15.17.2 Additive Operators (+ and -) for Numeric Types

The binary + operator performs addition when applied to two operands of numeric type, producing the sum of the operands. The binary - operator performs subtraction, producing the difference of two numeric operands.

Binary numeric promotion is performed on the operands (§5.6.2). The type of an additive expression on numeric operands is the promoted type of its operands. If this promoted type is int or long, then integer arithmetic is performed; if this promoted type is float or double, then floating-point arithmetic is performed.

Addition is a commutative operation if the operand expressions have no side effects. Integer addition is associative when the operands are all of the same type, but floating-point addition is not associative.

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

The result of a floating-point addition is determined using the following rules of IEEE arithmetic:

• If either operand is NaN, the result is NaN.
• The sum of two infinities of opposite sign is NaN.
• The sum of two infinities of the same sign is the infinity of that sign.
• The sum of an infinity and a finite value is equal to the infinite operand.
• The sum of two zeros of opposite sign is positive zero.
• The sum of two zeros of the same sign is the zero of that sign.
• The sum of a zero and a nonzero finite value is equal to the nonzero operand.
• The sum of two nonzero finite values of the same magnitude and opposite sign is positive zero.
• In the remaining cases, where neither an infinity, nor a zero, nor NaN is involved, and the operands have the same sign or have different magnitudes, the sum is computed. If the magnitude of the sum is too large to represent, we say the operation overflows; the result is then an infinity of appropriate sign. If the magnitude is too small to represent, we say the operation underflows; the result is then a zero of appropriate sign. Otherwise, the sum is rounded to the nearest representable value using IEEE 754 round-to-nearest mode. The Java language requires support of gradual underflow as defined by IEEE 754 (§4.2.4).

The binary - operator performs subtraction when applied to two operands of numeric type producing the difference of its operands; the left-hand operand is the minuend and the right-hand operand is the subtrahend. For both integer and floating-point subtraction, it is always the case that a-b produces the same result as a+(-b). Note that, for integer values, subtraction from zero is the same as negation. However, for floating-point operands, subtraction from zero is not the same as negation, because if x is +0.0, then 0.0-x equals +0.0, but -x equals -0.0.

Despite the fact that overflow, underflow, or loss of information may occur, evaluation of a numeric additive operator never throws a run-time exception.