BigInteger

public class BigInteger
extends Number implements Comparable<BigInteger>

java.lang.Object
   ↳ java.lang.Number
     ↳ java.math.BigInteger


Immutable arbitrary-precision integers. All operations behave as if BigIntegers were represented in two's-complement notation (like Java's primitive integer types). BigInteger provides analogues to all of Java's primitive integer operators, and all relevant methods from java.lang.Math. Additionally, BigInteger provides operations for modular arithmetic, GCD calculation, primality testing, prime generation, bit manipulation, and a few other miscellaneous operations.

Semantics of arithmetic operations exactly mimic those of Java's integer arithmetic operators, as defined in The Java Language Specification. For example, division by zero throws an ArithmeticException, and division of a negative by a positive yields a negative (or zero) remainder.

Semantics of shift operations extend those of Java's shift operators to allow for negative shift distances. A right-shift with a negative shift distance results in a left shift, and vice-versa. The unsigned right shift operator (>>>) is omitted since this operation only makes sense for a fixed sized word and not for a representation conceptually having an infinite number of leading virtual sign bits.

Semantics of bitwise logical operations exactly mimic those of Java's bitwise integer operators. The binary operators (and, or, xor) implicitly perform sign extension on the shorter of the two operands prior to performing the operation.

Comparison operations perform signed integer comparisons, analogous to those performed by Java's relational and equality operators.

Modular arithmetic operations are provided to compute residues, perform exponentiation, and compute multiplicative inverses. These methods always return a non-negative result, between 0 and (modulus - 1), inclusive.

Bit operations operate on a single bit of the two's-complement representation of their operand. If necessary, the operand is sign-extended so that it contains the designated bit. None of the single-bit operations can produce a BigInteger with a different sign from the BigInteger being operated on, as they affect only a single bit, and the arbitrarily large abstraction provided by this class ensures that conceptually there are infinitely many "virtual sign bits" preceding each BigInteger.

For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigInteger methods. The pseudo-code expression (i + j) is shorthand for "a BigInteger whose value is that of the BigInteger i plus that of the BigInteger j." The pseudo-code expression (i == j) is shorthand for "true if and only if the BigInteger i represents the same value as the BigInteger j." Other pseudo-code expressions are interpreted similarly.

All methods and constructors in this class throw NullPointerException when passed a null object reference for any input parameter. BigInteger must support values in the range -2Integer.MAX_VALUE (exclusive) to +2Integer.MAX_VALUE (exclusive) and may support values outside of that range. An ArithmeticException is thrown when a BigInteger constructor or method would generate a value outside of the supported range. The range of probable prime values is limited and may be less than the full supported positive range of BigInteger. The range must be at least 1 to 2500000000.

See also:

Summary

Fields

public static final BigInteger ONE

The BigInteger constant one.

public static final BigInteger TEN

The BigInteger constant ten.

public static final BigInteger TWO

The BigInteger constant two.

public static final BigInteger ZERO

The BigInteger constant zero.

Public constructors

BigInteger(byte[] val, int off, int len)

Translates a byte sub-array containing the two's-complement binary representation of a BigInteger into a BigInteger.

BigInteger(byte[] val)

Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger.

BigInteger(int signum, byte[] magnitude, int off, int len)

Translates the sign-magnitude representation of a BigInteger into a BigInteger.

BigInteger(int signum, byte[] magnitude)

Translates the sign-magnitude representation of a BigInteger into a BigInteger.

BigInteger(String val, int radix)

Translates the String representation of a BigInteger in the specified radix into a BigInteger.

BigInteger(String val)

Translates the decimal String representation of a BigInteger into a BigInteger.

BigInteger(int numBits, Random rnd)

Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2numBits - 1), inclusive.

BigInteger(int bitLength, int certainty, Random rnd)

Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength.

Public methods

BigInteger abs()

Returns a BigInteger whose value is the absolute value of this BigInteger.

BigInteger add(BigInteger val)

Returns a BigInteger whose value is (this + val).

BigInteger and(BigInteger val)

Returns a BigInteger whose value is (this & val).

BigInteger andNot(BigInteger val)

Returns a BigInteger whose value is (this & ~val).

int bitCount()

Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign bit.

int bitLength()

Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.

byte byteValueExact()

Converts this BigInteger to a byte, checking for lost information.

