Class MPZ

java.lang.Object

java.lang.Number

it.unich.jgmp.MPZ

All Implemented Interfaces:

Serializable, Comparable<MPZ>

public class MPZ
extends Number
implements Comparable<MPZ>

Multi-precision integer number. This class encapsulates the mpz_t data type, see the Integer Functions page of the GMP manual. In determining the names and prototypes of the methods of the MPZ class, we adopt the rules described in the documentation of the it.unich.jgmp package, enriched with the following ones:

• the functions in the categories I/O of Integers, Integer Import and Export and Special Functions are not exposed by the MPZ class.

See Also:

• Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private static class	MPZ.MPZCleaner	Cleaning action for the MPZ class.
static enum	MPZ.PrimalityStatus	Result enumeration for the invalid reference isProbabPrime method.

Field Summary

Fields

Modifier and Type	Field	Description
private MpzT	mpzNative	The pointer to the native mpz_t object.
private static final long	serialVersionUID	Version for serializability.

Constructor Summary

Constructors

Modifier	Constructor	Description
	MPZ()	Build an MPZ whose value is zero.
	MPZ(double op)	Build an MPZ whose value is the truncation of op.
	MPZ(long op)	Build an MPZ whose value is op.
	MPZ(MPF op)	Build an MPZ whose value is the truncation of op.
	MPZ(MPQ op)	Build an MPZ whose value is the truncation of op.
	MPZ(MPZ op)	Build an MPZ whose value is op.
private	MPZ(MpzT pointer)	A private constructor which build an MPZ starting from a pointer to its native data object.
	MPZ(String str)	Build an MPZ whose value is the number represented by the string str in decimal base.
	MPZ(String str, int base)	Build an MPZ whose value is the number represented by the string str in the specified base.
	MPZ(BigInteger op)	Builds an MPZ whose value is the same as op.

