- All Implemented Interfaces:
Serializable
,Comparable<BigInteger>
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.
- API Note:
- As
BigInteger
values are arbitrary precision integers, the algorithmic complexity of the methods of this class varies and may be superlinear in the size of the input. For example, a method likeintValue()
would be expected to run in O(1), that is constant time, since with the current internal representation only a fixed-size component of theBigInteger
needs to be accessed to perform the conversion toint
. In contrast, a method likenot()
would be expected to run in O(n) time where n is the size of theBigInteger
in bits, that is, to run in time proportional to the size of the input. For multiplying twoBigInteger
values of size n, a naive multiplication algorithm would run in time O(n2) and theoretical results indicate a multiplication algorithm for numbers using this category of representation must run in at least O(n log n). Common multiplication algorithms between the bounds of the naive and theoretical cases include the Karatsuba multiplication (O(n1.585)) and 3-way Toom-Cook multiplication (O(n1.465)).A particular implementation of
multiply
is free to switch between different algorithms for different inputs, such as to improve actual running time to produce the product by using simpler algorithms for smaller inputs even if the simpler algorithm has a larger asymptotic complexity.Operations may also allocate and compute on intermediate results, potentially those allocations may be as large as in proportion to the running time of the algorithm.
Users of
BigInteger
concerned with bounding the running time or space of operations can screen outBigInteger
values above a chosen magnitude. - Implementation Note:
- In the reference implementation, BigInteger constructors and
operations throw
ArithmeticException
when the result is out of the supported range of -2Integer.MAX_VALUE
(exclusive) to +2Integer.MAX_VALUE
(exclusive). - See Java Language Specification:
-
4.2.2 Integer Operations
- Since:
- 1.1
- See Also:
-
Field Summary
FieldsModifier and TypeFieldDescriptionstatic final BigInteger
The BigInteger constant one.static final BigInteger
The BigInteger constant ten.static final BigInteger
The BigInteger constant two.static final BigInteger
The BigInteger constant zero. -
Constructor Summary
ConstructorsConstructorDescriptionBigInteger
(byte[] val) Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger.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
(int signum, byte[] magnitude) Translates the sign-magnitude 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 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 (2numBits
- 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 TypeMethodDescriptionabs()
Returns a BigInteger whose value is the absolute value of this BigInteger.add
(BigInteger val) Returns a BigInteger whose value is(this + val)
.and
(BigInteger val) Returns a BigInteger whose value is(this & val)
.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
Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.byte
Converts thisBigInteger
to abyte
, checking for lost information.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.divide
(BigInteger val) Returns a BigInteger whose value is(this / val)
.Returns an array of two BigIntegers containing(this / val)
followed by(this % val)
.double
Converts this BigInteger to adouble
.boolean
Compares this BigInteger with the specified Object for equality.flipBit
(int n) Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped.float
Converts this BigInteger to afloat
.gcd
(BigInteger val) Returns a BigInteger whose value is the greatest common divisor ofabs(this)
andabs(val)
.int
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 anint
.int
Converts thisBigInteger
to anint
, checking for lost information.boolean
isProbablePrime
(int certainty) Returnstrue
if this BigInteger is probably prime,false
if it's definitely composite.long
Converts this BigInteger to along
.long
Converts thisBigInteger
to along
, checking for lost information.max
(BigInteger val) Returns the maximum of this BigInteger andval
.min
(BigInteger val) Returns the minimum of this BigInteger andval
.mod
(BigInteger m) Returns a BigInteger whose value is(this mod m
).Returns a BigInteger whose value is(this
-1mod m)
.modPow
(BigInteger exponent, BigInteger m) Returns a BigInteger whose value is(thisexponent mod m)
.multiply
(BigInteger val) Returns a BigInteger whose value is(this * val)
.negate()
Returns a BigInteger whose value is(-this)
.Returns the first integer greater than thisBigInteger
that is probably prime.not()
Returns a BigInteger whose value is(~this)
.or
(BigInteger val) Returns a BigInteger whose value is(this | val)
.Returns a BigInteger whose value is(this * val)
.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.remainder
(BigInteger val) Returns a BigInteger whose value is(this % val)
.setBit
(int n) Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set.shiftLeft
(int n) Returns a BigInteger whose value is(this << n)
.shiftRight
(int n) Returns a BigInteger whose value is(this >> n)
.short
Converts thisBigInteger
to ashort
, checking for lost information.int
signum()
Returns the signum function of this BigInteger.sqrt()
Returns the integer square root of this BigInteger.Returns an array of two BigIntegers containing the integer square roots
ofthis
and its remainderthis - s*s
, respectively.subtract
(BigInteger val) Returns a BigInteger whose value is(this - val)
.boolean
testBit
(int n) Returnstrue
if and only if the designated bit is set.byte[]
Returns a byte array containing the two's-complement representation of this BigInteger.toString()
Returns the decimal String representation of this BigInteger.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 specifiedlong
.xor
(BigInteger val) Returns a BigInteger whose value is(this ^ val)
.Methods declared in class java.lang.Number
byteValue, shortValue
-
Field Details
-
ZERO
-
ONE
-
TWO
-
TEN
-
-
Constructor Details
-
BigInteger
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 indexoff
. Theval
array is assumed to be unchanged for the duration of the constructor call. AnIndexOutOfBoundsException
is thrown if the length of the arrayval
is non-zero and eitheroff
is negative,len
is negative, oroff+len
is greater than the length ofval
.- Parameters:
val
- byte array containing a sub-array which is the big-endian two's-complement 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'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. Theval
array is assumed to be unchanged for the duration of the constructor call.- Parameters:
val
- big-endian two's-complement 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 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 indexoff
. A zero value of the lengthlen
is permissible, and will result in a BigInteger value of 0, whether signum is -1, 0 or 1. Themagnitude
array is assumed to be unchanged for the duration of the constructor call. AnIndexOutOfBoundsException
is thrown if the length of the arraymagnitude
is non-zero and eitheroff
is negative,len
is negative, oroff+len
is greater than the length ofmagnitude
.- Parameters:
signum
- signum of the number (-1 for negative, 0 for zero, 1 for positive).magnitude
- big-endian 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 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.- Since:
- 9
-
BigInteger
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. Themagnitude
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
- 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), orsignum
is 0 andmagnitude
contains one or more non-zero bytes.
