java.lang.Object | ||
↳ | java.lang.Number | |
↳ | java.math.BigInteger |
An immutable arbitrary-precision signed integer.
BitSet
for high-performance bitwise operations on
arbitrarily-large sequences of bits.
Fields | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
ONE | The BigInteger constant 1. |
||||||||||
TEN | The BigInteger constant 10. |
||||||||||
ZERO | The BigInteger constant 0. |
Public Constructors | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Constructs a random non-negative
BigInteger instance in the range
[0, pow(2, numBits)-1] . | |||||||||||
Constructs a random
BigInteger instance in the range [0,
pow(2, bitLength)-1] which is probably prime. | |||||||||||
Constructs a new
BigInteger by parsing value . | |||||||||||
Constructs a new
BigInteger instance by parsing value . | |||||||||||
Constructs a new
BigInteger instance with the given sign and
magnitude. | |||||||||||
Constructs a new
BigInteger from the given two's complement
representation. |
Public Methods | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Returns a
BigInteger whose value is the absolute value of this . | |||||||||||
Returns a
BigInteger whose value is this + value . | |||||||||||
Returns a
BigInteger whose value is this & value . | |||||||||||
Returns a
BigInteger whose value is this & ~value . | |||||||||||
Returns the number of bits in the two's complement representation of
this which differ from the sign bit. | |||||||||||
Returns the length of the value's two's complement representation without
leading zeros for positive numbers / without leading ones for negative
values.
| |||||||||||
Returns a
BigInteger which has the same binary representation
as this but with the bit at position n cleared. | |||||||||||
Compares this
BigInteger with value . | |||||||||||
Returns a
BigInteger whose value is this / divisor . | |||||||||||
Returns a two element
BigInteger array containing
this / divisor at index 0 and this % divisor at index 1. | |||||||||||
Returns this
BigInteger as a double. | |||||||||||
Compares this instance with the specified object and indicates if they
are equal.
| |||||||||||
Returns a
BigInteger which has the same binary representation
as this but with the bit at position n flipped. | |||||||||||
Returns this
BigInteger as a float. | |||||||||||
Returns a
BigInteger whose value is greatest common divisor
of this and value . | |||||||||||
Returns the position of the lowest set bit in the two's complement
representation of this
BigInteger . | |||||||||||
Returns an integer hash code for this object.
| |||||||||||
Returns this
BigInteger as an int value. | |||||||||||
Tests whether this
BigInteger is probably prime. | |||||||||||
Returns this
BigInteger as a long value. | |||||||||||
Returns the maximum of this
BigInteger and value . | |||||||||||
Returns the minimum of this
BigInteger and value . | |||||||||||
Returns a
BigInteger whose value is this mod m . | |||||||||||
Returns a
BigInteger whose value is 1/this mod m . | |||||||||||
Returns a
BigInteger whose value is pow(this, exponent) mod modulus . | |||||||||||
Returns a
BigInteger whose value is this * value . | |||||||||||
Returns a
BigInteger whose value is the -this . | |||||||||||
Returns the smallest integer x >
this which is probably prime as
a BigInteger instance. | |||||||||||
Returns a
BigInteger whose value is ~this . | |||||||||||
Returns a
BigInteger whose value is this | value . | |||||||||||
Returns a
BigInteger whose value is pow(this, exp) . | |||||||||||
Returns a random positive
BigInteger instance in the range [0, pow(2, bitLength)-1] which is probably prime. | |||||||||||
Returns a
BigInteger whose value is this % divisor . | |||||||||||
Returns a
BigInteger which has the same binary representation
as this but with the bit at position n set. | |||||||||||
Returns a
BigInteger whose value is this << n . | |||||||||||
Returns a
BigInteger whose value is this >> n . | |||||||||||
Returns the sign of this
BigInteger . | |||||||||||
Returns a
BigInteger whose value is this - value . | |||||||||||
Tests whether the bit at position n in
this is set. | |||||||||||
Returns the two's complement representation of this
BigInteger in
a byte array. | |||||||||||
Returns a string representation of this
BigInteger in decimal
form. | |||||||||||
Returns a string containing a string representation of this
BigInteger with base radix. | |||||||||||
Returns a
BigInteger whose value is equal to value . | |||||||||||
Returns a
BigInteger whose value is this ^ value . |
[Expand]
Inherited Methods | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
From class
java.lang.Number
| |||||||||||
From class
java.lang.Object
| |||||||||||
From interface
java.lang.Comparable
|
Constructs a random non-negative BigInteger
instance in the range
[0, pow(2, numBits)-1]
.
