jdk.math.BigInteger

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Clojure only.

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. 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 2Integer.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.

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.
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
2Integer.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.

jdk.math.BigInteger

*-oneclj

*-tenclj

*-zeroclj

*probable-primeclj

*value-ofclj

->big-integerclj

absclj

addclj

andclj

and-notclj

bit-countclj

bit-lengthclj

byte-value-exactclj

clear-bitclj

compare-toclj

divideclj

divide-and-remainderclj

double-valueclj

equalsclj

flip-bitclj

float-valueclj

gcdclj

get-lowest-set-bitclj

hash-codeclj

int-valueclj

int-value-exactclj

long-valueclj

long-value-exactclj

maxclj

minclj

modclj

mod-inverseclj

mod-powclj

multiplyclj

negateclj

next-probable-primeclj

notclj

orclj

powclj

probable-prime?clj

remainderclj

set-bitclj

shift-leftclj

shift-rightclj

short-value-exactclj

signumclj

subtractclj

test-bitclj

to-byte-arrayclj

to-stringclj

xorclj

*-one^clj

*-ten^clj

*-zero^clj

*probable-prime^clj

*value-of^clj

->big-integer^clj

abs^clj

add^clj

and^clj

and-not^clj

bit-count^clj

bit-length^clj

byte-value-exact^clj

clear-bit^clj

compare-to^clj

divide^clj

divide-and-remainder^clj

double-value^clj

equals^clj

flip-bit^clj

float-value^clj

gcd^clj

get-lowest-set-bit^clj

hash-code^clj

int-value^clj

int-value-exact^clj

long-value^clj

long-value-exact^clj

max^clj

min^clj

mod^clj

mod-inverse^clj

mod-pow^clj

multiply^clj

negate^clj

next-probable-prime^clj

not^clj

or^clj

pow^clj

probable-prime?^clj

remainder^clj

set-bit^clj

shift-left^clj

shift-right^clj

short-value-exact^clj

signum^clj

subtract^clj

test-bit^clj

to-byte-array^clj

to-string^clj

xor^clj