operator % and signed integers

[Thomas Matthews]

Hi,

We had an applications guy use a {signed} int and the operator % in an
embedded system. None of us could figure out if this was a valid
operation, and if so, what is sign of the result?

In searching the newsgroup, I found an article stating that the
operator % is a "remainder operator" not a modulus operator.
Is this true? If so, is the result ever negative?

{Posted to comp.lang.c and comp.lang.c++ because it pertains
to both languages.}

Given:
signed int A;
signed int B;

What are the signs of the result column below
where Result = A % B; /* B != 0, A != 0 */?
A B Result
----------------------------------------------
positive, > B positive
positive, < B positive
negative, magnitude < B positive
-2 * B positive
positive, magnitude > B negative
positive, magnitude < B negative
negative, magnitude < B negative
negative, magnitude > B negative

--
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[Ivan Vecerina]

: We had an applications guy use a {signed} int and the operator % in an
: embedded system. None of us could figure out if this was a valid
: operation, and if so, what is sign of the result?

It is a valid operation. However, to allow the compiler to use
the best-performing signed division operation supported on a
given hardware, the C language had chosen not to specify the
sign of the result. (and this remains the case in C++ today).

The result is therefore defined, but platform-dependent.
This also applies to the division operator:
int x = (-3)/2; // x might be -1 or -2 !!!

: In searching the newsgroup, I found an article stating that the
: operator % is a "remainder operator" not a modulus operator.
: Is this true? If so, is the result ever negative?
It might be.

The only guarantee you have is that / and % are to
behave consistently. I.e.:
void f(int a, int b)
{
int d = a/b;
int r = a%b;
assert( d*b + r == a ); //safe
assert( abs(r) < abs(b) ); //also safe
// And for given signs of a and b, the
// sign of d and r will always be consistent.
}


Yes this situation is akward.
Many are of the opinion that the result of signed
/ and % shall be specified strictly, and that
performance-conscious users will always have the
option to rely on unsigned / and %, which would
still provide the same (best possible) performance
on all platforms.


I hope this helps,
Ivan

 

[jat]

dear sir,
The result will be remainder having the sign of
numerator.

so result can be calculated like this remainder( magnitude(A),
magnitude(B)) * sign(A)

sign of denominator does have any effect on the result.

 

[Keith Thompson]

We had an applications guy use a {signed} int and the operator % in an
embedded system. None of us could figure out if this was a valid
operation, and if so, what is sign of the result?

In searching the newsgroup, I found an article stating that the
operator % is a "remainder operator" not a modulus operator.
Is this true? If so, is the result ever negative?

{Posted to comp.lang.c and comp.lang.c++ because it pertains
to both languages.}

C99 6.5.5 says:

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.

When integers are divided, the result of the / operator is the
algebraic quotient with any fractional part discarded (88). If the
quotient a/b is representable, the expression (a/b)*b + a%b shall
equal a.

with a footnote:

(88) This is often called "truncation toward zero".

 

[Jack Klein]

Hi,

We had an applications guy use a {signed} int and the operator % in an
embedded system. None of us could figure out if this was a valid
operation, and if so, what is sign of the result?

In searching the newsgroup, I found an article stating that the
operator % is a "remainder operator" not a modulus operator.
Is this true? If so, is the result ever negative?

{Posted to comp.lang.c and comp.lang.c++ because it pertains
to both languages.}

The statement above raises a serious issue, at least as far as posting
in comp.lang.c is concerned. As far as the C language is concerned,
C++ does not exist. Actually, I exaggerate. The C language and
standard take no notice, nor any responsibility, for languages "based
on C" or that adopt part of C's syntax. As far as the C standard, and
comp.lang.c are concerned, there is no "Objective C", "Java", "C#",
"D", and who knows how many others.

Where did I exaggerate? The C language and its ISO standard do barely
acknowledge that C++. It is mentioned in no less than four footnotes
in the current C standard, basically at the request of the C++
standard committee. And the C standard specifically forbids a
conforming C implementation from defining a macro "__cplusplus". So
since 1999, C acknowledges that C++ exists.

Why am I making such a point of this? Because C++ adopts part of, but
not all of, an earlier (1995) version of the C standard, and makes
subtle changes to other parts, some of them quiet and likely to trap
the unwary.

So here in comp.lang.c, the only answer is what the C standard
requires and/or allows to happen in C. Whether C++ requires/allows
the same, or something different, is quite off-topic here.

