The Java Language Specification, Third Edition

EXPRESSIONS Remainder Operator % 15.17.3
15.17.3 Remainder Operator %
And on the pedestal these words appear:
“My name is Ozymandias, king of kings:
Look on my works, ye Mighty, and despair!”
Nothing beside remains.
—Ozymandias
The binary % operator is said to yield the remainder of its operands from an
implied division; the left-hand operand is the dividend and the right-hand operand
is the divisor.
In C and C++, the remainder operator accepts only integral operands, but in
the Java programming language, it also accepts floating-point operands.
The remainder operation for operands that are integers after binary numeric
promotion (§5.6.2) produces a result value such that (a/b)*b+(a%b) is equal to
a. This identity holds even in the special case that the dividend is the negative
integer of largest possible magnitude for its type and the divisor is -1 (the remainder
is 0). It follows from this rule that the result of the remainder operation can be
negative only if the dividend is negative, and can be positive only if the dividend is
positive; moreover, the magnitude of the result is always less than the magnitude
of the divisor. If the value of the divisor for an integer remainder operator is 0,
then an ArithmeticException is thrown.Examples:
5%3 produces 2 (note that 5/3 produces 1)
5%(-3) produces 2 (note that 5/(-3) produces -1)
(-5)%3 produces -2 (note that (-5)/3 produces -1)
(-5)%(-3) produces -2 (note that (-5)/(-3) produces 1)
The result of a floating-point remainder operation as computed by the % operator
is not the same as that produced by the remainder operation defined by IEEE
754. The IEEE 754 remainder operation computes the remainder from a rounding
division, not a truncating division, and so its behavior is not analogous to that of
the usual integer remainder operator. Instead, the Java programming language
defines % on floating-point operations to behave in a manner analogous to that of
the integer remainder operator; this may be compared with the C library function
fmod. The IEEE 754 remainder operation may be computed by the library routine
Math.IEEEremainder.
The result of a floating-point remainder operation is determined by the rules
of IEEE arithmetic:
• If either operand is NaN, the result is NaN.
• If the result is not NaN, the sign of the result equals the sign of the dividend.
• If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.
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