Package org.teavm.classlib.java.math

Class TBigInteger

java.lang.Object

java.lang.Number

org.teavm.classlib.java.math.TBigInteger

All Implemented Interfaces:

Serializable, Comparable<TBigInteger>

public class TBigInteger
extends Number
implements Comparable<TBigInteger>, Serializable

This class represents immutable integer numbers of arbitrary length. Large numbers are typically used in security applications and therefore BigIntegers offer dedicated functionality like the generation of large prime numbers or the computation of modular inverse.

Since the class was modeled to offer all the functionality as the Integer class does, it provides even methods that operate bitwise on a two's complement representation of large integers. Note however that the implementations favors an internal representation where magnitude and sign are treated separately. Hence such operations are inefficient and should be discouraged. In simple words: Do NOT implement any bit fields based on BigInteger.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final TBigInteger	ONE	The BigInteger constant 1.
static final TBigInteger	TEN	The BigInteger constant 10.
static final TBigInteger	ZERO	The BigInteger constant 0.

Constructor Summary

Constructors

Constructor	Description
TBigInteger(byte[] val)	Constructs a new BigInteger from the given two's complement representation.
TBigInteger(int signum, byte[] magnitude)	Constructs a new BigInteger instance with the given sign and the given magnitude.
TBigInteger(int bitLength, int certainty, Random rnd)	Constructs a random BigInteger instance in the range [0, 2^(bitLength)-1] which is probably prime.
TBigInteger(int numBits, Random rnd)	Constructs a random non-negative BigInteger instance in the range [0, 2^(numBits)-1].
TBigInteger(String val)	Constructs a new BigInteger instance from the string representation.
TBigInteger(String val, int radix)	Constructs a new BigInteger instance from the string representation.

Method Summary

Modifier and Type	Method	Description
TBigInteger	abs()	Returns a (new) BigInteger whose value is the absolute value of this.
TBigInteger	add(TBigInteger val)	Returns a new BigInteger whose value is this + val.
TBigInteger	and(TBigInteger val)	Returns a new BigInteger whose value is this & val.
TBigInteger	andNot(TBigInteger val)	Returns a new BigInteger whose value is this & ~val.
int	bitCount()	Use bitLength(0) if you want to know the length of the binary value in bits.
int	bitLength()	Returns the length of the value's two's complement representation without leading zeros for positive numbers / without leading ones for negative values.
TBigInteger	clearBit(int n)	Returns a new BigInteger which has the same binary representation as this but with the bit at position n cleared.
int	compareTo(TBigInteger val)	Compares this BigInteger with val.
TBigInteger	divide(TBigInteger divisor)	Returns a new BigInteger whose value is this / divisor.
TBigInteger[]	divideAndRemainder(TBigInteger divisor)	Returns a BigInteger array which contains this / divisor at index 0 and this % divisor at index 1.
double	doubleValue()	Returns this BigInteger as an double value.
boolean	equals(Object x)	Returns true if x is a BigInteger instance and if this instance is equal to this BigInteger.
TBigInteger	flipBit(int n)	Returns a new BigInteger which has the same binary representation as this but with the bit at position n flipped.
float	floatValue()	Returns this BigInteger as an float value.
TBigInteger	gcd(TBigInteger val)	Returns a new BigInteger whose value is greatest common divisor of this and val.
int	getLowestSetBit()	Returns the position of the lowest set bit in the two's complement representation of this BigInteger.
int	hashCode()	Returns a hash code for this BigInteger.
int	intValue()	Returns this BigInteger as an int value.
boolean	isProbablePrime(int certainty)	Tests whether this BigInteger is probably prime.
long	longValue()	Returns this BigInteger as an long value.
TBigInteger	max(TBigInteger val)	Returns the maximum of this BigInteger and val.
TBigInteger	min(TBigInteger val)	Returns the minimum of this BigInteger and val.
TBigInteger	mod(TBigInteger m)	Returns a new BigInteger whose value is this mod m.
TBigInteger	modInverse(TBigInteger m)	Returns a new BigInteger whose value is 1/this mod m.
TBigInteger	modPow(TBigInteger exponent, TBigInteger m)	Returns a new BigInteger whose value is this^exponent mod m.
TBigInteger	multiply(TBigInteger val)	Returns a new BigInteger whose value is this * val.
TBigInteger	negate()	Returns a new BigInteger whose value is the -this.
TBigInteger	nextProbablePrime()	Returns the smallest integer x > this which is probably prime as a BigInteger instance.
TBigInteger	not()	Returns a new BigInteger whose value is ~this.
TBigInteger	or(TBigInteger val)	Returns a new BigInteger whose value is this | val.
TBigInteger	pow(int exp)	Returns a new BigInteger whose value is this ^ exp.
static TBigInteger	probablePrime(int bitLength, Random rnd)	Returns a random positive BigInteger instance in the range [0, 2^(bitLength)-1] which is probably prime.
TBigInteger	remainder(TBigInteger divisor)	Returns a new BigInteger whose value is this % divisor.
TBigInteger	setBit(int n)	Returns a new BigInteger which has the same binary representation as this but with the bit at position n set.
TBigInteger	shiftLeft(int n)	Returns a new BigInteger whose value is this << n.
TBigInteger	shiftRight(int n)	Returns a new BigInteger whose value is this >> n.
int	signum()	Returns the sign of this BigInteger.
TBigInteger	subtract(TBigInteger val)	Returns a new BigInteger whose value is this - val.
boolean	testBit(int n)	Tests whether the bit at position n in this is set.
byte[]	toByteArray()	Returns the two's complement representation of this BigInteger in a byte array.
String	toString()	Returns a string representation of this BigInteger in decimal form.
String	toString(int radix)	Returns a string containing a string representation of this BigInteger with base radix.
static TBigInteger	valueOf(long val)
TBigInteger	xor(TBigInteger val)	Returns a new BigInteger whose value is this ^ val.

