15.16.1 Multiplication Operator *

Entia non sunt multiplicanda praeter necessitatem.
—William of Occam (c. 1320)

The binary * operator performs multiplication, producing the product of its operands. Multiplication is a commutative operation if the operand expressions have no side effects. While integer multiplication is associative when the operands are all of the same type, floating-point multiplication is not associative.

If an integer multiplication overflows, then the result is the low-order bits of the mathematical product as represented in some sufficiently large two's-complement format. As a result, if overflow occurs, then the sign of the result may not be the same as the sign of the mathematical product of the two operand values.

The result of a floating-point multiplication is governed by the rules of IEEE 754 arithmetic:

• If either operand is NaN, the result is NaN.
• If the result is not NaN, the sign of the result is positive if both operands have the same sign, and negative if the operands have different signs.
• Multiplication of an infinity by a zero results in NaN.
• Multiplication of an infinity by a finite value results in a signed infinity. The sign is determined by the rule stated above.
• In the remaining cases, where neither an infinity or NaN is involved, the product is computed. If the magnitude of the product 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 product 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).

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