numBits | maximum length of the new BigInteger in bits. |
---|---|
random | is the random number generator to be used. |
IllegalArgumentException | if numBits < 0.
|
---|
Constructs a random BigInteger
instance in the range [0,
pow(2, bitLength)-1]
which is probably prime. The probability that the
returned BigInteger
is prime is greater than
1 - 1/2certainty)
.
Note: the Random
argument is ignored if
bitLength >= 16
, where this implementation will use OpenSSL's
BN_generate_prime_ex
as a source of cryptographically strong pseudo-random numbers.
bitLength | length of the new BigInteger in bits. |
---|---|
certainty | tolerated primality uncertainty. |
ArithmeticException | if bitLength < 2 . |
---|
Constructs a new BigInteger
by parsing value
. The string
representation consists of an optional plus or minus sign followed by a
non-empty sequence of decimal digits. Digits are interpreted as if by
Character.digit(char,10)
.
value | string representation of the new BigInteger . |
---|
NullPointerException | if value == null . |
---|---|
NumberFormatException | if value is not a valid
representation of a BigInteger .
|
Constructs a new BigInteger
instance by parsing value
.
The string representation consists of an optional plus or minus sign
followed by a non-empty sequence of digits in the specified radix. Digits
are interpreted as if by Character.digit(char, radix)
.
value | string representation of the new BigInteger . |
---|---|
radix | the base to be used for the conversion. |
NullPointerException | if value == null . |
---|---|
NumberFormatException | if value is not a valid
representation of a BigInteger or if radix <
Character.MIN_RADIX or radix > Character.MAX_RADIX .
|
Constructs a new BigInteger
instance with the given sign and
magnitude.
signum | sign of the new BigInteger (-1 for negative, 0 for
zero, 1 for positive). |
---|---|
magnitude | magnitude of the new BigInteger with the most
significant byte first. |
NullPointerException | if magnitude == null . |
---|---|
NumberFormatException | if the sign is not one of -1, 0, 1 or if the sign is zero and the magnitude contains non-zero entries. |
Constructs a new BigInteger
from the given two's complement
representation. The most significant byte is the entry at index 0. The
most significant bit of this entry determines the sign of the new BigInteger
instance. The array must be nonempty.
value | two's complement representation of the new BigInteger . |
---|
NullPointerException | if value == null . |
---|---|
NumberFormatException | if the length of value is zero.
|
Returns a BigInteger
whose value is the absolute value of this
.
Returns a BigInteger
whose value is this + value
.
Returns a BigInteger
whose value is this & value
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
value | value to be and'ed with this . |
---|
NullPointerException | if value == null .
|
---|
Returns a BigInteger
whose value is this & ~value
.
Evaluating x.andNot(value)
returns the same result as x.and(value.not())
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
value | value to be not'ed and then and'ed with this . |
---|
NullPointerException | if value == null .
|
---|
Returns the number of bits in the two's complement representation of
this
which differ from the sign bit. If this
is negative,
the result is equivalent to the number of bits set in the two's
complement representation of -this - 1
.
Use bitLength(0)
to find the length of the binary value in
bits.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
Returns the length of the value's two's complement representation without leading zeros for positive numbers / without leading ones for negative values.
The two's complement representation of this
will be at least
bitLength() + 1
bits long.
The value will fit into an int
if bitLength() < 32
or
into a long
if bitLength() < 64
.
this
without the sign bit.
