Question

Why do such operations:

std::cout << (-7 % 3) << std::endl;
std::cout << (7 % -3) << std::endl;

give different results?

-1
1

Answer 1

From ISO14882:2011(e) 5.6-4:

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.

The rest is basic math:

(-7 / 3) => -2
-2 * 3   => -6
so a % b => -1

(7 / -3) => -2
-2 * -3  => 6
so a % b => 1

Note that

If both operands are nonnegative then the remainder is nonnegative; if
not, the sign of the remainder is implementation-defined.

from ISO14882:2003(e) is no longer present in ISO14882:2011(e)