public class BigInteger extends Number implements 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. All of the details in the Spec concerning overflow
are ignored, as BigIntegers are made as large as necessary to accommodate the results of an operation.
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, as this operation makes little sense in combination with the "infinite word size"
abstraction provided by this class.
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 "infinite word size" abstraction provided by this class ensures that 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 +2
Integer.MAX_VALUE
(exclusive) and may support values outside of that 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.
implNote: BigInteger constructors and operations throw ArithmeticException
when the result is out of the
supported range of -2Integer.MAX_VALUE
(exclusive) to +2 Integer.MAX_VALUE
(exclusive).
BigDecimal
,
Serialized FormModifier and Type | Field and Description |
---|---|
static BigInteger |
ONE
The BigInteger constant one.
|
static BigInteger |
TEN
The BigInteger constant ten.
|
static BigInteger |
ZERO
The BigInteger constant zero.
|
Constructor and Description |
---|
BigInteger(byte[] val)
Translates a byte array containing the two's-complement binary representation of a BigInteger into a BigInteger.
|
BigInteger(int signum,
byte[] magnitude)
Translates the sign-magnitude representation of a BigInteger into a BigInteger.
|
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.
|
Modifier and Type | Method and 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
(this + val) . |
BigInteger |
and(BigInteger val)
Returns a BigInteger whose value is
(this & val) . |
BigInteger |
andNot(BigInteger val)
Returns a BigInteger whose value is
(this & ~val) . |
int |
bitCount()
Returns the number of bits in the two's complement representation of this BigInteger that differ from its sign
bit.
|
int |
bitLength()
Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a
sign bit.
|
byte |
byteValueExact()
Converts this
BigInteger to a byte , checking for lost information. |
BigInteger |
clearBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit cleared.
|
int |
compareTo(BigInteger val)
Compares this BigInteger with the specified BigInteger.
|
BigInteger |
divide(BigInteger val)
Returns a BigInteger whose value is
(this / val) . |
BigInteger[] |
divideAndRemainder(BigInteger val)
Returns an array of two BigIntegers containing
(this / val) followed by (this % val) . |
double |
doubleValue()
Converts this BigInteger to a
double . |
boolean |
equals(Object x)
Compares this BigInteger with the specified Object for equality.
|
BigInteger |
flipBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit flipped.
|
float |
floatValue()
Converts this BigInteger to a
float . |
BigInteger |
gcd(BigInteger val)
Returns a BigInteger whose value is the greatest common divisor of
abs(this) and abs(val) . |
int |
getLowestSetBit()
Returns the index of the rightmost (lowest-order) one bit in this BigInteger (the number of zero bits to the
right of the rightmost one bit).
|
int |
hashCode()
Returns the hash code for this BigInteger.
|
int |
intValue()
Converts this BigInteger to an
int . |
int |
intValueExact()
Converts this
BigInteger to an int , checking for lost information. |
long |
longValue()
Converts this BigInteger to a
long . |
long |
longValueExact()
Converts this
BigInteger to a long , checking for lost information. |
BigInteger |
max(BigInteger val)
Returns the maximum of this BigInteger and
val . |
BigInteger |
min(BigInteger val)
Returns the minimum of this BigInteger and
val . |
BigInteger |
mod(BigInteger m)
Returns a BigInteger whose value is
(this mod m ). |
BigInteger |
modInverse(BigInteger m)
Returns a BigInteger whose value is
(this -1 mod m) . |
BigInteger |
modPow(BigInteger exponent,
BigInteger m)
Returns a BigInteger whose value is (thisexponent mod m).
|
BigInteger |
multiply(BigInteger val)
Returns a BigInteger whose value is
(this * val) . |
BigInteger |
negate()
Returns a BigInteger whose value is
(-this) . |
BigInteger |
not()
Returns a BigInteger whose value is
(~this) . |
BigInteger |
or(BigInteger val)
Returns a BigInteger whose value is
(this | val) . |
BigInteger |
pow(int exponent)
Returns a BigInteger whose value is (thisexponent).
|
BigInteger |
remainder(BigInteger val)
Returns a BigInteger whose value is
(this % val) . |
BigInteger |
setBit(int n)
Returns a BigInteger whose value is equivalent to this BigInteger with the designated bit set.
|
BigInteger |
shiftLeft(int n)
Returns a BigInteger whose value is
(this << n) . |
BigInteger |
shiftRight(int n)
Returns a BigInteger whose value is
(this >> n) . |
short |
shortValueExact()
Converts this
BigInteger to a short , checking for lost information. |
int |
signum()
Returns the signum function of this BigInteger.