BigInteger clearBit(int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared.

int compareTo(BigInteger val)

Compares this BigInteger with the specified BigInteger.

BigInteger divide(BigInteger val)

Returns a BigInteger whose value is (this / val).

BigInteger[] divideAndRemainder(BigInteger val)

Returns an array of two BigIntegers containing (this / val) followed by (this % val).

double doubleValue()

Converts this BigInteger to a double.

boolean equals(Object x)

Compares this BigInteger with the specified Object for equality.

BigInteger flipBit(int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped.

float floatValue()

Converts this BigInteger to a float.

BigInteger gcd(BigInteger val)

Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val).

int getLowestSetBit()

Returns the index of the rightmost (lowest-order) one bit in this BigInteger (the number of zero bits to the right of the rightmost one bit).

int hashCode()

Returns the hash code for this BigInteger.

int intValue()

Converts this BigInteger to an int.

int intValueExact()

Converts this BigInteger to an int, checking for lost information.

boolean isProbablePrime(int certainty)

Returns true if this BigInteger is probably prime, false if it's definitely composite.

long longValue()

Converts this BigInteger to a long.

long longValueExact()

Converts this BigInteger to a long, checking for lost information.

BigInteger max(BigInteger val)

Returns the maximum of this BigInteger and val.

BigInteger min(BigInteger val)

Returns the minimum of this BigInteger and val.

BigInteger mod(BigInteger m)

Returns a BigInteger whose value is (this mod m).

BigInteger modInverse(BigInteger m)

Returns a BigInteger whose value is (this-1 mod m).

BigInteger modPow(BigInteger exponent, BigInteger m)

Returns a BigInteger whose value is (thisexponent mod m).

BigInteger multiply(BigInteger val)

Returns a BigInteger whose value is (this * val).

BigInteger negate()

Returns a BigInteger whose value is (-this).

BigInteger nextProbablePrime()

Returns the first integer greater than this BigInteger that is probably prime.

BigInteger not()

Returns a BigInteger whose value is (~this).

BigInteger or(BigInteger val)

Returns a BigInteger whose value is (this | val).

BigInteger pow(int exponent)

Returns a BigInteger whose value is (thisexponent).

static BigInteger probablePrime(int bitLength, Random rnd)

Returns a positive BigInteger that is probably prime, with the specified bitLength.

BigInteger remainder(BigInteger val)

Returns a BigInteger whose value is (this % val).

BigInteger setBit(int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set.

BigInteger shiftLeft(int n)

Returns a BigInteger whose value is (this << n).

BigInteger shiftRight(int n)

Returns a BigInteger whose value is (this >> n).

short shortValueExact()

Converts this BigInteger to a short, checking for lost information.

int signum()

Returns the signum function of this BigInteger.

BigInteger sqrt()

Returns the integer square root of this BigInteger.

BigInteger[] sqrtAndRemainder()

Returns an array of two BigIntegers containing the integer square root s of this and its remainder this - s*s, respectively.

BigInteger subtract(BigInteger val)

Returns a BigInteger whose value is (this - val).

boolean testBit(int n)

Returns true if and only if the designated bit is set.

byte[] toByteArray()

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

String toString()

Returns the decimal String representation of this BigInteger.

String toString(int radix)

Returns the String representation of this BigInteger in the given radix.

static BigInteger valueOf(long val)

Returns a BigInteger whose value is equal to that of the specified long.

BigInteger xor(BigInteger val)

Returns a BigInteger whose value is (this ^ val).

Inherited methods

Fields

ONE

Added in API level 1
public static final BigInteger ONE

The BigInteger constant one.

TEN

Added in API level 1
public static final BigInteger TEN

The BigInteger constant ten.

TWO

Added in API level 33
public static final BigInteger TWO

The BigInteger constant two.

ZERO

Added in API level 1
public static final BigInteger ZERO

The BigInteger constant zero.

Public constructors

BigInteger

Added in API level 1
public BigInteger (byte[] val, 
                int off, 
                int len)

Translates a byte sub-array containing the two's-complement binary representation of a BigInteger into a BigInteger. The sub-array is specified via an offset into the array and a length. The sub-array is assumed to be in big-endian byte-order: the most significant byte is the element at index off. The val array is assumed to be unchanged for the duration of the constructor call. An IndexOutOfBoundsException is thrown if the length of the array val is non-zero and either off is negative, len is negative, or off+len is greater than the length of val.