Method Summary

Modifier and Type	Method	Description
MPZ	abs()	Return an MPZ whose value is the absolute value of this.
MPZ	absAssign()	Set this MPZ to its absolute value.
MPZ	absAssign(MPZ op)	Set this MPZ to the absolute value of op.
MPZ	add(MPZ op)	Return an MPZ whose value is (this + op).
MPZ	addAssign(MPZ op)	Set this MPZ to (this + op)
MPZ	addAssign(MPZ op1, MPZ op2)	Set this MPZ to (op1 + op2).
MPZ	addmul(MPZ op1, MPZ op2)	Return an MPZ whose value is (this + op1 * op2).
MPZ	addmulAssign(MPZ op1, MPZ op2)	Add (op1 * op2) to this MPZ.
MPZ	addmulUi(MPZ op1, long op2)	Return an MPZ whose value is (this + op1 * op2).
MPZ	addmulUiAssign(MPZ op1, long op2)	Add (op1 * op2) to this MPZ.
MPZ	addUi(long op)	Return an MPZ whose value is (this + op).
MPZ	addUiAssign(long op)	Set this MPZ to (this + op)
MPZ	addUiAssign(MPZ op1, long op2)	Set this MPZ to (op1 + op2).
MPZ	and(MPZ op)	Return an MPZ whose value is (this & op).
MPZ	andAssign(MPZ op)	Set this MPZ to (this & op).
MPZ	andAssign(MPZ op1, MPZ op2)	Set this MPZ to (op1 & op2).
MPZ	binUi(long k)	Return an MPZ whose value is the binomial coefficient this over k.
MPZ	binUiAssign(long k)	Set this MPZ to the binomial coefficient this over k.
MPZ	binUiAssign(MPZ n, long k)	Set this MPZ to the binomial coefficient n over k.
static MPZ	binUiUi(long n, long k)	Return an MPZ whose value is the binomial coefficient n over k.
MPZ	binUiUiAssign(long n, long k)	Set this MPZ to the binomial coefficient n over k.
ByteBuffer	bufferExport(int order, int size, int endian, long nails)	Return a ByteBuffer filled with word data from this MPZ.
static MPZ	bufferImport(int order, int size, int endian, long nails, ByteBuffer op)	Return an MPZ whose value is determined from the buffer of word data at op.
MPZ	bufferImportAssign(int order, int size, int endian, long nails, ByteBuffer op)	Set this MPZ from the buffer of word data at op.
MPZ	cdivq(MPZ d)	Return an MPZ whose value is the quotient of the integer division (this / d), rounded towards +∞.
MPZ	cdivq2Exp(long b)	Return an MPZ whose value is the quotient of the integer division (this / 2b), rounded towards +∞.
MPZ	cdivq2ExpAssign(long b)	Set this MPZ to the quotient of the integer division (this / 2b), rounded toward +∞.
MPZ	cdivq2ExpAssign(MPZ n, long b)	Set this MPZ to the quotient of the integer division (n / 2b), rounded toward +∞.
MPZ	cdivqAssign(MPZ d)	Set this MPZ to the quotient of the integer division (this / d), rounded towards +∞.
MPZ	cdivqAssign(MPZ n, MPZ d)	Set this MPZ to the quotient of the integer division (n / d), rounded towards +∞.
org.javatuples.Pair<MPZ,MPZ>	cdivqr(MPZ d)	Return a pair of MPZs whose values are the quotient and remainder of the integer division (this / d), rounded towards +∞.
MPZ	cdivqrAssign(MPZ r, MPZ d)	Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards +∞.
MPZ	cdivqrAssign(MPZ r, MPZ n, MPZ d)	Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards +∞.
long	cdivqrUiAssign(MPZ r, long d)	Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards +∞; it also returns the remainder.
long	cdivqrUiAssign(MPZ r, MPZ n, long d)	Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards +∞; it also returns the remainder.
long	cdivqUiAssign(long d)	Set this MPZ to the quotient of the integer division (this / d), rounded towards +∞; it also returns the remainder.
long	cdivqUiAssign(MPZ n, long d)	Set this MPZ to the quotient of the integer division (n / d), rounded towards +∞; it also Return the remainder.
MPZ	cdivr(MPZ d)	Return an MPZ whose value is the remainder of the integer division (this / d), rounded towards +∞.
MPZ	cdivr2Exp(long b)	Return an MPZ whose value is the remainder of the integer division (this / 2b), rounded towards +∞.
MPZ	cdivr2ExpAssign(long b)	Set this MPZ to the remainder of the integer division (this / 2b), rounded toward +∞.
MPZ	cdivr2ExpAssign(MPZ n, long b)	Set this MPZ to the remainder of the integer division (n / 2b), rounded toward +∞.
MPZ	cdivrAssign(MPZ d)	Set this MPZ to the remainder of the integer division (this / d), rounded towards +∞.
MPZ	cdivrAssign(MPZ n, MPZ d)	Set this MPZ to the remainder of the integer division (n / d), rounded towards +∞.
long	cdivrUiAssign(long d)	Set this MPZ to the remainder of the integer division (this / d), rounded towards +∞; it also returns the remainder.
long	cdivrUiAssign(MPZ n, long d)	Set this MPZ to the remainder of the integer division (n / d), rounded towards +∞; it also returns the remainder.
long	cdivUi(long d)	Return the remainder of the integer division (this / d), rounded towards +∞.
MPZ	clrbit(long index)	Return an MPZ whose value is (this & ~ 2index).
MPZ	clrbitAssign(long index)	Clear the bit index of this MPZ.
int	cmp(double op)	Compare this with op.
int	cmp(long op)	Compare this with op.
int	cmp(MPZ op)	Compare this with op.
int	cmpabs(double op)	Compare the absolute values of this and op.
int	cmpabs(MPZ op)	Compare the absolute values of this and op.
int	cmpabsUi(long op)	Compare the absolute values of this and op.
int	cmpUi(long op)	Compare this with op.
MPZ	com()	Return an MPZ whose value is (~ op).
MPZ	comAssign()	Set this MPZ to (~ this).
MPZ	comAssign(MPZ op)	Set this MPZ to (~ op).
MPZ	combit(long index)	Return an MPZ whose value is (this ^ 2index).
MPZ	combitAssign(long index)	Complement the bit index of this MPZ.
int	compareTo(MPZ op)	Compare this MPZ with op.
static MPZ	dfacUi(long n)	Return an MPZ whose value the double factorial of n.
MPZ	dfacUiAssign(long n)	Set this MPZ to the double factorial of n.
MPZ	divexact(MPZ d)	Return an MPZ whose value is the quotient of (this / d).
MPZ	divexactAssign(MPZ d)	Set this MPZ to the quotient of (this / d).
MPZ	divexactAssign(MPZ n, MPZ d)	Set this MPZ to the quotient of (n / d).
MPZ	divexactUi(long d)	Return an MPZ whose value is the quotient of (this / d).
MPZ	divexactUiAssign(long d)	Set this MPZ to the quotient of (this / d).
MPZ	divexactUiAssign(MPZ n, long d)	Set this MPZ to the quotient of (n / d).
double	doubleValue()	Convert this MPZ to a double, truncating if necessary.
boolean	equals(Object obj)	Compare this MPZ with the object op for equality.
static MPZ	facUi(long n)	Return an MPZ whose value is the factorial of n.
MPZ	facUiAssign(long n)	Set this MPZ to the factorial of n.
MPZ	fdivq(MPZ d)	Return an MPZ whose value is the quotient of the integer division (this / d), rounded towards -∞.
MPZ	fdivq2Exp(long b)	Return an MPZ whose value is the quotient of the integer division (this / 2b), rounded towards -∞.
MPZ	fdivq2ExpAssign(long b)	Set this MPZ to the quotient of the integer division (this / 2b), rounded toward -∞.
MPZ	fdivq2ExpAssign(MPZ n, long b)	Set this MPZ to the quotient of the integer division (n / 2b), rounded toward -∞.
MPZ	fdivqAssign(MPZ d)	Set this MPZ to the quotient of the integer division (this / d), rounded towards -∞.
MPZ	fdivqAssign(MPZ n, MPZ d)	Set this MPZ to the quotient of the integer division (n / d), rounded towards -∞.
org.javatuples.Pair<MPZ,MPZ>	fdivqr(MPZ d)	Return two MPZs whose values are the quotient and remainder of the integer division (this / d), rounded towards -∞.
MPZ	fdivqrAssign(MPZ r, MPZ d)	Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards -∞.
MPZ	fdivqrAssign(MPZ r, MPZ n, MPZ d)	Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards -∞.
long	fdivqrUiAssign(MPZ r, long d)	Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards -∞; it also returns the absolute value of the remainder.
long	fdivqrUiAssign(MPZ r, MPZ n, long d)	Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards -∞; it also returns the absolute value of the remainder.
long	fdivqUiAssign(long d)	Set this MPZ to the quotient of the integer division (this / d), rounded towards -∞; it also returns the absolute value of the remainder.
long	fdivqUiAssign(MPZ n, long d)	Set this MPZ to the quotient of the integer division (n / d), rounded towards -∞; it also returns the absolute value of the remainder.
MPZ	fdivr(MPZ d)	Return an MPZ whose value is the remainder of the integer division (this / d), rounded towards -∞.
MPZ	fdivr2Exp(long b)	Return an MPZ whose value is the remainder of the integer division (this / 2b), rounded towards -∞.
MPZ	fdivr2ExpAssign(long b)	Set this MPZ to the remainder of the integer division (this / 2b), rounded toward -∞.
MPZ	fdivr2ExpAssign(MPZ n, long b)	Set this MPZ to the remainder of the integer division (n / 2b), rounded toward -∞.
MPZ	fdivrAssign(MPZ d)	Set this MPZ to the remainder of the integer division (this / d), rounded towards -∞.
MPZ	fdivrAssign(MPZ n, MPZ d)	Set this MPZ to the remainder of the integer division (n / d), rounded towards -∞.
long	fdivrUiAssign(long d)	Set this MPZ to the remainder of the integer division (this / d), rounded towards -∞; it also returns the absolute value of the remainder.
long	fdivrUiAssign(MPZ n, long d)	Set this MPZ to the remainder of the integer division (n / d), rounded towards -∞; it also returns the absolute value of the remainder.
long	fdivUi(long d)	Return the remainder of the integer division (this / d), rounded towards -∞.
static org.javatuples.Pair<MPZ,MPZ>	fib2Ui(long n)	Return two MPZ whose values are the n-th and (n-1)-th Fibonacci numbers.
MPZ	fib2UiAssign(MPZ fnsub1, long n)	Set the value of this and fnsub1 to the n-th and (n-1)-th Fibonacci numbers respecively.
static MPZ	fibUi(long n)	Return an MPZ whose value is the n-th Fibonacci number.
MPZ	fibUiAssign(long n)	Set this MPZ to the n-th Fibonacci number.
boolean	fitsSint()	Return true if and only if this MPZ fits into a native signed int.
boolean	fitsSlong()	Return true if and only if this MPZ fits into a native signed long.
boolean	fitsSshort()	Return true if and only if this MPZ fits into a native signed short.
boolean	fitsUint()	Return true if and only if this MPZ fits into a native unsigned int.
boolean	fitsUlong()	Return true if and only if this MPZ fits into a native unsigned long.
boolean	fitsUshort()	Return true if and only if this MPZ fits into a native unsigned short.
float	floatValue()	Convert this MPZ to a float, truncating if necessary.
MPZ	gcd(MPZ op)	Return an MPZ whose value is the greatest commond divisor of this and op.
MPZ	gcdAssign(MPZ op)	Set this MPZ to the greatest commond divisor of this and op.
MPZ	gcdAssign(MPZ op1, MPZ op2)	Set this MPZ to the greatest commond divisor of op1 and op2.
org.javatuples.Triplet<MPZ,MPZ,MPZ>	gcdext(MPZ op)	Return the greatest common divisor of this and op, together with numbers s and t satisfying (a*this + b*op = g) See the GMP function mpz_gcdext.
MPZ	gcdextAssign(MPZ s, MPZ t, MPZ op)	Set this MPZ to the greatest common divisor of this and op, and in addition Set s and t to coefficients satisfying (this*s + op*t = gcd).
MPZ	gcdextAssign(MPZ s, MPZ t, MPZ a, MPZ b)	Set this MPZ to the greatest common divisor of a and b, and in addition Set s and t to coefficients satisfying (a*s + b*t = gcd).
long	gcdUi(long op)	Return the greatest commond divisor of this and op.
long	gcdUiAssign(long op)	Set this MPZ to the greatest commond divisor of op1 and op2, and returns it.
long	gcdUiAssign(MPZ op1, long op2)	Set this MPZ to the greatest commond divisor of op1 and op2, and return it.
BigInteger	getBigInteger()	Converts this MPZ to BigInteger.
double	getD()	Convert this MPZ to a double, truncating if necessary.
org.javatuples.Pair<Double,Long>	getD2Exp()	Convert this MPZ to a pair made of mantissa and exponent, truncating if necessary.
MpzT	getNative()	Return the native pointer to the GMP object.
long	getSi()	Convert this MPZ to a signed long.
String	getStr(int base)	Return the String representation of this MPZ in the specified base, or null if the base is not valid.
long	getUi()	Convert this MPZ to an unsigned long.
long	hamdist(MPZ op)	If this and op are both >= 0 or both < 0, return the Hamming distance between them, which is the number of bit positions where this and op have different bit values.
int	hashCode()	Return a hash code value for this MPZ.
static MPZ	init()	Return an MPZ whose value is zero.
static MPZ	init2(long n)	Return an MPZ whose value is zero, with pre-allocated space for n-bit numbers.
static MPZ	initSet(double op)	Return an MPZ whose value is the truncation of op.
static MPZ	initSet(long op)	Return an MPZ whose value is op.
static MPZ	initSet(MPZ op)	Return an MPZ whose value is op.
static org.javatuples.Pair<Integer,MPZ>	initSet(String str, int base)	Return an MPZ whose value is the number represented by the string str in the specified base.
static MPZ	initSetUi(long op)	Return an MPZ whose value is op.
int	intValue()	Convert this MPZ to a signed int, truncating if necessary.
Optional<MPZ>	invert(MPZ op)	Optionally return, when it exists, an MPZ whose value is the inverse of this modulo op.
boolean	invertAssign(MPZ op)	Set this MPZ to the inverse of this modulo op.
boolean	invertAssign(MPZ op1, MPZ op2)	Set this MPZ to the inverse of op1 modulo op2.
MPZ	ior(MPZ op)	Return an MPZ whose value is (this | op).
MPZ	iorAssign(MPZ op)	Set this MPZ to (this | op).
MPZ	iorAssign(MPZ op1, MPZ op2)	Set this MPZ to (op1 | op2).
boolean	isCongruent(MPZ c, MPZ d)	Return true if and only if this is congruent to c modulo d.
boolean	isCongruent2Exp(MPZ c, long b)	Return true if and only if this is congruent to c modulo 2b.
boolean	isCongruentUi(long c, long d)	Return true if and only if this is congruent to c modulo d.
boolean	isDivisible(MPZ d)	Return true if and only if this is exactly divisible by d.
boolean	isDivisible2Exp(long b)	Return true if and only if this is exactly divisible by 2b.
boolean	isDivisibleUi(long d)	Return true if and only if this is exactly divisible by d.
boolean	isEven()	Return true if and only if this MPZ is even
boolean	isOdd()	Return true if and only if this MPZ is odd.
boolean	isPerfectPower()	Return true if and only if this number is a perfect power, i.e., if there exist integers a and b, with (b > 1), such that this equals (ab).
boolean	isPerfectSquare()	Return true if and only if this number is a perfect square.
MPZ.PrimalityStatus	isProbabPrime(int reps)	Return true if and only if this is prime.
boolean	isZero()	Return true if and only if this MPZ is zero.
