C++ operator % guarantees

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In addition to Luchian‘s answer, this is the corresponding part from the C++11 standard:

The binary / operator yields the quotient, and the binary % operator
yields the remainder from the division of the first expression by the
second. If the second operand of / or % is zero the behavior is
undefined. For integral operands the / operator yields the algebraic
quotient with any fractional part discarded; if the quotient a/b is
representable in the type of the result, (a/b)*b + a%b is equal to a.

Which misses the last sentence. So the part

(a/b)*b + a%b is equal to a

Is the only reference to rely on, and that implies that a % b will always have the sign of a, given the truncating behaviour of /. So if your implementation adheres to the C++11 standard in this regard, the sign and value of a modulo operation is indeed perfectly defined for negative operands.

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