public static BigInteger operator *(BigInteger bi1, BigInteger bi2)
{
if (bi1 == 0 || bi2 == 0)
{
return(0);
}
//
// Validate pointers
//
if (bi1.data.Length < bi1.length)
{
throw new IndexOutOfRangeException("bi1 out of range");
}
if (bi2.data.Length < bi2.length)
{
throw new IndexOutOfRangeException("bi2 out of range");
}
var ret = new BigInteger(Sign.Positive, bi1.length + bi2.length);
Kernel.Multiply(bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);
ret.Normalize();
return(ret);
}
public static BigInteger RightShift(BigInteger bi, int n)
{
if (n == 0)
{
return(new BigInteger(bi));
}
var w = n >> 5;
var s = n & ((1 << 5) - 1);
var ret = new BigInteger(Sign.Positive, bi.length - (uint)w + 1);
var l = (uint)ret.data.Length - 1;
if (s != 0)
{
uint x, carry = 0;
while (l-- > 0)
{
x = bi.data[l + w];
ret.data[l] = (x >> n) | carry;
carry = x << (32 - n);
}
}
else
{
while (l-- > 0)
{
ret.data[l] = bi.data[l + w];
}
}
ret.Normalize();
return(ret);
}
public static BigInteger Subtract(BigInteger big, BigInteger small)
{
var result = new BigInteger(Sign.Positive, big.length);
uint[] r = result.data, b = big.data, s = small.data;
uint i = 0, c = 0;
do
{
var x = s[i];
if (((x += c) < c) | ((r[i] = b[i] - x) > ~x))
{
c = 1;
}
else
{
c = 0;
}
} while (++i < small.length);
if (i == big.length)
{
goto fixup;
}
if (c == 1)
{
do
{
r[i] = b[i] - 1;
} while (b[i++] == 0 && i < big.length);
if (i == big.length)
{
goto fixup;
}
}
do
{
r[i] = b[i];
} while (++i < big.length);
fixup:
result.Normalize();
return(result);
}
/// <summary>
/// Performs n / d and n % d in one operation.
/// </summary>
/// <param name="n">A BigInteger, upon exit this will hold n / d</param>
/// <param name="d">The divisor</param>
/// <returns>n % d</returns>
public static uint SingleByteDivideInPlace(BigInteger n, uint d)
{
ulong r = 0;
var i = n.length;
while (i-- > 0)
{
r <<= 32;
r |= n.data[i];
n.data[i] = (uint)(r / d);
r %= d;
}
n.Normalize();
return((uint)r);
}
public static BigInteger MultiplyByDword(BigInteger n, uint f)
{
var ret = new BigInteger(Sign.Positive, n.length + 1);
uint i = 0;
ulong c = 0;
do
{
c += n.data[i] * (ulong)f;
ret.data[i] = (uint)c;
c >>= 32;
} while (++i < n.length);
ret.data[i] = (uint)c;
ret.Normalize();
return(ret);
}
public static BigInteger DwordDiv(BigInteger n, uint d)
{
var ret = new BigInteger(Sign.Positive, n.length);
ulong r = 0;
var i = n.length;
while (i-- > 0)
{
r <<= 32;
r |= n.data[i];
ret.data[i] = (uint)(r / d);
r %= d;
}
ret.Normalize();
return(ret);
}
public static BigInteger LeftShift(BigInteger bi, int n)
{
if (n == 0)
{
return(new BigInteger(bi, bi.length + 1));
}
var w = n >> 5;
n &= ((1 << 5) - 1);
var ret = new BigInteger(Sign.Positive, bi.length + 1 + (uint)w);
uint i = 0, l = bi.length;
if (n != 0)
{
uint x, carry = 0;
while (i < l)
{
x = bi.data[i];
ret.data[i + w] = (x << n) | carry;
carry = x >> (32 - n);
i++;
}
ret.data[i + w] = carry;
}
else
{
while (i < l)
{
ret.data[i + w] = bi.data[i];
i++;
}
}
ret.Normalize();
return(ret);
}
public static BigInteger[] multiByteDivide(BigInteger bi1, BigInteger bi2)
{
if (Compare(bi1, bi2) == Sign.Negative)
{
return new BigInteger[2] {
0, new BigInteger(bi1)
}
}
;
bi1.Normalize();
bi2.Normalize();
if (bi2.length == 1)
{
return(DwordDivMod(bi1, bi2.data[0]));
}
var remainderLen = bi1.length + 1;
var divisorLen = (int)bi2.length + 1;
var mask = 0x80000000;
var val = bi2.data[bi2.length - 1];
var shift = 0;
var resultPos = (int)bi1.length - (int)bi2.length;
while (mask != 0 && (val & mask) == 0)
{
shift++;
mask >>= 1;
}
var quot = new BigInteger(Sign.Positive, bi1.length - bi2.length + 1);
var rem = (bi1 << shift);
var remainder = rem.data;
bi2 = bi2 << shift;
var j = (int)(remainderLen - bi2.length);
var pos = (int)remainderLen - 1;
var firstDivisorByte = bi2.data[bi2.length - 1];
ulong secondDivisorByte = bi2.data[bi2.length - 2];
while (j > 0)
{
var dividend = ((ulong)remainder[pos] << 32) + remainder[pos - 1];
var q_hat = dividend / firstDivisorByte;
var r_hat = dividend % firstDivisorByte;
do
{
if (q_hat == 0x100000000 ||
(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
{
continue;
}
}
break;
} while (true);
//
// At this point, q_hat is either exact, or one too large
// (more likely to be exact) so, we attempt to multiply the
// divisor by q_hat, if we get a borrow, we just subtract
// one from q_hat and add the divisor back.