Parameters
val byte: byte array containing a sub-array which is the big-endian two's-complement binary representation of a BigInteger.

off int: the start offset of the binary representation.

len int: the number of bytes to use.

Throws
NumberFormatException val is zero bytes long.
IndexOutOfBoundsException if the provided array offset and length would cause an index into the byte array to be negative or greater than or equal to the array length.

BigInteger

Added in API level 1
public BigInteger (byte[] val)

Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger. The input array is assumed to be in big-endian byte-order: the most significant byte is in the zeroth element. The val array is assumed to be unchanged for the duration of the constructor call.

Parameters
val byte: big-endian two's-complement binary representation of a BigInteger.

Throws
NumberFormatException val is zero bytes long.

BigInteger

Added in API level 1
public BigInteger (int signum, 
                byte[] magnitude, 
                int off, 
                int len)

Translates the sign-magnitude representation of a BigInteger into a BigInteger. The sign is represented as an integer signum value: -1 for negative, 0 for zero, or 1 for positive. The magnitude is a sub-array of a byte array in big-endian byte-order: the most significant byte is the element at index off. A zero value of the length len is permissible, and will result in a BigInteger value of 0, whether signum is -1, 0 or 1. The magnitude array is assumed to be unchanged for the duration of the constructor call. An IndexOutOfBoundsException is thrown if the length of the array magnitude is non-zero and either off is negative, len is negative, or off+len is greater than the length of magnitude.

Parameters
signum int: signum of the number (-1 for negative, 0 for zero, 1 for positive).

magnitude byte: big-endian binary representation of the magnitude of the number.

off int: the start offset of the binary representation.

len int: the number of bytes to use.

Throws
NumberFormatException signum is not one of the three legal values (-1, 0, and 1), or signum is 0 and magnitude contains one or more non-zero bytes.
IndexOutOfBoundsException if the provided array offset and length would cause an index into the byte array to be negative or greater than or equal to the array length.

BigInteger

Added in API level 1
public BigInteger (int signum, 
                byte[] magnitude)

Translates the sign-magnitude representation of a BigInteger into a BigInteger. The sign is represented as an integer signum value: -1 for negative, 0 for zero, or 1 for positive. The magnitude is a byte array in big-endian byte-order: the most significant byte is the zeroth element. A zero-length magnitude array is permissible, and will result in a BigInteger value of 0, whether signum is -1, 0 or 1. The magnitude array is assumed to be unchanged for the duration of the constructor call.

Parameters
signum int: signum of the number (-1 for negative, 0 for zero, 1 for positive).

magnitude byte: big-endian binary representation of the magnitude of the number.

Throws
NumberFormatException signum is not one of the three legal values (-1, 0, and 1), or signum is 0 and magnitude contains one or more non-zero bytes.

BigInteger

Added in API level 1
public BigInteger (String val, 
                int radix)

Translates the String representation of a BigInteger in the specified radix into a BigInteger. The String representation consists of an optional minus or plus sign followed by a sequence of one or more digits in the specified radix. The character-to-digit mapping is provided by Character.digit. The String may not contain any extraneous characters (whitespace, for example).

Parameters
val String: String representation of BigInteger.

radix int: radix to be used in interpreting val.

Throws
NumberFormatException val is not a valid representation of a BigInteger in the specified radix, or radix is outside the range from Character#MIN_RADIX to Character#MAX_RADIX, inclusive.

BigInteger

Added in API level 1
public BigInteger (String val)

Translates the decimal String representation of a BigInteger into a BigInteger. The String representation consists of an optional minus or plus sign followed by a sequence of one or more decimal digits. The character-to-digit mapping is provided by Character.digit. The String may not contain any extraneous characters (whitespace, for example).

Parameters
val String: decimal String representation of BigInteger.

Throws
NumberFormatException val is not a valid representation of a BigInteger.

BigInteger

Added in API level 1
public BigInteger (int numBits, 
                Random rnd)

Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2numBits - 1), inclusive. The uniformity of the distribution assumes that a fair source of random bits is provided in rnd. Note that this constructor always constructs a non-negative BigInteger.

Parameters
numBits int: maximum bitLength of the new BigInteger.

rnd Random: source of randomness to be used in computing the new BigInteger.

Throws
IllegalArgumentException numBits is negative.

