Mpz

java.lang.Object
- gmp.Mpz

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, java.lang.Comparable<Mpz>

Direct Known Subclasses:

MpzRef
```
public class Mpz
extends java.lang.Object
implements java.io.Serializable, java.lang.Comparable<Mpz>, java.lang.Cloneable
```
GMP arbitrary precision integers.
This class wraps mpz_t GMP objects.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

static int infinite
This value can be returned by bit-searching or bit-counting operations.

Fields
Modifier and Type	Field and Description
`static int`	`infinite` This value can be returned by bit-searching or bit-counting operations.

Constructor Summary

Constructors
Constructor and Description
`Mpz()` Constructs an uninitialized number.
`Mpz(java.math.BigInteger b)` Constructs a number initialized from a Java big integer.
`Mpz(double d)` Constructs a number initialized with a double.
`Mpz(int i)` Constructs a number initialized with an integer.
`Mpz(int sign, byte[] mag)` Constructs a number from a unsigned stored in a big-endian byte array and a sign.
`Mpz(Mpz v)` Constructs a copy of its argument.
`Mpz(java.lang.String s)` Constructs a number initialized from a string representation.
`Mpz(java.lang.String s, int b)` Constructs a number initialized from a string representation in base b.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`abs()` Replaces this with \|this\|.
`void`	`abs(Mpz arg)` Stores \|arg\| into this.
`void`	`add(int arg)` Adds arg to this.
`void`	`add(Mpz arg)` Adds arg to this.
`void`	`add(Mpz arg1, int arg2)` Stores arg1+arg2 into this.
`void`	`add(Mpz arg1, Mpz arg2)` Stores arg1+arg2 into this.
`void`	`addMul(Mpz arg1, int arg2)` Stores this+arg1*arg2 into this.
`void`	`addMul(Mpz arg1, Mpz arg2)` Stores this+arg1*arg2 into this.
`void`	`and(Mpz op)` Stores the bitwise and of this and op into this.
`void`	`and(Mpz op1, Mpz op2)` Stores the bitwise and of op1 and op2 into this.
`java.math.BigInteger`	`bigIntegerValue()` Returns this as a Java big integer.
`void`	`bin(int n, int k)` Stores into this the binomial coefficient (n k).
`void`	`bin(Mpz n, int k)` Stores into this the binomial coefficient (n k).
`byte[]`	`byteArrayValue()` Returns the magnitude of this.
`int`	`cdivQ(int d)` Divides this by d, rounds towards +oo, and returns the remainder.
`void`	`cdivQ(Mpz d)` Divides this by d and rounds towards +oo.
`int`	`cdivQ(Mpz n, int d)` Stores the quotient of n/d rounded towards +oo into this, and returns the remainder.
`void`	`cdivQ(Mpz n, Mpz d)` Stores the quotient of n/d rounded towards +oo into this.
`void`	`cdivQ2exp(Mpz n, int d)` Stores the quotient of n/(2^d) rounded towards +oo into this.
`int`	`cdivQR(Mpz r, Mpz n, int d)` Stores the quotient of n/d rounded towards +oo into this, the remainder into r, and returns the remainder.
`void`	`cdivQR(Mpz r, Mpz n, Mpz d)` Stores the quotient of n/d rounded towards +oo into this and the remainder into r.
`int`	`cdivR(int d)` Returns the remainder of of this/d rounded towards +oo.
`int`	`cdivR(Mpz n, int d)` Stores the remainder of n/d rounded towards +oo into this, and returns the remainder.
`void`	`cdivR(Mpz n, Mpz d)` Stores the remainder of n/d rounded towards +oo into this.
`void`	`cdivR2exp(Mpz n, int d)` Stores the remainder of n/(2^d) rounded towards +oo into this.
`Mpz`	`clone()` Creates a new Mpz initialized with the value of this.
`void`	`clrBit(int pos)` Sets the pos-th bit to 0 in this.
`int`	`cmp(double op)` Returns a positive, null, or negative number when this is respectively strictly greater, equal, or strictly smaller than op.
`int`	`cmp(int op)` Returns a positive, null, or negative number when this is respectively strictly greater, equal, or strictly smaller than op.
`int`	`cmp(Mpz op)` Returns a positive, null, or negative number when this is respectively strictly greater, equal, or strictly smaller than op.
`int`	`cmpAbs(double op)` Returns a positive, null, or negative number when \|this\| is respectively strictly greater, equal, or strictly smaller than \|op\|.
`int`	`cmpAbs(int op)` Returns a positive, null, or negative number when \|this\| is respectively strictly greater, equal, or strictly smaller than \|op\|.
`int`	`cmpAbs(Mpz op)` Returns a positive, null, or negative number when \|this\| is respectively strictly greater, equal, or strictly smaller than \|op\|.
`int`	`compareTo(Mpz x)` Compare the value of this and x.
`void`	`divExact(int d)` Divides this by d, assuming that d divides this. d must be positive.
`void`	`divExact(Mpz d)` Divides this by d, assuming that d divides this.
`void`	`divExact(Mpz n, int d)` Stores n/d into this, assuming that d divides n. d must be positive.
