*This is an unofficial snapshot of the ISO/IEC JTC1 SC22 WG21
Core Issues List revision 110b.
See http://www.open-std.org/jtc1/sc22/wg21/ for the official
list.*

2023-01-15

#### 614.
Results of integer `/` and `%`

**Section: **7.6.5 [expr.mul]
**Status: **CD1
**Submitter: **Gabriel Dos Reis
**Date: **15 January 2007

[Voted into the WP at the September, 2008 meeting as part of
paper N2757.]

The current Standard leaves it implementation-defined whether
integer division rounds the result toward 0 or toward negative
infinity and thus whether the result of `%` may be negative.
C99, apparently reflecting (nearly?) unanimous hardware practice, has
adopted the rule that integer division rounds toward 0, thus requiring
that the result of `-1 % 5` be `-1`. Should the C++
Standard follow suit?

On a related note, does `INT_MIN % -1` invoke undefined
behavior? The `%` operator is defined in terms of the
`/` operator, and `INT_MIN / -1` overflows, which by
Clause 7 [expr] paragraph 5 causes undefined behavior;
however, that is not the “result” of the `%`
operation, so it's not clear. The wording of 7.6.5 [expr.mul] paragraph 4
appears to allow `%` to cause undefined behavior
only when the second operand is 0.

**Proposed resolution (August, 2008):**

Change 7.6.5 [expr.mul] paragraph 4 as follows:

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~~;
otherwise ~~`(a/b)*b + a%b` is equal to `a`. If both
operands are nonnegative then the remainder is nonnegative; if
not, the sign of the remainder is
implementation-defined. [*Footnote:* According to work
underway toward the revision of ISO C, the preferred algorithm
for integer division follows the rules defined in the ISO Fortran
standard, ISO/IEC 1539:1991, in which the quotient is always
rounded toward zero. —*end footnote*]. For
integral operands, the `/` operator yields the
algebraic quotient with any fractional part discarded;
[*Footnote:* This is often called “truncation towards
zero.” —*end footnote*] if the quotient
`a/b` is representable in the type of the result,
`(a/b)*b + a%b` is equal to `a`.

*[Drafting note: see C99 6.5.5 paragraph 6.]*