public BigInteger modPow(BigInteger exponent, BigInteger m)
{
if (m.sign <= 0)
{
throw new ArithmeticException("BigInteger: modulus not positive");
}
BigInteger _base = this;
if (m.isOne() | (exponent.sign > 0 & _base.sign == 0))
{
return(BigInteger.ZERO);
}
if (_base.sign == 0 && exponent.sign == 0)
{
return(BigInteger.ONE);
}
if (exponent.sign < 0)
{
_base = modInverse(m);
exponent = exponent.negate();
}
// From now on: (m > 0) and (exponent >= 0)
BigInteger res = (m.testBit(0)) ? Division.oddModPow(_base.abs(),
exponent, m) : Division.evenModPow(_base.abs(), exponent, m);
if ((_base.sign < 0) && exponent.testBit(0))
{
// -b^e mod m == ((-1 mod m) * (b^e mod m)) mod m
res = m.subtract(BigInteger.ONE).multiply(res).mod(m);
}
// else exponent is even, so base^exp is positive
return(res);
}
internal static BigInteger subtract(BigInteger op1, BigInteger op2)
{
int resSign;
int[] resDigits;
int op1Sign = op1.sign;
int op2Sign = op2.sign;
if (op2Sign == 0)
{
return(op1);
}
if (op1Sign == 0)
{
return(op2.negate());
}
int op1Len = op1.numberLength;
int op2Len = op2.numberLength;
if (op1Len + op2Len == 2)
{
long a = (op1.digits[0] & 0xFFFFFFFFL);
long b = (op2.digits[0] & 0xFFFFFFFFL);
if (op1Sign < 0)
{
a = -a;
}
if (op2Sign < 0)
{
b = -b;
}
return(BigInteger.valueOf(a - b));
}
int cmp = ((op1Len != op2Len) ? ((op1Len > op2Len) ? 1 : -1)
: Elementary.compareArrays(op1.digits, op2.digits, op1Len));
if (cmp == BigInteger.LESS)
{
resSign = -op2Sign;
resDigits = (op1Sign == op2Sign) ? subtract(op2.digits, op2Len,
op1.digits, op1Len) : add(op2.digits, op2Len, op1.digits,
op1Len);
}
else
{
resSign = op1Sign;
if (op1Sign == op2Sign)
{
if (cmp == BigInteger.EQUALS)
{
return(BigInteger.ZERO);
}
resDigits = subtract(op1.digits, op1Len, op2.digits, op2Len);
}
else
{
resDigits = add(op1.digits, op1Len, op2.digits, op2Len);
}
}
BigInteger res = new BigInteger(resSign, resDigits.Length, resDigits);
res.cutOffLeadingZeroes();
return(res);
}
public BigInteger modPow(BigInteger exponent, BigInteger m)
{
if (m.sign <= 0) {
throw new ArithmeticException("BigInteger: modulus not positive");
}
BigInteger _base = this;
if (m.isOne() | (exponent.sign > 0 & _base.sign == 0)) {
return BigInteger.ZERO;
}
if (_base.sign == 0 && exponent.sign == 0) {
return BigInteger.ONE;
}
if (exponent.sign < 0) {
_base = modInverse(m);
exponent = exponent.negate();
}
// From now on: (m > 0) and (exponent >= 0)
BigInteger res = (m.testBit(0)) ? Division.oddModPow(_base.abs(),
exponent, m) : Division.evenModPow(_base.abs(), exponent, m);
if ((_base.sign < 0) && exponent.testBit(0)) {
// -b^e mod m == ((-1 mod m) * (b^e mod m)) mod m
res = m.subtract(BigInteger.ONE).multiply(res).mod(m);
}
// else exponent is even, so base^exp is positive
return res;
}
internal static BigInteger modInverseLorencz(BigInteger a, BigInteger modulo)
{
int max = Math.Max(a.numberLength, modulo.numberLength);
int[] uDigits = new int[max + 1]; // enough place to make all the inplace operation
int[] vDigits = new int[max + 1];
Array.Copy(modulo.digits, uDigits, modulo.numberLength);
Array.Copy(a.digits, vDigits, a.numberLength);
BigInteger u = new BigInteger(modulo.sign, modulo.numberLength,
uDigits);
BigInteger v = new BigInteger(a.sign, a.numberLength, vDigits);
BigInteger r = new BigInteger(0, 1, new int[max + 1]); // BigInteger.ZERO;
BigInteger s = new BigInteger(1, 1, new int[max + 1]);
s.digits[0] = 1;
// r == 0 && s == 1, but with enough place
int coefU = 0, coefV = 0;
int n = modulo.bitLength();
int k;
while (!isPowerOfTwo(u, coefU) && !isPowerOfTwo(v, coefV)) {
// modification of original algorithm: I calculate how many times the algorithm will enter in the same branch of if
k = howManyIterations(u, n);
if (k != 0) {
BitLevel.inplaceShiftLeft(u, k);
if (coefU >= coefV) {
BitLevel.inplaceShiftLeft(r, k);
} else {
BitLevel.inplaceShiftRight(s, Math.Min(coefV - coefU, k));
if (k - ( coefV - coefU ) > 0) {
BitLevel.inplaceShiftLeft(r, k - coefV + coefU);
}
}
coefU += k;
}
k = howManyIterations(v, n);
if (k != 0) {
BitLevel.inplaceShiftLeft(v, k);
if (coefV >= coefU) {
BitLevel.inplaceShiftLeft(s, k);
} else {
BitLevel.inplaceShiftRight(r, Math.Min(coefU - coefV, k));
if (k - ( coefU - coefV ) > 0) {
BitLevel.inplaceShiftLeft(s, k - coefU + coefV);
