Package gmp

Class Mpz

java.lang.Object

gmp.Mpz

All Implemented Interfaces:

Serializable, Cloneable, Comparable<Mpz>

Direct Known Subclasses:

MpzRef

public class Mpz
extends Object
implements Serializable, Comparable<Mpz>, Cloneable

GMP arbitrary precision integers.

This class wraps mpz_t GMP objects.

See Also:

• Serialized Form

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor	Description
Mpz()	Constructs an uninitialized number.
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(String s)	Constructs a number initialized from a string representation.
Mpz(String s, int b)	Constructs a number initialized from a string representation in base b.
Mpz(BigInteger b)	Constructs a number initialized from a Java big integer.

Method Summary

Modifier and Type	Method	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.
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(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.
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(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(String s)	Sets this to the String s.
void	set(String s, int b)	Sets this to the String s expressed in base b.
void	set(BigInteger b)	Sets this to a Java big integer.
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.
String	toString()	Returns a String representation this in base 10.
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

finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

infinite

public static final int infinite

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

See Also:

• Constant Field Values

Constructor Details

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(BigInteger b)

Constructs a number initialized from a Java big integer.

Mpz

public Mpz(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(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 Details

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.

clone

public Mpz clone()
          throws CloneNotSupportedException

Creates a new Mpz initialized with the value of this.

Overrides:

clone in class Object

Throws:

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(BigInteger b)

Sets this to a Java big integer.

set

public void set(String s,
 int b)

Sets this to the String s expressed in base b.

See Also:

• Mpz(String,int)

set

public void set(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 BigInteger bigIntegerValue()

Returns this as a Java big integer.

toString

public String toString(int b)

Returns a String representation of this in base b.

Parameters:

b - must be between 2 and 62.

toString

public String toString()

Returns a String representation this in base 10.

Overrides:

toString in class 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 ArithmeticException

Stores the quotient of n/d rounded towards +oo into this.

Throws:

ArithmeticException

cdivQ

public void cdivQ(Mpz d)
           throws ArithmeticException

Divides this by d and rounds towards +oo.

Throws:

ArithmeticException

cdivR

public void cdivR(Mpz n,
 Mpz d)
           throws ArithmeticException

Stores the remainder of n/d rounded towards +oo into this.

Throws:

ArithmeticException

cdivQR

public void cdivQR(Mpz r,
 Mpz n,
 Mpz d)
            throws ArithmeticException

Stores the quotient of n/d rounded towards +oo into this and the remainder into r.

Throws:

ArithmeticException

cdivQ

public int cdivQ(Mpz n,
 int d)
          throws ArithmeticException

Stores the quotient of n/d rounded towards +oo into this, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

cdivQ

public int cdivQ(int d)
          throws ArithmeticException

Divides this by d, rounds towards +oo, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

cdivR

public int cdivR(Mpz n,
 int d)
          throws ArithmeticException

Stores the remainder of n/d rounded towards +oo into this, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

cdivQR

public int cdivQR(Mpz r,
 Mpz n,
 int d)
           throws 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:

ArithmeticException

cdivR

public int cdivR(int d)
          throws ArithmeticException

Returns the remainder of of this/d rounded towards +oo.

this is unchanged.

d must be positive.

Throws:

ArithmeticException

cdivQ2exp

public void cdivQ2exp(Mpz n,
 int d)
               throws ArithmeticException

Stores the quotient of n/(2^d) rounded towards +oo into this.

d must be positive.

Throws:

ArithmeticException

cdivR2exp

public void cdivR2exp(Mpz n,
 int d)
               throws ArithmeticException

Stores the remainder of n/(2^d) rounded towards +oo into this.

d must be positive.

Throws:

ArithmeticException

fdivQ

public void fdivQ(Mpz n,
 Mpz d)
           throws ArithmeticException

Stores the quotient of n/d rounded towards -oo into this.

Throws:

ArithmeticException

fdivQ

public void fdivQ(Mpz d)
           throws ArithmeticException

Divides this by d and rounds towards -oo.

Throws:

ArithmeticException

fdivR

public void fdivR(Mpz n,
 Mpz d)
           throws ArithmeticException

Stores the remainder of n/d rounded towards -oo into this.

Throws:

ArithmeticException

fdivQR

public void fdivQR(Mpz r,
 Mpz n,
 Mpz d)
            throws ArithmeticException

Stores the quotient of n/d rounded towards -oo into this and the remainder into r.

