Class BigInteger
 java.lang.Object

 java.lang.Number

 java.math.BigInteger
 All Implemented Interfaces:

Serializable
,Comparable<BigInteger>
public class BigInteger extends Number implements Comparable<BigInteger>
Immutable arbitraryprecision integers. All operations behave as if BigIntegers were represented in two'scomplement 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 rightshift with a negative shift distance results in a left shift, and viceversa. 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 nonnegative result, between 0
and (modulus  1)
, inclusive.
Bit operations operate on a single bit of the two'scomplement representation of their operand. If necessary, the operand is sign extended so that it contains the designated bit. None of the singlebit 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, pseudocode is used throughout the descriptions of BigInteger methods. The pseudocode expression (i + j)
is shorthand for "a BigInteger whose value is that of the BigInteger i
plus that of the BigInteger j
." The pseudocode expression (i == j)
is shorthand for "true
if and only if the BigInteger i
represents the same value as the BigInteger j
." Other pseudocode 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 2^{Integer.MAX_VALUE} (exclusive) to +2^{Integer.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 2^{500000000}.
 Implementation Note:
 In the reference implementation, BigInteger constructors and operations throw
ArithmeticException
when the result is out of the supported range of 2^{Integer.MAX_VALUE} (exclusive) to +2^{Integer.MAX_VALUE} (exclusive).  Since:
 1.1
 See Also:

BigDecimal
, Serialized Form
Field Summary
Modifier and Type  Field  Description 

static BigInteger  ONE  The BigInteger constant one. 
static BigInteger  TEN  The BigInteger constant ten. 
static BigInteger  TWO  The BigInteger constant two. 
static BigInteger  ZERO  The BigInteger constant zero. 
Constructor Summary
Constructor  Description 

BigInteger(byte[] val)  Translates a byte array containing the two'scomplement binary representation of a BigInteger into a BigInteger. 
BigInteger(byte[] val,
int off,
int len)  Translates a byte subarray containing the two'scomplement binary representation of a BigInteger into a BigInteger. 
BigInteger(int signum,
byte[] magnitude)  Translates the signmagnitude representation of a BigInteger into a BigInteger. 
BigInteger(int signum,
byte[] magnitude,
int off,
int len)  Translates the signmagnitude representation of a BigInteger into a BigInteger. 
BigInteger(int bitLength,
int certainty,
Random rnd)  Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength. 
BigInteger(int numBits,
Random rnd)  Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2^{numBits}  1), inclusive. 
BigInteger(String val)  Translates the decimal String 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. 
Method Summary
Modifier and Type  Method  Description 

BigInteger  abs()  Returns a BigInteger whose value is the absolute value of this BigInteger. 
BigInteger  add(BigInteger val)  Returns a BigInteger whose value is 
BigInteger  and(BigInteger val)  Returns a BigInteger whose value is 
BigInteger  andNot(BigInteger val)  Returns a BigInteger whose value is 
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'scomplement representation of this BigInteger, excluding a sign bit. 
byte  byteValueExact()  Converts this 
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 
BigInteger[]  divideAndRemainder(BigInteger val)  Returns an array of two BigIntegers containing 
double  doubleValue()  Converts this BigInteger to a 
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 
BigInteger  gcd(BigInteger val)  Returns a BigInteger whose value is the greatest common divisor of 
int  getLowestSetBit()  Returns the index of the rightmost (lowestorder) 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  intValueExact()  Converts this 
boolean  isProbablePrime(int certainty)  Returns 
long  longValue()  Converts this BigInteger to a 
long  longValueExact()  Converts this 
BigInteger  max(BigInteger val)  Returns the maximum of this BigInteger and 
BigInteger  min(BigInteger val)  Returns the minimum of this BigInteger and 
BigInteger  mod(BigInteger m)  Returns a BigInteger whose value is 
BigInteger  modInverse(BigInteger m)  Returns a BigInteger whose value is 
BigInteger  modPow(BigInteger exponent,
BigInteger m)  Returns a BigInteger whose value is 
BigInteger  multiply(BigInteger val)  Returns a BigInteger whose value is 
BigInteger  negate()  Returns a BigInteger whose value is 
BigInteger  nextProbablePrime()  Returns the first integer greater than this 
BigInteger  not()  Returns a BigInteger whose value is 
BigInteger  or(BigInteger val)  Returns a BigInteger whose value is 
BigInteger  pow(int exponent)  Returns a BigInteger whose value is 
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 
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 
BigInteger  shiftRight(int n)  Returns a BigInteger whose value is 
short  shortValueExact()  Converts this 
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 
BigInteger  subtract(BigInteger val)  Returns a BigInteger whose value is 
boolean  testBit(int n)  Returns 
byte[]  toByteArray()  Returns a byte array containing the two'scomplement 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 
BigInteger  xor(BigInteger val)  Returns a BigInteger whose value is 
Methods declared in class java.lang.Number
byteValue, shortValue
Methods declared in class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Field Detail
ZERO
public static final BigInteger ZERO
The BigInteger constant zero.
 Since:
 1.2
ONE
public static final BigInteger ONE
The BigInteger constant one.
 Since:
 1.2
TWO
public static final BigInteger TWO
The BigInteger constant two.
 Since:
 9
TEN
public static final BigInteger TEN
The BigInteger constant ten.
 Since:
 1.5
Constructor Detail
BigInteger
public BigInteger(byte[] val, int off, int len)
Translates a byte subarray containing the two'scomplement binary representation of a BigInteger into a BigInteger. The subarray is specified via an offset into the array and a length. The subarray is assumed to be in bigendian byteorder: 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 nonzero and either off
is negative, len
is negative, or off+len
is greater than the length of val
.
 Parameters:

val
 byte array containing a subarray which is the bigendian two'scomplement binary representation of a BigInteger. 
off
 the start offset of the binary representation. 
len
 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.  Since:
 9
BigInteger
public BigInteger(byte[] val)
Translates a byte array containing the two'scomplement binary representation of a BigInteger into a BigInteger. The input array is assumed to be in bigendian byteorder: 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
 bigendian two'scomplement binary representation of a BigInteger.  Throws:

NumberFormatException
val
is zero bytes long.
BigInteger
public BigInteger(int signum, byte[] magnitude, int off, int len)
Translates the signmagnitude 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 subarray of a byte array in bigendian byteorder: 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 nonzero and either off
is negative, len
is negative, or off+len
is greater than the length of magnitude
.
 Parameters:

signum
 signum of the number (1 for negative, 0 for zero, 1 for positive). 
magnitude
 bigendian binary representation of the magnitude of the number. 
off
 the start offset of the binary representation. 
len
 the number of bytes to use.  Throws:

NumberFormatException
signum
is not one of the three legal values (1, 0, and 1), orsignum
is 0 andmagnitude
contains one or more nonzero 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.  Since:
 9
BigInteger
public BigInteger(int signum, byte[] magnitude)
Translates the signmagnitude 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 bigendian byteorder: the most significant byte is the zeroth element. A zerolength 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
 signum of the number (1 for negative, 0 for zero, 1 for positive). 
magnitude
 bigendian binary representation of the magnitude of the number.  Throws:

NumberFormatException
signum
is not one of the three legal values (1, 0, and 1), orsignum
is 0 andmagnitude
contains one or more nonzero bytes.
BigInteger
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 charactertodigit mapping is provided by
Character.digit
. The String may not contain any extraneous characters (whitespace, for example).
 Parameters:

val
 String representation of BigInteger. 
radix
 radix to be used in interpretingval
.  Throws:

NumberFormatException
val
is not a valid representation of a BigInteger in the specified radix, orradix
is outside the range fromCharacter.MIN_RADIX
toCharacter.MAX_RADIX
, inclusive.  See Also:
Character.digit(char, int)
BigInteger
public BigInteger(String val)
Translates the decimal String representation of a BigInteger into a BigInteger. The String representation consists of an optional minus sign followed by a sequence of one or more decimal digits. The charactertodigit mapping is provided by Character.digit
. The String may not contain any extraneous characters (whitespace, for example).
 Parameters:

val
 decimal String representation of BigInteger.  Throws:

NumberFormatException
val
is not a valid representation of a BigInteger.  See Also:
Character.digit(char, int)
BigInteger
public BigInteger(int numBits, Random rnd)
Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2^{numBits}  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 nonnegative BigInteger.
 Parameters:

numBits
 maximum bitLength of the new BigInteger. 
rnd
 source of randomness to be used in computing the new BigInteger.  Throws:

IllegalArgumentException
numBits
is negative.  See Also:
bitLength()
BigInteger
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
 bitLength of the returned BigInteger. 
certainty
 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  1/2^{certainty}). The execution time of this constructor is proportional to the value of this parameter. 
rnd
 source of random bits used to select candidates to be tested for primality.  Throws:

ArithmeticException
bitLength < 2
orbitLength
is too large.  See Also:
bitLength()
Method Detail
probablePrime
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
 bitLength of the returned BigInteger. 
rnd
 source of random bits used to select candidates to be tested for primality.  Returns:
 a BigInteger of
bitLength
bits that is probably prime  Throws:

ArithmeticException
bitLength < 2
orbitLength
is too large.  Since:
 1.4
 See Also:
bitLength()
nextProbablePrime
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:
 the first integer greater than this
BigInteger
that is probably prime.  Throws:

ArithmeticException
this < 0
orthis
is too large.  Since:
 1.5
valueOf
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
 value of the BigInteger to return.  Returns:
 a BigInteger with the specified value.
add
public BigInteger add(BigInteger val)
Returns a BigInteger whose value is (this + val)
.
 Parameters:

val
 value to be added to this BigInteger.  Returns:
this + val
subtract
public BigInteger subtract(BigInteger val)
Returns a BigInteger whose value is (this  val)
.
 Parameters:

val
 value to be subtracted from this BigInteger.  Returns:
this  val
multiply
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
 value to be multiplied by this BigInteger.  Returns:
this * val
divide
public BigInteger divide(BigInteger val)
Returns a BigInteger whose value is (this / val)
.
 Parameters:

val
 value by which this BigInteger is to be divided.  Returns:
this / val
 Throws:

ArithmeticException
 ifval
is zero.
divideAndRemainder
public BigInteger[] divideAndRemainder(BigInteger val)
Returns an array of two BigIntegers containing (this / val)
followed by (this % val)
.
 Parameters:

val
 value by which this BigInteger is to be divided, and the remainder computed.  Returns:
 an array of two BigIntegers: the quotient
(this / val)
is the initial element, and the remainder(this % val)
is the final element.  Throws:

ArithmeticException
 ifval
is zero.
remainder
public BigInteger remainder(BigInteger val)
Returns a BigInteger whose value is (this % val)
.
 Parameters:

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

ArithmeticException
 ifval
is zero.
pow
public BigInteger pow(int exponent)
Returns a BigInteger whose value is (this^{exponent})
. Note that exponent
is an integer rather than a BigInteger.
 Parameters:

exponent
 exponent to which this BigInteger is to be raised.  Returns:
this^{exponent}
 Throws:

ArithmeticException
exponent
is negative. (This would cause the operation to yield a noninteger value.)
sqrt
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:
 the integer square root of
this
 Throws:

ArithmeticException
 ifthis
is negative. (The square root of a negative integerval
is(i * sqrt(val))
where i is the imaginary unit and is equal tosqrt(1)
.)  Since:
 9
sqrtAndRemainder
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:
 an array of two BigIntegers with the integer square root at offset 0 and the remainder at offset 1
 Throws:

ArithmeticException
 ifthis
is negative. (The square root of a negative integerval
is(i * sqrt(val))
where i is the imaginary unit and is equal tosqrt(1)
.)  Since:
 9
 See Also:
sqrt()
gcd
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
 value with which the GCD is to be computed.  Returns:
GCD(abs(this), abs(val))
abs
public BigInteger abs()
Returns a BigInteger whose value is the absolute value of this BigInteger.
 Returns:
abs(this)
negate
public BigInteger negate()
Returns a BigInteger whose value is (this)
.
 Returns:
this
signum
public int signum()
Returns the signum function of this BigInteger.
 Returns:
 1, 0 or 1 as the value of this BigInteger is negative, zero or positive.
mod
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 nonnegative BigInteger.
 Parameters:

m
 the modulus.  Returns:
this mod m
 Throws:

ArithmeticException
m
≤ 0  See Also:
remainder(java.math.BigInteger)
modPow
public BigInteger modPow(BigInteger exponent, BigInteger m)
Returns a BigInteger whose value is (this^{exponent} mod m)
. (Unlike pow
, this method permits negative exponents.)
 Parameters:

exponent
 the exponent. 
m
 the modulus.  Returns:
this^{exponent} mod m
 Throws:

ArithmeticException
m
≤ 0 or the exponent is negative and this BigInteger is not relatively prime tom
.  See Also:
modInverse(java.math.BigInteger)
modInverse
public BigInteger modInverse(BigInteger m)
Returns a BigInteger whose value is (this
^{1} mod m)
.
 Parameters:

m
 the modulus.  Returns:

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).
shiftLeft
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 * 2^{n})
.)
 Parameters:

n
 shift distance, in bits.  Returns:
this << n
 See Also:
shiftRight(int)
shiftRight
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 / 2^{n})
.)
 Parameters:

n
 shift distance, in bits.  Returns:
this >> n
 See Also:
shiftLeft(int)
and
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
 value to be AND'ed with this BigInteger.  Returns:
this & val
or
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
 value to be OR'ed with this BigInteger.  Returns:
this  val
xor
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
 value to be XOR'ed with this BigInteger.  Returns:
this ^ val
not
public BigInteger not()
Returns a BigInteger whose value is (~this)
. (This method returns a negative value if and only if this BigInteger is nonnegative.)
 Returns:
~this
andNot
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
 value to be complemented and AND'ed with this BigInteger.  Returns:
this & ~val
testBit
public boolean testBit(int n)
Returns true
if and only if the designated bit is set. (Computes ((this & (1<<n)) != 0)
.)
 Parameters:

n
 index of bit to test.  Returns:

true
if and only if the designated bit is set.  Throws:

ArithmeticException
n
is negative.
setBit
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
 index of bit to set.  Returns:
this  (1<<n)
 Throws:

ArithmeticException
n
is negative.
clearBit
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
 index of bit to clear.  Returns:
this & ~(1<<n)
 Throws:

ArithmeticException
n
is negative.
flipBit
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
 index of bit to flip.  Returns:
this ^ (1<<n)
 Throws:

ArithmeticException
n
is negative.
getLowestSetBit
public int getLowestSetBit()
Returns the index of the rightmost (lowestorder) 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:
 index of the rightmost one bit in this BigInteger.
bitLength
public int bitLength()
Returns the number of bits in the minimal two'scomplement 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:
 number of bits in the minimal two'scomplement representation of this BigInteger, excluding a sign bit.
bitCount
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 bitvector style sets atop BigIntegers.
 Returns:
 number of bits in the two's complement representation of this BigInteger that differ from its sign bit.
isProbablePrime
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
 a measure of the uncertainty that the caller is willing to tolerate: if the call returnstrue
the probability that this BigInteger is prime exceeds (1  1/2^{certainty}). The execution time of this method is proportional to the value of this parameter.  Returns:

true
if this BigInteger is probably prime,false
if it's definitely composite.
compareTo
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.
 Specified by:

compareTo
in interfaceComparable<BigInteger>
 Parameters:

val
 BigInteger to which this BigInteger is to be compared.  Returns:
 1, 0 or 1 as this BigInteger is numerically less than, equal to, or greater than
val
.
equals
public boolean equals(Object x)
Compares this BigInteger with the specified Object for equality.
 Overrides:

equals
in classObject
 Parameters:

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

true
if and only if the specified Object is a BigInteger whose value is numerically equal to this BigInteger.  See Also:

Object.hashCode()
,HashMap
min
public BigInteger min(BigInteger val)
Returns the minimum of this BigInteger and val
.
 Parameters:

val
 value with which the minimum is to be computed.  Returns:
 the BigInteger whose value is the lesser of this BigInteger and
val
. If they are equal, either may be returned.
max
public BigInteger max(BigInteger val)
Returns the maximum of this BigInteger and val
.
 Parameters:

val
 value with which the maximum is to be computed.  Returns:
 the BigInteger whose value is the greater of this and
val
. If they are equal, either may be returned.
hashCode
public int hashCode()
Returns the hash code for this BigInteger.
 Overrides:

hashCode
in classObject
 Returns:
 hash code for this BigInteger.
 See Also:

Object.equals(java.lang.Object)
,System.identityHashCode(java.lang.Object)
toString
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 digittocharacter 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
 radix of the String representation.  Returns:
 String representation of this BigInteger in the given radix.
 See Also:

Integer.toString(int, int)
,Character.forDigit(int, int)
,BigInteger(java.lang.String, int)
toString
public String toString()
Returns the decimal String representation of this BigInteger. The digittocharacter 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.)
 Overrides:

toString
in classObject
 Returns:
 decimal String representation of this BigInteger.
 See Also:

Character.forDigit(int, int)
,BigInteger(java.lang.String)
toByteArray
public byte[] toByteArray()
Returns a byte array containing the two'scomplement representation of this BigInteger. The byte array will be in bigendian byteorder: 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:
 a byte array containing the two'scomplement representation of this BigInteger.
 See Also:
BigInteger(byte[])
intValue
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 loworder 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.
 Specified by:

intValue
in classNumber
 Returns:
 this BigInteger converted to an
int
.  See Also:
intValueExact()
longValue
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 loworder 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.
 Specified by:

longValue
in classNumber
 Returns:
 this BigInteger converted to a
long
.  See Also:
longValueExact()
floatValue
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.
 Specified by:

floatValue
in classNumber
 Returns:
 this BigInteger converted to a
float
.
doubleValue
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.
 Specified by:

doubleValue
in classNumber
 Returns:
 this BigInteger converted to a
double
.
longValueExact
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:
 this
BigInteger
converted to along
.  Throws:

ArithmeticException
 if the value ofthis
will not exactly fit in along
.  Since:
 1.8
 See Also:
longValue()
intValueExact
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:
 this
BigInteger
converted to anint
.  Throws:

ArithmeticException
 if the value ofthis
will not exactly fit in anint
.  Since:
 1.8
 See Also:
intValue()
shortValueExact
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:
 this
BigInteger
converted to ashort
.  Throws:

ArithmeticException
 if the value ofthis
will not exactly fit in ashort
.  Since:
 1.8
 See Also:
Number.shortValue()
byteValueExact
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:
 this
BigInteger
converted to abyte
.  Throws:

ArithmeticException
 if the value ofthis
will not exactly fit in abyte
.  Since:
 1.8
 See Also:
Number.byteValue()