`void`	`divExact(Mpz n, Mpz d)` Stores n/d into this, assuming that d divides n.
`double`	`doubleExponentValue(int[] r)` Converts the integer to a mantissa and exponent.
`double`	`doubleValue()` Returns this as a double.
`boolean`	`equals(java.lang.Object x)` Whether x is a Mpz and has the same value as this.
`void`	`fac(int op)` Stores op!
`int`	`fdivQ(int d)` Divides this by d, rounds towards -oo, and returns the remainder.
`void`	`fdivQ(Mpz d)` Divides this by d and rounds towards -oo.
`int`	`fdivQ(Mpz n, int d)` Stores the quotient of n/d rounded towards -oo into this, and returns the remainder.
`void`	`fdivQ(Mpz n, Mpz d)` Stores the quotient of n/d rounded towards -oo into this.
`void`	`fdivQ2exp(Mpz n, int d)` Stores the quotient of n/(2^d) rounded towards -oo into this.
`int`	`fdivQR(Mpz r, Mpz n, int d)` Stores the quotient of n/d rounded towards -oo into this, the remainder into r, and returns the remainder.
`void`	`fdivQR(Mpz r, Mpz n, Mpz d)` Stores the quotient of n/d rounded towards -oo into this and the remainder into r.
`int`	`fdivR(int d)` Returns the remainder of of this/d rounded towards -oo.
`int`	`fdivR(Mpz n, int d)` Stores the remainder of n/d rounded towards -oo into this, and returns the remainder.
`void`	`fdivR(Mpz n, Mpz d)` Stores the remainder of n/d rounded towards -oo into this.
`void`	`fdivR2exp(Mpz n, int d)` Stores the remainder of n/(2^d) rounded towards -oo into this.
`void`	`fib(int n)` Stores into this the n-th Fibonacci number.
`void`	`fib(Mpz r, int n)` Stores into this the n-th Fibonacci number, and into r the n-1-th Fibonacci number.
`protected void`	`finalize()` Deallocates the underlying mpz_t GMP object.
`boolean`	`fitsInt()` Whether this can fit in an int.
`int`	`gcd(Mpz op1, int op2)` Returns the greatest common divisor of op1 and op2.
`void`	`gcd(Mpz op1, Mpz op2)` Stores into this the greatest common divisor of op1 and op2.
`void`	`gcd(Mpz s, Mpz t, Mpz op1, Mpz op2)` Stores the greatest common divisor of op1 and op2 into this.
`int`	`hamDist(Mpz op)` Returns the Hamming distance between this and op.
`int`	`hashCode()` Returns a hash of the value of this.
`int`	`intValue()` Returns this as an integer.
`boolean`	`invert(Mpz op1, Mpz op2)` Stores the inverse of op1 modulo op2 into this.
`boolean`	`isCongruent(int c, int d)` Returns true if this equals c modulo d.
`boolean`	`isCongruent(Mpz c, Mpz d)` Returns true if this equals c modulo d.
`boolean`	`isCongruent2exp(Mpz c, int d)` Returns true if this equals c modulo 2^d.
`boolean`	`isDivisible(int d)` Returns true if d divides this.
`boolean`	`isDivisible(Mpz d)` Returns true if d divides this.
`boolean`	`isDivisible2exp(int d)` Returns true if 2^d divides this.
`boolean`	`isEqual(Mpz x)` Whether this and x have the same value.
`boolean`	`isEven()` Whether this is even.
`boolean`	`isOdd()` Whether this is odd.
`boolean`	`isPerfectPower()` Returns true if this has the form a^b for some a and b > 1.
`boolean`	`isPerfectSquare()` Returns true if this has the form a^2 for some a.
`boolean`	`isPhysicalEqual(Mpz x)` Whether this and x have the same address in memory.
`int`	`isProbabPrime(int r)` Returns 2 if this is definitely prime, 1 if it is probably prime, and 0 if it is definitely composite.
`static int`	`jacobi(Mpz b, Mpz p)` Returns the Jacobi symbol of a and b.
`static int`	`kronecker(int a, Mpz b)` Returns the Jacobi symbol with the Kronecker extension.
`static int`	`kronecker(Mpz a, int b)` Returns the Jacobi symbol with the Kronecker extension.
`static int`	`kronecker(Mpz a, Mpz b)` Returns the Jacobi symbol with the Kronecker extension.
`void`	`lcm(Mpz op1, int op2)` Stores into this the least common multiple of op1 and op2.
`void`	`lcm(Mpz op1, Mpz op2)` Stores into this the least common multiple of op1 and op2.
`static int`	`legendre(Mpz a, Mpz p)` Returns the Legendre symbol.
`void`	`lucnum(int n)` Stores into this the n-th Lucas number.
`void`	`lucnum(Mpz r, int n)` Stores into this the n-th Lucas number, and into r the n-1-th Lucas number.
`int`	`mod(int d)` Replaces this with this mod \|d\|.
`void`	`mod(Mpz d)` Replaces this with this mod \|d\|.
`int`	`mod(Mpz n, int d)` Stores n mod \|d\| into this and returns it.
`void`	`mod(Mpz n, Mpz d)` Stores n mod \|d\| into this.
`void`	`mul(int arg)` Multiplies this by arg.
`void`	`mul(Mpz arg)` Multiplies this by arg.
`void`	`mul(Mpz arg1, int arg2)` Stores arg1*arg2 into this.
`void`	`mul(Mpz arg1, Mpz arg2)` Stores arg1*arg2 into this.
`void`	`mul2exp(int arg)` Multiplies this by 2^arg.
`void`	`mul2exp(Mpz arg1, int arg2)` Stores arg1*2^arg2 into this.
`void`	`neg()` Replaces this with -this.
`void`	`neg(Mpz arg)` Stores -arg into this.