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

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

Field Details

ZERO

public static final TBigInteger ZERO

The BigInteger constant 0.

ONE

public static final TBigInteger ONE

The BigInteger constant 1.

TEN

public static final TBigInteger TEN

The BigInteger constant 10.

Constructor Details

TBigInteger

public TBigInteger(int numBits,
 Random rnd)

Constructs a random non-negative BigInteger instance in the range [0, 2^(numBits)-1].

Parameters:

numBits - maximum length of the new BigInteger in bits.

rnd - is an optional random generator to be used.

Throws:

IllegalArgumentException - if numBits invalid input: '<' 0.

TBigInteger

public TBigInteger(int bitLength,
 int certainty,
 Random rnd)

Constructs a random BigInteger instance in the range [0, 2^(bitLength)-1] which is probably prime. The probability that the returned BigInteger is prime is beyond (1-1/2^certainty).

Parameters:

bitLength - length of the new BigInteger in bits.

certainty - tolerated primality uncertainty.

rnd - is an optional random generator to be used.

Throws:

ArithmeticException - if bitLength invalid input: '<' 2.

TBigInteger

public TBigInteger(String val)

Constructs a new BigInteger instance from the string representation. The string representation consists of an optional minus sign followed by a non-empty sequence of decimal digits.

Parameters:

val - string representation of the new BigInteger.

Throws:

NullPointerException - if val == null.

NumberFormatException - if val is not a valid representation of a BigInteger.

TBigInteger

public TBigInteger(String val,
 int radix)

Constructs a new BigInteger instance from the string representation. The string representation consists of an optional minus sign followed by a non-empty sequence of digits in the specified radix. For the conversion the method Character.digit(char, radix) is used.

Parameters:

val - string representation of the new BigInteger.

radix - the base to be used for the conversion.

Throws:

NullPointerException - if val == null.

NumberFormatException - if val is not a valid representation of a BigInteger or if radix < Character.MIN_RADIX or radix > Character.MAX_RADIX.

TBigInteger

public TBigInteger(int signum,
 byte[] magnitude)

Constructs a new BigInteger instance with the given sign and the given magnitude. The sign is given as an integer (-1 for negative, 0 for zero, 1 for positive). The magnitude is specified as a byte array. The most significant byte is the entry at index 0.

Parameters:

signum - sign of the new BigInteger (-1 for negative, 0 for zero, 1 for positive).

magnitude - magnitude of the new BigInteger with the most significant byte first.

Throws:

NullPointerException - if magnitude == null.

NumberFormatException - if the sign is not one of -1, 0, 1 or if the sign is zero and the magnitude contains non-zero entries.

TBigInteger

public TBigInteger(byte[] val)

Constructs a new BigInteger from the given two's complement representation. The most significant byte is the entry at index 0. The most significant bit of this entry determines the sign of the new BigInteger instance. The given array must not be empty.

