The Java Language Specification, Third Edition

EXPRESSIONS Division Operator / 15.17.2
❖ If the type of the multiplication expression is float, then either the float
value set or the float-extended-exponent value set may be chosen, at the
whim of the implementation.
❖ If the type of the multiplication expression is double, then either the double
value set or the double-extended-exponent value set may be chosen, at
the whim of the implementation.
Next, a value must be chosen from the chosen value set to represent the product.
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. Otherwise,
the product is rounded to the nearest value in the chosen value set using IEEE
754 round-to-nearest mode. The Java programming 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.
15.17.2 Division Operator /
Gallia est omnis divisa in partes tres.
— Commentaries on the Gallic Wars
The binary / operator performs division, producing the quotient of its operands.
The left-hand operand is the dividend and the right-hand operand is the divisor.
Integer division rounds toward 0. That is, the quotient produced for operands
n and d that are integers after binary numeric promotion (§5.6.2) is an integer
value q whose magnitude is as large as possible while satisfying d ⋅ q ≤ n ;
moreover, q is positive when n ≥ d and n and d have the same sign, but q is negative
when n ≥
d and n and d have opposite signs. There is one special case that
does not satisfy this rule: if the dividend is the negative integer of largest possible
magnitude for its type, and the divisor is -1, then integer overflow occurs and the
result is equal to the dividend. Despite the overflow, no exception is thrown in this
case. On the other hand, if the value of the divisor in an integer division is 0, then
an ArithmeticException is thrown.
The result of a floating-point division is determined by the specification of
IEEE 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, negative if the operands have different signs.
DRAFT
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