`void`	`nextPrime(Mpz op)` Stores into this the next prime greater than op.
`void`	`not()` Stores the bitwise complement of this into this.
`void`	`not(Mpz op)` Stores the bitwise complement of op into this.
`void`	`notBit(int pos)` Inverts the pos-th bit in this.
`void`	`or(Mpz op)` Stores the bitwise or of this and op into this.
`void`	`or(Mpz op1, Mpz op2)` Stores the bitwise or of op1 and op2 into this.
`int`	`popCount()` Returns the number of bits set to 1 in this.
`void`	`pow(int e)` Takes the e-th power of this.
`void`	`pow(int b, int e)` Stores b^e into this.
`void`	`pow(Mpz b, int e)` Stores b^e into this.
`void`	`pow(Mpz b, int e, Mpz m)` Stores b^e mod m into this.
`void`	`pow(Mpz b, Mpz e, Mpz m)` Stores b^e mod m into this.
`void`	`random(RandState r, Mpz n)` Stores into this a uniformly distributed random number in 0..n-1.
`void`	`randomBits(RandState r, int n)` Stores into this a uniformly distributed random number with n bits (i.e., in 0..2^n-1).
`int`	`remove(Mpz f)` Removes from this all occurrences of factor f.
`int`	`remove(Mpz op, Mpz f)` Stores into this op with all occurrences of factor f removed.
`boolean`	`root(int n)` Takes the n-th root of this, truncated.
`boolean`	`root(Mpz op, int n)` Stores the n-th root of op into this, truncated.
`void`	`root(Mpz r, Mpz op, int n)` Stores the n-th root of op into this, truncated, and the remainder op-this^n into r.
`void`	`rRandomBits(RandState r, int n)` Stores into this a random number with n bits, and long strings of zeros and ones in its binary representation.
`int`	`scan0(int pos)` Returns the position of the first bit set to 0 at or after position pos.
`int`	`scan1(int pos)` Returns the position of the first bit set to 1 at or after position pos.
`void`	`set(java.math.BigInteger b)` Sets this to a Java big integer.
`void`	`set(double d)` Sets this to a double.
`void`	`set(int i)` Sets this to an integer.
`void`	`set(int sign, byte[] mag)` Sets the value of this given a magnitude and a sign.
`void`	`set(Mpz v)` Copies the argument into this.
`void`	`set(java.lang.String s)` Sets this to the String s.
`void`	`set(java.lang.String s, int b)` Sets this to the String s expressed in base b.
`void`	`setBit(int pos)` Sets the pos-th bit to 1 in this.
`int`	`sgn()` Returns +1, 0, or -1 when this is respectively strictly positive, null, or strictly negative.
`int`	`size()` Returns the size (in GMP limbs) of the internal representation of this.
`int`	`sizeInBase(int b)` Returns the number of digits necessary to represent \|this\| in base b.
`void`	`sqrt()` Takes the truncated square root of this.
`void`	`sqrt(Mpz op)` Stores the truncated square root of op into this.
`void`	`sqrt(Mpz r, Mpz op)` Stores the square root of op into this, truncated, and the remainder op-this^2 into r.
`void`	`sub(int arg)` Subtracts arg from this.
`void`	`sub(int arg1, Mpz arg2)` Stores arg1-arg2 into this.
`void`	`sub(Mpz arg)` Subtracts arg from this.
`void`	`sub(Mpz arg1, int arg2)` Stores arg1-arg2 into this.
`void`	`sub(Mpz arg1, Mpz arg2)` Stores arg1-arg2 into this.
`void`	`subMul(Mpz arg1, int arg2)` Stores this-arg1*arg2 into this.
`void`	`subMul(Mpz arg1, Mpz arg2)` Stores this-arg1*arg2 into this.
`void`	`subRev(int arg)` Replaces this with arg-this.
`int`	`tdivQ(int d)` Divides this by d, rounds towards 0, and returns the remainder.
`void`	`tdivQ(Mpz d)` Divides this by d and rounds towards 0.
`int`	`tdivQ(Mpz n, int d)` Stores the quotient of n/d rounded towards 0 into this, and returns the remainder.
`void`	`tdivQ(Mpz n, Mpz d)` Stores the quotient of n/d rounded towards 0 into this.
`void`	`tdivQ2exp(Mpz n, int d)` Stores the quotient of n/(2^d) rounded towards 0 into this.
`int`	`tdivQR(Mpz r, Mpz n, int d)` Stores the quotient of n/d rounded towards 0 into this, the remainder into r, and returns the remainder.
`void`	`tdivQR(Mpz r, Mpz n, Mpz d)` Stores the quotient of n/d rounded towards 0 into this and the remainder into r.
`int`	`tdivR(int d)` Returns the remainder of of this/d rounded towards 0.
`int`	`tdivR(Mpz n, int d)` Stores the remainder of n/d rounded towards 0 into this, and returns the remainder.
`void`	`tdivR(Mpz n, Mpz d)` Stores the remainder of n/d rounded towards 0 into this.
`void`	`tdivR2exp(Mpz n, int d)` Stores the remainder of n/(2^d) rounded towards 0 into this.
`java.lang.String`	`toString()` Returns a String representation this in base 10.
`java.lang.String`	`toString(int b)` Returns a String representation of this in base b.
`boolean`	`tstBit(int pos)` Returns true if the pos-th bit in this is 1.
`void`	`xor(Mpz op)` Stores the bitwise xor of this and op into this.
`void`	`xor(Mpz op1, Mpz op2)` Stores the bitwise xor of op1 and op2 into this.