|
BigInteger |
subtract(BigInteger val)
Returns a BigInteger whose value is
(this - val) . |
boolean |
testBit(int n)
Returns
true if and only if the designated bit is set. |
byte[] |
toByteArray()
Returns a byte array containing the two's-complement representation of this BigInteger.
|
String |
toString()
Returns the decimal String representation of this BigInteger.
|
String |
toString(int radix)
Returns the String representation of this BigInteger in the given radix.
|
static BigInteger |
valueOf(long val)
Returns a BigInteger whose value is equal to that of the specified
long . |
BigInteger |
xor(BigInteger val)
Returns a BigInteger whose value is
(this ^ val) . |
byteValue, shortValue
public static final BigInteger ONE
public static final BigInteger TEN
public static final BigInteger ZERO
public BigInteger(byte[] val)
val
- big-endian two's-complement binary representation of BigInteger.NumberFormatException
- val
is zero bytes long.public BigInteger(int signum, byte[] magnitude)
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.NumberFormatException
- signum
is not one of the three legal values (-1, 0, and 1), or signum
is 0 and
magnitude
contains one or more non-zero bytes.public BigInteger(int numBits, Random rnd)
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 non-negative BigInteger.numBits
- maximum bitLength of the new BigInteger.rnd
- source of randomness to be used in computing the new BigInteger.IllegalArgumentException
- numBits
is negative.bitLength()
public BigInteger(String val)
Character.digit
. The String may not contain any extraneous characters (whitespace,
for example).val
- decimal String representation of BigInteger.NumberFormatException
- val
is not a valid representation of a BigInteger.Character.digit(char, int)
public BigInteger(String val, int radix)
Character.digit
. The String may not contain any extraneous characters (whitespace, for example).val
- String representation of BigInteger.radix
- radix to be used in interpreting val
.NumberFormatException
- val
is not a valid representation of a BigInteger in the specified radix, or radix
is
outside the range from Character.MIN_RADIX
to Character.MAX_RADIX
, inclusive.Character.digit(char, int)
public BigInteger abs()
abs(this)
public BigInteger add(BigInteger val)
(this + val)
.val
- value to be added to this BigInteger.this + val
public BigInteger and(BigInteger val)
(this & val)
. (This method returns a negative BigInteger if and only
if this and val are both negative.)val
- value to be AND'ed with this BigInteger.this & val
public BigInteger andNot(BigInteger val)
(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.)val
- value to be complemented and AND'ed with this BigInteger.this & ~val
public int bitCount()
public int bitLength()
(ceil(log2(this < 0 ? -this : this+1)))
.)public byte byteValueExact()
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.BigInteger
converted to a byte
.ArithmeticException
- if the value of this
will not exactly fit in a byte
.Number.byteValue()
public BigInteger clearBit(int n)
(this & ~(1<<n))
.)n
- index of bit to clear.this & ~(1<<n)
ArithmeticException
- n
is negative.public int compareTo(BigInteger val)
(x.compareTo(y)
<op> 0)
, where <op> is one of the six comparison operators.compareTo
in interface Comparable<BigInteger>
val
- BigInteger to which this BigInteger is to be compared.val
.public BigInteger divide(BigInteger val)
(this / val)
.val
- value by which this BigInteger is to be divided.this / val
ArithmeticException
- if val
is zero.public BigInteger[] divideAndRemainder(BigInteger val)
(this / val)
followed by (this % val)
.val
- value by which this BigInteger is to be divided, and the remainder computed.(this / val)
is the initial element, and the remainder
(this % val)
is the final element.ArithmeticException
- if val
is zero.public double doubleValue()
double
. This conversion is similar to the narrowing primitive
conversion from double
to float
as defined in section 5.1.3 of 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.doubleValue
in class Number
double
.public boolean equals(@Nullable Object x)
equals
in class Object
x
- Object to which this BigInteger is to be compared.true
if and only if the specified Object is a BigInteger whose value is numerically equal to this
BigInteger.Object.hashCode()
,
HashMap
public BigInteger flipBit(int n)
(this ^ (1<<n))
.)n
- index of bit to flip.this ^ (1<<n)
ArithmeticException
- n
is negative.public float floatValue()
float
. This conversion is similar to the narrowing primitive
conversion from double
to float
as defined in section 5.1.3 of 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.floatValue
in class Number
float
.public BigInteger gcd(BigInteger val)
abs(this)
and abs(val)
.