//
uint t;
uint dPos = 0;
var nPos = pos - divisorLen + 1;
ulong mc = 0;
var uint_q_hat = (uint)q_hat;
do
{
mc += bi2.data[dPos] * (ulong)uint_q_hat;
t = remainder[nPos];
remainder[nPos] -= (uint)mc;
mc >>= 32;
if (remainder[nPos] > t)
{
mc++;
}
dPos++;
nPos++;
} while (dPos < divisorLen);
nPos = pos - divisorLen + 1;
dPos = 0;
// Overestimate
if (mc != 0)
{
uint_q_hat--;
ulong sum = 0;
do
{
sum = remainder[nPos] + ((ulong)bi2.data[dPos]) + sum;
remainder[nPos] = (uint)sum;
sum >>= 32;
dPos++;
nPos++;
} while (dPos < divisorLen);
}
quot.data[resultPos--] = uint_q_hat;
pos--;
j--;
}
quot.Normalize();
rem.Normalize();
var ret = new BigInteger[2] {
quot, rem
};
if (shift != 0)
{
ret[1] >>= shift;
}
return(ret);
}
public static BigInteger MultiplyByDword(BigInteger n, uint f)
{
var ret = new BigInteger(Sign.Positive, n.length + 1);
uint i = 0;
ulong c = 0;
do
{
c += n.data[i]*(ulong) f;
ret.data[i] = (uint) c;
c >>= 32;
} while (++i < n.length);
ret.data[i] = (uint) c;
ret.Normalize();
return ret;
}
public static BigInteger Subtract(BigInteger big, BigInteger small)
{
var result = new BigInteger(Sign.Positive, big.length);
uint[] r = result.data, b = big.data, s = small.data;
uint i = 0, c = 0;
do
{
var x = s[i];
if (((x += c) < c) | ((r[i] = b[i] - x) > ~x))
c = 1;
else
c = 0;
} while (++i < small.length);
if (i == big.length) goto fixup;
if (c == 1)
{
do
r[i] = b[i] - 1; while (b[i++] == 0 && i < big.length);
if (i == big.length) goto fixup;
}
do
r[i] = b[i]; while (++i < big.length);
fixup:
result.Normalize();
return result;
}
/// <summary>
/// Adds two numbers with the same sign.