Parameters:

val - two's complement representation of the new BigInteger.

Throws:

NullPointerException - if val == null.

NumberFormatException - if the length of val is zero.

Method Details

valueOf

public static TBigInteger valueOf(long val)

toByteArray

public byte[] toByteArray()

Returns the two's complement representation of this BigInteger in a byte array.

Returns:

two's complement representation of this.

abs

public TBigInteger abs()

Returns a (new) BigInteger whose value is the absolute value of this.

Returns:

abs(this).

negate

public TBigInteger negate()

Returns a new BigInteger whose value is the -this.

Returns:

-this.

add

public TBigInteger add(TBigInteger val)

Returns a new BigInteger whose value is this + val.

Parameters:

val - value to be added to this.

Returns:

this + val.

Throws:

NullPointerException - if val == null.

subtract

public TBigInteger subtract(TBigInteger val)

Returns a new BigInteger whose value is this - val.

Parameters:

val - value to be subtracted from this.

Returns:

this - val.

Throws:

NullPointerException - if val == null.

signum

public int signum()

Returns the sign of this BigInteger.

Returns:

-1 if this < 0, 0 if this == 0, 1 if this > 0.

shiftRight

public TBigInteger shiftRight(int n)

Returns a new BigInteger whose value is this >> n. For negative arguments, the result is also negative. The shift distance may be negative which means that this is shifted left.

Implementation Note: Usage of this method on negative values is not recommended as the current implementation is not efficient.

Parameters:

n - shift distance

Returns:

this >> n if n >= 0; this << (-n) otherwise

shiftLeft

public TBigInteger shiftLeft(int n)

Returns a new BigInteger whose value is this << n. The result is equivalent to this * 2^n if n >= 0. The shift distance may be negative which means that this is shifted right. The result then corresponds to floor(this / 2^(-n)).

Implementation Note: Usage of this method on negative values is not recommended as the current implementation is not efficient.

Parameters:

n - shift distance.

Returns:

this << n if n >= 0; this >> (-n). otherwise

bitLength

public int bitLength()

Returns the length of the value's two's complement representation without leading zeros for positive numbers / without leading ones for negative values.

The two's complement representation of this will be at least bitLength() + 1 bits long.

The value will fit into an int if bitLength() < 32 or into a long if bitLength() < 64.

Returns:

the length of the minimal two's complement representation for this without the sign bit.

testBit

public boolean testBit(int n)

Tests whether the bit at position n in this is set. The result is equivalent to this & (2^n) != 0.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

n - position where the bit in this has to be inspected.

Returns:

this & (2^n) != 0.

Throws:

ArithmeticException - if n < 0.

setBit

public TBigInteger setBit(int n)

Returns a new BigInteger which has the same binary representation as this but with the bit at position n set. The result is equivalent to this | 2^n.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

n - position where the bit in this has to be set.

Returns:

this | 2^n.

Throws:

ArithmeticException - if n < 0.

clearBit

public TBigInteger clearBit(int n)

Returns a new BigInteger which has the same binary representation as this but with the bit at position n cleared. The result is equivalent to this & ~(2^n).

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

n - position where the bit in this has to be cleared.

Returns:

this & ~(2^n).

Throws:

ArithmeticException - if n < 0.

flipBit

public TBigInteger flipBit(int n)

Returns a new BigInteger which has the same binary representation as this but with the bit at position n flipped. The result is equivalent to this ^ 2^n.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

n - position where the bit in this has to be flipped.

Returns:

this ^ 2^n.

Throws:

ArithmeticException - if n < 0.

getLowestSetBit

public int getLowestSetBit()

Returns the position of the lowest set bit in the two's complement representation of this BigInteger. If all bits are zero (this=0) then -1 is returned as result.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Returns:

position of lowest bit if this != 0, -1 otherwise

bitCount

public int bitCount()

Use bitLength(0) if you want to know the length of the binary value in bits.

Returns the number of bits in the binary representation of this which differ from the sign bit. If this is positive the result is equivalent to the number of bits set in the binary representation of this. If this is negative the result is equivalent to the number of bits set in the binary representation of -this-1.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Returns:

number of bits in the binary representation of this which differ from the sign bit

not

public TBigInteger not()

Returns a new BigInteger whose value is ~this. The result of this operation is -this-1.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Returns:

~this.

and

public TBigInteger and(TBigInteger val)

Returns a new BigInteger whose value is this & val.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

val - value to be and'ed with this.