int	jacobi(MPZ b)	Return the Jacobi symbol (this / b).
int	kronecker(long b)	Return the Jacobi symbol (this / b) with the Kronecker extension.
int	kronecker(MPZ b)	Return the Jacobi symbol (this / n) with the Kronecker extension (this/2)=(2/this) when this is odd, or (this/2)=0 when this is even.
int	kroneckerReverse(long a)	Return the Jacobi symbol (a / this) with the Kronecker extension.
int	kroneckerUi(long b)	Return the Jacobi symbol (this / b) with the Kronecker extension.
MPZ	lcm(MPZ op)	Return an MPZ whose value is the least common multiple of this and op.
MPZ	lcmAssign(MPZ op)	Set this MPZ to the least common multiple of this and op.
MPZ	lcmAssign(MPZ op1, MPZ op2)	Set this MPZ to the least common multiple of op1 and op2.
MPZ	lcmUi(long op)	Return the least common multiple of this and op.
MPZ	lcmUiAssign(long op)	Set this MPZ to the least common multiple of this and op.
MPZ	lcmUiAssign(MPZ op1, long op2)	Set this MPZ to the least common multiple of op1 and op2.
int	legendre(MPZ p)	Return the Legendre symbol (this / p).
long	longValue()	Convert this MPZ to a signed long.
static org.javatuples.Pair<MPZ,MPZ>	lucnum2Ui(long n)	Return two MPZ whose values are the n-th and (n-1)-th Lucas numbers.
MPZ	lucnum2UiAssign(MPZ fnsub1, long n)	Set the value of this and fnsub1 to the n-th and (n-1)-th Lucas numbers respecively.
static MPZ	lucnumUi(long n)	Return an MPZ whose value is the n-th Lucas number.
MPZ	lucnumUiAssign(long n)	Set this MPZ to the n-th Lucas number.
static MPZ	mfacUiUi(long n, long m)	Return an MPZ whose value is the m-multi factorial of n.
MPZ	mfacUiUiAssign(long n, long m)	Set this MPZ to the m-multi factorial of n.
MPZ	mod(MPZ d)	Return an MPZ whose value is (this mod d).
MPZ	modAssign(MPZ d)	Set this MPZ to (this mod d).
MPZ	modAssign(MPZ n, MPZ d)	Set this MPZ to (n mod d).
long	modUi(long d)	Return an MPZ whose value is (this mod d).
long	modUiAssign(long d)	Set this MPZ to (n mod d); it also returns the result.
long	modUiAssign(MPZ n, long d)	Set this MPZ to (n mod d); it also returns the result.
MPZ	mul(long op)	Return an MPZ whose value is (this * op).
MPZ	mul(MPZ op)	Return an MPZ whose value is (this * op).
MPZ	mul2Exp(long b)	Return an MPZ whose value is (this * 2b).
MPZ	mul2ExpAssign(long b)	Set this MPZ to (this * 2b).
MPZ	mul2ExpAssign(MPZ op, long b)	Set this MPZ to (op * 2b).
MPZ	mulAssign(long op)	Set this MPZ to (this * op)
MPZ	mulAssign(MPZ op)	Set this MPZ to (this * op)
MPZ	mulAssign(MPZ op1, long op2)	Set this MPZ to (op1 * op2).
MPZ	mulAssign(MPZ op1, MPZ op2)	Set this MPZ to (op1 * op2).
MPZ	mulUi(long op)	Return an MPZ whose value is (this * op).
MPZ	mulUiAssign(long op)	Set this MPZ to (this * op)
MPZ	mulUiAssign(MPZ op1, long op2)	Set this MPZ to (op1 * op2).
MPZ	neg()	Return an MPZ whose value is the quotient of (- this).
MPZ	negAssign()	Set this MPZ to its opposite.
MPZ	negAssign(MPZ op)	Set this MPZ to (- op).
MPZ	nextprime()	Return an MPZ whose value is the next prime greater then this.
MPZ	nextprimeAssign()	Set this MPZ to the next prime greater then itself.
MPZ	nextprimeAssign(MPZ op)	Set this MPZ to the next prime greater then op.
long	popcount()	If this MPZ is non-negative, return its population count, which is the number of 1 bits in its binary representation.
MPZ	powm(MPZ exp, MPZ mod)	Return an MPZ whose value is (thisexp) modulo mod.
MPZ	powmAssign(MPZ exp, MPZ mod)	Set this MPZ to (thisexp) modulo mod.
MPZ	powmAssign(MPZ base, MPZ exp, MPZ mod)	Set this MPZ to (baseexp) modulo mod.
MPZ	powmSec(MPZ exp, MPZ mod)	Return an MPZ whose value is (thisexp) modulo mod.
MPZ	powmSecAssign(MPZ exp, MPZ mod)	Set this MPZ to (thisexp) modulo mod.
MPZ	powmSecAssign(MPZ base, MPZ exp, MPZ mod)	Set this MPZ to (baseexp) modulo mod.
MPZ	powmUi(long exp, MPZ mod)	Return an MPZ whose value is (thisexp) modulo mod.
MPZ	powmUiAssign(long exp, MPZ mod)	Set this MPZ to (thisexp) modulo mod.
MPZ	powmUiAssign(MPZ base, long exp, MPZ mod)	Set this MPZ to (baseexp) modulo mod.
MPZ	powUi(long exp)	Return an MPZ whose value is (thisexp).
static MPZ	powUi(long base, long exp)	Return an MPZ whose value is (baseexp).
MPZ	powUiAssign(long exp)	Set this MPZ to (thisexp).
MPZ	powUiAssign(long base, long exp)	Set this MPZ to (baseexp).
MPZ	powUiAssign(MPZ base, long exp)	Set this MPZ to (baseexp).
static MPZ	primorialUi(long n)	Return an MPZ whose value is the primorial of n, i.e., the product of all positive prime numbers <= n.
MPZ	primorialUiAssign(long n)	Set this MPZ to the primorial of n, i.e., the product of all positive prime numbers <= n.
static MPZ	random(long max_size)	Deprecated. use urandomb(it.unich.jgmp.RandState,long) or urandomm(it.unich.jgmp.RandState,it.unich.jgmp.MPZ) instead, since this method uses a global random state and it is not reentrant.
static MPZ	random2(long max_size)	Deprecated. use rrandomb(it.unich.jgmp.RandState,long) instead, since this method uses a global random state and it is not reentrant.
MPZ	random2Assign(long max_size)	Deprecated. use rrandombAssign(it.unich.jgmp.RandState,long) instead, since this method uses a global random state and it is not reentrant.
MPZ	randomAssign(long max_size)	Deprecated. use urandombAssign(it.unich.jgmp.RandState,long) or urandommAssign(it.unich.jgmp.RandState,it.unich.jgmp.MPZ) instead, since this method uses a global random state and it is not reentrant.
private void	readObject(ObjectInputStream in)
private void	readObjectNoData()
MPZ	realloc2(long n)	Changes the space allocated for this number to n bits.
org.javatuples.Pair<Long,MPZ>	remove(MPZ f)	Return the result of removing the factorf from this, together with the number of occurrences which were removed.
long	removeAssign(MPZ f)	Remove all occurrences of the factor f from this MPZ.
long	removeAssign(MPZ op, MPZ f)	Remove all occurrences of the factor f from op and stores the result in this MPZ.
org.javatuples.Pair<Boolean,MPZ>	root(long n)	Return an MPZ whose value is the truncated integer part of the nth root of this, and a boolean flag which is true when the result is exact.
boolean	rootAssign(long n)	Set this MPZ to the truncated integer part of its nth root.
boolean	rootAssign(MPZ op, long n)	Set this MPZ to the truncated integer part of the nth root of op.
org.javatuples.Pair<MPZ,MPZ>	rootrem(long n)	Return two MPZs whose values are the truncated integer part of the nth root of this and the remainder, i.e., (u - rootn).
MPZ	rootremAssign(MPZ rem, long n)	Set this MPZ to the truncated integer part of the its nth root and rem to the remainder, i.e., (this - rootn).
MPZ	rootremAssign(MPZ rem, MPZ u, long n)	Set this MPZ to the truncated integer part of the nth root of u and rem to the remainder, i.e., (u - rootn).
static MPZ	rrandomb(RandState s, long n)	Return an MPZ whose value is a random integer with long strings of zeros and ones in the binary representation.
MPZ	rrandombAssign(RandState s, long n)	Set this MPZ to a random integer with long strings of zeros and ones in the binary representation.
long	scan0(long starting_bit)	Scan this MPZ, starting from bit starting_bit, towards more significant bits, until the first 0 bit is found.
long	scan1(long starting_bit)	Scan this, starting from bit starting_bit, towards more significant bits, until the first 1 bit is found.
MPZ	set(double op)	Set this MPZ to the truncation of op.
MPZ	set(long op)	Set this MPZ to op.
MPZ	set(MPF op)	Set this MPZ to the truncation of op.
MPZ	set(MPQ op)	Set this MPZ to the truncation of op.
MPZ	set(MPZ op)	Set this MPZ to op.
(package private) static void	set(MpzT mpzNative, BigInteger op)
int	set(String str, int base)	Set this MPZ to the number represented by the string str in the specified base.
MPZ	set(BigInteger op)	Sets this MPZ to op.
MPZ	setbit(long index)	Return an MPZ whose value is (this | 2index).
MPZ	setbitAssign(long index)	Set the bit index of this MPZ.
MPZ	setUi(long op)	Set this MPZ to op.
MPZ	setValue(double op)	Set this MPZ to the truncation op op.
MPZ	setValue(long op)	Set this MPZ to signed long op.
MPZ	setValue(MPF op)	Set this MPZ to the truncation op op.
MPZ	setValue(MPQ op)	Set this MPZ to the truncation op op.
MPZ	setValue(MPZ op)	Set this MPZ to op.
MPZ	setValue(String str)	Set this MPZ to the value represented by the string str in decimal base.
MPZ	setValue(String str, int base)	Set this MPZ to the number represented by the string str in the specified base.
MPZ	setValue(BigInteger op)	Sets this MPZ to op.
int	sgn()	Return +1 if (this > 0), 0 if (this = 0) and -1 if this < 0.
long	sizeinbase(int base)	Return the size of this MPZ measured in number of digits in the specified base.
MPZ	sqrt()	Return an MPZ whose value is the truncated integer part of the square root of this.
MPZ	sqrtAssign()	Set this MPZ to the truncated integer part of its square root.
MPZ	sqrtAssign(MPZ op)	Set this MPZ to the truncated integer part of the square root of op.
org.javatuples.Pair<MPZ,MPZ>	sqrtrem()	Return two MPZs whose values are the truncated integer part of the square root of this and the remainder, i.e., (op - root2).
MPZ	sqrtremAssign(MPZ rem)	Set this MPZ to the truncated integer part of its square root and rem to the remainder, i.e., (this - root2).
MPZ	sqrtremAssign(MPZ rem, MPZ op)	Set this MPZ to the truncated integer part of the square root of op and rem to the remainder, i.e., (op - root2).
MPZ	sub(MPZ op)	Return an MPZ whose value is (this - op).
MPZ	subAssign(MPZ op)	Set this MPZ to (this - op)
MPZ	subAssign(MPZ op1, MPZ op2)	Set this MPZ to (op1 - op2).
MPZ	submul(MPZ op1, MPZ op2)	Return an MPZ whose value is (this - op1 * op2).
MPZ	submulAssign(MPZ op1, MPZ op2)	Subtract (op1 * op2) to this MPZ.
MPZ	submulUi(MPZ op1, long op2)	Return an MPZ whose value is (this - op1 * op2).
MPZ	submulUiAssign(MPZ op1, long op2)	Subtract (op1 * op2) to this MPZ.
MPZ	subUi(long op)	Return an MPZ whose value is (this - op).
MPZ	subUiAssign(long op)	Set this MPZ to (this - op)
MPZ	subUiAssign(MPZ op1, long op2)	Set this MPZ to (op1 - op2).
MPZ	swap(MPZ op)	Swap the value of this MPZ with the value of op.
MPZ	tdivq(MPZ d)	Return an MPZ whose value is the quotient of the integer division (this / d), rounded towards zero.
MPZ	tdivq2Exp(long b)	Return an MPZ whose value is the quotient of the integer division (this / 2b), rounded towards zero.
MPZ	tdivq2ExpAssign(long b)	Set this MPZ to the quotient of the integer division (this / 2b), rounded toward zero.
MPZ	tdivq2ExpAssign(MPZ n, long b)	Set this MPZ to the quotient of the integer division (n / 2b), rounded toward zero.
MPZ	tdivqAssign(MPZ d)	Set this MPZ to the quotient of the integer division (this / d), rounded towards zero.
MPZ	tdivqAssign(MPZ n, MPZ d)	Set this MPZ to the quotient of the integer division (n / d), rounded towards zero.
org.javatuples.Pair<MPZ,MPZ>	tdivqr(MPZ d)	Return two MPZs whose values are the quotient and remainder of the integer division (this / d), rounded towards zero.
MPZ	tdivqrAssign(MPZ r, MPZ d)	Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards zero.
MPZ	tdivqrAssign(MPZ r, MPZ n, MPZ d)	Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards zero.
long	tdivqrUiAssign(MPZ r, long d)	Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards zero; it also returns the absolute value of the remainder.
long	tdivqrUiAssign(MPZ r, MPZ n, long d)	Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards zero; it also returns the absolute value of the remainder.
long	tdivqUiAssign(long d)	Set this MPZ to the quotient of the integer division (this / d), rounded towards zero; it also returns the absolute value of the remainder.
long	tdivqUiAssign(MPZ n, long d)	Set this MPZ to the quotient of the integer division (n / d), rounded towards zero; it also returns the absolute value of the remainder.
MPZ	tdivr(MPZ d)	Return an MPZ whose value is the remainder of the integer division (this / d), rounded towards zero.
MPZ	tdivr2Exp(long b)	Return an MPZ whose value is the remainder of the integer division (this / 2b), rounded towards zero.
MPZ	tdivr2ExpAssign(long b)	Set this MPZ to the remainder of the integer division (this / 2b), rounded toward zero.
MPZ	tdivr2ExpAssign(MPZ n, long b)	Set this MPZ to the remainder of the integer division (n / 2b), rounded toward zero.
MPZ	tdivrAssign(MPZ d)	Set this MPZ to the remainder of the integer division (this / d), rounded towards zero.
MPZ	tdivrAssign(MPZ n, MPZ d)	Set this MPZ to the remainder of the integer division (n / d), rounded towards zero.
long	tdivrUiAssign(long d)	Set this MPZ to the remainder of the integer division (this / d), rounded towards zero; it also returns the absolute value of the remainder.
long	tdivrUiAssign(MPZ n, long d)	Set this MPZ to the remainder of the integer division (n / d), rounded towards zero; it also returns the absolute value of the remainder.
long	tdivUi(long d)	Return the remainder of the integer division (this / d), rounded towards zero.
String	toString()	Convert this MPZ to its decimal string representation.
String	toString(int base)	Convert this MPZ to its string representation in the specified base, or null if the base is not valid.
int	tstbit(long index)	Return the bit index of this MPZ.
int	uiKronecker(long a)	Return the Jacobi symbol (a / this) with the Kronecker extension.
MPZ	uiSub(long op)	Return an MPZ whose value is (op - this).
MPZ	uiSubAssign(long op)	Set this MPZ to (op - this)
MPZ	uiSubAssign(long op1, MPZ op2)	Set this MPZ to (op1 - op2).
static MPZ	urandomb(RandState s, long n)	Return an MPZ whose value is an uniformly distributed random integer in the range 0} to (2n - 1), inclusive.
MPZ	urandombAssign(RandState s, long n)	Set this MPZ to a uniformly distributed random integer in the range 0 to (2n - 1), inclusive.
static MPZ	urandomm(RandState s, MPZ n)	Return an MPZ whose value is an uniformly distributed random integer in the range 0 to (n - 1), inclusive.
MPZ	urandommAssign(RandState s, MPZ n)	Set this MPZ to a uniformly distributed random integer in the range 0 to (n - 1), inclusive.
private void	writeObject(ObjectOutputStream out)
MPZ	xor(MPZ op)	Return an MPZ whose value is (this ^ op).
MPZ	xorAssign(MPZ op)	Set this MPZ to (this ^ op).
MPZ	xorAssign(MPZ op1, MPZ op2)	Set this MPZ to (op1 ^ op2).

