Why Does the Modulo Operator Sometimes Produce Negative Results?

Why Modulo Operations Produce Negative Results

The modulo operator (%) calculates the remainder after dividing the first operand (a) by the second operand (b). However, understanding why negative values might arise in certain modulo operations requires delving into the details of the operator's behavior.

The ISO14882:2011(e) 5.6-4 standard states: "For integral operands, the / operator yields the algebraic quotient with any fractional part discarded". This implies that the quotient (a/b) is an integer with no fractional part. Moreover, "if the quotient a/b is representable in the type of the result, (a/b)*b a%b is equal to a".

Let's consider the operation (-7 % 3). The quotient (-7 / 3) is -2, since it discards any fractional part (-7.0 / 3.0 would yield -2.33, but we keep only the integer part). Multiplying the quotient by the divisor (-2 * 3 = -6) and adding the result to the remainder (a%b), we get (-6) (-1) = -7, matching the original value.

Now, let's examine (7 % -3). The quotient (7 / -3) is also -2, but the sign of the remainder a%b is implementation-defined according to ISO14882:2011(e). In this case, some implementations choose a negative sign, resulting in 1.

Therefore, the modulo operation's behavior with negative operands depends on the implementation and may produce either positive or negative remainders. However, the standard ensures that the original value can always be reconstructed from the quotient and the remainder in certain conditions.

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