java.lang.Object
|
+----java.lang.Number
|
+----java.math.BigInteger
public class BigInteger
extends Number
Immutable arbitrary-precision integers. All operations behave as if BigIntegers were represented in two's-complement notation (like Java's primitive integer types). BigIntegers provide analogues to all of Java's primitive integer operators, and all relevant static methods from java.lang.Math. Additionally, BigIntegers provide operations for modular arithmetic, GCD calculation, primality testing, prime generation, single-bit manipulation, and a few other odds and ends.
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 are are 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.
Single-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 number with a different sign from the 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.