Methods inherited from class Number

byteValue, shortValue

Methods inherited from class Object

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

Field Details

serialVersionUID

private static final long serialVersionUID

Version for serializability.

See Also:

• Constant Field Values

mpzNative

private transient MpzT mpzNative

The pointer to the native mpz_t object.

Constructor Details

MPZ

private MPZ(MpzT pointer)

A private constructor which build an MPZ starting from a pointer to its native data object. The native object needs to be already initialized.

MPZ

public MPZ()

Build an MPZ whose value is zero.

MPZ

public MPZ(MPZ op)

Build an MPZ whose value is op.

MPZ

public MPZ(long op)

Build an MPZ whose value is op.

MPZ

public MPZ(double op)

Build an MPZ whose value is the truncation of op.

Throws:

ArithmeticException - if op is not a finite number.

MPZ

public MPZ(MPQ op)

Build an MPZ whose value is the truncation of op.

MPZ

public MPZ(MPF op)

Build an MPZ whose value is the truncation of op.

MPZ

public MPZ(String str,
 int base)

Build an MPZ whose value is the number represented by the string str in the specified base. See the GMP function mpz_init_set_str.

Throws:

NumberFormatException - if either base is not valid or str is not a valid string in the specified base.

MPZ

public MPZ(String str)

Build an MPZ whose value is the number represented by the string str in decimal base. See the GMP function mpz_init_set_str.

Throws:

NumberFormatException - if str is not a valid number representation in decimal base.

MPZ

public MPZ(BigInteger op)

Builds an MPZ whose value is the same as op.

Method Details

getNative

public MpzT getNative()

Return the native pointer to the GMP object.

init

public static MPZ init()

Return an MPZ whose value is zero.

init2

public static MPZ init2(long n)

Return an MPZ whose value is zero, with pre-allocated space for n-bit numbers. Calling this method is never necessary; reallocation is handled automatically by GMP when needed. See the GMP function mpz_init2.

realloc2

public MPZ realloc2(long n)

Changes the space allocated for this number to n bits. The value is preserved if it fits, otherwise it is set to 0. Calling this function is never necessary; reallocation is handled automatically by GMP when needed. This function can be used to increase the space for a variable in order to avoid repeated automatic reallocations, or to decrease it to give memory back to the heap.

Returns:

this MPZ.

set

public MPZ set(MPZ op)

Set this MPZ to op.

Returns:

this MPZ.

set

public MPZ set(long op)

Set this MPZ to op.

Returns:

this MPZ.

setUi

public MPZ setUi(long op)

Set this MPZ to op.

Returns:

this MPZ.

set

public MPZ set(double op)

Set this MPZ to the truncation of op.

Returns:

this MPZ.

Throws:

ArithmeticException - if op is not a finite number. In this case, this is not altered.

set

public MPZ set(MPQ op)

Set this MPZ to the truncation of op.

Returns:

this MPZ.

set

public MPZ set(MPF op)

Set this MPZ to the truncation of op.

Returns:

this MPZ.

set

public int set(String str,
 int base)

Set this MPZ to the number represented by the string str in the specified base. See the GMP function mpz_set_str.

Returns:

0 if the operation succeeded, -1 otherwise. In the latter case, this is not altered.

set

static void set(MpzT mpzNative,
 BigInteger op)

set

public MPZ set(BigInteger op)

Sets this MPZ to op.

Returns:

this MPZ.

swap

public MPZ swap(MPZ op)

Swap the value of this MPZ with the value of op.

Returns:

this MPZ.

initSet

public static MPZ initSet(MPZ op)

Return an MPZ whose value is op.

initSet

public static MPZ initSet(long op)

Return an MPZ whose value is op.

initSetUi

public static MPZ initSetUi(long op)

Return an MPZ whose value is op.

initSet

public static MPZ initSet(double op)

Return an MPZ whose value is the truncation of op.

Throws:

ArithmeticException - if op is not a finite number.

initSet

public static org.javatuples.Pair<Integer,MPZ> initSet(String str,
 int base)

Return an MPZ whose value is the number represented by the string str in the specified base. See the GMP function mpz_init_set_str.

Returns:

a pair whose first component is 0 if the operation succeeded, and -1 if either base is not valid, or str is not a valid numeric representation in the specified base. The second component of the pair is the number represented in str if the operation succeeded, 0 otherwise.

getUi

public long getUi()

Convert this MPZ to an unsigned long. If this number is too big to fit a native unsigned long, then just the least significant bits that do fit are returned. The sign of this number is ignored, only the absolute value is used.

getSi

public long getSi()

Convert this MPZ to a signed long. If this number is too big to fit a native signed long, return the least significant part, preserving the sign.

getD

public double getD()

Convert this MPZ to a double, truncating if necessary. If the exponent from the conversion is too big, the result is system dependent. An infinity is returned where available. A hardware overflow trap may or may not occur.

getD2Exp

public org.javatuples.Pair<Double,Long> getD2Exp()

Convert this MPZ to a pair made of mantissa and exponent, truncating if necessary. See the GMP function mpz_get_d_2exp.

getStr

public String getStr(int base)

Return the String representation of this MPZ in the specified base, or null if the base is not valid. See the GMP function mpz_get_str.

getBigInteger

public BigInteger getBigInteger()

Converts this MPZ to BigInteger.

addAssign

public MPZ addAssign(MPZ op1,
 MPZ op2)

Set this MPZ to (op1 + op2).

Returns:

this MPZ.

addAssign

public MPZ addAssign(MPZ op)

Set this MPZ to (this + op)

Returns:

this MPZ

add

public MPZ add(MPZ op)

Return an MPZ whose value is (this + op).

addUiAssign

public MPZ addUiAssign(MPZ op1,
 long op2)

Set this MPZ to (op1 + op2).

Returns:

this MPZ.

addUiAssign

public MPZ addUiAssign(long op)

Set this MPZ to (this + op)

Returns:

this MPZ

addUi

public MPZ addUi(long op)

Return an MPZ whose value is (this + op).

subAssign

public MPZ subAssign(MPZ op1,
 MPZ op2)

Set this MPZ to (op1 - op2).

Returns:

this MPZ.

subAssign

public MPZ subAssign(MPZ op)

Set this MPZ to (this - op)

Returns:

this MPZ

sub

public MPZ sub(MPZ op)

Return an MPZ whose value is (this - op).

subUiAssign

public MPZ subUiAssign(MPZ op1,
 long op2)

Set this MPZ to (op1 - op2).

Returns:

this MPZ.

subUiAssign

public MPZ subUiAssign(long op)

Set this MPZ to (this - op)

Returns:

this MPZ

subUi

public MPZ subUi(long op)

Return an MPZ whose value is (this - op).

uiSubAssign

public MPZ uiSubAssign(long op1,
 MPZ op2)

Set this MPZ to (op1 - op2).

Returns:

this MPZ.

uiSubAssign

public MPZ uiSubAssign(long op)

Set this MPZ to (op - this)

Returns:

this MPZ

uiSub

public MPZ uiSub(long op)

Return an MPZ whose value is (op - this).

mulAssign

public MPZ mulAssign(MPZ op1,
 MPZ op2)

Set this MPZ to (op1 * op2).

Returns:

this MPZ.

mulAssign

public MPZ mulAssign(MPZ op)

Set this MPZ to (this * op)

Returns:

this MPZ

mul

public MPZ mul(MPZ op)

Return an MPZ whose value is (this * op).

mulUiAssign

public MPZ mulUiAssign(MPZ op1,
 long op2)

Set this MPZ to (op1 * op2).

Returns:

this MPZ.

mulUiAssign

public MPZ mulUiAssign(long op)

Set this MPZ to (this * op)

Returns:

this MPZ

mulUi

public MPZ mulUi(long op)

Return an MPZ whose value is (this * op).

mulAssign

public MPZ mulAssign(MPZ op1,
 long op2)

Set this MPZ to (op1 * op2).

Returns:

this MPZ.

mulAssign

public MPZ mulAssign(long op)

Set this MPZ to (this * op)

Returns:

this MPZ

mul

public MPZ mul(long op)

Return an MPZ whose value is (this * op).

addmulAssign

public MPZ addmulAssign(MPZ op1,
 MPZ op2)

Add (op1 * op2) to this MPZ.

Returns:

this MPZ.

addmul

public MPZ addmul(MPZ op1,
 MPZ op2)

Return an MPZ whose value is (this + op1 * op2).

addmulUiAssign

public MPZ addmulUiAssign(MPZ op1,
 long op2)

Add (op1 * op2) to this MPZ.

Returns:

this MPZ.

addmulUi

public MPZ addmulUi(MPZ op1,
 long op2)

Return an MPZ whose value is (this + op1 * op2).

submulAssign

public MPZ submulAssign(MPZ op1,
 MPZ op2)

Subtract (op1 * op2) to this MPZ.

Returns:

this MPZ.

submul

public MPZ submul(MPZ op1,
 MPZ op2)

Return an MPZ whose value is (this - op1 * op2).

submulUiAssign

public MPZ submulUiAssign(MPZ op1,
 long op2)

Subtract (op1 * op2) to this MPZ.

Returns:

this MPZ.

submulUi

public MPZ submulUi(MPZ op1,
 long op2)

Return an MPZ whose value is (this - op1 * op2).

mul2ExpAssign

public MPZ mul2ExpAssign(MPZ op,
 long b)

Set this MPZ to (op * 2b).

Returns:

this MPZ.

mul2ExpAssign

public MPZ mul2ExpAssign(long b)

Set this MPZ to (this * 2b).

Returns:

this MPZ.

mul2Exp

public MPZ mul2Exp(long b)

Return an MPZ whose value is (this * 2b).

negAssign

public MPZ negAssign(MPZ op)

Set this MPZ to (- op).

Returns:

this MPZ.

negAssign

public MPZ negAssign()

Set this MPZ to its opposite.

Returns:

this MPZ.

neg

public MPZ neg()

Return an MPZ whose value is the quotient of (- this).

absAssign

public MPZ absAssign(MPZ op)

Set this MPZ to the absolute value of op.

