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 {@code 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 BigInteger2s 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 ( {@code >>>}) 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 ( {@code and}, {@code or}, {@code 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 {@code 0} and {@code (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 BigInteger2 with a different sign from the BigInteger2 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 BigInteger2.
For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigInteger2 methods. The pseudo-code expression {@code (i + j)} is shorthand for "a BigInteger2 whose value isthat of the BigInteger2 {@code i} plus that of the BigInteger2 {@code j}." The pseudo-code expression {@code (i == j)} is shorthand for" {@code true} if and only if the BigInteger2 {@code i} represents the samevalue as the BigInteger2 {@code j}." Other pseudo-code expressions are interpreted similarly.
All methods and constructors in this class throw {@code NullPointerException} when passeda null object reference for any input parameter. @see BigDecimal @author Josh Bloch @author Michael McCloskey @since JDK1.1
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