See also:

BigInteger

Added in API level 1
public BigInteger (int bitLength, 
                int certainty, 
                Random rnd)

Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength.

API Note:
  • It is recommended that the probablePrime method be used in preference to this constructor unless there is a compelling need to specify a certainty.
Parameters
bitLength int: bitLength of the returned BigInteger.

certainty int: a measure of the uncertainty that the caller is willing to tolerate. The probability that the new BigInteger represents a prime number will exceed (1 - 1/2certainty). The execution time of this constructor is proportional to the value of this parameter.

rnd Random: source of random bits used to select candidates to be tested for primality.

Throws
ArithmeticException bitLength < 2 or bitLength is too large.

See also:

Public methods

abs

Added in API level 1
public BigInteger abs ()

Returns a BigInteger whose value is the absolute value of this BigInteger.

Returns
BigInteger abs(this)

add

Added in API level 1
public BigInteger add (BigInteger val)

Returns a BigInteger whose value is (this + val).

Parameters
val BigInteger: value to be added to this BigInteger.

Returns
BigInteger this + val

and

Added in API level 1
public BigInteger and (BigInteger val)

Returns a BigInteger whose value is (this & val). (This method returns a negative BigInteger if and only if this and val are both negative.)

Parameters
val BigInteger: value to be AND'ed with this BigInteger.

Returns
BigInteger this & val

andNot

Added in API level 1
public BigInteger andNot (BigInteger val)

Returns a BigInteger whose value is (this & ~val). This method, which is equivalent to and(val.not()), is provided as a convenience for masking operations. (This method returns a negative BigInteger if and only if this is negative and val is positive.)

Parameters
val BigInteger: value to be complemented and AND'ed with this BigInteger.

Returns
BigInteger this & ~val

bitCount

Added in API level 1
public int bitCount ()

Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign bit. This method is useful when implementing bit-vector style sets atop BigIntegers.

Returns
int number of bits in the two's complement representation of this BigInteger that differ from its sign bit.

bitLength

Added in API level 1
public int bitLength ()

Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit. For positive BigIntegers, this is equivalent to the number of bits in the ordinary binary representation. For zero this method returns 0. (Computes (ceil(log2(this < 0 ? -this : this+1))).)

Returns
int number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.

byteValueExact

Added in API level 31
public byte byteValueExact ()

Converts this BigInteger to a byte, checking for lost information. If the value of this BigInteger is out of the range of the byte type, then an ArithmeticException is thrown.

Returns
byte this BigInteger converted to a byte.

Throws
ArithmeticException if the value of this will not exactly fit in a byte.

See also:

clearBit

Added in API level 1
public BigInteger clearBit (int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared. (Computes (this & ~(1<<n)).)

Parameters
n int: index of bit to clear.

Returns
BigInteger this & ~(1<<n)

Throws
ArithmeticException n is negative.

compareTo

Added in API level 1
public int compareTo (BigInteger val)

Compares this BigInteger with the specified BigInteger. This method is provided in preference to individual methods for each of the six boolean comparison operators (<, ==, >, >=, !=, <=). The suggested idiom for performing these comparisons is: (x.compareTo(y) <op> 0), where <op> is one of the six comparison operators.

Parameters
val BigInteger: BigInteger to which this BigInteger is to be compared.

Returns
int -1, 0 or 1 as this BigInteger is numerically less than, equal to, or greater than val.

divide

Added in API level 1
public BigInteger divide (BigInteger val)

Returns a BigInteger whose value is (this / val).

Parameters
val BigInteger: value by which this BigInteger is to be divided.

Returns
BigInteger this / val

Throws
ArithmeticException if val is zero.

divideAndRemainder

Added in API level 1
public BigInteger[] divideAndRemainder (BigInteger val)

Returns an array of two BigIntegers containing (this / val) followed by (this % val).

Parameters
val BigInteger: value by which this BigInteger is to be divided, and the remainder computed.

Returns
BigInteger[] an array of two BigIntegers: the quotient (this / val) is the initial element, and the remainder (this % val) is the final element.

Throws
ArithmeticException if val is zero.

doubleValue

Added in API level 1
public double doubleValue ()

Converts this BigInteger to a double. This conversion is similar to the narrowing primitive conversion from double to float as defined in The Java Language Specification: if this BigInteger has too great a magnitude to represent as a double, it will be converted to Double#NEGATIVE_INFINITY or Double.POSITIVE_INFINITY as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigInteger value.