Methods inherited from class java.lang.Object
getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - infinite
```
public static final int infinite
```
    This value can be returned by bit-searching or bit-counting operations.
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - Mpz
```
public Mpz()
```
    Constructs an uninitialized number.
  - Mpz
```
public Mpz(Mpz v)
```
    Constructs a copy of its argument.
  - Mpz
```
public Mpz(int i)
```
    Constructs a number initialized with an integer.
  - Mpz
```
public Mpz(double d)
```
    Constructs a number initialized with a double.
    The value is truncated to an integer.
  - Mpz
```
public Mpz(java.math.BigInteger b)
```
    Constructs a number initialized from a Java big integer.
  - Mpz
```
public Mpz(java.lang.String s,
           int b)
```
    Constructs a number initialized from a string representation in base b.
    
    Parameters:
    
    b - must be either 0, or between 2 and 62. When b is 0, the leading characters are used to determine the base (0x and 0X for hexadecimal, 0b and 0B for binary, 0 for octal, decimal otherwise).
  - Mpz
```
public Mpz(java.lang.String s)
```
    Constructs a number initialized from a string representation.
    The leading characters are used to determine whether base: 0x and 0X for hexadecimal, 0b and 0B for binary, 0 for octal, and decimal otherwise.
  - Mpz
```
public Mpz(int sign,
           byte[] mag)
```
    Constructs a number from a unsigned stored in a big-endian byte array and a sign.
- Method Detail
  - set
```
public void set(int sign,
                byte[] mag)
```
    Sets the value of this given a magnitude and a sign.
    Used during deserialization.
    mag is the absolute value encoded in a byte array in big endian order.
  - byteArrayValue
```
public byte[] byteArrayValue()
```
    Returns the magnitude of this.
    User during serialization.
    The magnitude is the absolute value, and it is returned as a byte array stored in big-endian order.
  - finalize
```
protected void finalize()
```
    Deallocates the underlying mpz_t GMP object.
    
    Overrides:
    
    finalize in class java.lang.Object
  - clone
```
public Mpz clone()
          throws java.lang.CloneNotSupportedException
```
    Creates a new Mpz initialized with the value of this.
    
    Overrides:
    
    clone in class java.lang.Object
    
    Throws:
    
    java.lang.CloneNotSupportedException
  - set
```
public void set(Mpz v)
```
    Copies the argument into this.
  - set
```
public void set(int i)
```
    Sets this to an integer.
  - set
```
public void set(double d)
```
    Sets this to a double.
    The value is truncated.
  - set
```
public void set(java.math.BigInteger b)
```
    Sets this to a Java big integer.
  - set
```
public void set(java.lang.String s,
                int b)
```
    Sets this to the String s expressed in base b.
    
    See Also:
    
    Mpz(String,int)
  - set
```
public void set(java.lang.String s)
```
    Sets this to the String s.
    
    See Also:
    
    Mpz(String)
  - intValue
```
public int intValue()
```
    Returns this as an integer.
    The result is truncated if it does not fit in an integer.
    
    See Also:
    
    fitsInt()
  - doubleValue
```
public double doubleValue()
```
    Returns this as a double.
    If this cannot be represented as a double, the result is truncated.
    Overflows cause infinities to be returned.
  - doubleExponentValue
```
public double doubleExponentValue(int[] r)
```
    Converts the integer to a mantissa and exponent.
    The mantissa m returned is such that 0.5 <= |m| < 1, truncated to fit double.
    The exponent is stored into r[0].
  - bigIntegerValue
```
public java.math.BigInteger bigIntegerValue()
```
    Returns this as a Java big integer.
  - toString
```
public java.lang.String toString(int b)
```
    Returns a String representation of this in base b.
    
    Parameters:
    
    b - must be between 2 and 62.
  - toString
```
public java.lang.String toString()
```
    Returns a String representation this in base 10.
    