Returns a BigInteger
which has the same binary representation
as this
but with the bit at position n cleared. The result is
equivalent to this & ~pow(2, n)
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
n | position where the bit in this has to be cleared. |
---|
ArithmeticException | if n < 0 .
|
---|
Compares this BigInteger
with value
. Returns -1
if this < value
, 0
if this == value
and 1
if this > value
, .
value | value to be compared with this . |
---|
NullPointerException | if value == null .
|
---|
Returns a BigInteger
whose value is this / divisor
.
divisor | value by which this is divided. |
---|
this / divisor
.NullPointerException | if divisor == null . |
---|---|
ArithmeticException | if divisor == 0 .
|
Returns a two element BigInteger
array containing
this / divisor
at index 0 and this % divisor
at index 1.
divisor | value by which this is divided. |
---|
NullPointerException | if divisor == null . |
---|---|
ArithmeticException | if divisor == 0 . |
Returns this BigInteger
as a double. If this
is too big
to be represented as a double, then Double.POSITIVE_INFINITY
or
Double.NEGATIVE_INFINITY
is returned. Note that not all integers
in the range [-Double.MAX_VALUE, Double.MAX_VALUE]
can be exactly
represented as a double.
Compares this instance with the specified object and indicates if they
are equal. In order to be equal, o
must represent the same object
as this instance using a class-specific comparison. The general contract
is that this comparison should be reflexive, symmetric, and transitive.
Also, no object reference other than null is equal to null.
The default implementation returns true
only if this ==
o
. See Writing a correct
equals
method
if you intend implementing your own equals
method.
The general contract for the equals
and hashCode()
methods is that if equals
returns true
for
any two objects, then hashCode()
must return the same value for
these objects. This means that subclasses of Object
usually
override either both methods or neither of them.
x | the object to compare this instance with. |
---|
true
if the specified object is equal to this Object
; false
otherwise.Returns a BigInteger
which has the same binary representation
as this
but with the bit at position n flipped. The result is
equivalent to this ^ pow(2, n)
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
n | position where the bit in this has to be flipped. |
---|
ArithmeticException | if n < 0 .
|
---|
Returns this BigInteger
as a float. If this
is too big to
be represented as a float, then Float.POSITIVE_INFINITY
or
Float.NEGATIVE_INFINITY
is returned. Note that not all integers
in the range [-Float.MAX_VALUE, Float.MAX_VALUE]
can be exactly
represented as a float.
Returns a BigInteger
whose value is greatest common divisor
of this
and value
. If this == 0
and value == 0
then zero is returned, otherwise the result is positive.
value | value with which the greatest common divisor is computed. |
---|
NullPointerException | if value == null .
|
---|
Returns the position of the lowest set bit in the two's complement
representation of this BigInteger
. If all bits are zero (this==0)
then -1 is returned as result.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
Returns an integer hash code for this object. By contract, any two
objects for which equals(Object)
returns true
must return
the same hash code value. This means that subclasses of Object
usually override both methods or neither method.
Note that hash values must not change over time unless information used in equals comparisons also changes.
See Writing a correct
hashCode
method
if you intend implementing your own hashCode
method.
Returns this BigInteger
as an int value. If this
is too
big to be represented as an int, then this % (1 << 32)
is
returned.
Tests whether this BigInteger
is probably prime. If true
is returned, then this is prime with a probability greater than
1 - 1/2certainty)
. If false
is returned, then this
is definitely composite. If the argument certainty
<= 0, then
this method returns true.
certainty | tolerated primality uncertainty. |
---|
true
, if this
is probably prime, false
otherwise.
Returns this BigInteger
as a long value. If this
is too
big to be represented as a long, then this % pow(2, 64)
is
returned.
Returns the maximum of this BigInteger
and value
.
value | value to be used to compute the maximum with this |
---|
NullPointerException | if value == null
|
---|
Returns the minimum of this BigInteger
and value
.
value | value to be used to compute the minimum with this . |
---|
NullPointerException | if value == null .
|
---|
Returns a BigInteger
whose value is this mod m
. The
modulus m
must be positive. The result is guaranteed to be in the
interval [0, m)
(0 inclusive, m exclusive). The behavior of this
function is not equivalent to the behavior of the % operator defined for
the built-in int
's.
m | the modulus. |
---|
this mod m
.NullPointerException | if m == null . |
---|---|
ArithmeticException | if m < 0 .
|
Returns a BigInteger
whose value is 1/this mod m
. The
modulus m
must be positive. The result is guaranteed to be in the
interval [0, m)
(0 inclusive, m exclusive). If this
is
not relatively prime to m, then an exception is thrown.
m | the modulus. |
---|
NullPointerException | if m == null |
---|---|
ArithmeticException | if m < 0 or if this is not
relatively prime to m
|
Returns a BigInteger
whose value is pow(this, exponent) mod modulus
. The modulus must be positive. The
result is guaranteed to be in the interval [0, modulus)
.