}
}
coefV += k;
}
if (u.signum() == v.signum()) {
if (coefU <= coefV) {
Elementary.completeInPlaceSubtract(u, v);
Elementary.completeInPlaceSubtract(r, s);
} else {
Elementary.completeInPlaceSubtract(v, u);
Elementary.completeInPlaceSubtract(s, r);
}
} else {
if (coefU <= coefV) {
Elementary.completeInPlaceAdd(u, v);
Elementary.completeInPlaceAdd(r, s);
} else {
Elementary.completeInPlaceAdd(v, u);
Elementary.completeInPlaceAdd(s, r);
}
}
if (v.signum() == 0 || u.signum() == 0){
throw new ArithmeticException("BigInteger not invertible");
}
}
if (isPowerOfTwo(v, coefV)) {
r = s;
if (v.signum() != u.signum())
u = u.negate();
}
if (u.testBit(n)) {
if (r.signum() < 0) {
r = r.negate();
} else {
r = modulo.subtract(r);
}
}
if (r.signum() < 0) {
r = r.add(modulo);
}
return r;
}
internal static BigInteger modInverseLorencz(BigInteger a, BigInteger modulo)
{
int max = Math.Max(a.numberLength, modulo.numberLength);
int[] uDigits = new int[max + 1]; // enough place to make all the inplace operation
int[] vDigits = new int[max + 1];
Array.Copy(modulo.digits, uDigits, modulo.numberLength);
Array.Copy(a.digits, vDigits, a.numberLength);
BigInteger u = new BigInteger(modulo.sign, modulo.numberLength,
uDigits);
BigInteger v = new BigInteger(a.sign, a.numberLength, vDigits);
BigInteger r = new BigInteger(0, 1, new int[max + 1]); // BigInteger.ZERO;
BigInteger s = new BigInteger(1, 1, new int[max + 1]);
s.digits[0] = 1;
// r == 0 && s == 1, but with enough place
int coefU = 0, coefV = 0;
int n = modulo.bitLength();
int k;
while (!isPowerOfTwo(u, coefU) && !isPowerOfTwo(v, coefV))
{
// modification of original algorithm: I calculate how many times the algorithm will enter in the same branch of if
k = howManyIterations(u, n);
if (k != 0)
{
BitLevel.inplaceShiftLeft(u, k);
if (coefU >= coefV)
{
BitLevel.inplaceShiftLeft(r, k);
}
else
{
BitLevel.inplaceShiftRight(s, Math.Min(coefV - coefU, k));
if (k - (coefV - coefU) > 0)
{
BitLevel.inplaceShiftLeft(r, k - coefV + coefU);
}
}
coefU += k;
}
k = howManyIterations(v, n);
if (k != 0)
{
BitLevel.inplaceShiftLeft(v, k);
if (coefV >= coefU)
{
BitLevel.inplaceShiftLeft(s, k);
}
else
{
BitLevel.inplaceShiftRight(r, Math.Min(coefU - coefV, k));
if (k - (coefU - coefV) > 0)
{
BitLevel.inplaceShiftLeft(s, k - coefU + coefV);
}
}
coefV += k;
}
if (u.signum() == v.signum())
{
if (coefU <= coefV)
{
Elementary.completeInPlaceSubtract(u, v);
Elementary.completeInPlaceSubtract(r, s);
}
else
{
Elementary.completeInPlaceSubtract(v, u);
Elementary.completeInPlaceSubtract(s, r);
}
}
else
{
if (coefU <= coefV)
{
Elementary.completeInPlaceAdd(u, v);
Elementary.completeInPlaceAdd(r, s);
}
else
{
Elementary.completeInPlaceAdd(v, u);
Elementary.completeInPlaceAdd(s, r);
}
}
if (v.signum() == 0 || u.signum() == 0)
{
throw new ArithmeticException("BigInteger not invertible");
}
}
if (isPowerOfTwo(v, coefV))
{
r = s;
if (v.signum() != u.signum())
{
u = u.negate();
}
}
if (u.testBit(n))
{
if (r.signum() < 0)
{
r = r.negate();
}
else
{
r = modulo.subtract(r);
}
}
if (r.signum() < 0)
{
r = r.add(modulo);
}
return(r);
}
internal static BigInteger subtract(BigInteger op1, BigInteger op2)
{
int resSign;
int[] resDigits;
int op1Sign = op1.sign;
int op2Sign = op2.sign;
if (op2Sign == 0) {
return op1;
}
if (op1Sign == 0) {
return op2.negate ();
}
int op1Len = op1.numberLength;
int op2Len = op2.numberLength;
if (op1Len + op2Len == 2) {
long a = ( op1.digits[0] & 0xFFFFFFFFL );
long b = ( op2.digits[0] & 0xFFFFFFFFL );
if (op1Sign < 0) {
a = -a;
}
if (op2Sign < 0) {
b = -b;
}
return BigInteger.valueOf (a - b);
}
int cmp = ( ( op1Len != op2Len ) ? ( ( op1Len > op2Len ) ? 1 : -1 )
: Elementary.compareArrays (op1.digits, op2.digits, op1Len) );
if (cmp == BigInteger.LESS) {
resSign = -op2Sign;
resDigits = ( op1Sign == op2Sign ) ? subtract (op2.digits, op2Len,
op1.digits, op1Len) : add (op2.digits, op2Len, op1.digits,
op1Len);
} else {
resSign = op1Sign;
if (op1Sign == op2Sign) {
if (cmp == BigInteger.EQUALS) {
return BigInteger.ZERO;
}
resDigits = subtract (op1.digits, op1Len, op2.digits, op2Len);
} else {
resDigits = add (op1.digits, op1Len, op2.digits, op2Len);
}
}
BigInteger res = new BigInteger (resSign, resDigits.Length, resDigits);
res.cutOffLeadingZeroes();
return res;
}