Throws:

ArithmeticException

fdivQ

public int fdivQ(Mpz n,
 int d)
          throws ArithmeticException

Stores the quotient of n/d rounded towards -oo into this, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

fdivQ

public int fdivQ(int d)
          throws ArithmeticException

Divides this by d, rounds towards -oo, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

fdivR

public int fdivR(Mpz n,
 int d)
          throws ArithmeticException

Stores the remainder of n/d rounded towards -oo into this, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

fdivQR

public int fdivQR(Mpz r,
 Mpz n,
 int d)
           throws 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:

ArithmeticException

fdivR

public int fdivR(int d)
          throws ArithmeticException

Returns the remainder of of this/d rounded towards -oo.

this is unchanged.

d must be positive.

Throws:

ArithmeticException

fdivQ2exp

public void fdivQ2exp(Mpz n,
 int d)
               throws ArithmeticException

Stores the quotient of n/(2^d) rounded towards -oo into this.

Throws:

ArithmeticException

fdivR2exp

public void fdivR2exp(Mpz n,
 int d)
               throws ArithmeticException

Stores the remainder of n/(2^d) rounded towards -oo into this.

d must be positive.

Throws:

ArithmeticException

tdivQ

public void tdivQ(Mpz n,
 Mpz d)
           throws ArithmeticException

Stores the quotient of n/d rounded towards 0 into this.

Throws:

ArithmeticException

tdivQ

public void tdivQ(Mpz d)
           throws ArithmeticException

Divides this by d and rounds towards 0.

Throws:

ArithmeticException

tdivR

public void tdivR(Mpz n,
 Mpz d)
           throws ArithmeticException

Stores the remainder of n/d rounded towards 0 into this.

Throws:

ArithmeticException

tdivQR

public void tdivQR(Mpz r,
 Mpz n,
 Mpz d)
            throws ArithmeticException

Stores the quotient of n/d rounded towards 0 into this and the remainder into r.

Throws:

ArithmeticException

tdivQ

public int tdivQ(Mpz n,
 int d)
          throws ArithmeticException

Stores the quotient of n/d rounded towards 0 into this, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

tdivQ

public int tdivQ(int d)
          throws ArithmeticException

Divides this by d, rounds towards 0, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

tdivR

public int tdivR(Mpz n,
 int d)
          throws ArithmeticException

Stores the remainder of n/d rounded towards 0 into this, and returns the remainder.

d must be positive.

Throws:

ArithmeticException

tdivQR

public int tdivQR(Mpz r,
 Mpz n,
 int d)
           throws 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:

ArithmeticException

tdivR

public int tdivR(int d)
          throws ArithmeticException

Returns the remainder of of this/d rounded towards 0.

this is unchanged.

d must be positive.

Throws:

ArithmeticException

tdivQ2exp

public void tdivQ2exp(Mpz n,
 int d)
               throws ArithmeticException

Stores the quotient of n/(2^d) rounded towards 0 into this.

d must be positive.

Throws:

ArithmeticException

tdivR2exp

public void tdivR2exp(Mpz n,
 int d)
               throws ArithmeticException

Stores the remainder of n/(2^d) rounded towards 0 into this.

d must be positive.

Throws:

ArithmeticException

mod

public void mod(Mpz n,
 Mpz d)
         throws ArithmeticException

Stores n mod |d| into this.

Throws:

ArithmeticException

mod

public void mod(Mpz d)
         throws ArithmeticException

Replaces this with this mod |d|.

Throws:

ArithmeticException

mod

public int mod(Mpz n,
 int d)
        throws ArithmeticException

Stores n mod |d| into this and returns it.

Throws:

ArithmeticException

mod

public int mod(int d)
        throws ArithmeticException

Replaces this with this mod |d|.

Throws:

ArithmeticException

divExact

public void divExact(Mpz n,
 Mpz d)
              throws ArithmeticException

Stores n/d into this, assuming that d divides n.

Throws:

ArithmeticException

divExact

public void divExact(Mpz d)
              throws ArithmeticException

Divides this by d, assuming that d divides this.

Throws:

ArithmeticException

divExact

public void divExact(Mpz n,
 int d)
              throws ArithmeticException

Stores n/d into this, assuming that d divides n. d must be positive.

Throws:

ArithmeticException

divExact

public void divExact(int d)
              throws ArithmeticException

Divides this by d, assuming that d divides this. d must be positive.

Throws:

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 ArithmeticException

Stores b^e mod m into this.

Throws an ArithmeticException if e < 0 and b has no inverse modulo m.

Throws:

ArithmeticException

pow

public void pow(Mpz b,
 int e,
 Mpz m)
         throws ArithmeticException

Stores b^e mod m into this.

e must be positive.

Throws:

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(Object x)

Whether x is a Mpz and has the same value as this.

Overrides:

equals in class Object

compareTo

public int compareTo(Mpz x)

Compare the value of this and x.

Specified by:

compareTo in interface Comparable<Mpz>

hashCode

public int hashCode()

Returns a hash of the value of this.

Overrides:

hashCode in class 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.