If the exponent is negative, then
pow(this.modInverse(modulus), -exponent) mod modulus
is computed.
The inverse of this only exists if this
is relatively prime to the modulus,
otherwise an exception is thrown.
NullPointerException | if modulus == null or exponent == null . |
---|---|
ArithmeticException | if modulus < 0 or if exponent < 0 and
not relatively prime to modulus .
|
Returns a BigInteger
whose value is this * value
.
NullPointerException | if value == null .
|
---|
Returns the smallest integer x > this
which is probably prime as
a BigInteger
instance. The probability that the returned BigInteger
is prime is greater than 1 - 1/2100
.
this
which is probably prime.ArithmeticException | if this < 0 .
|
---|
Returns a BigInteger
whose value is ~this
. The result
of this operation is -this-1
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
Returns a BigInteger
whose value is this | value
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
value | value to be or'ed with this . |
---|
NullPointerException | if value == null .
|
---|
Returns a BigInteger
whose value is pow(this, exp)
.
ArithmeticException | if exp < 0 .
|
---|
Returns a random positive BigInteger
instance in the range [0, pow(2, bitLength)-1]
which is probably prime. The probability that
the returned BigInteger
is prime is greater than 1 - 1/2100)
.
bitLength | length of the new BigInteger in bits. |
---|
BigInteger
instance.IllegalArgumentException | if bitLength < 2 .
|
---|
Returns a BigInteger
whose value is this % divisor
.
Regarding signs this methods has the same behavior as the % operator on
ints: the sign of the remainder is the same as the sign of this.
divisor | value by which this is divided. |
---|
NullPointerException | if divisor == null . |
---|---|
ArithmeticException | if divisor == 0 .
|
Returns a BigInteger
which has the same binary representation
as this
but with the bit at position n set. The result is
equivalent to this | pow(2, n)
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
n | position where the bit in this has to be set. |
---|
ArithmeticException | if n < 0 .
|
---|
Returns a BigInteger
whose value is this << n
. The
result is equivalent to this * pow(2, n)
if n >= 0. The shift
distance may be negative which means that this
is shifted right.
The result then corresponds to floor(this / pow(2, -n))
.
Implementation Note: Usage of this method on negative values is not recommended as the current implementation is not efficient.
n | shift distance. |
---|
this << n
if n >= 0
; this >> (-n)
.
otherwise
Returns a BigInteger
whose value is this >> n
. For
negative arguments, the result is also negative. The shift distance may
be negative which means that this
is shifted left.
Implementation Note: Usage of this method on negative values is not recommended as the current implementation is not efficient.
n | shift distance |
---|
this >> n
if n >= 0
; this << (-n)
otherwise
Returns the sign of this BigInteger
.
-1
if this < 0
, 0
if this == 0
,
1
if this > 0
.
Returns a BigInteger
whose value is this - value
.
Tests whether the bit at position n in this
is set. The result is
equivalent to this & pow(2, n) != 0
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
n | position where the bit in this has to be inspected. |
---|
ArithmeticException | if n < 0 .
|
---|
Returns the two's complement representation of this BigInteger
in
a byte array.
Returns a string representation of this BigInteger
in decimal
form.
Returns a string containing a string representation of this BigInteger
with base radix. If radix < Character.MIN_RADIX
or
radix > Character.MAX_RADIX
then a decimal representation is
returned. The characters of the string representation are generated with
method Character.forDigit
.
radix | base to be used for the string representation. |
---|
Returns a BigInteger
whose value is equal to value
.
Returns a BigInteger
whose value is this ^ value
.
Implementation Note: Usage of this method is not recommended as the current implementation is not efficient.
value | value to be xor'ed with this |
---|
NullPointerException | if value == null
|
---|