Returns:

this MPZ.

absAssign

public MPZ absAssign()

Set this MPZ to its absolute value.

Returns:

this MPZ.

abs

public MPZ abs()

Return an MPZ whose value is the absolute value of this.

cdivqAssign

public MPZ cdivqAssign(MPZ n,
 MPZ d)

Set this MPZ to the quotient of the integer division (n / d), rounded towards +∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

cdivqAssign

public MPZ cdivqAssign(MPZ d)

Set this MPZ to the quotient of the integer division (this / d), rounded towards +∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

cdivrAssign

public MPZ cdivrAssign(MPZ n,
 MPZ d)

Set this MPZ to the remainder of the integer division (n / d), rounded towards +∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

cdivrAssign

public MPZ cdivrAssign(MPZ d)

Set this MPZ to the remainder of the integer division (this / d), rounded towards +∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

cdivqrAssign

public MPZ cdivqrAssign(MPZ r,
 MPZ n,
 MPZ d)

Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards +∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

cdivqrAssign

public MPZ cdivqrAssign(MPZ r,
 MPZ d)

Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards +∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

cdivqUiAssign

public long cdivqUiAssign(MPZ n,
 long d)

Set this MPZ to the quotient of the integer division (n / d), rounded towards +∞; it also Return the remainder.

Throws:

ArithmeticException - if d is zero.

cdivqUiAssign

public long cdivqUiAssign(long d)

Set this MPZ to the quotient of the integer division (this / d), rounded towards +∞; it also returns the remainder.

Throws:

ArithmeticException - if d is zero.

cdivrUiAssign

public long cdivrUiAssign(MPZ n,
 long d)

Set this MPZ to the remainder of the integer division (n / d), rounded towards +∞; it also returns the remainder.

Throws:

ArithmeticException - if d is zero.

cdivrUiAssign

public long cdivrUiAssign(long d)

Set this MPZ to the remainder of the integer division (this / d), rounded towards +∞; it also returns the remainder.

Throws:

ArithmeticException - if d is zero.

cdivqrUiAssign

public long cdivqrUiAssign(MPZ r,
 MPZ n,
 long d)

Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards +∞; it also returns the remainder.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

cdivqrUiAssign

public long cdivqrUiAssign(MPZ r,
 long d)

Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards +∞; it also returns the remainder.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

cdivUi

public long cdivUi(long d)

Return the remainder of the integer division (this / d), rounded towards +∞.

Throws:

ArithmeticException - if d is zero.

cdivq2ExpAssign

public MPZ cdivq2ExpAssign(MPZ n,
 long b)

Set this MPZ to the quotient of the integer division (n / 2b), rounded toward +∞.

Returns:

this MPZ.

cdivq2ExpAssign

public MPZ cdivq2ExpAssign(long b)

Set this MPZ to the quotient of the integer division (this / 2b), rounded toward +∞.

Returns:

this MPZ.

cdivr2ExpAssign

public MPZ cdivr2ExpAssign(MPZ n,
 long b)

Set this MPZ to the remainder of the integer division (n / 2b), rounded toward +∞.

Returns:

this MPZ.

cdivr2ExpAssign

public MPZ cdivr2ExpAssign(long b)

Set this MPZ to the remainder of the integer division (this / 2b), rounded toward +∞.

Returns:

this MPZ.

cdivq

public MPZ cdivq(MPZ d)

Return an MPZ whose value is the quotient of the integer division (this / d), rounded towards +∞.

Throws:

ArithmeticException - if d is zero.

cdivr

public MPZ cdivr(MPZ d)

Return an MPZ whose value is the remainder of the integer division (this / d), rounded towards +∞.

Throws:

ArithmeticException - if d is zero.

cdivqr

public org.javatuples.Pair<MPZ,MPZ> cdivqr(MPZ d)

Return a pair of MPZs whose values are the quotient and remainder of the integer division (this / d), rounded towards +∞.

Throws:

ArithmeticException - if d is zero.

cdivq2Exp

public MPZ cdivq2Exp(long b)

Return an MPZ whose value is the quotient of the integer division (this / 2b), rounded towards +∞.

cdivr2Exp

public MPZ cdivr2Exp(long b)

Return an MPZ whose value is the remainder of the integer division (this / 2b), rounded towards +∞.

fdivqAssign

public MPZ fdivqAssign(MPZ n,
 MPZ d)

Set this MPZ to the quotient of the integer division (n / d), rounded towards -∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

fdivqAssign

public MPZ fdivqAssign(MPZ d)

Set this MPZ to the quotient of the integer division (this / d), rounded towards -∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

fdivrAssign

public MPZ fdivrAssign(MPZ n,
 MPZ d)

Set this MPZ to the remainder of the integer division (n / d), rounded towards -∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

fdivrAssign

public MPZ fdivrAssign(MPZ d)

Set this MPZ to the remainder of the integer division (this / d), rounded towards -∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

fdivqrAssign

public MPZ fdivqrAssign(MPZ r,
 MPZ n,
 MPZ d)

Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards -∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

fdivqrAssign

public MPZ fdivqrAssign(MPZ r,
 MPZ d)

Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards -∞.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

fdivqUiAssign

public long fdivqUiAssign(MPZ n,
 long d)

Set this MPZ to the quotient of the integer division (n / d), rounded towards -∞; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

fdivqUiAssign

public long fdivqUiAssign(long d)

Set this MPZ to the quotient of the integer division (this / d), rounded towards -∞; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

fdivrUiAssign

public long fdivrUiAssign(MPZ n,
 long d)

Set this MPZ to the remainder of the integer division (n / d), rounded towards -∞; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

fdivrUiAssign

public long fdivrUiAssign(long d)

Set this MPZ to the remainder of the integer division (this / d), rounded towards -∞; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

fdivqrUiAssign

public long fdivqrUiAssign(MPZ r,
 MPZ n,
 long d)

Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards -∞; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

fdivqrUiAssign

public long fdivqrUiAssign(MPZ r,
 long d)

Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards -∞; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

fdivUi

public long fdivUi(long d)

Return the remainder of the integer division (this / d), rounded towards -∞.

Throws:

ArithmeticException - if d is zero.

fdivq2ExpAssign

public MPZ fdivq2ExpAssign(MPZ n,
 long b)

Set this MPZ to the quotient of the integer division (n / 2b), rounded toward -∞.

Returns:

this MPZ.

fdivq2ExpAssign

public MPZ fdivq2ExpAssign(long b)

Set this MPZ to the quotient of the integer division (this / 2b), rounded toward -∞.

Returns:

this MPZ.

fdivr2ExpAssign

public MPZ fdivr2ExpAssign(MPZ n,
 long b)

Set this MPZ to the remainder of the integer division (n / 2b), rounded toward -∞.

Returns:

this MPZ.

fdivr2ExpAssign

public MPZ fdivr2ExpAssign(long b)

Set this MPZ to the remainder of the integer division (this / 2b), rounded toward -∞.

Returns:

this MPZ.

fdivq

public MPZ fdivq(MPZ d)

Return an MPZ whose value is the quotient of the integer division (this / d), rounded towards -∞.

Throws:

ArithmeticException - if d is zero.

fdivr

public MPZ fdivr(MPZ d)

Return an MPZ whose value is the remainder of the integer division (this / d), rounded towards -∞.

Throws:

ArithmeticException - if d is zero.

fdivqr

public org.javatuples.Pair<MPZ,MPZ> fdivqr(MPZ d)

Return two MPZs whose values are the quotient and remainder of the integer division (this / d), rounded towards -∞.

Throws:

ArithmeticException - if d is zero.

fdivq2Exp

public MPZ fdivq2Exp(long b)

Return an MPZ whose value is the quotient of the integer division (this / 2b), rounded towards -∞.

fdivr2Exp

public MPZ fdivr2Exp(long b)

Return an MPZ whose value is the remainder of the integer division (this / 2b), rounded towards -∞.

tdivqAssign

public MPZ tdivqAssign(MPZ n,
 MPZ d)

Set this MPZ to the quotient of the integer division (n / d), rounded towards zero.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

tdivqAssign

public MPZ tdivqAssign(MPZ d)

Set this MPZ to the quotient of the integer division (this / d), rounded towards zero.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

tdivrAssign

public MPZ tdivrAssign(MPZ n,
 MPZ d)

Set this MPZ to the remainder of the integer division (n / d), rounded towards zero.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

tdivrAssign

public MPZ tdivrAssign(MPZ d)

Set this MPZ to the remainder of the integer division (this / d), rounded towards zero.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

tdivqrAssign

public MPZ tdivqrAssign(MPZ r,
 MPZ n,
 MPZ d)

Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards zero.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

tdivqrAssign

public MPZ tdivqrAssign(MPZ r,
 MPZ d)

Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards zero.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

tdivqUiAssign

public long tdivqUiAssign(MPZ n,
 long d)

Set this MPZ to the quotient of the integer division (n / d), rounded towards zero; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

tdivqUiAssign

public long tdivqUiAssign(long d)

Set this MPZ to the quotient of the integer division (this / d), rounded towards zero; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

tdivrUiAssign

public long tdivrUiAssign(MPZ n,
 long d)

Set this MPZ to the remainder of the integer division (n / d), rounded towards zero; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

tdivrUiAssign

public long tdivrUiAssign(long d)

Set this MPZ to the remainder of the integer division (this / d), rounded towards zero; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

tdivqrUiAssign

public long tdivqrUiAssign(MPZ r,
 MPZ n,
 long d)

Set this MPZ and r to the quotient and remainder of the integer division (n / d), rounded towards zero; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

tdivqrUiAssign

public long tdivqrUiAssign(MPZ r,
 long d)

Set this MPZ and r to the quotient and remainder of the integer division (this / d), rounded towards zero; it also returns the absolute value of the remainder.

Throws:

ArithmeticException - if d is zero.

IllegalArgumentException - if this and r are the same object.

tdivUi

public long tdivUi(long d)

Return the remainder of the integer division (this / d), rounded towards zero.

Throws:

ArithmeticException - if d is zero.

tdivq2ExpAssign

public MPZ tdivq2ExpAssign(MPZ n,
 long b)

Set this MPZ to the quotient of the integer division (n / 2b), rounded toward zero.

Returns:

this MPZ.

tdivq2ExpAssign

public MPZ tdivq2ExpAssign(long b)

Set this MPZ to the quotient of the integer division (this / 2b), rounded toward zero.

Returns:

this MPZ.

tdivr2ExpAssign

public MPZ tdivr2ExpAssign(MPZ n,
 long b)

Set this MPZ to the remainder of the integer division (n / 2b), rounded toward zero.

Returns:

this MPZ.

tdivr2ExpAssign

public MPZ tdivr2ExpAssign(long b)

Set this MPZ to the remainder of the integer division (this / 2b), rounded toward zero.

Returns:

this MPZ.

tdivq

public MPZ tdivq(MPZ d)

Return an MPZ whose value is the quotient of the integer division (this / d), rounded towards zero.