/// </summary>
/// <param name="bi1">A BigInteger</param>
/// <param name="bi2">A BigInteger</param>
/// <returns>bi1 + bi2</returns>
public static BigInteger AddSameSign(BigInteger bi1, BigInteger bi2)
{
uint[] x, y;
uint yMax, xMax, i = 0;
// x should be bigger
if (bi1.length < bi2.length)
{
x = bi2.data;
xMax = bi2.length;
y = bi1.data;
yMax = bi1.length;
}
else
{
x = bi1.data;
xMax = bi1.length;
y = bi2.data;
yMax = bi2.length;
}
var result = new BigInteger(Sign.Positive, xMax + 1);
var r = result.data;
ulong sum = 0;
// Add common parts of both numbers
do
{
sum = x[i] + ((ulong) y[i]) + sum;
r[i] = (uint) sum;
sum >>= 32;
} while (++i < yMax);
// Copy remainder of longer number while carry propagation is required
var carry = (sum != 0);
if (carry)
{
if (i < xMax)
{
do
carry = ((r[i] = x[i] + 1) == 0); while (++i < xMax && carry);
}
if (carry)
{
r[i] = 1;
result.length = ++i;
return result;
}
}
// Copy the rest
if (i < xMax)
{
do
r[i] = x[i]; while (++i < xMax);
}
result.Normalize();
return result;
}
public static void PlusEq(BigInteger bi1, BigInteger bi2)
{
uint[] x, y;
uint yMax, xMax, i = 0;
var flag = false;
// x should be bigger
if (bi1.length < bi2.length)
{
flag = true;
x = bi2.data;
xMax = bi2.length;
y = bi1.data;
yMax = bi1.length;
}
else
{
x = bi1.data;
xMax = bi1.length;
y = bi2.data;
yMax = bi2.length;
}
var r = bi1.data;
ulong sum = 0;
// Add common parts of both numbers
do
{
sum += x[i] + ((ulong) y[i]);
r[i] = (uint) sum;
sum >>= 32;
} while (++i < yMax);
// Copy remainder of longer number while carry propagation is required
var carry = (sum != 0);
if (carry)
{
if (i < xMax)
{
do
carry = ((r[i] = x[i] + 1) == 0); while (++i < xMax && carry);
}
if (carry)
{
r[i] = 1;
bi1.length = ++i;
return;
}
}
// Copy the rest
if (flag && i < xMax - 1)
{
do
r[i] = x[i]; while (++i < xMax);
}
bi1.length = xMax + 1;
bi1.Normalize();
}
public static void PlusEq(BigInteger bi1, BigInteger bi2)
{
uint[] x, y;
uint yMax, xMax, i = 0;
var flag = false;
// x should be bigger
if (bi1.length < bi2.length)
{
flag = true;
x = bi2.data;
xMax = bi2.length;
y = bi1.data;
yMax = bi1.length;
}
else
{
x = bi1.data;
xMax = bi1.length;
y = bi2.data;
yMax = bi2.length;
}
var r = bi1.data;
ulong sum = 0;
// Add common parts of both numbers
do
{
sum += x[i] + ((ulong)y[i]);
r[i] = (uint)sum;
sum >>= 32;
} while (++i < yMax);
// Copy remainder of longer number while carry propagation is required
var carry = (sum != 0);
if (carry)
{
if (i < xMax)
{
do
{
carry = ((r[i] = x[i] + 1) == 0);
} while (++i < xMax && carry);
}
if (carry)
{
r[i] = 1;
bi1.length = ++i;
return;
}
}
// Copy the rest
if (flag && i < xMax - 1)
{
do
{
r[i] = x[i];
} while (++i < xMax);
}
bi1.length = xMax + 1;
bi1.Normalize();
}
/// <summary>
/// Performs n / d and n % d in one operation.
/// </summary>
/// <param name="n">A BigInteger, upon exit this will hold n / d</param>
/// <param name="d">The divisor</param>
/// <returns>n % d</returns>
public static uint SingleByteDivideInPlace(BigInteger n, uint d)
{
ulong r = 0;
var i = n.length;
while (i-- > 0)
{
r <<= 32;
r |= n.data[i];
n.data[i] = (uint) (r/d);
r %= d;
}
n.Normalize();
return (uint) r;
}
/// <summary>
/// Adds two numbers with the same sign.