Returns
double this BigInteger converted to a double.

equals

Added in API level 1
public boolean equals (Object x)

Compares this BigInteger with the specified Object for equality.

Parameters
x Object: Object to which this BigInteger is to be compared.

Returns
boolean true if and only if the specified Object is a BigInteger whose value is numerically equal to this BigInteger.

flipBit

Added in API level 1
public BigInteger flipBit (int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped. (Computes (this ^ (1<<n)).)

Parameters
n int: index of bit to flip.

Returns
BigInteger this ^ (1<<n)

Throws
ArithmeticException n is negative.

floatValue

Added in API level 1
public float floatValue ()

Converts this BigInteger to a float. This conversion is similar to the narrowing primitive conversion from double to float as defined in The Java Language Specification: if this BigInteger has too great a magnitude to represent as a float, it will be converted to Float#NEGATIVE_INFINITY or Float.POSITIVE_INFINITY as appropriate. Note that even when the return value is finite, this conversion can lose information about the precision of the BigInteger value.

Returns
float this BigInteger converted to a float.

gcd

Added in API level 1
public BigInteger gcd (BigInteger val)

Returns a BigInteger whose value is the greatest common divisor of abs(this) and abs(val). Returns 0 if this == 0 && val == 0.

Parameters
val BigInteger: value with which the GCD is to be computed.

Returns
BigInteger GCD(abs(this), abs(val))

getLowestSetBit

Added in API level 1
public int getLowestSetBit ()

Returns the index of the rightmost (lowest-order) one bit in this BigInteger (the number of zero bits to the right of the rightmost one bit). Returns -1 if this BigInteger contains no one bits. (Computes (this == 0? -1 : log2(this & -this)).)

Returns
int index of the rightmost one bit in this BigInteger.

hashCode

Added in API level 1
public int hashCode ()

Returns the hash code for this BigInteger.

Returns
int hash code for this BigInteger.

intValue

Added in API level 1
public int intValue ()

Converts this BigInteger to an int. This conversion is analogous to a narrowing primitive conversion from long to int as defined in The Java Language Specification: if this BigInteger is too big to fit in an int, only the low-order 32 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInteger value as well as return a result with the opposite sign.

Returns
int this BigInteger converted to an int.

See also:

intValueExact

Added in API level 31
public int intValueExact ()

Converts this BigInteger to an int, checking for lost information. If the value of this BigInteger is out of the range of the int type, then an ArithmeticException is thrown.

Returns
int this BigInteger converted to an int.

Throws
ArithmeticException if the value of this will not exactly fit in an int.

See also:

isProbablePrime

Added in API level 1
public boolean isProbablePrime (int certainty)

Returns true if this BigInteger is probably prime, false if it's definitely composite. If certainty is ≤ 0, true is returned.

Parameters
certainty int: a measure of the uncertainty that the caller is willing to tolerate: if the call returns true the probability that this BigInteger is prime exceeds (1 - 1/2certainty). The execution time of this method is proportional to the value of this parameter.

Returns
boolean true if this BigInteger is probably prime, false if it's definitely composite.

longValue

Added in API level 1
public long longValue ()

Converts this BigInteger to a long. This conversion is analogous to a narrowing primitive conversion from long to int as defined in The Java Language Specification: if this BigInteger is too big to fit in a long, only the low-order 64 bits are returned. Note that this conversion can lose information about the overall magnitude of the BigInteger value as well as return a result with the opposite sign.

Returns
long this BigInteger converted to a long.

See also:

longValueExact

Added in API level 31
public long longValueExact ()

Converts this BigInteger to a long, checking for lost information. If the value of this BigInteger is out of the range of the long type, then an ArithmeticException is thrown.

Returns
long this BigInteger converted to a long.

Throws
ArithmeticException if the value of this will not exactly fit in a long.

See also:

max

Added in API level 1
public BigInteger max (BigInteger val)

Returns the maximum of this BigInteger and val.

Parameters
val BigInteger: value with which the maximum is to be computed.

Returns
BigInteger the BigInteger whose value is the greater of this and val. If they are equal, either may be returned.

min

Added in API level 1
public BigInteger min (BigInteger val)

Returns the minimum of this BigInteger and val.

Parameters
val BigInteger: value with which the minimum is to be computed.

