Range analysis of floating point values?

Question

I have an image processing program which uses floating point calculations. However, I need to port it to a processor which does not have floating point support in it. So, I have to change the program to use fixed point calculations. For that I need proper scaling of those floating point numbers, for which I need to know the range of all values, including intermediate values of the floating point calculations.

Is there a method where I just run the program and it automatically give me the range of all the floating point calculations in the program? Trying to figure out the ranges manually would be too cumbersome, so if there is some tool for doing it, that would be awesome!

Answer 1

You could use some "measuring" replacement for your floating type, along these lines (live example):

template<typename T>
class foo
{
    T val;

    using lim = std::numeric_limits<int>;

    static int& min_val() { static int e = lim::max(); return e; }
    static int& max_val() { static int e = lim::min(); return e; }

    static void sync_min(T e) { if (e < min_val()) min_val() = int(e); }
    static void sync_max(T e) { if (e > max_val()) max_val() = int(e); }

    static void sync(T v)
    {
        v = std::abs(v);
        T e = v == 0 ? T(1) : std::log10(v);
        sync_min(std::floor(e)); sync_max(std::ceil(e));
    }

public:
    foo(T v = T()) : val(v) { sync(v); }
    foo& operator=(T v) { val = v; sync(v); return *this; }

    template<typename U> foo(U v) : foo(T(v)) {}
    template<typename U> foo& operator=(U v) { return *this = T(v); }

    operator T&() { return val; }
    operator const T&() const { return val; }

    static int min() { return min_val(); }
    static int max() { return max_val(); }
};

to be used like

int main ()
{
    using F = foo<float>;
    F x;

    for (F e = -10.2; e <= 30.4; e += .2)
        x = std::pow(10, e);

    std::cout << F::min() << " " << F::max() << std::endl;  // -11 31
}

This means you need to define an alias (say, Float) for your floating type (float or double) and use it consistently throughout your program. This may be inconvenient but it may prove beneficial eventually (because then your program is more generic). If your code is already templated on the floating type, even better.

After this parametrization, you can switch your program to "measuring" or "release" mode by defining Float to be either foo<T> or T, where T is your float or double.

The good thing is that you don't need external tools, your own code carries out the measurements. The bad thing is that, as currently designed, it won't catch all intermediate results. You would have to define all (e.g. arithmetic) operators on foo for this. This can be done but needs some more work.