Throws:

ArithmeticException - if d is zero.

tdivr

public MPZ tdivr(MPZ d)

Return an MPZ whose value is the remainder of the integer division (this / d), rounded towards zero.

Throws:

ArithmeticException - if d is zero.

tdivqr

public org.javatuples.Pair<MPZ,MPZ> tdivqr(MPZ d)

Return two MPZs whose values are the quotient and remainder of the integer division (this / d), rounded towards zero.

Throws:

ArithmeticException - if d is zero.

tdivq2Exp

public MPZ tdivq2Exp(long b)

Return an MPZ whose value is the quotient of the integer division (this / 2b), rounded towards zero.

tdivr2Exp

public MPZ tdivr2Exp(long b)

Return an MPZ whose value is the remainder of the integer division (this / 2b), rounded towards zero.

modAssign

public MPZ modAssign(MPZ n,
 MPZ d)

Set this MPZ to (n mod d). The sign of the divisor is ignored, the result is always non-negative.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

modAssign

public MPZ modAssign(MPZ d)

Set this MPZ to (this mod d). The sign of the divisor is ignored, the result is always non-negative.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

mod

public MPZ mod(MPZ d)

Return an MPZ whose value is (this mod d). The sign of the divisor is ignored, the result is always non-negative.

modUiAssign

public long modUiAssign(MPZ n,
 long d)

Set this MPZ to (n mod d); it also returns the result. The sign of the divisor is ignored, the result is always non-negative.

Throws:

ArithmeticException - if d is zero.

modUiAssign

public long modUiAssign(long d)

Set this MPZ to (n mod d); it also returns the result. The sign of the divisor is ignored, the result is always non-negative.

Throws:

ArithmeticException - if d is zero.

modUi

public long modUi(long d)

Return an MPZ whose value is (this mod d). The sign of the divisor is ignored, the result is always non-negative.

Throws:

ArithmeticException - if d is zero.

divexactAssign

public MPZ divexactAssign(MPZ n,
 MPZ d)

Set this MPZ to the quotient of (n / d). This method produces correct results only when it is known in advance that d divides n.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

divexactAssign

public MPZ divexactAssign(MPZ d)

Set this MPZ to the quotient of (this / d). This method produces correct results only when it is known in advance that d divides this.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

divexact

public MPZ divexact(MPZ d)

Return an MPZ whose value is the quotient of (this / d). This method produces correct results only when it is known in advance that d divides this.

Throws:

ArithmeticException - if d is zero.

divexactUiAssign

public MPZ divexactUiAssign(MPZ n,
 long d)

Set this MPZ to the quotient of (n / d). This method produces correct results only when it is known in advance that d divides n.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

divexactUiAssign

public MPZ divexactUiAssign(long d)

Set this MPZ to the quotient of (this / d). This method produces correct results only when it is known in advance that d divides this.

Returns:

this MPZ.

Throws:

ArithmeticException - if d is zero.

divexactUi

public MPZ divexactUi(long d)

Return an MPZ whose value is the quotient of (this / d). This method produces correct results only when it is known in advance that d divides this.

Throws:

ArithmeticException - if d is zero.

isDivisible

public boolean isDivisible(MPZ d)

Return true if and only if this is exactly divisible by d. This means that there exists an integer qsatisfying (n = q*d). Unlike the other division functions, the case d=0 is accepted and following the rule it can be seen that only 0 is considered divisible by 0.

isDivisibleUi

public boolean isDivisibleUi(long d)

Return true if and only if this is exactly divisible by d. This means that there exists an integer q satisfying (n = q*d). The case d=0 is accepted and following the rule it can be seen that only 0 is considered divisible by 0.

isDivisible2Exp

public boolean isDivisible2Exp(long b)

Return true if and only if this is exactly divisible by 2b. This means that there exists an integer q satisfying (n = q * 2^b).

isCongruent

public boolean isCongruent(MPZ c,
 MPZ d)

Return true if and only if this is congruent to c modulo d. This means that there exists an integer q satisfying (n = c + q*d). Unlike the other division functions, d=0 is accepted and following the rule it can be seen that n and c are considered congruent modulo 0 only when exactly equal.

isCongruentUi

public boolean isCongruentUi(long c,
 long d)

Return true if and only if this is congruent to c modulo d. This means that there exists an integer q satisfying (n = c + q*d). Unlike the other division functions, d=0 is accepted and following the rule it can be seen that n and c are considered congruent modulo 0 only when exactly equal.

isCongruent2Exp

public boolean isCongruent2Exp(MPZ c,
 long b)

Return true if and only if this is congruent to c modulo 2b. This means that there exists an integer q satisfying (n = c + q*2^b).

powmAssign

public MPZ powmAssign(MPZ base,
 MPZ exp,
 MPZ mod)

Set this MPZ to (baseexp) modulo mod. Negative exp is supported if the inverse of base modulo mod exists, otherwise an ArithmeticExpection is thrown.

Returns:

this MPZ.

Throws:

ArithmeticException - if mod is zero or base has no inverse modulo mod.

powmAssign

public MPZ powmAssign(MPZ exp,
 MPZ mod)

Set this MPZ to (thisexp) modulo mod.

Returns:

this MPZ.

Throws:

ArithmeticException - if mod is zero.

powm

public MPZ powm(MPZ exp,
 MPZ mod)

Return an MPZ whose value is (thisexp) modulo mod.

powmUiAssign

public MPZ powmUiAssign(MPZ base,
 long exp,
 MPZ mod)

Set this MPZ to (baseexp) modulo mod.

Returns:

this MPZ.

Throws:

ArithmeticException - if mod is zero.

powmUiAssign

public MPZ powmUiAssign(long exp,
 MPZ mod)

Set this MPZ to (thisexp) modulo mod.

Returns:

this MPZ.

Throws:

ArithmeticException - if mod is zero.

powmUi

public MPZ powmUi(long exp,
 MPZ mod)

Return an MPZ whose value is (thisexp) modulo mod.

powmSecAssign

public MPZ powmSecAssign(MPZ base,
 MPZ exp,
 MPZ mod)

Set this MPZ to (baseexp) modulo mod. It is required that (exp > 0 and that mod is odd. This function is intended for cryptographic purposes, where resilience to side-channel attacks is desired.

Returns:

this MPZ.

Throws:

ArithmeticException - if mod is even or exp is negative.

powmSecAssign

public MPZ powmSecAssign(MPZ exp,
 MPZ mod)

Set this MPZ to (thisexp) modulo mod. It is required that (exp > 0 and that mod is odd. This function is intended for cryptographic purposes, where resilience to side-channel attacks is desired.

Returns:

this MPZ.

Throws:

ArithmeticException - if mod is zero.

powmSec

public MPZ powmSec(MPZ exp,
 MPZ mod)

Return an MPZ whose value is (thisexp) modulo mod. It is required that (exp > 0) and that mod is odd. This function is intended for cryptographic purposes, where resilience to side-channel attacks is desired.

powUiAssign

public MPZ powUiAssign(MPZ base,
 long exp)

Set this MPZ to (baseexp). The case 00 yields 1.

Returns:

this MPZ.

powUiAssign

public MPZ powUiAssign(long exp)

Set this MPZ to (thisexp). The case 00 yields 1.

Returns:

this MPZ.

powUi

public MPZ powUi(long exp)

Return an MPZ whose value is (thisexp). The case 00 yields 1.

powUiAssign

public MPZ powUiAssign(long base,
 long exp)

Set this MPZ to (baseexp). The case 00 yields 1.

Returns:

this MPZ.

powUi

public static MPZ powUi(long base,
 long exp)

Return an MPZ whose value is (baseexp). The case 00 yields 1.

rootAssign

public boolean rootAssign(MPZ op,
 long n)

Set this MPZ to the truncated integer part of the nth root of op.

Returns:

true if the computation is exact.

Throws:

ArithmeticException - if n is even and op is negative.

rootAssign

public boolean rootAssign(long n)

Set this MPZ to the truncated integer part of its nth root.

Returns:

true if the computation is exact.

Throws:

ArithmeticException - if n is even and this is negative.

root

public org.javatuples.Pair<Boolean,MPZ> root(long n)

Return an MPZ whose value is the truncated integer part of the nth root of this, and a boolean flag which is true when the result is exact.

Throws:

ArithmeticException - if n is even and this is negative.

rootremAssign

public MPZ rootremAssign(MPZ rem,
 MPZ u,
 long n)

Set this MPZ to the truncated integer part of the nth root of u and rem to the remainder, i.e., (u - rootn).

Returns:

this MPZ.

Throws:

ArithmeticException - if n is even and u is negative.

rootremAssign

public MPZ rootremAssign(MPZ rem,
 long n)

Set this MPZ to the truncated integer part of the its nth root and rem to the remainder, i.e., (this - rootn).

Returns:

this MPZ.

Throws:

ArithmeticException - if n is even and this is negative.

rootrem

public org.javatuples.Pair<MPZ,MPZ> rootrem(long n)

Return two MPZs whose values are the truncated integer part of the nth root of this and the remainder, i.e., (u - rootn).

Throws:

ArithmeticException - if n is even and this is negative.

sqrtAssign

public MPZ sqrtAssign(MPZ op)

Set this MPZ to the truncated integer part of the square root of op.

Returns:

this MPZ.

Throws:

ArithmeticException - if op is negative.

sqrtAssign

public MPZ sqrtAssign()

Set this MPZ to the truncated integer part of its square root.

Returns:

this MPZ.

Throws:

ArithmeticException - if this is negative.

sqrt

public MPZ sqrt()

Return an MPZ whose value is the truncated integer part of the square root of this.

Throws:

ArithmeticException - if this is negative.

sqrtremAssign

public MPZ sqrtremAssign(MPZ rem,
 MPZ op)

Set this MPZ to the truncated integer part of the square root of op and rem to the remainder, i.e., (op - root2).

Returns:

this MPZ.

Throws:

ArithmeticException - if op is negative.

sqrtremAssign

public MPZ sqrtremAssign(MPZ rem)

Set this MPZ to the truncated integer part of its square root and rem to the remainder, i.e., (this - root2).

Returns:

this MPZ.

Throws:

ArithmeticException - if this is negative.

sqrtrem

public org.javatuples.Pair<MPZ,MPZ> sqrtrem()

Return two MPZs whose values are the truncated integer part of the square root of this and the remainder, i.e., (op - root2).

Throws:

ArithmeticException - if this is negative.

isPerfectPower

public boolean isPerfectPower()

Return true if and only if this number is a perfect power, i.e., if there exist integers a and b, with (b > 1), such that this equals (ab). Under this definition both 0 and 1 are considered to be perfect powers. Negative values are accepted, but of course can only be odd perfect powers.

isPerfectSquare

public boolean isPerfectSquare()

Return true if and only if this number is a perfect square. Under this definition both 0 and 1 are considered to be perfect squares.

isProbabPrime

public MPZ.PrimalityStatus isProbabPrime(int reps)

Return true if and only if this is prime. See the GMP function mpz_probab_prime_p.

Parameters:

reps - can be used to tune the probability of a non-prime being identified as “probably prime”. Reasonable values of reps are between 15 and 50.

