C++ for Scientists - Technische Universität Dresden

5.2. PROVIDING TYPE INFORMATION 135
This requires the evaluation of fibonacci::value as
template
struct fibonacci
{
static const long value= 0 < 3 ? 1 : fibonacci< −1>::value + fibonacci< −2>::value; // error
};
which needs fibonacci< −1>::value . . . . Although the values for N < 3 are not used in the end,
the compiler will nevertheless generate these terms infinitely and die at some point.
We said before that we implement the computation recursively. In fact, all repetive calculations
must be realized recursively as there is no iteration for 2 meta-functions.
If we write for instance
std::cout ≪ fibonacci::value ≪ ”\n”;
the value would be already calculated during the compilation and the program just prints
it. If you do not believe us, you can read the assembler code (e.g. compile with ‘g++ -S
fibonacci.cpp -o fibonacci.asm’).
We mentioned long compilations with meta-programming at the beginning of the chapter. The
compilation for Fibonacci number 45 took less than a second. Compared to it, a naïve run-time
implemtation:
long fibonacci2(long x)
{
return x < 3 ? 1 : fibonacci2(x−1) + fibonacci2(x−2);
}
took 14s on the same computer. The reason is that the compiler remember intermediate results
while the run-time version recomputes everything. We are, however, convinced that every reader
of this book can rewrite fibonacci2 without the exponential overhead of recomputations.
5.2 Providing Type Information
5.2.1 Type Traits
When we write template functions, we can easily define temporary values because they have
usually the same type as one of the template arguments. But not always. Imagine you have a
function that returns from two value that with the minimal magnitude:
template
T inline min magnitude(const T& x, const T& y)
{
using std::abs;
T ax= abs(x), ay= abs(y);
return ax < ay ? x : y;
}
We can call this for int, unsigned, double values:
2 The Meta Programming Library provides compile-time iterators but even those are recursive internally.