Re: [boost] Re: rational.hpp: !!m? no way, jose!

From: Stephen Silver (boost_at_[hidden])
Date: 2001-01-12 09:51:33

Dean Sturtevant wrote:

> And the comparison within the algorithm is a 
> little strange: Why would n % m be < 0 ? I would have thought that 
> any reasonable def of '%' would always yield non-negative numbers?

Unfortunately, the definition is not reasonable.  The original ANSI C
standard did not specify the direction of rounding in integer division
if either operand is negative, and the C++ standard simply adopts
this lax approach.  Worse still, the C99 standard actually requires
truncation towards zero, and this is what most current C++ compilers
do in practice.  Quotients and remainders are linked by the formula

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

so truncation towards zero inevitably leads to negative remainders.
Also note that the boost::rational documentation says "division should
truncate", which I take to mean "towards zero" (although perhaps this
should be clarified).

But if gcd() started by taking the abs() of its arguments, then it
would have no need to make this negativity test inside the loop.

Stephen