    Overrides:
    
    toString in class java.lang.Object
  - add
```
public void add(Mpz arg1,
                Mpz arg2)
```
    Stores arg1+arg2 into this.
  - add
```
public void add(Mpz arg1,
                int arg2)
```
    Stores arg1+arg2 into this.
  - add
```
public void add(Mpz arg)
```
    Adds arg to this.
  - add
```
public void add(int arg)
```
    Adds arg to this.
  - sub
```
public void sub(Mpz arg1,
                Mpz arg2)
```
    Stores arg1-arg2 into this.
  - sub
```
public void sub(Mpz arg1,
                int arg2)
```
    Stores arg1-arg2 into this.
  - sub
```
public void sub(int arg1,
                Mpz arg2)
```
    Stores arg1-arg2 into this.
  - sub
```
public void sub(Mpz arg)
```
    Subtracts arg from this.
  - sub
```
public void sub(int arg)
```
    Subtracts arg from this.
  - subRev
```
public void subRev(int arg)
```
    Replaces this with arg-this.
  - mul
```
public void mul(Mpz arg1,
                Mpz arg2)
```
    Stores arg1*arg2 into this.
  - mul
```
public void mul(Mpz arg1,
                int arg2)
```
    Stores arg1*arg2 into this.
  - mul
```
public void mul(Mpz arg)
```
    Multiplies this by arg.
  - mul
```
public void mul(int arg)
```
    Multiplies this by arg.
  - addMul
```
public void addMul(Mpz arg1,
                   Mpz arg2)
```
    Stores this+arg1*arg2 into this.
  - addMul
```
public void addMul(Mpz arg1,
                   int arg2)
```
    Stores this+arg1*arg2 into this.
  - subMul
```
public void subMul(Mpz arg1,
                   Mpz arg2)
```
    Stores this-arg1*arg2 into this.
  - subMul
```
public void subMul(Mpz arg1,
                   int arg2)
```
    Stores this-arg1*arg2 into this.
  - mul2exp
```
public void mul2exp(Mpz arg1,
                    int arg2)
```
    Stores arg1*2^arg2 into this.
    arg2 must be positive.
  - mul2exp
```
public void mul2exp(int arg)
```
    Multiplies this by 2^arg.
    arg must be positive.
  - neg
```
public void neg(Mpz arg)
```
    Stores -arg into this.
  - neg
```
public void neg()
```
    Replaces this with -this.
  - abs
```
public void abs(Mpz arg)
```
    Stores |arg| into this.
  - abs
```
public void abs()
```
    Replaces this with |this|.
  - cdivQ
```
public void cdivQ(Mpz n,
                  Mpz d)
           throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards +oo into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivQ
```
public void cdivQ(Mpz d)
           throws java.lang.ArithmeticException
```
    Divides this by d and rounds towards +oo.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivR
```
public void cdivR(Mpz n,
                  Mpz d)
           throws java.lang.ArithmeticException
```
    Stores the remainder of n/d rounded towards +oo into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivQR
```
public void cdivQR(Mpz r,
                   Mpz n,
                   Mpz d)
            throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards +oo into this and the remainder into r.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivQ
```
public int cdivQ(Mpz n,
                 int d)
          throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards +oo into this, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivQ
```
public int cdivQ(int d)
          throws java.lang.ArithmeticException
```
    Divides this by d, rounds towards +oo, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivR
```
public int cdivR(Mpz n,
                 int d)
          throws java.lang.ArithmeticException
```
    Stores the remainder of n/d rounded towards +oo into this, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivQR
```
public int cdivQR(Mpz r,
                  Mpz n,
                  int d)
           throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards +oo into this, the remainder into r, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivR
```
public int cdivR(int d)
          throws java.lang.ArithmeticException
```
    Returns the remainder of of this/d rounded towards +oo.
    this is unchanged.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivQ2exp
```
public void cdivQ2exp(Mpz n,
                      int d)
               throws java.lang.ArithmeticException
```
    Stores the quotient of n/(2^d) rounded towards +oo into this.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - cdivR2exp
```
public void cdivR2exp(Mpz n,
                      int d)
               throws java.lang.ArithmeticException
```
    Stores the remainder of n/(2^d) rounded towards +oo into this.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQ
```
public void fdivQ(Mpz n,
                  Mpz d)
           throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards -oo into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQ
```
public void fdivQ(Mpz d)
           throws java.lang.ArithmeticException
```
    Divides this by d and rounds towards -oo.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivR
```
public void fdivR(Mpz n,
                  Mpz d)
           throws java.lang.ArithmeticException
```
    Stores the remainder of n/d rounded towards -oo into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQR
```
public void fdivQR(Mpz r,
                   Mpz n,
                   Mpz d)
            throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards -oo into this and the remainder into r.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQ
```
public int fdivQ(Mpz n,
                 int d)
          throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards -oo into this, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQ
```
public int fdivQ(int d)
          throws java.lang.ArithmeticException
```
    Divides this by d, rounds towards -oo, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivR
```
public int fdivR(Mpz n,
                 int d)
          throws java.lang.ArithmeticException
```
    Stores the remainder of n/d rounded towards -oo into this, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQR
```
public int fdivQR(Mpz r,
                  Mpz n,
                  int d)
           throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards -oo into this, the remainder into r, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivR
```
public int fdivR(int d)
          throws java.lang.ArithmeticException
```
    Returns the remainder of of this/d rounded towards -oo.
    this is unchanged.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivQ2exp
```
public void fdivQ2exp(Mpz n,
                      int d)
               throws java.lang.ArithmeticException
```
    Stores the quotient of n/(2^d) rounded towards -oo into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - fdivR2exp
```
public void fdivR2exp(Mpz n,
                      int d)
               throws java.lang.ArithmeticException
```
    Stores the remainder of n/(2^d) rounded towards -oo into this.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQ
```
public void tdivQ(Mpz n,
                  Mpz d)
           throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards 0 into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQ
```
public void tdivQ(Mpz d)
           throws java.lang.ArithmeticException
```
    Divides this by d and rounds towards 0.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivR
```
public void tdivR(Mpz n,
                  Mpz d)
           throws java.lang.ArithmeticException
```
    Stores the remainder of n/d rounded towards 0 into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQR
```
public void tdivQR(Mpz r,
                   Mpz n,
                   Mpz d)
            throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards 0 into this and the remainder into r.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQ
```
public int tdivQ(Mpz n,
                 int d)
          throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards 0 into this, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQ
```
public int tdivQ(int d)
          throws java.lang.ArithmeticException
```
    Divides this by d, rounds towards 0, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivR
```
public int tdivR(Mpz n,
                 int d)
          throws java.lang.ArithmeticException
```
    Stores the remainder of n/d rounded towards 0 into this, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQR
```
public int tdivQR(Mpz r,
                  Mpz n,
                  int d)
           throws java.lang.ArithmeticException
```
    Stores the quotient of n/d rounded towards 0 into this, the remainder into r, and returns the remainder.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivR
```
public int tdivR(int d)
          throws java.lang.ArithmeticException
```
    Returns the remainder of of this/d rounded towards 0.
    this is unchanged.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivQ2exp
```
public void tdivQ2exp(Mpz n,
                      int d)
               throws java.lang.ArithmeticException
```
    Stores the quotient of n/(2^d) rounded towards 0 into this.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - tdivR2exp
```
public void tdivR2exp(Mpz n,
                      int d)
               throws java.lang.ArithmeticException
```
    Stores the remainder of n/(2^d) rounded towards 0 into this.
    d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - mod
```
public void mod(Mpz n,
                Mpz d)
         throws java.lang.ArithmeticException
```
    Stores n mod |d| into this.
    
    Throws:
    
    java.lang.ArithmeticException
  - mod
```
public void mod(Mpz d)
         throws java.lang.ArithmeticException
```
    Replaces this with this mod |d|.
    
    Throws:
    
    java.lang.ArithmeticException
  - mod
```
public int mod(Mpz n,
               int d)
        throws java.lang.ArithmeticException
```
    Stores n mod |d| into this and returns it.
    
    Throws:
    
    java.lang.ArithmeticException
  - mod
```
public int mod(int d)
        throws java.lang.ArithmeticException
```
    Replaces this with this mod |d|.
    
    Throws:
    
    java.lang.ArithmeticException
  - divExact
```
public void divExact(Mpz n,
                     Mpz d)
              throws java.lang.ArithmeticException
```
    Stores n/d into this, assuming that d divides n.
    
    Throws:
    
    java.lang.ArithmeticException
  - divExact
```
public void divExact(Mpz d)
              throws java.lang.ArithmeticException
```
    Divides this by d, assuming that d divides this.
    
    Throws:
    
    java.lang.ArithmeticException
  - divExact
```
public void divExact(Mpz n,
                     int d)
              throws java.lang.ArithmeticException
```
    Stores n/d into this, assuming that d divides n. d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - divExact
```
public void divExact(int d)
              throws java.lang.ArithmeticException
```
    Divides this by d, assuming that d divides this. d must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - isDivisible
```
public boolean isDivisible(Mpz d)
```
    Returns true if d divides this.
    Only 0 is divisible by 0.
  - isDivisible
```
public boolean isDivisible(int d)
```
    Returns true if d divides this.
    d must be positive.
    Only 0 is divisible by 0.
  - isDivisible2exp
```
public boolean isDivisible2exp(int d)
```
    Returns true if 2^d divides this.
    d must be positive.
  - isCongruent
```
public boolean isCongruent(Mpz c,
                           Mpz d)
```
    Returns true if this equals c modulo d.
    When d=0, returns true if this equals c.