Returns
BigInteger the BigInteger whose value is the lesser of this BigInteger and val. If they are equal, either may be returned.

mod

Added in API level 1
public BigInteger mod (BigInteger m)

Returns a BigInteger whose value is (this mod m). This method differs from remainder in that it always returns a non-negative BigInteger.

Parameters
m BigInteger: the modulus.

Returns
BigInteger this mod m

Throws
ArithmeticException m ≤ 0

modInverse

Added in API level 1
public BigInteger modInverse (BigInteger m)

Returns a BigInteger whose value is (this-1 mod m).

Parameters
m BigInteger: the modulus.

Returns
BigInteger this-1 mod m.

Throws
ArithmeticException m ≤ 0, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger is not relatively prime to m).

modPow

Added in API level 1
public BigInteger modPow (BigInteger exponent, 
                BigInteger m)

Returns a BigInteger whose value is (thisexponent mod m). (Unlike pow, this method permits negative exponents.)

Parameters
exponent BigInteger: the exponent.

m BigInteger: the modulus.

Returns
BigInteger thisexponent mod m

Throws
ArithmeticException m ≤ 0 or the exponent is negative and this BigInteger is not relatively prime to m.

multiply

Added in API level 1
public BigInteger multiply (BigInteger val)

Returns a BigInteger whose value is (this * val).

Implementation Note:
  • An implementation may offer better algorithmic performance when val == this.
Parameters
val BigInteger: value to be multiplied by this BigInteger.

Returns
BigInteger this * val

negate

Added in API level 1
public BigInteger negate ()

Returns a BigInteger whose value is (-this).

Returns
BigInteger -this

nextProbablePrime

Added in API level 1
public BigInteger nextProbablePrime ()

Returns the first integer greater than this BigInteger that is probably prime. The probability that the number returned by this method is composite does not exceed 2-100. This method will never skip over a prime when searching: if it returns p, there is no prime q such that this < q < p.

Returns
BigInteger the first integer greater than this BigInteger that is probably prime.

Throws
ArithmeticException this < 0 or this is too large.

not

Added in API level 1
public BigInteger not ()

Returns a BigInteger whose value is (~this). (This method returns a negative value if and only if this BigInteger is non-negative.)

Returns
BigInteger ~this

or

Added in API level 1
public BigInteger or (BigInteger val)

Returns a BigInteger whose value is (this | val). (This method returns a negative BigInteger if and only if either this or val is negative.)

Parameters
val BigInteger: value to be OR'ed with this BigInteger.

Returns
BigInteger this | val

pow

Added in API level 1
public BigInteger pow (int exponent)

Returns a BigInteger whose value is (thisexponent). Note that exponent is an integer rather than a BigInteger.

Parameters
exponent int: exponent to which this BigInteger is to be raised.

Returns
BigInteger thisexponent

Throws
ArithmeticException exponent is negative. (This would cause the operation to yield a non-integer value.)

probablePrime

Added in API level 1
public static BigInteger probablePrime (int bitLength, 
                Random rnd)

Returns a positive BigInteger that is probably prime, with the specified bitLength. The probability that a BigInteger returned by this method is composite does not exceed 2-100.

Parameters
bitLength int: bitLength of the returned BigInteger.

rnd Random: source of random bits used to select candidates to be tested for primality.

Returns
BigInteger a BigInteger of bitLength bits that is probably prime

Throws
ArithmeticException bitLength < 2 or bitLength is too large.

See also:

remainder

Added in API level 1
public BigInteger remainder (BigInteger val)

Returns a BigInteger whose value is (this % val).

Parameters
val BigInteger: value by which this BigInteger is to be divided, and the remainder computed.

Returns
BigInteger this % val

Throws
ArithmeticException if val is zero.

setBit

Added in API level 1
public BigInteger setBit (int n)

Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set. (Computes (this | (1<<n)).)

Parameters
n int: index of bit to set.

Returns
BigInteger this | (1<<n)

Throws
ArithmeticException n is negative.

shiftLeft

Added in API level 1
public BigInteger shiftLeft (int n)

Returns a BigInteger whose value is (this << n). The shift distance, n, may be negative, in which case this method performs a right shift. (Computes floor(this * 2n).)

Parameters
n int: shift distance, in bits.