-
BigInteger
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 byCharacter.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.
-
BigInteger
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 byCharacter.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.
-
BigInteger
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 inrnd
. Note that this constructor always constructs a non-negative 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:
-
BigInteger
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 - 1/2certainty
). 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:
-
-
Method Details
-
probablePrime
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:
-
nextProbablePrime
Returns the first integer greater than thisBigInteger
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 returnsp
, there is no primeq
such thatthis < q < p
.- Implementation Note:
- Due to the nature of the underlying algorithm,
and depending on the size of
this
, this method could consume a large amount of memory, up to exhaustion of available heap space, or could run for a long time. - Returns:
- the first integer greater than this
BigInteger
that is probably prime. - Throws:
ArithmeticException
-this < 0
orthis
is too large.- Since:
- 1.5
-
valueOf
Returns a BigInteger whose value is equal to that of the specifiedlong
.- 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
Returns a BigInteger whose value is(this + val)
.- Parameters:
val
- value to be added to this BigInteger.- Returns:
this + val
-
subtract
Returns a BigInteger whose value is(this - val)
.- Parameters:
val
- value to be subtracted from this BigInteger.- Returns:
this - val
-
multiply
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
-
parallelMultiply
Returns a BigInteger whose value is(this * val)
. When boththis
andval
are large, typically in the thousands of bits, parallel multiply might be used. This method returns the exact same mathematical result asmultiply(java.math.BigInteger)
.- Implementation Note:
- This implementation may offer better algorithmic
performance when
val == this
., Compared tomultiply(java.math.BigInteger)
, an implementation's parallel multiplication algorithm would typically use more CPU resources to compute the result faster, and may do so with a slight increase in memory consumption. - Parameters:
val
- value to be multiplied by this BigInteger.- Returns:
this * val
- Since:
- 19
- See Also:
-
divide
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
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
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
Returns a BigInteger whose value is(thisexponent)
. Note thatexponent
is an integer rather than a BigInteger.- Parameters:
exponent
- exponent to which this BigInteger is to be raised.- Returns:
thisexponent
- Throws:
ArithmeticException
-exponent
is negative. (This would cause the operation to yield a non-integer value.)
-
sqrt
Returns the integer square root of this BigInteger. The integer square root of the corresponding mathematical integern
is the largest mathematical integers
such thats*s <= n
. It is equal to the value offloor(sqrt(n))
, wheresqrt(n)
denotes the real square root ofn
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
Returns an array of two BigIntegers containing the integer square roots
ofthis
and its remainderthis - 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:
-
gcd
Returns a BigInteger whose value is the greatest common divisor ofabs(this)
andabs(val)
. Returns 0 ifthis == 0 && val == 0
.- Parameters:
val
- value with which the GCD is to be computed.- Returns:
GCD(abs(this), abs(val))
-
abs
Returns a BigInteger whose value is the absolute value of this BigInteger.- Returns:
abs(this)
-
negate
-
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
Returns a BigInteger whose value is(this mod m
). This method differs fromremainder
in that it always returns a non-negative BigInteger.- Parameters:
m
- the modulus.- Returns:
this mod m
- Throws:
ArithmeticException
-m
≤ 0- See Also:
-
modPow
Returns a BigInteger whose value is(thisexponent mod m)
. (Unlikepow
, this method permits negative exponents.)- Parameters:
exponent
- the exponent.m
- the modulus.- Returns:
thisexponent mod m
- Throws:
ArithmeticException
-m
≤ 0 or the exponent is negative and this BigInteger is not relatively prime tom
.- See Also:
-
modInverse
Returns a BigInteger whose value is(this
-1mod m)
.- Parameters:
m
- the modulus.- Returns:
this
-1mod 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
Returns a BigInteger whose value is(this << n)
. The shift distance,n
, may be negative, in which case this method performs a right shift. (Computesfloor(this * 2n)
.)- Parameters:
n
- shift distance, in bits.- Returns:
this << n
- See Also:
-
shiftRight
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. (Computesfloor(this / 2n)
.)- Parameters:
n
- shift distance, in bits.- Returns:
this >> n
- See Also:
-
and
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
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
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
Returns a BigInteger whose value is(~this)
. (This method returns a negative value if and only if this BigInteger is non-negative.)- Returns:
~this
-
andNot
Returns a BigInteger whose value is(this & ~val)
. This method, which is equivalent toand(val.not())
, is provided as a convenience for masking operations. (This method returns a negative BigInteger if and only ifthis
is negative andval
is positive.)- Parameters:
val
- value to be complemented and AND'ed with this BigInteger.- Returns:
this & ~val
-
testBit
public boolean testBit(int n) Returnstrue
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
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
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
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 (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:
- index of the rightmost one bit in this BigInteger.