  - isCongruent
```
public boolean isCongruent(int c,
                           int d)
```
    Returns true if this equals c modulo d.
    d must be positive.
    When d=0, returns true if this equals c.
  - isCongruent2exp
```
public boolean isCongruent2exp(Mpz c,
                               int d)
```
    Returns true if this equals c modulo 2^d.
    d must be positive.
  - pow
```
public void pow(Mpz b,
                Mpz e,
                Mpz m)
         throws java.lang.ArithmeticException
```
    Stores b^e mod m into this.
    Throws an ArithmeticException if e < 0 and b has no inverse modulo m.
    
    Throws:
    
    java.lang.ArithmeticException
  - pow
```
public void pow(Mpz b,
                int e,
                Mpz m)
         throws java.lang.ArithmeticException
```
    Stores b^e mod m into this.
    e must be positive.
    
    Throws:
    
    java.lang.ArithmeticException
  - pow
```
public void pow(Mpz b,
                int e)
```
    Stores b^e into this.
    e must be positive.
    0^0 is 1.
  - pow
```
public void pow(int e)
```
    Takes the e-th power of this.
    e must be positive.
    0^0 is 1.
  - pow
```
public void pow(int b,
                int e)
```
    Stores b^e into this.
    b and e must be positive.
    0^0 is 1.
  - root
```
public boolean root(Mpz op,
                    int n)
```
    Stores the n-th root of op into this, truncated.
    Returns true if the computation was exact.
    n must be positive.
  - root
```
public boolean root(int n)
```
    Takes the n-th root of this, truncated.
    Returns true if the computation was exact.
    n must be positive.
  - root
```
public void root(Mpz r,
                 Mpz op,
                 int n)
```
    Stores the n-th root of op into this, truncated, and the remainder op-this^n into r.
    n must be positive.
  - sqrt
```
public void sqrt(Mpz op)
```
    Stores the truncated square root of op into this.
  - sqrt
```
public void sqrt()
```
    Takes the truncated square root of this.
  - sqrt
```
public void sqrt(Mpz r,
                 Mpz op)
```
    Stores the square root of op into this, truncated, and the remainder op-this^2 into r.
  - isPerfectPower
```
public boolean isPerfectPower()
```
    Returns true if this has the form a^b for some a and b > 1.
    0 and 1 are perfect powers.
  - isPerfectSquare
```
public boolean isPerfectSquare()
```
    Returns true if this has the form a^2 for some a.
    0 and 1 are perfect squares.
  - isProbabPrime
```
public int isProbabPrime(int r)
```
    Returns 2 if this is definitely prime, 1 if it is probably prime, and 0 if it is definitely composite.
    r is the number of tests; high numbers increasing the certainty. A value between 5 and 10 is reasonable.
  - nextPrime
```
public void nextPrime(Mpz op)
```
    Stores into this the next prime greater than op.
    This uses a probabilistic algorithm so that the chance of getting a composite are non-null but extremely small.
  - gcd
```
public void gcd(Mpz op1,
                Mpz op2)
```
    Stores into this the greatest common divisor of op1 and op2.
    The result is always positive, even for negative inputs.
  - gcd
```
public int gcd(Mpz op1,
               int op2)
```
    Returns the greatest common divisor of op1 and op2.
    this is unchanged.
    op2 must be strictly positive.
  - gcd
```
public void gcd(Mpz s,
                Mpz t,
                Mpz op1,
                Mpz op2)
```
    Stores the greatest common divisor of op1 and op2 into this.
    Sets s and t to values such that s*op1+t*op2 = gcd and |s| <= |op2|, |t| <= |op1|.
  - lcm
```
public void lcm(Mpz op1,
                Mpz op2)
```
    Stores into this the least common multiple of op1 and op2.
  - lcm
```
public void lcm(Mpz op1,
                int op2)
```
    Stores into this the least common multiple of op1 and op2.
    op2 must be positive.
  - invert
```
public boolean invert(Mpz op1,
                      Mpz op2)
```
    Stores the inverse of op1 modulo op2 into this.
    Returns true if this inverse exists. Otherwise, returns false; this is undefined.
  - jacobi
```
public static int jacobi(Mpz b,
                         Mpz p)
```
    Returns the Jacobi symbol of a and b.
    b must be odd.
  - legendre
```
public static int legendre(Mpz a,
                           Mpz p)
```
    Returns the Legendre symbol.
    p must be an odd positive prime.
  - kronecker
```
public static int kronecker(Mpz a,
                            Mpz b)
```
    Returns the Jacobi symbol with the Kronecker extension.
  - kronecker
```
public static int kronecker(Mpz a,
                            int b)
```
    Returns the Jacobi symbol with the Kronecker extension.
  - kronecker
```
public static int kronecker(int a,
                            Mpz b)
```
    Returns the Jacobi symbol with the Kronecker extension.
  - remove
```
public int remove(Mpz op,
                  Mpz f)
```
    Stores into this op with all occurrences of factor f removed.
    Returns the number of removed factors.
  - remove
```
public int remove(Mpz f)
```
    Removes from this all occurrences of factor f.
    Returns the number of removed factors.
  - fac
```
public void fac(int op)
```
    Stores op! into this.
    op must be positive.
  - bin
```
public void bin(Mpz n,
                int k)
```
    Stores into this the binomial coefficient (n k).
    k must be positive.
  - bin
```
public void bin(int n,
                int k)
```
    Stores into this the binomial coefficient (n k).
    n and k must be positive.
  - fib
```
public void fib(int n)
```
    Stores into this the n-th Fibonacci number.
    n must be positive.
  - fib
```
public void fib(Mpz r,
                int n)
```
    Stores into this the n-th Fibonacci number, and into r the n-1-th Fibonacci number.
