Question

I was reading the section on C portability in the book C Traps and Pitfalls by Andrew Koening..

On an integer divison

q = a/b;
r = a%b;

If a is a negative number, apparently the reminder r can be a negative or positive number, while satisfying the property

q * b + r == a

Normally I would expect r to be negative if dividend a is negative. And that is what I see in a intel machine with gcc. I am just curious have you ever seen a machine that would return a positive reminder when the dividend is a negative number ?

Answer 1

C99 formalized the remainder as having the same sign as the dividend. Prior to C99 (C89 and K&R), it could have gone either way as both results meet the technical requirements. There are indeed compilers out there non-conforming to the C99 spec in this matter, though I don’t know of any off the top of my head.

In particular, section 6.5.5 (Multiplicative operators) states:

¶5 The result of the / operator is the quotient from the division of the
first operand by the second; the result of the % operator is the
remainder. In both operations, if the value of the second operand is
zero, the behavior is undefined.

¶6 When integers are divided, the result of the / operator is the algebraic quotient with any
fractional part discarded.⁸⁷⁾ If the quotient a/b is representable, the expression
(a/b)*b + a%b shall equal a.

⁸⁷⁾ This is often called “truncation toward zero”.

With this new definition, the remainder is basically defined as what you’d expect it to be mathematically speaking.

EDIT

To address a question in the comments, the C99 spec also specifies (footnote 240) that if the remainder is zero, on systems where zero is not signed the sign of r will be the same as that of divisor, x.

‘‘When y ≠ 0, the remainder r = x REM y is defined regardless of the
rounding mode by the mathematical relation r = x − ny, where n is the
integer nearest the exact value of x/y; whenever | n − x/y | = 1/2,
then n is even. Thus, the remainder is always exact. If r = 0, its
sign shall be that of x.’’ This definition is applicable for all
implementations.