/// </summary>
/// <param name="bi1">A BigInteger</param>
/// <param name="bi2">A BigInteger</param>
/// <returns>bi1 + bi2</returns>
public static BigInteger AddSameSign(BigInteger bi1, BigInteger bi2)
{
uint[] x, y;
uint yMax, xMax, i = 0;
// x should be bigger
if (bi1.length < bi2.length)
{
x = bi2.data;
xMax = bi2.length;
y = bi1.data;
yMax = bi1.length;
}
else
{
x = bi1.data;
xMax = bi1.length;
y = bi2.data;
yMax = bi2.length;
}
var result = new BigInteger(Sign.Positive, xMax + 1);
var r = result.data;
ulong sum = 0;
// Add common parts of both numbers
do
{
sum = x[i] + ((ulong)y[i]) + sum;
r[i] = (uint)sum;
sum >>= 32;
} while (++i < yMax);
// Copy remainder of longer number while carry propagation is required
var carry = (sum != 0);
if (carry)
{
if (i < xMax)
{
do
{
carry = ((r[i] = x[i] + 1) == 0);
} while (++i < xMax && carry);
}
if (carry)
{
r[i] = 1;
result.length = ++i;
return(result);
}
}
// Copy the rest
if (i < xMax)
{
do
{
r[i] = x[i];
} while (++i < xMax);
}
result.Normalize();
return(result);
}
public static BigInteger operator *(BigInteger bi1, BigInteger bi2)
{
if (bi1 == 0 || bi2 == 0) return 0;
//
// Validate pointers
//
if (bi1.data.Length < bi1.length) throw new IndexOutOfRangeException("bi1 out of range");
if (bi2.data.Length < bi2.length) throw new IndexOutOfRangeException("bi2 out of range");
var ret = new BigInteger(Sign.Positive, bi1.length + bi2.length);
Kernel.Multiply(bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);
ret.Normalize();
return ret;
}
public static BigInteger[] DwordDivMod(BigInteger n, uint d)
{
var ret = new BigInteger(Sign.Positive, n.length);
ulong r = 0;
var i = n.length;
while (i-- > 0)
{
r <<= 32;
r |= n.data[i];
ret.data[i] = (uint) (r/d);
r %= d;
}
ret.Normalize();
BigInteger rem = (uint) r;
return new[] {ret, rem};
}
public static BigInteger RightShift(BigInteger bi, int n)
{
if (n == 0) return new BigInteger(bi);
var w = n >> 5;
var s = n & ((1 << 5) - 1);
var ret = new BigInteger(Sign.Positive, bi.length - (uint) w + 1);
var l = (uint) ret.data.Length - 1;
if (s != 0)
{
uint x, carry = 0;
while (l-- > 0)
{
x = bi.data[l + w];
ret.data[l] = (x >> n) | carry;
carry = x << (32 - n);
}
}
else
{
while (l-- > 0)
ret.data[l] = bi.data[l + w];
}
ret.Normalize();
return ret;
}
public static BigInteger LeftShift(BigInteger bi, int n)
{
if (n == 0) return new BigInteger(bi, bi.length + 1);
var w = n >> 5;
n &= ((1 << 5) - 1);
var ret = new BigInteger(Sign.Positive, bi.length + 1 + (uint) w);
uint i = 0, l = bi.length;
if (n != 0)
{
uint x, carry = 0;
while (i < l)
{
x = bi.data[i];
ret.data[i + w] = (x << n) | carry;
carry = x >> (32 - n);
i++;
}
ret.data[i + w] = carry;
}
else
{
while (i < l)
{
ret.data[i + w] = bi.data[i];
i++;
}
}
ret.Normalize();
return ret;
}
public static BigInteger[] multiByteDivide(BigInteger bi1, BigInteger bi2)
{
if (Compare(bi1, bi2) == Sign.Negative)
return new BigInteger[2] {0, new BigInteger(bi1)};
bi1.Normalize();
bi2.Normalize();
if (bi2.length == 1)
return DwordDivMod(bi1, bi2.data[0]);
var remainderLen = bi1.length + 1;
var divisorLen = (int) bi2.length + 1;
var mask = 0x80000000;
var val = bi2.data[bi2.length - 1];
var shift = 0;
var resultPos = (int) bi1.length - (int) bi2.length;
while (mask != 0 && (val & mask) == 0)
{
shift++;
mask >>= 1;
}
var quot = new BigInteger(Sign.Positive, bi1.length - bi2.length + 1);
var rem = (bi1 << shift);
var remainder = rem.data;
bi2 = bi2 << shift;
var j = (int) (remainderLen - bi2.length);
var pos = (int) remainderLen - 1;
var firstDivisorByte = bi2.data[bi2.length - 1];
ulong secondDivisorByte = bi2.data[bi2.length - 2];
while (j > 0)
{
var dividend = ((ulong) remainder[pos] << 32) + remainder[pos - 1];
var q_hat = dividend/firstDivisorByte;
var r_hat = dividend%firstDivisorByte;
do
{
if (q_hat == 0x100000000 ||
(q_hat*secondDivisorByte) > ((r_hat << 32) + remainder[pos - 2]))
{
q_hat--;
r_hat += firstDivisorByte;
if (r_hat < 0x100000000)
continue;
}
break;
} while (true);
//
// At this point, q_hat is either exact, or one too large
// (more likely to be exact) so, we attempt to multiply the
// divisor by q_hat, if we get a borrow, we just subtract
// one from q_hat and add the divisor back.
