Re: Modulus and negative operands



August Karlstrom wrote On 01/12/06 14:01,:
> Michael Mair wrote:
>
>>% is defined in terms of / (see below).
>>If / rounds down, then % yields positive values.
>>If / rounds to zero, you get the observed behaviour.
>
> [snip]
>
> OK, but what's the benefit of this behavior?

The benefit of "truncate toward zero" on division are
mostly conventional: That's the way practically all known
hardware does division, and that's also the way Fortran
defines it. According to the C99 Rationale, compatibility
with Fortran was the main reason for requiring "truncate
toward zero."

Quotient and remainder are governed by the identity

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

(unless the division itself is undefined). Whichever
way the quotient is chosen on an inexact division, the
modulus must "balance" the truncation error. If division
truncates toward zero, the truncated negative quotient
will be larger than the true mathematical quotient, so
the "correction" must be negative.

> If I want to decrement a
> cyclic variable n by k I have to write something like
>
> n = ((n - k) % length + length) % length

If k <= length, this can be simplified to

n = (n - k + length) % length

or to

if ((n -= k) < 0)
n += length;

--
Eric.Sosman@xxxxxxx



.

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