Returns:

an instance of the MPZ.PrimalityStatus enum, telling whether this is definitely prime, probably prime or definitely non-prime.

nextprimeAssign

public MPZ nextprimeAssign(MPZ op)

Set this MPZ to the next prime greater then op. This function uses a probabilistic algorithm to identify primes. For practical purposes it’s adequate, the chance of a composite passing will be extremely small.

nextprimeAssign

public MPZ nextprimeAssign()

Set this MPZ to the next prime greater then itself. This function uses a probabilistic algorithm to identify primes. For practical purposes it’s adequate, the chance of a composite passing will be extremely small.

nextprime

public MPZ nextprime()

Return an MPZ whose value is the next prime greater then this.

See Also:

• nextprimeAssign(it.unich.jgmp.MPZ)

gcdAssign

public MPZ gcdAssign(MPZ op1,
 MPZ op2)

Set this MPZ to the greatest commond divisor of op1 and op2. The result is always positive even if one or both input operands are negative. Except if both inputs are zero; then this function defines gcd(0,0) = 0.

gcdAssign

public MPZ gcdAssign(MPZ op)

Set this MPZ to the greatest commond divisor of this and op. The result is always positive even if one or both operands are negative. Except if both this and op are zero; then this function Return zero.

gcd

public MPZ gcd(MPZ op)

Return an MPZ whose value is the greatest commond divisor of this and op.

See Also:

• gcdAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

gcdUiAssign

public long gcdUiAssign(MPZ op1,
 long op2)

Set this MPZ to the greatest commond divisor of op1 and op2, and return it. If the result does not fit into an unsigned long, then 0 si returned.

See Also:

• gcdAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

gcdUiAssign

public long gcdUiAssign(long op)

Set this MPZ to the greatest commond divisor of op1 and op2, and returns it. If the result does not fit into an unsigned long, then 0 si returned.

See Also:

• gcdAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

gcdUi

public long gcdUi(long op)

Return the greatest commond divisor of this and op. If the result does not fit into an unsigned long, 0 is returned.

gcdextAssign

public MPZ gcdextAssign(MPZ s,
 MPZ t,
 MPZ a,
 MPZ b)

Set this MPZ to the greatest common divisor of a and b, and in addition Set s and t to coefficients satisfying (a*s + b*t = gcd). If s or t is null, that value is not computed. See the GMP function mpz_gcdext.

gcdextAssign

public MPZ gcdextAssign(MPZ s,
 MPZ t,
 MPZ op)

Set this MPZ to the greatest common divisor of this and op, and in addition Set s and t to coefficients satisfying (this*s + op*t = gcd). If s or t is null, that value is not computed. See the GMP function mpz_gcdext.

gcdext

public org.javatuples.Triplet<MPZ,MPZ,MPZ> gcdext(MPZ op)

Return the greatest common divisor of this and op, together with numbers s and t satisfying (a*this + b*op = g) See the GMP function mpz_gcdext.

lcmAssign

public MPZ lcmAssign(MPZ op1,
 MPZ op2)

Set this MPZ to the least common multiple of op1 and op2. The result is always non-negative even if one or both input operands are negative. The result will be zero if either op1 or op2 is zero.

lcmAssign

public MPZ lcmAssign(MPZ op)

Set this MPZ to the least common multiple of this and op. The result is always non-negative even if one or both input operands are negative. The result will be zero if either this or op is zero.

lcm

public MPZ lcm(MPZ op)

Return an MPZ whose value is the least common multiple of this and op.

See Also:

• lcmAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

lcmUiAssign

public MPZ lcmUiAssign(MPZ op1,
 long op2)

Set this MPZ to the least common multiple of op1 and op2.

See Also:

• lcmAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

lcmUiAssign

public MPZ lcmUiAssign(long op)

Set this MPZ to the least common multiple of this and op.

See Also:

• lcmAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

lcmUi

public MPZ lcmUi(long op)

Return the least common multiple of this and op.

See Also:

• lcmAssign(it.unich.jgmp.MPZ,it.unich.jgmp.MPZ)

invertAssign

public boolean invertAssign(MPZ op1,
 MPZ op2)

Set this MPZ to the inverse of op1 modulo op2. If the inverse does not exist, the new value of this MPZ is undefined.

Returns:

true if the inverse exists, false otherwise.

invertAssign

public boolean invertAssign(MPZ op)

Set this MPZ to the inverse of this modulo op. If the inverse does not exist, the new value of this MPZ is undefined.

Returns:

true if the inverse exists, false otherwise.

invert

public Optional<MPZ> invert(MPZ op)

Optionally return, when it exists, an MPZ whose value is the inverse of this modulo op.

jacobi

public int jacobi(MPZ b)

Return the Jacobi symbol (this / b). This is defined only for b odd.

legendre

public int legendre(MPZ p)

Return the Legendre symbol (this / p). This is defined only for p an odd positive prime, and for such p it’s identical to the Jacobi symbol.

kronecker

public int kronecker(MPZ b)

Return the Jacobi symbol (this / n) with the Kronecker extension (this/2)=(2/this) when this is odd, or (this/2)=0 when this is even. When b is odd the Jacobi symbol and Kronecker symbol are identical. See the GMP function mpz_kronecker.

kronecker

public int kronecker(long b)

Return the Jacobi symbol (this / b) with the Kronecker extension.

See Also:

• kronecker(it.unich.jgmp.MPZ)

kroneckerUi

public int kroneckerUi(long b)

Return the Jacobi symbol (this / b) with the Kronecker extension.

See Also:

• kronecker(it.unich.jgmp.MPZ)

kroneckerReverse

public int kroneckerReverse(long a)

Return the Jacobi symbol (a / this) with the Kronecker extension.

See Also:

• kronecker(it.unich.jgmp.MPZ)

uiKronecker

public int uiKronecker(long a)

Return the Jacobi symbol (a / this) with the Kronecker extension.

See Also:

• kronecker(it.unich.jgmp.MPZ)

removeAssign

public long removeAssign(MPZ op,
 MPZ f)

Remove all occurrences of the factor f from op and stores the result in this MPZ. The return value is the number of occurrences of f which were removed.

removeAssign

public long removeAssign(MPZ f)

Remove all occurrences of the factor f from this MPZ. The return value is the number of occurrences of f which were removed.

remove

public org.javatuples.Pair<Long,MPZ> remove(MPZ f)

Return the result of removing the factorf from this, together with the number of occurrences which were removed.

facUiAssign

public MPZ facUiAssign(long n)

Set this MPZ to the factorial of n.

facUi

public static MPZ facUi(long n)

Return an MPZ whose value is the factorial of n.

dfacUiAssign

public MPZ dfacUiAssign(long n)

Set this MPZ to the double factorial of n.

dfacUi

public static MPZ dfacUi(long n)

Return an MPZ whose value the double factorial of n.

mfacUiUiAssign

public MPZ mfacUiUiAssign(long n,
 long m)

Set this MPZ to the m-multi factorial of n.

mfacUiUi

public static MPZ mfacUiUi(long n,
 long m)

Return an MPZ whose value is the m-multi factorial of n.

primorialUiAssign

public MPZ primorialUiAssign(long n)

Set this MPZ to the primorial of n, i.e., the product of all positive prime numbers <= n.

primorialUi

public static MPZ primorialUi(long n)

Return an MPZ whose value is the primorial of n, i.e., the product of all positive prime numbers <= n.

binUiAssign

public MPZ binUiAssign(MPZ n,
 long k)

Set this MPZ to the binomial coefficient n over k. Negative values of n are supported using the identity (bin(-n,k) = (-1)^k * bin(n+k-1,k)), see Knuth volume 1 section 1.2.6 part G.

binUiAssign

public MPZ binUiAssign(long k)

Set this MPZ to the binomial coefficient this over k. Negative values of this are supported using the identity (bin(-n,k) = (-1)^k * bin(n+k-1,k)), see Knuth volume 1 section 1.2.6 part G.

binUi

public MPZ binUi(long k)

Return an MPZ whose value is the binomial coefficient this over k. Negative values of this are supported as in binUiAssign(it.unich.jgmp.MPZ,long).

binUiUiAssign

public MPZ binUiUiAssign(long n,
 long k)

Set this MPZ to the binomial coefficient n over k.

binUiUi

public static MPZ binUiUi(long n,
 long k)

Return an MPZ whose value is the binomial coefficient n over k.

fibUiAssign

public MPZ fibUiAssign(long n)

Set this MPZ to the n-th Fibonacci number.

fibUi

public static MPZ fibUi(long n)

Return an MPZ whose value is the n-th Fibonacci number.

fib2UiAssign

public MPZ fib2UiAssign(MPZ fnsub1,
 long n)

Set the value of this and fnsub1 to the n-th and (n-1)-th Fibonacci numbers respecively.

fib2Ui

public static org.javatuples.Pair<MPZ,MPZ> fib2Ui(long n)

Return two MPZ whose values are the n-th and (n-1)-th Fibonacci numbers.

lucnumUiAssign

public MPZ lucnumUiAssign(long n)

Set this MPZ to the n-th Lucas number.

lucnumUi

public static MPZ lucnumUi(long n)

Return an MPZ whose value is the n-th Lucas number.

lucnum2UiAssign

public MPZ lucnum2UiAssign(MPZ fnsub1,
 long n)

Set the value of this and fnsub1 to the n-th and (n-1)-th Lucas numbers respecively.

lucnum2Ui

public static org.javatuples.Pair<MPZ,MPZ> lucnum2Ui(long n)

Return two MPZ whose values are the n-th and (n-1)-th Lucas numbers.

cmp

public int cmp(MPZ op)

Compare this with op. Return a positive value if (this > op), zero if this = op, or a negative value if this < op.

cmp

public int cmp(double op)

Compare this with op. Return a positive value if (this > op), zero if this = op, or a negative value if this < op. The value of op may be infinite, but the result is undefined on NaNs.

Throws:

ArithmeticException - if op is a NaN.

cmp

public int cmp(long op)

Compare this with op. Return a positive value if (this > op), zero if this = op, or a negative value if this < op.

cmpUi

public int cmpUi(long op)

Compare this with op. Return a positive value if (this > op), zero if this = op, or a negative value if this < op.

cmpabs

public int cmpabs(MPZ op)

Compare the absolute values of this and op. Return a positive value if (abs(this) > abs(op)), zero if abs(this) = abs(op), or a negative value if abs(this) < abs(op).

cmpabs

public int cmpabs(double op)

Compare the absolute values of this and op. Return a positive value if (abs(this) > abs(op)), zero if abs(this) = abs(op), or a negative value if abs(this) < abs(op). The value of op may be infinite, but the result is undefined on NaNs.