//
uint t;
uint dPos = 0;
var nPos = pos - divisorLen + 1;
ulong mc = 0;
var uint_q_hat = (uint) q_hat;
do
{
mc += bi2.data[dPos]*(ulong) uint_q_hat;
t = remainder[nPos];
remainder[nPos] -= (uint) mc;
mc >>= 32;
if (remainder[nPos] > t) mc++;
dPos++;
nPos++;
} while (dPos < divisorLen);
nPos = pos - divisorLen + 1;
dPos = 0;
// Overestimate
if (mc != 0)
{
uint_q_hat--;
ulong sum = 0;
do
{
sum = remainder[nPos] + ((ulong) bi2.data[dPos]) + sum;
remainder[nPos] = (uint) sum;
sum >>= 32;
dPos++;
nPos++;
} while (dPos < divisorLen);
}
quot.data[resultPos--] = uint_q_hat;
pos--;
j--;
}
quot.Normalize();
rem.Normalize();
var ret = new BigInteger[2] {quot, rem};
if (shift != 0)
ret[1] >>= shift;
return ret;
}
public void BarrettReduction(BigInteger x)
{
var n = mod;
uint k = n.length,
kPlusOne = k + 1,
kMinusOne = k - 1;
// x < mod, so nothing to do.
if (x.length < k)
{
return;
}
BigInteger q3;
//
// Validate pointers
//
if (x.data.Length < x.length)
{
throw new IndexOutOfRangeException("x out of range");
}
// q1 = x / b^ (k-1)
// q2 = q1 * constant
// q3 = q2 / b^ (k+1), Needs to be accessed with an offset of kPlusOne
// TODO: We should the method in HAC p 604 to do this (14.45)
q3 = new BigInteger(Sign.Positive, x.length - kMinusOne + constant.length);
Kernel.Multiply(x.data, kMinusOne, x.length - kMinusOne, constant.data, 0, constant.length, q3.data, 0);
// r1 = x mod b^ (k+1)
// i.e. keep the lowest (k+1) words
var lengthToCopy = (x.length > kPlusOne) ? kPlusOne : x.length;
x.length = lengthToCopy;
x.Normalize();
// r2 = (q3 * n) mod b^ (k+1)
// partial multiplication of q3 and n
var r2 = new BigInteger(Sign.Positive, kPlusOne);
Kernel.MultiplyMod2p32pmod(q3.data, (int)kPlusOne, (int)q3.length - (int)kPlusOne, n.data, 0,
(int)n.length, r2.data, 0, (int)kPlusOne);
r2.Normalize();
if (r2 <= x)
{
Kernel.MinusEq(x, r2);
}
else
{
var val = new BigInteger(Sign.Positive, kPlusOne + 1);
val.data[kPlusOne] = 0x00000001;
Kernel.MinusEq(val, r2);
Kernel.PlusEq(x, val);
}
while (x >= n)
{
Kernel.MinusEq(x, n);
}
}
public void BarrettReduction(BigInteger x)
{
var n = mod;
uint k = n.length,
kPlusOne = k + 1,
kMinusOne = k - 1;
// x < mod, so nothing to do.
if (x.length < k) return;
BigInteger q3;
//
// Validate pointers
//
if (x.data.Length < x.length) throw new IndexOutOfRangeException("x out of range");
// q1 = x / b^ (k-1)
// q2 = q1 * constant
// q3 = q2 / b^ (k+1), Needs to be accessed with an offset of kPlusOne
// TODO: We should the method in HAC p 604 to do this (14.45)
q3 = new BigInteger(Sign.Positive, x.length - kMinusOne + constant.length);
Kernel.Multiply(x.data, kMinusOne, x.length - kMinusOne, constant.data, 0, constant.length, q3.data, 0);
// r1 = x mod b^ (k+1)
// i.e. keep the lowest (k+1) words
var lengthToCopy = (x.length > kPlusOne) ? kPlusOne : x.length;
x.length = lengthToCopy;
x.Normalize();
// r2 = (q3 * n) mod b^ (k+1)
// partial multiplication of q3 and n
var r2 = new BigInteger(Sign.Positive, kPlusOne);
Kernel.MultiplyMod2p32pmod(q3.data, (int) kPlusOne, (int) q3.length - (int) kPlusOne, n.data, 0,
(int) n.length, r2.data, 0, (int) kPlusOne);
r2.Normalize();
if (r2 <= x)
{
Kernel.MinusEq(x, r2);
}
else
{
var val = new BigInteger(Sign.Positive, kPlusOne + 1);
val.data[kPlusOne] = 0x00000001;
Kernel.MinusEq(val, r2);
Kernel.PlusEq(x, val);
}
while (x >= n)
Kernel.MinusEq(x, n);
}
