Andrei Alexandrescu wrote:
Ok, here's how I rewrote the section on multiplicative operations. The
text is hardly intelligible due to all formatting, sorry about that (but
it looks much better in a specialized editor). Comments and suggestions
welcome.
\subsection{Multiplicative Expressions}
The multiplicative expressions are multiplication (\ccbox{a * b}),
division (\ccbox{a / b}), and remainder (\ccbox{a \% b}). They
operate on numeric types only. The result type of either of these
operations is same as the type of \ccbox{true ? a : b}
(see~\S~\ref{sec:conditional-operator}).
i...@b@ is zero in the integral operation \ccbox{a / b} or \ccbox{a \%
b}, a hardware exception is thrown. If the division would yield a
fractional number, it is always truncated towards zero (for example,
\ccbox{7 / 3} yiel...@2@ and \ccbox{-7 / 3} yiel...@-2@). The
expression \ccbox{a \% b} is defined such that \cc{a == (a / b) * b +
a \% b}, so \ccbox{7 \% 3} yiel...@1@ and \ccbox{-7 / 3}
yiel...@-1@.
\dee also defines modulus for floating-point numbers. The definition
is more involved. When at least one of @a@ and @b@ is a floating-point
value in \cc{a \% b}, the result is the largest (in absolute value)
floating-point number @r@ satisfying the following conditions:
\begin{itemize*}
\item @a@ and @r@ do not have opposite signs;
\item @r@ is smaller than @b@ in absolute value, \ccbox{abs(r) <
abs(b)};
\item there exists a number @q@ of type @long@ such that \ccbox{r == a
- q * b}.
\end{itemize*}
If such a number cannot be found, \ccbox{a \% b} yields the Not A
Number (NaN) special value.
Andrei
Close, but that's technically not true in the case where abs(a/b) >
long.max. (The integer doesn't have to fit into a 'long').
In IEEE754, r= a % b is defined by the mathematical relation r = a – b
* n , where n is the integer nearest the exact number a/b ; whenever
abs( n – a/b) = 0.5 , then n is even. If r == 0 , its sign is the same
as a.
