Division and Modular Reduction

[Jeffrey Walton]

Hi All,

I'm building test cases for a third party library, and wanted a
clarification. Searching the FAQ did not turn up hits for division and
modulo or reduction [1].

INT_MIN / -1 = overflow since the result is INT_MAX+1. For example
(using int16 types):

32768 = -32768 / -1

Below, the result is within the reange of the datattype.

32767 = -32768 % -1

However Seacord tells us the result is undefined in CERT's Secure
Programming Guide [2]. Also, I seem to recall that reduction is
defined similar to division for consistency.

What is the state of modular reduction (eg, INT_MIN % -1)?

Jeff

[1] http://www.parashift.com/c++-faq-lite/
[2]
https://www.securecoding.cert.org/c...ations+do+not+result+in+divide-by-zero+errors

 

[Victor Bazarov]

Hi All,

I'm building test cases for a third party library, and wanted a
clarification. Searching the FAQ did not turn up hits for division and
modulo or reduction [1].

INT_MIN / -1 = overflow since the result is INT_MAX+1. For example
(using int16 types):

32768 = -32768 / -1

Actually, 5/4 says the result is not overflow, it's undefined: "If
during the evaluation of an expression, the result is not mathematically
defined or not in the range of representable values for its type, the
behavior is undefined."

Below, the result is within the reange of the datattype.

32767 = -32768 % -1

The modulo operand (or the remainder) (a % b) is defined to produce the
number (c) such that

(a / b) * b + c == a

So, if we allow the division to go through (i.e. not be undefined), then
the remainder should satisfy the equation

(-32768 / -1) * -1 + c = -32768,

which yields c==0 (if I didn't mess up).

Generally speaking for any 'i' (i % 1) => 0. Considering that the
remainder is specified to have the same sign as the left operand, if
negative zero is representable on the system, then for any negative
number 'j' (j % 1) => -0 and (j %-1) => 0.

At least that's how I understand it.

However Seacord tells us the result is undefined in CERT's Secure
Programming Guide [2]. Also, I seem to recall that reduction is
defined similar to division for consistency.

What is the state of modular reduction (eg, INT_MIN % -1)?

Jeff

[1] http://www.parashift.com/c++-faq-lite/
[2]
https://www.securecoding.cert.org/c...ations+do+not+result+in+divide-by-zero+errors

V