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 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.
- 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). - 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'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 (2 |
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's-complement 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 (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 | 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'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 |
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 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 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. The val
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 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
- 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. 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
- 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
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 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 character-to-digit 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 (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
- 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 - 1/2certainty
). 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:
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 (thisexponent)
. Note that exponent
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
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 non-negative 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 (thisexponent mod m)
. (Unlike pow
, 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(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
-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
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
- 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 / 2n)
.)
- 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 non-negative.)
- 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 (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 returns 0
. (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)
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 - 1/2certainty
). 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.
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 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
- 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 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.)
- 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'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:
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 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 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 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 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()