Throws:

ArithmeticException - if op is a NaN.

cmpabsUi

public int cmpabsUi(long op)

Compare the absolute values of this and op. Return a positive value if (abs(this) > abs(op)), zero if abs(this) = abs(op), or a negative value if abs(this) < abs(op).

sgn

public int sgn()

Return +1 if (this > 0), 0 if (this = 0) and -1 if this < 0.

andAssign

public MPZ andAssign(MPZ op1,
 MPZ op2)

Set this MPZ to (op1 & op2).

andAssign

public MPZ andAssign(MPZ op)

Set this MPZ to (this & op).

and

public MPZ and(MPZ op)

Return an MPZ whose value is (this & op).

iorAssign

public MPZ iorAssign(MPZ op1,
 MPZ op2)

Set this MPZ to (op1 | op2).

iorAssign

public MPZ iorAssign(MPZ op)

Set this MPZ to (this | op).

ior

public MPZ ior(MPZ op)

Return an MPZ whose value is (this | op).

xorAssign

public MPZ xorAssign(MPZ op1,
 MPZ op2)

Set this MPZ to (op1 ^ op2).

xorAssign

public MPZ xorAssign(MPZ op)

Set this MPZ to (this ^ op).

xor

public MPZ xor(MPZ op)

Return an MPZ whose value is (this ^ op).

comAssign

public MPZ comAssign(MPZ op)

Set this MPZ to (~ op).

comAssign

public MPZ comAssign()

Set this MPZ to (~ this).

com

public MPZ com()

Return an MPZ whose value is (~ op).

popcount

public long popcount()

If this MPZ is non-negative, return its population count, which is the number of 1 bits in its binary representation. If this MPZ is negative, the number of 1s is infinite, and the return value is the largest possible value for the native type mp_bitcnt_t.

hamdist

public long hamdist(MPZ op)

If this and op are both >= 0 or both < 0, return the Hamming distance between them, which is the number of bit positions where this and op have different bit values. If one operand is >= 0 and the other < 0 then the number of bits different is infinite, and the return value is the largest possible value for the native type mp_bitcnt_t.

scan0

public long scan0(long starting_bit)

Scan this MPZ, starting from bit starting_bit, towards more significant bits, until the first 0 bit is found. Return the index of the found bit.

scan1

public long scan1(long starting_bit)

Scan this, starting from bit starting_bit, towards more significant bits, until the first 1 bit is found. Return the index of the found bit.

setbitAssign

public MPZ setbitAssign(long index)

Set the bit index of this MPZ.

setbit

public MPZ setbit(long index)

Return an MPZ whose value is (this | 2index).

clrbitAssign

public MPZ clrbitAssign(long index)

Clear the bit index of this MPZ.

clrbit

public MPZ clrbit(long index)

Return an MPZ whose value is (this & ~ 2index).

combitAssign

public MPZ combitAssign(long index)

Complement the bit index of this MPZ.

combit

public MPZ combit(long index)

Return an MPZ whose value is (this ^ 2index).

tstbit

public int tstbit(long index)

Return the bit index of this MPZ.

urandombAssign

public MPZ urandombAssign(RandState s,
 long n)

Set this MPZ to a uniformly distributed random integer in the range 0 to (2n - 1), inclusive.

urandomb

public static MPZ urandomb(RandState s,
 long n)

Return an MPZ whose value is an uniformly distributed random integer in the range 0} to (2n - 1), inclusive.

urandommAssign

public MPZ urandommAssign(RandState s,
 MPZ n)

Set this MPZ to a uniformly distributed random integer in the range 0 to (n - 1), inclusive.

urandomm

public static MPZ urandomm(RandState s,
 MPZ n)

Return an MPZ whose value is an uniformly distributed random integer in the range 0 to (n - 1), inclusive.

rrandombAssign

public MPZ rrandombAssign(RandState s,
 long n)

Set this MPZ to a random integer with long strings of zeros and ones in the binary representation. Useful for testing functions and algorithms, since this kind of random numbers have proven to be more likely to trigger corner-case bugs. The random number will be in the range (2n - 1) to (2n - 1), inclusive.

rrandomb

public static MPZ rrandomb(RandState s,
 long n)

Return an MPZ whose value is a random integer with long strings of zeros and ones in the binary representation. Useful for testing functions and algorithms, since this kind of random numbers have proven to be more likely to trigger corner-case bugs. The random number will be in the range (2n - 1) to (2n - 1), inclusive.

randomAssign

@Deprecated
public MPZ randomAssign(long max_size)

Deprecated.

use urandombAssign(it.unich.jgmp.RandState,long) or urandommAssign(it.unich.jgmp.RandState,it.unich.jgmp.MPZ) instead, since this method uses a global random state and it is not reentrant.

Set this MPZ to a random integer of at most max_size limbs. The generated random number doesn’t satisfy any particular requirements of randomness. Negative random numbers are generated when max_size is negative.

Returns:

this MPZ.

random

@Deprecated
public static MPZ random(long max_size)

Deprecated.

use urandomb(it.unich.jgmp.RandState,long) or urandomm(it.unich.jgmp.RandState,it.unich.jgmp.MPZ) instead, since this method uses a global random state and it is not reentrant.

Return an MPZ whose value is a random integer of at most max_size limbs. The generated random number doesn’t satisfy any particular requirements of randomness. Negative random numbers are generated when max_size is negative.

random2Assign

@Deprecated
public MPZ random2Assign(long max_size)

Deprecated.

use rrandombAssign(it.unich.jgmp.RandState,long) instead, since this method uses a global random state and it is not reentrant.

Set this MPZ to a random integer of at most max_size limbs, with long strings of zeros and ones in the binary representation. Useful for testing functions and algorithms, since this kind of random numbers have proven to be more likely to trigger corner-case bugs. Negative random numbers are generated when max_size is negative.

Returns:

this MPZ.

random2

@Deprecated
public static MPZ random2(long max_size)

Deprecated.

use rrandomb(it.unich.jgmp.RandState,long) instead, since this method uses a global random state and it is not reentrant.

Return an MPZ whose value is a random integer of at most max_size limbs, with long strings of zeros and ones in the binary representation. Useful for testing functions and algorithms, since this kind of random numbers have proven to be more likely to trigger corner-case bugs. Negative random numbers are generated when max_size is negative.

bufferImportAssign

public MPZ bufferImportAssign(int order,
 int size,
 int endian,
 long nails,
 ByteBuffer op)

Set this MPZ from the buffer of word data at op. See the detailed description in the documentation of the GMP function mpz_import. The parameter count in the prototype of mpz_import is automatically computed by the capacity of the buffer op. The size parameter is declared as int instead of long since Java does not allow byte buffers to be longer than 4GB.

bufferImport

public static MPZ bufferImport(int order,
 int size,
 int endian,
 long nails,
 ByteBuffer op)

Return an MPZ whose value is determined from the buffer of word data at op. The size parameter is declared as int instead of long since Java does not allow byte buffers to be longer than 4GB.

See Also:

• bufferImportAssign(int,int,int,long,java.nio.ByteBuffer)

bufferExport

public ByteBuffer bufferExport(int order,
 int size,
 int endian,
 long nails)

Return a ByteBuffer filled with word data from this MPZ. See the detailed description in the documentation of the GMP function mpz_export. We let the function allocate the buffer, since it the easier and safer. The output count of the original GMP function is not needed, since it corresponds to the capacity of the resulting ByteBuffer. The size parameter is declared as int instead of long since Java does not allow byte buffers to be longer than 4GB.

fitsUlong

public boolean fitsUlong()

Return true if and only if this MPZ fits into a native unsigned long.

fitsSlong

public boolean fitsSlong()

Return true if and only if this MPZ fits into a native signed long.

fitsUint

public boolean fitsUint()

Return true if and only if this MPZ fits into a native unsigned int.

fitsSint

public boolean fitsSint()

Return true if and only if this MPZ fits into a native signed int.

fitsUshort

public boolean fitsUshort()

Return true if and only if this MPZ fits into a native unsigned short.

fitsSshort

public boolean fitsSshort()

Return true if and only if this MPZ fits into a native signed short.

isOdd

public boolean isOdd()

Return true if and only if this MPZ is odd.

isEven

public boolean isEven()

Return true if and only if this MPZ is even

isZero

public boolean isZero()

Return true if and only if this MPZ is zero.

sizeinbase

public long sizeinbase(int base)

Return the size of this MPZ measured in number of digits in the specified base. See the the GMP function mpz_sizeinbase.

Throws:

IllegalArgumentException - if base is not between 2 and 62.

setValue

public MPZ setValue(MPZ op)

Set this MPZ to op.

Returns:

this MPZ.

setValue

public MPZ setValue(long op)

Set this MPZ to signed long op.

Returns:

this MPZ.

setValue

public MPZ setValue(double op)

Set this MPZ to the truncation op op.

Returns:

this MPZ.

Throws:

ArithmeticException - if op is not a finite number. In this case, this is not altered.

setValue

public MPZ setValue(MPQ op)

Set this MPZ to the truncation op op.

Returns:

this MPZ.

setValue

public MPZ setValue(MPF op)

Set this MPZ to the truncation op op.

Returns:

this MPZ.

setValue

public MPZ setValue(String str,
 int base)

Set this MPZ to the number represented by the string str in the specified base. See the GMP function mpz_set_str.

Throws:

NumberFormatException - if either base is not valid or str is not a valid number representation in the specified base. In this case, this is not altered.

setValue

public MPZ setValue(String str)

Set this MPZ to the value represented by the string str in decimal base.

Throws:

NumberFormatException - if str is not a valid number representation in decimal base.

See Also:

• setValue(java.lang.String,int)

setValue

public MPZ setValue(BigInteger op)

Sets this MPZ to op.

Returns:

this MPZ.

compareTo

public int compareTo(MPZ op)

Compare this MPZ with op. Return a positive value if (this > op), zero if this = op, or a negative value if this < op. This order is compatible with equality.

Specified by:

compareTo in interface Comparable<MPZ>

equals

public boolean equals(Object obj)

Compare this MPZ with the object op for equality. It returns true if and only if op is an MPZ with the same value of this.

Overrides:

equals in class Object

hashCode

public int hashCode()

Return a hash code value for this MPZ.

Overrides:

hashCode in class Object

longValue

public long longValue()

Convert this MPZ to a signed long. If this number is too big to fit a native signed long, return the least significant part, preserving the sign.

Specified by:

longValue in class Number

intValue

public int intValue()

Convert this MPZ to a signed int, truncating if necessary.

Specified by:

intValue in class Number

doubleValue

public double doubleValue()

Convert this MPZ to a double, truncating if necessary. If the exponent from the conversion is too big, the result is system dependent. An infinity is returned where available. A hardware overflow trap may or may not occur.

Specified by:

doubleValue in class Number

floatValue

public float floatValue()

Convert this MPZ to a float, truncating if necessary.

Specified by:

floatValue in class Number

toString

public String toString(int base)

Convert this MPZ to its string representation in the specified base, or null if the base is not valid. See the GMP function mpz_get_str.

toString

public String toString()

Convert this MPZ to its decimal string representation.

Overrides:

toString in class Object

writeObject

private void writeObject(ObjectOutputStream out)
                  throws IOException

Throws:

IOException

readObject

private void readObject(ObjectInputStream in)
                 throws IOException,
ClassNotFoundException

Throws:

IOException

ClassNotFoundException

readObjectNoData

private void readObjectNoData()
                       throws ObjectStreamException

Throws:

ObjectStreamException