Given:
signed int A;
signed int B;

What are the signs of the result column below
where Result = A % B; /* B != 0, A != 0 */?
A B Result
----------------------------------------------
positive, > B positive
positive, < B positive
negative, magnitude < B positive
-2 * B positive
positive, magnitude > B negative
positive, magnitude < B negative
negative, magnitude < B negative
negative, magnitude > B negative

As for the C language, the operation is valid regardless of the signs
of the operands, as long as B is not 0.

Here is exactly what the C standard guarantees for A % B given that A
and B are signed int:

A positive or 0, B positive: result positive or 0.

Any other case: result positive, negative, or 0.

The sign of a non-zero result of the % operator when either or both of
the operands is negative is implementation-defined.

 

[Chuck F.]

We had an applications guy use a {signed} int and the operator
% in an embedded system. None of us could figure out if this
was a valid operation, and if so, what is sign of the result?

In searching the newsgroup, I found an article stating that the
operator % is a "remainder operator" not a modulus operator.
Is this true? If so, is the result ever negative?

{Posted to comp.lang.c and comp.lang.c++ because it pertains
to both languages.}

I suspect this is a bad idea, inasmuch as the answer is very likely
to be different in the two languages, and can probably only be
answered by careful perusal of the appropriate standards. I also
seem to remember that the answer changed between C90 and C99 (for
C), which further emphasizes the uselessness of the crosspost.

F'ups set.

--
Some useful references about C:
<http://www.ungerhu.com/jxh/clc.welcome.txt>
<http://www.eskimo.com/~scs/C-faq/top.html>
<http://benpfaff.org/writings/clc/off-topic.html>
<http://anubis.dkuug.dk/jtc1/sc22/wg14/www/docs/n869/> (C99)
<http://www.dinkumware.com/refxc.html> (C-library}
<http://gcc.gnu.org/onlinedocs/> (GNU docs)

 

[Pete Becker]

The result is therefore defined, but platform-dependent.

It's also implementation-defined, that is, the implementation is
required to document what the behavior is.

 

[Chuck F.]

C99 6.5.5 says:

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.

When integers are divided, the result of the / operator is the
algebraic quotient with any fractional part discarded (88). If
the quotient a/b is representable, the expression (a/b)*b + a%b
shall equal a.

with a footnote:

(88) This is often called "truncation toward zero".

I believe this is different from the C90 specification. If I am
right it probably also means that the C and C++ specifications
differ, showing once more how silly it is to cross-post between
c.l.c and c.l.c++. They are different languages. F'ups set.

--
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the broken "Reply" link at the bottom of the article. Click on
"show options" at the top of the article, then click on the
"Reply" at the bottom of the article headers." - Keith Thompson
More details at: <http://cfaj.freeshell.org/google/>

 

[Tim Rentsch]

Hi,

We had an applications guy use a {signed} int and the operator % in an
embedded system. None of us could figure out if this was a valid
operation, and if so, what is sign of the result?

In searching the newsgroup, I found an article stating that the
operator % is a "remainder operator" not a modulus operator.
Is this true? If so, is the result ever negative?

{Posted to comp.lang.c and comp.lang.c++ because it pertains
to both languages.}

[C++ portion snipped]

Given:
signed int A;
signed int B;

What are the signs of the result column below
where Result = A % B; /* B != 0, A != 0 */?
A B Result
----------------------------------------------
positive, > B positive
positive, < B positive
negative, magnitude < B positive
-2 * B positive
positive, magnitude > B negative
positive, magnitude < B negative
negative, magnitude < B negative
negative, magnitude > B negative

As for the C language, the operation is valid regardless of the signs
of the operands, as long as B is not 0.

If the result is representable. The expression 'INT_MIN / -1'
might not be representable. Such cases aren't valid either.

Here is exactly what the C standard guarantees for A % B given that A
and B are signed int:

A positive or 0, B positive: result positive or 0.

Any other case: result positive, negative, or 0.

The sign of a non-zero result of the % operator when either or both of
the operands is negative is implementation-defined.

It _was_ implementation-defined in C90. In C99 it's well-defined
(division truncates toward zero, remainder consistent with division)
as long as the results are representable.

 

[Jordan Abel]

As for the C language, the operation is valid regardless of the signs
of the operands, as long as B is not 0.

Here is exactly what the C standard guarantees for A % B given that A
and B are signed int:

A positive or 0, B positive: result positive or 0.

Any other case: result positive, negative, or 0.

The sign of a non-zero result of the % operator when either or both of
the operands is negative is implementation-defined.

Is it still required that, for C = A%B and D = A/B, that D*B+C==A? [i.e.
the two results are related in a way that makes that expression true,
with the sign of the % result determined by the rounding of the /
result]