Making gcc optimize deep recursion

Question

I'm testing functional style programming with C++. Having the compiler to optimize recursion to a loop when possible is necessary to avoid stack overflows. The below program crashes due to stack overflow when BlendingTable::print() is called. I don't know why it doesn't crash in the constructor of BlendingTable, which does a same form of recursion as print. I need to allocate 1GB of stack to avoid stack overflow, and this is not acceptable.

Do I need to pass some special options to hint gcc to optimize the recursion? How do functional programming languages handle the problem of deep recursion? Or is it simply an unsolvable problem with current compiler technology?

---

EDIT1

I kind of solved the problem by placing __attribute__((always_inline)) at Stdout::print. Then gcc does remove the recursion in BlendingTable::print.

#include <cstdlib>
#include <iostream>
#include <memory>
#include <array>
#include <limits>

class Stdout {
public:
    template<typename T, typename... Ts>
    static void print(const T& t, const Ts&... ts) {
        std::cout << t << std::flush;
        print(ts...);
    }

    static void print() {}

    template<typename... Ts>
    static void printLine(const Ts&... ts) {
        print(ts..., '\n');
    }
};

class Error {
public:
    template<typename... Ts>
    static void assert(bool b, const Ts&... ts) {
        if (!b) {
            Stdout::printLine(ts...);
            throw;
        }
    }
};

template<typename T, int dimension = 1>
class Array {
private:
    std::unique_ptr<T[]> pointer;
    std::array<int, dimension> sizes;
    int realSize;

public:
    template<typename... Ns>
    Array(Ns... ns):
    realSize(1) {
        checkArguments(ns...);
        create(1, ns...);
    }

    Array() {}

private:
    template<typename... Ns>
    static constexpr void checkArguments(Ns...) {
        static_assert(sizeof...(Ns) == dimension, "dimension mismatch");
    }

    template<typename... Ns>
    void create(int d, int n, Ns... ns) {
        realSize *= n;
        sizes[d - 1] = n;
        create(d + 1, ns...);
    }

    void create(int) {
        pointer = std::unique_ptr<T[]>(new T[realSize]);
    }

    int computeSubSize(int d) const {
        if (d == dimension) {
            return 1;
        }
        return sizes[d] * computeSubSize(d + 1);
    }

    template<typename... Ns>
    int getIndex(int d, int n, Ns... ns) const {
        return n * computeSubSize(d) + getIndex(d + 1, ns...);
    }

    int getIndex(int) const {
        return 0;
    }

public:
    template<typename... Ns>
    T& operator()(Ns... ns) const {
        checkArguments(ns...);
        return pointer[getIndex(1, ns...)];
    }

    int getSize(int d = 1) const {
        return sizes[d - 1];
    }
};

class BlendingTable : public Array<unsigned char, 3> {
private:
    enum {
        SIZE = 0x100,
        FF = SIZE - 1,
    };

public:
    BlendingTable():
    Array<unsigned char, 3>(SIZE, SIZE, SIZE) {
        static_assert(std::numeric_limits<unsigned char>::max() == FF, "unsupported byte format");
        create(FF, FF, FF);
    }

private:
    void create(int dst, int src, int a) {
        (*this)(dst, src, a) = (src * a + dst * (FF - a)) / FF;
        if (a > 0) {
            create(dst, src, a - 1);
        } else if (src > 0) {
            create(dst, src - 1, FF);
        } else if (dst > 0) {
            create(dst - 1, FF, FF);
        } else {
            return;
        }
    }

    void print(int dst, int src, int a) {
        Stdout::print(static_cast<int>((*this)(FF - dst, FF - src, FF - a)), ' ');
        if (a > 0) {
            print(dst, src, a - 1);
        } else if (src > 0) {
            print(dst, src - 1, FF);
        } else if (dst > 0) {
            print(dst - 1, FF, FF);
        } else {
            Stdout::printLine();
            return;
        }
    }

public:
    void print() {
        print(FF, FF, FF);
    }
};

int main() {
    BlendingTable().print();
    return EXIT_SUCCESS;
}