInteger n)
{
if((exp.Data[maxLength-1] & 0x80000000) != 0)
throw (new ArithmeticException("Positive exponents only."));
BigInteger resultNum = 1;
BigInteger tempNum;
bool thisNegative = false;
if((this.Data[maxLength-1] & 0x80000000) != 0) // negative this
{
tempNum = -this % n;
thisNegative = true;
}
else
tempNum = this % n; // ensures (tempNum * tempNum) < b^(2k)
if((n.Data[maxLength-1] & 0x80000000) != 0) // negative n
n = -n;
// calculate constant = b^(2k) / m
var constant = new BigInteger(0);
int i = n.Length << 1;
constant.Data[i] = 0x00000001;
constant.Length = i + 1;
constant.Divide(n);
//constant /= n;
int totalBits = exp.bitCount();
int count = 0;
var temp = new BigInteger(0);
// perform squaring and multiply exponentiation
for(var pos = 0; pos < exp.Length; pos++)
{
uint mask = 0x01;
//Console.WriteLine("pos = " + pos);
for(var index = 0; index < 32; index++)
{
if ((exp.Data[pos] & mask) != 0)
{
BarrettReduction(ref resultNum, tempNum, n, constant, ref temp);
}
mask <<= 1;
BarrettReduction(ref tempNum, tempNum, n, constant, ref temp);
if(tempNum.Length == 1 && tempNum.Data[0] == 1)
{
if(thisNegative && (exp.Data[0] & 0x1) != 0) //odd exp
resultNum.Negative();
return resultNum;
}
count++;
if(count == totalBits)
break;
}
}
constant.Recycle();
temp.Recycle();
if(thisNegative && (exp.Data[0] & 0x1) != 0) //odd exp
resultNum.Negative();
return resultNum;
}