Returns:

this & val.

Throws:

NullPointerException - if val == null.

or

public TBigInteger or(TBigInteger val)

Returns a new BigInteger whose value is this | val.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

val - value to be or'ed with this.

Returns:

this | val.

Throws:

NullPointerException - if val == null.

xor

public TBigInteger xor(TBigInteger val)

Returns a new BigInteger whose value is this ^ val.

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

val - value to be xor'ed with this

Returns:

this ^ val

Throws:

NullPointerException - if val == null

andNot

public TBigInteger andNot(TBigInteger val)

Returns a new BigInteger whose value is this & ~val. Evaluating x.andNot(val) returns the same result as x.and(val.not()).

Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.

Parameters:

val - value to be not'ed and then and'ed with this.

Returns:

this & ~val.

Throws:

NullPointerException - if val == null.

intValue

public int intValue()

Returns this BigInteger as an int value. If this is too big to be represented as an int, then this % 2^32 is returned.

Specified by:

intValue in class Number

Returns:

this BigInteger as an int value.

longValue

public long longValue()

Returns this BigInteger as an long value. If this is too big to be represented as an long, then this % 2^64 is returned.

Specified by:

longValue in class Number

Returns:

this BigInteger as a long value.

floatValue

public float floatValue()

Returns this BigInteger as an float value. If this is too big to be represented as an float, then Float.POSITIVE_INFINITY or Float.NEGATIVE_INFINITY is returned. Note, that not all integers x in the range [-Float.MAX_VALUE, Float.MAX_VALUE] can be represented as a float. The float representation has a mantissa of length 24. For example, 2^24+1 = 16777217 is returned as float 16777216.0.

Specified by:

floatValue in class Number

Returns:

this BigInteger as a float value.

doubleValue

public double doubleValue()

Returns this BigInteger as an double value. If this is too big to be represented as an double, then Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY is returned. Note, that not all integers x in the range [-Double.MAX_VALUE, Double.MAX_VALUE] can be represented as a double. The double representation has a mantissa of length 53. For example, 2^53+1 = 9007199254740993 is returned as double 9007199254740992.0.

Specified by:

doubleValue in class Number

Returns:

this BigInteger as a double value

compareTo

public int compareTo(TBigInteger val)

Compares this BigInteger with val. Returns one of the three values 1, 0, or -1.

Specified by:

compareTo in interface Comparable<TBigInteger>

Parameters:

val - value to be compared with this.

Returns:

1 if this > val, -1 if this < val , 0 if this == val.

Throws:

NullPointerException - if val == null.

min

public TBigInteger min(TBigInteger val)

Returns the minimum of this BigInteger and val.

Parameters:

val - value to be used to compute the minimum with this.

Returns:

min(this, val).

Throws:

NullPointerException - if val == null.

max

public TBigInteger max(TBigInteger val)

Returns the maximum of this BigInteger and val.

Parameters:

val - value to be used to compute the maximum with this

Returns:

max(this, val)

Throws:

NullPointerException - if val == null

hashCode

public int hashCode()

Returns a hash code for this BigInteger.

Overrides:

hashCode in class Object

Returns:

hash code for this.

equals

public boolean equals(Object x)

Returns true if x is a BigInteger instance and if this instance is equal to this BigInteger.

Overrides:

equals in class Object

Parameters:

x - object to be compared with this.

Returns:

true if x is a BigInteger and this == x, false otherwise.

toString

public String toString()

Returns a string representation of this BigInteger in decimal form.

Overrides:

toString in class Object

Returns:

a string representation of this in decimal form.

toString

public String toString(int radix)

Returns a string containing a string representation of this BigInteger with base radix. If radix < Character.MIN_RADIX or radix > Character.MAX_RADIX then a decimal representation is returned. The characters of the string representation are generated with method Character.forDigit.

Parameters:

radix - base to be used for the string representation.

Returns:

a string representation of this with radix 10.

gcd

public TBigInteger gcd(TBigInteger val)

Returns a new BigInteger whose value is greatest common divisor of this and val. If this==0 and val==0 then zero is returned, otherwise the result is positive.

Parameters:

val - value with which the greatest common divisor is computed.

Returns:

gcd(this, val).

Throws:

NullPointerException - if val == null.

multiply

public TBigInteger multiply(TBigInteger val)

Returns a new BigInteger whose value is this * val.