Returns
BigInteger this << n

See also:

shiftRight

Added in API level 1
public BigInteger shiftRight (int n)

Returns a BigInteger whose value is (this >> n). Sign extension is performed. The shift distance, n, may be negative, in which case this method performs a left shift. (Computes floor(this / 2n).)

Parameters
n int: shift distance, in bits.

Returns
BigInteger this >> n

See also:

shortValueExact

Added in API level 31
public short shortValueExact ()

Converts this BigInteger to a short, checking for lost information. If the value of this BigInteger is out of the range of the short type, then an ArithmeticException is thrown.

Returns
short this BigInteger converted to a short.

Throws
ArithmeticException if the value of this will not exactly fit in a short.

signum

Added in API level 1
public int signum ()

Returns the signum function of this BigInteger.

Returns
int -1, 0 or 1 as the value of this BigInteger is negative, zero or positive.

sqrt

Added in API level 33
public BigInteger sqrt ()

Returns the integer square root of this BigInteger. The integer square root of the corresponding mathematical integer n is the largest mathematical integer s such that s*s <= n. It is equal to the value of floor(sqrt(n)), where sqrt(n) denotes the real square root of n treated as a real. Note that the integer square root will be less than the real square root if the latter is not representable as an integral value.

Returns
BigInteger the integer square root of this

Throws
ArithmeticException if this is negative. (The square root of a negative integer val is (i * sqrt(-val)) where i is the imaginary unit and is equal to sqrt(-1).)

sqrtAndRemainder

Added in API level 33
public BigInteger[] sqrtAndRemainder ()

Returns an array of two BigIntegers containing the integer square root s of this and its remainder this - s*s, respectively.

Returns
BigInteger[] an array of two BigIntegers with the integer square root at offset 0 and the remainder at offset 1

Throws
ArithmeticException if this is negative. (The square root of a negative integer val is (i * sqrt(-val)) where i is the imaginary unit and is equal to sqrt(-1).)

See also:

subtract

Added in API level 1
public BigInteger subtract (BigInteger val)

Returns a BigInteger whose value is (this - val).

Parameters
val BigInteger: value to be subtracted from this BigInteger.

Returns
BigInteger this - val

testBit

Added in API level 1
public boolean testBit (int n)

Returns true if and only if the designated bit is set. (Computes ((this & (1<<n)) != 0).)

Parameters
n int: index of bit to test.

Returns
boolean true if and only if the designated bit is set.

Throws
ArithmeticException n is negative.

toByteArray

Added in API level 1
public byte[] toByteArray ()

Returns a byte array containing the two's-complement representation of this BigInteger. The byte array will be in big-endian byte-order: the most significant byte is in the zeroth element. The array will contain the minimum number of bytes required to represent this BigInteger, including at least one sign bit, which is (ceil((this.bitLength() + 1)/8)). (This representation is compatible with the (byte[]) constructor.)

Returns
byte[] a byte array containing the two's-complement representation of this BigInteger.

See also:

toString

Added in API level 1
public String toString ()

Returns the decimal String representation of this BigInteger. The digit-to-character mapping provided by Character.forDigit is used, and a minus sign is prepended if appropriate. (This representation is compatible with the (String) constructor, and allows for String concatenation with Java's + operator.)

Returns
String decimal String representation of this BigInteger.

toString

Added in API level 1
public String toString (int radix)

Returns the String representation of this BigInteger in the given radix. If the radix is outside the range from Character.MIN_RADIX to Character#MAX_RADIX inclusive, it will default to 10 (as is the case for Integer.toString). The digit-to-character mapping provided by Character.forDigit is used, and a minus sign is prepended if appropriate. (This representation is compatible with the (String, int) constructor.)

Parameters
radix int: radix of the String representation.

Returns
String String representation of this BigInteger in the given radix.

valueOf

Added in API level 1
public static BigInteger valueOf (long val)

Returns a BigInteger whose value is equal to that of the specified long.

API Note:
  • This static factory method is provided in preference to a (long) constructor because it allows for reuse of frequently used BigIntegers.
Parameters
val long: value of the BigInteger to return.

Returns
BigInteger a BigInteger with the specified value.

xor

Added in API level 1
public BigInteger xor (BigInteger val)

Returns a BigInteger whose value is (this ^ val). (This method returns a negative BigInteger if and only if exactly one of this and val are negative.)

Parameters
val BigInteger: value to be XOR'ed with this BigInteger.

Returns
BigInteger this ^ val