Returns 0 if this == 0 && val == 0
.val
- value with which the GCD is to be computed.GCD(abs(this), abs(val))
public int getLowestSetBit()
(this == 0? -1 : log2(this & -this))
.)public int hashCode()
hashCode
in class Object
Object.equals(java.lang.Object)
,
System.identityHashCode(java.lang.Object)
public int intValue()
int
. This conversion is analogous to a narrowing primitive
conversion from long
to int
as defined in section 5.1.3 of 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.intValue
in class Number
int
.intValueExact()
public int intValueExact()
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.BigInteger
converted to an int
.ArithmeticException
- if the value of this
will not exactly fit in a int
.intValue()
public long longValue()
long
. This conversion is analogous to a narrowing primitive
conversion from long
to int
as defined in section 5.1.3 of 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.longValue
in class Number
long
.longValueExact()
public long longValueExact()
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.BigInteger
converted to a long
.ArithmeticException
- if the value of this
will not exactly fit in a long
.longValue()
public BigInteger max(BigInteger val)
val
.val
- value with which the maximum is to be computed.val
. If they are equal, either may be
returned.public BigInteger min(BigInteger val)
val
.val
- value with which the minimum is to be computed.val
. If they are equal, either
may be returned.public BigInteger mod(BigInteger m)
(this mod m
). This method differs from remainder
in that it
always returns a non-negative BigInteger.m
- the modulus.this mod m
ArithmeticException
- m
≤ 0remainder(java.math.BigInteger)
public BigInteger modInverse(BigInteger m)
(this
-1 mod m)
.m
- the modulus.this
-1 mod m
.ArithmeticException
- m
≤ 0, or this BigInteger has no multiplicative inverse mod m (that is, this BigInteger
is not relatively prime to m).public BigInteger modPow(BigInteger exponent, BigInteger m)
pow
, this method
permits negative exponents.)exponent
- the exponent.m
- the modulus.ArithmeticException
- m
≤ 0 or the exponent is negative and this BigInteger is not relatively prime to
m
.modInverse(java.math.BigInteger)
public BigInteger multiply(BigInteger val)
(this * val)
.
implNote: An implementation may offer better algorithmic performance when val == this
.val
- value to be multiplied by this BigInteger.this * val
public BigInteger negate()
(-this)
.-this
public BigInteger not()
(~this)
. (This method returns a negative value if and only if this
BigInteger is non-negative.)~this
public BigInteger or(BigInteger val)
(this | val)
. (This method returns a negative BigInteger if and only
if either this or val is negative.)val
- value to be OR'ed with this BigInteger.this | val
public BigInteger pow(int exponent)
exponent
is an integer
rather than a BigInteger.exponent
- exponent to which this BigInteger is to be raised.ArithmeticException
- exponent
is negative. (This would cause the operation to yield a non-integer value.)public BigInteger remainder(BigInteger val)
(this % val)
.val
- value by which this BigInteger is to be divided, and the remainder computed.this % val
ArithmeticException
- if val
is zero.public BigInteger setBit(int n)
(this | (1<<n))
.)n
- index of bit to set.this | (1<<n)
ArithmeticException
- n
is negative.public BigInteger shiftLeft(int n)
(this << n)
. The shift distance, n
, may be negative, in which
case this method performs a right shift. (Computes floor(this * 2n).)n
- shift distance, in bits.this << n
shiftRight(int)
public BigInteger shiftRight(int n)
(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).)n
- shift distance, in bits.this >> n
shiftLeft(int)
public short shortValueExact()
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.BigInteger
converted to a short
.ArithmeticException
- if the value of this
will not exactly fit in a short
.Number.shortValue()
public int signum()
public BigInteger subtract(BigInteger val)
(this - val)
.val
- value to be subtracted from this BigInteger.this - val
public boolean testBit(int n)
true
if and only if the designated bit is set. (Computes ((this & (1<<n)) != 0)
.)n
- index of bit to test.true
if and only if the designated bit is set.ArithmeticException
- n
is negative.public byte[] toByteArray()
(ceil((this.bitLength() +
1)/8))
. (This representation is compatible with the (byte[])
constructor.)BigInteger(byte[])
public String toString()
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.)toString
in class Object
Character.forDigit(int, int)
,
BigInteger(java.lang.String)
public String toString(int radix)
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.)radix
- radix of the String representation.Integer.toString(int)
,
Character.forDigit(int, int)
,
BigInteger(java.lang.String, int)
public static BigInteger valueOf(long val)
long
. This "static factory method" is
provided in preference to a (long
) constructor because it allows for reuse of frequently used
BigIntegers.val
- value of the BigInteger to return.public BigInteger xor(BigInteger val)
(this ^ val)
. (This method returns a negative BigInteger if and only
if exactly one of this and val are negative.)val
- value to be XOR'ed with this BigInteger.this ^ val