Parameters:

val - value to be multiplied with this.

Returns:

this * val.

Throws:

NullPointerException - if val == null.

pow

public TBigInteger pow(int exp)

Returns a new BigInteger whose value is this ^ exp.

Parameters:

exp - exponent to which this is raised.

Returns:

this ^ exp.

Throws:

ArithmeticException - if exp < 0.

divideAndRemainder

public TBigInteger[] divideAndRemainder(TBigInteger divisor)

Returns a BigInteger array which contains this / divisor at index 0 and this % divisor at index 1.

Parameters:

divisor - value by which this is divided.

Returns:

[this / divisor, this % divisor].

Throws:

NullPointerException - if divisor == null.

ArithmeticException - if divisor == 0.

See Also:

• divide(org.teavm.classlib.java.math.TBigInteger)
• remainder(org.teavm.classlib.java.math.TBigInteger)

divide

public TBigInteger divide(TBigInteger divisor)

Returns a new BigInteger whose value is this / divisor.

Parameters:

divisor - value by which this is divided.

Returns:

this / divisor.

Throws:

NullPointerException - if divisor == null.

ArithmeticException - if divisor == 0.

remainder

public TBigInteger remainder(TBigInteger divisor)

Returns a new BigInteger whose value is this % divisor. Regarding signs this methods has the same behavior as the % operator on int's, i.e. the sign of the remainder is the same as the sign of this.

Parameters:

divisor - value by which this is divided.

Returns:

this % divisor.

Throws:

NullPointerException - if divisor == null.

ArithmeticException - if divisor == 0.

modInverse

public TBigInteger modInverse(TBigInteger m)

Returns a new BigInteger whose value is 1/this mod m. The modulus m must be positive. The result is guaranteed to be in the interval [0, m) (0 inclusive, m exclusive). If this is not relatively prime to m, then an exception is thrown.

Parameters:

m - the modulus.

Returns:

1/this mod m.

Throws:

NullPointerException - if m == null

ArithmeticException - if m < 0 or if this is not relatively prime to m

modPow

public TBigInteger modPow(TBigInteger exponent,
 TBigInteger m)

Returns a new BigInteger whose value is this^exponent mod m. The modulus m must be positive. The result is guaranteed to be in the interval [0, m) (0 inclusive, m exclusive). If the exponent is negative, then this.modInverse(m)^(-exponent) mod m) is computed. The inverse of this only exists if this is relatively prime to m, otherwise an exception is thrown.

Parameters:

exponent - the exponent.

m - the modulus.

Returns:

this^exponent mod val.

Throws:

NullPointerException - if m == null or exponent == null.

ArithmeticException - if m < 0 or if exponent<0 and this is not relatively prime to m.

mod

public TBigInteger mod(TBigInteger m)

Returns a new BigInteger whose value is this mod m. The modulus m must be positive. The result is guaranteed to be in the interval [0, m) (0 inclusive, m exclusive). The behavior of this function is not equivalent to the behavior of the % operator defined for the built-in int's.

Parameters:

m - the modulus.

Returns:

this mod m.

Throws:

NullPointerException - if m == null.

ArithmeticException - if m < 0.

isProbablePrime

public boolean isProbablePrime(int certainty)

Tests whether this BigInteger is probably prime. If true is returned, then this is prime with a probability beyond (1-1/2^certainty). If false is returned, then this is definitely composite. If the argument certainty invalid input: '<'= 0, then this method returns true.

Parameters:

certainty - tolerated primality uncertainty.

Returns:

true, if this is probably prime, false otherwise.

nextProbablePrime

public TBigInteger nextProbablePrime()

Returns the smallest integer x > this which is probably prime as a BigInteger instance. The probability that the returned BigInteger is prime is beyond (1-1/2^80).

Returns:

smallest integer > this which is robably prime.

Throws:

ArithmeticException - if this < 0.

probablePrime

public static TBigInteger probablePrime(int bitLength,
 Random rnd)

Returns a random positive BigInteger instance in the range [0, 2^(bitLength)-1] which is probably prime. The probability that the returned BigInteger is prime is beyond (1-1/2^80).

Implementation Note: Currently rnd is ignored.

Parameters:

bitLength - length of the new BigInteger in bits.

rnd - random generator used to generate the new BigInteger.

Returns:

probably prime random BigInteger instance.

Throws:

IllegalArgumentException - if bitLength < 2.