    n must be positive.
  - lucnum
```
public void lucnum(int n)
```
    Stores into this the n-th Lucas number.
    n must be positive.
  - lucnum
```
public void lucnum(Mpz r,
                   int n)
```
    Stores into this the n-th Lucas number, and into r the n-1-th Lucas number.
    n must be positive.
  - cmp
```
public int cmp(Mpz op)
```
    Returns a positive, null, or negative number when this is respectively strictly greater, equal, or strictly smaller than op.
  - cmp
```
public int cmp(int op)
```
    Returns a positive, null, or negative number when this is respectively strictly greater, equal, or strictly smaller than op.
  - cmp
```
public int cmp(double op)
```
    Returns a positive, null, or negative number when this is respectively strictly greater, equal, or strictly smaller than op.
  - cmpAbs
```
public int cmpAbs(Mpz op)
```
    Returns a positive, null, or negative number when |this| is respectively strictly greater, equal, or strictly smaller than |op|.
  - cmpAbs
```
public int cmpAbs(int op)
```
    Returns a positive, null, or negative number when |this| is respectively strictly greater, equal, or strictly smaller than |op|.
  - cmpAbs
```
public int cmpAbs(double op)
```
    Returns a positive, null, or negative number when |this| is respectively strictly greater, equal, or strictly smaller than |op|.
  - sgn
```
public int sgn()
```
    Returns +1, 0, or -1 when this is respectively strictly positive, null, or strictly negative.
  - isEqual
```
public boolean isEqual(Mpz x)
```
    Whether this and x have the same value.
  - equals
```
public boolean equals(java.lang.Object x)
```
    Whether x is a Mpz and has the same value as this.
    
    Overrides:
    
    equals in class java.lang.Object
  - compareTo
```
public int compareTo(Mpz x)
```
    Compare the value of this and x.
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<Mpz>
  - hashCode
```
public int hashCode()
```
    Returns a hash of the value of this.
    
    Overrides:
    
    hashCode in class java.lang.Object
  - isPhysicalEqual
```
public boolean isPhysicalEqual(Mpz x)
```
    Whether this and x have the same address in memory.
  - and
```
public void and(Mpz op1,
                Mpz op2)
```
    Stores the bitwise and of op1 and op2 into this.
  - and
```
public void and(Mpz op)
```
    Stores the bitwise and of this and op into this.
  - or
```
public void or(Mpz op1,
               Mpz op2)
```
    Stores the bitwise or of op1 and op2 into this.
  - or
```
public void or(Mpz op)
```
    Stores the bitwise or of this and op into this.
  - xor
```
public void xor(Mpz op1,
                Mpz op2)
```
    Stores the bitwise xor of op1 and op2 into this.
  - xor
```
public void xor(Mpz op)
```
    Stores the bitwise xor of this and op into this.
  - not
```
public void not(Mpz op)
```
    Stores the bitwise complement of op into this.
  - not
```
public void not()
```
    Stores the bitwise complement of this into this.
  - popCount
```
public int popCount()
```
    Returns the number of bits set to 1 in this.
    Returns infinite if this is negative.
  - hamDist
```
public int hamDist(Mpz op)
```
    Returns the Hamming distance between this and op.
    Returns infinite if this and op have different signs.
  - scan0
```
public int scan0(int pos)
```
    Returns the position of the first bit set to 0 at or after position pos.
    pos must be positive.
    May return infinite, if this is negative.
  - scan1
```
public int scan1(int pos)
```
    Returns the position of the first bit set to 1 at or after position pos.
    pos must be positive.
    May return infinite, if this is positive.
  - setBit
```
public void setBit(int pos)
```
    Sets the pos-th bit to 1 in this.
    pos must be positive.
  - clrBit
```
public void clrBit(int pos)
```
    Sets the pos-th bit to 0 in this.
    pos must be positive.
  - notBit
```
public void notBit(int pos)
```
    Inverts the pos-th bit in this.
    pos must be positive.
  - tstBit
```
public boolean tstBit(int pos)
```
    Returns true if the pos-th bit in this is 1.
    pos must be positive.
  - fitsInt
```
public boolean fitsInt()
```
    Whether this can fit in an int.
  - isOdd
```
public boolean isOdd()
```
    Whether this is odd.
  - isEven
```
public boolean isEven()
```
    Whether this is even.
  - sizeInBase
```
public int sizeInBase(int b)
```
    Returns the number of digits necessary to represent |this| in base b.
  - size
```
public int size()
```
    Returns the size (in GMP limbs) of the internal representation of this.
  - randomBits
```
public void randomBits(RandState r,
                       int n)
```
    Stores into this a uniformly distributed random number with n bits (i.e., in 0..2^n-1).
    n must be positive.
  - random
```
public void random(RandState r,
                   Mpz n)
```
    Stores into this a uniformly distributed random number in 0..n-1.
  - rRandomBits
```
public void rRandomBits(RandState r,
                        int n)
```
    Stores into this a random number with n bits, and long strings of zeros and ones in its binary representation.
    Useful to trigger corner-case bugs when testing.

Class Mpz

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

infinite

Constructor Detail

Mpz

Mpz

Mpz

Mpz

Mpz

Mpz

Mpz

Mpz

Method Detail

set

byteArrayValue

finalize

clone

set

set

set

set

set

set

intValue

doubleValue

doubleExponentValue

bigIntegerValue

toString

toString

add

add

add

add

sub

sub

sub

sub

sub

subRev

mul

mul

mul

mul

addMul

addMul

subMul

subMul

mul2exp

mul2exp

neg

neg

abs

abs

cdivQ

cdivQ

cdivR

cdivQR

cdivQ

cdivQ

cdivR

cdivQR

cdivR

cdivQ2exp

cdivR2exp

fdivQ

fdivQ

fdivR

fdivQR

fdivQ

fdivQ

fdivR

fdivQR

fdivR

fdivQ2exp

fdivR2exp

tdivQ