-
bitLength
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 returns0
. (Computes(ceil(log2(this < 0 ? -this : this+1)))
.)- Returns:
- number of bits in the minimal two's-complement 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 bit-vector 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) Returnstrue
if this BigInteger is probably prime,false
if it's definitely composite. Ifcertainty
is ≤ 0,true
is returned.- Implementation Note:
- Due to the nature of the underlying primality test algorithm,
and depending on the size of
this
andcertainty
, this method could consume a large amount of memory, up to exhaustion of available heap space, or could run for a long time. - 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 - 1/2certainty
). 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.- Throws:
ArithmeticException
-this
is too large.
-
compareTo
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
Compares this BigInteger with the specified Object for equality. -
min
Returns the minimum of this BigInteger andval
.- 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
Returns the maximum of this BigInteger andval
.- 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
-
toString
Returns the String representation of this BigInteger in the given radix. If the radix is outside the range fromCharacter.MIN_RADIX
toCharacter.MAX_RADIX
inclusive, it will default to 10 (as is the case forInteger.toString
). The digit-to-character mapping provided byCharacter.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:
-
toString
Returns the decimal String representation of this BigInteger. The digit-to-character mapping provided byCharacter.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.) -
toByteArray
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:
- a byte array containing the two's-complement representation of this BigInteger.
- See Also:
-
intValue
public int intValue()Converts this BigInteger to anint
. This conversion is analogous to a narrowing primitive conversion fromlong
toint
as defined in The Java Language Specification: if this BigInteger is too big to fit in anint
, 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.- Specified by:
intValue
in classNumber
- Returns:
- this BigInteger converted to an
int
. - See Java Language Specification:
-
5.1.3 Narrowing Primitive Conversion
- See Also:
-
longValue
public long longValue()Converts this BigInteger to along
. This conversion is analogous to a narrowing primitive conversion fromlong
toint
as defined in The Java Language Specification: if this BigInteger is too big to fit in along
, 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.- Specified by:
longValue
in classNumber
- Returns:
- this BigInteger converted to a
long
. - See Java Language Specification:
-
5.1.3 Narrowing Primitive Conversion
- See Also:
-
floatValue
public float floatValue()Converts this BigInteger to afloat
. This conversion is similar to the narrowing primitive conversion fromdouble
tofloat
as defined in The Java Language Specification: if this BigInteger has too great a magnitude to represent as afloat
, it will be converted toFloat.NEGATIVE_INFINITY
orFloat.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
. - See Java Language Specification:
-
5.1.3 Narrowing Primitive Conversion
-
doubleValue
public double doubleValue()Converts this BigInteger to adouble
. This conversion is similar to the narrowing primitive conversion fromdouble
tofloat
as defined in The Java Language Specification: if this BigInteger has too great a magnitude to represent as adouble
, it will be converted toDouble.NEGATIVE_INFINITY
orDouble.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
. - See Java Language Specification:
-
5.1.3 Narrowing Primitive Conversion
-
longValueExact
public long longValueExact()Converts thisBigInteger
to along
, checking for lost information. If the value of thisBigInteger
is out of the range of thelong
type, then anArithmeticException
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:
-
intValueExact
public int intValueExact()Converts thisBigInteger
to anint
, checking for lost information. If the value of thisBigInteger
is out of the range of theint
type, then anArithmeticException
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:
-
shortValueExact
public short shortValueExact()Converts thisBigInteger
to ashort
, checking for lost information. If the value of thisBigInteger
is out of the range of theshort
type, then anArithmeticException
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:
-
byteValueExact
public byte byteValueExact()Converts thisBigInteger
to abyte
, checking for lost information. If the value of thisBigInteger
is out of the range of thebyte
type, then anArithmeticException
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:
-