In my C++ programme, I often need to build a vector of values of a function on all the possible values of its arguments over some small finite field. For example, something like this:
int q = 7;
vector<int> GFq;
for (int x = 0; x < q; x++) GFq.push_back(x);
auto P = [q](int x, int y) -> int { return (x*x+y) % q; };
auto Q = [q](int x, int y) -> int { return (x+2*y) % q; };
auto f = [q,P,Q](int x1, int y1, int x2, int y2)
-> int {return (P(x1,y1) + Q(x2,y2)) % q; }
vector<int> table;
for (int x1: GFq) for (int y1: GFq) for (int x2: GFq) for (int y2: GFq)
table.push_back(f(x1,y1,x2,y2));
This pattern is so often repeated in my code that I naturally want to make it a function. So I need something like this:
template<typename F> // not sure if I need to use templates
vector<int> tabulate(int q, F f) {
// run through values 0..q-1 for all arguments of f
// and store the values of f to the resulting vector
}
Some questions/issues:
tabulate()
including those of different arity (ie f(x)
, f(x,y)
, etc.) f
is constructed from P
and Q
in the first code snippet f
(ie 0..q-1
for each of its arguments) inside tabulate()
? I want to be able to pass an arbitrary function to tabulate() including those of different arity (ie f(x), f(x,y), etc.)
Make tabulate
a template that accepts objects of arbitrary types as functions.
I want to construct the function I pass "on the fly", including usage of other functions (the same way as f is constructed from P and Q in the first code snippet
You can use a lambda directly as a function parameter.
if I manage to pass such a function, how can I run a loop over all possible arguments of f (ie 0..q-1 for each of its arguments) inside tabulate()?
In pseudocode:
params = {0, ..., 0};
while (1)
{
// Call function with `params` here.
int i = 0;
for (i = 0; i < params.size(); i++)
{
params[i]++;
if (params[i] == q)
params[i] = 0;
else
break;
}
if (i == params.size())
break;
}
In practice you need to store parameters in a std::array
(or std::tuple
, as the code below does), and use std::apply
to call your function with these parameters.
A complete implementation:
#include <cstddef>
#include <iostream>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>
template <typename T, typename ...P, std::size_t ...I>
bool increment_tuple_impl(T q, std::tuple<P...> &t, std::index_sequence<I...>)
{
auto lambda = [&](auto index) -> bool
{
auto &elem = std::get<index.value>(t);
elem++;
if (elem == q)
{
elem = 0;
return 0;
}
else
{
return 1;
}
};
return (lambda(std::integral_constant<std::size_t, I>{}) || ...);
}
template <typename T, typename ...P>
bool increment_tuple(T q, std::tuple<P...> &t)
{
return increment_tuple_impl(q, t, std::make_index_sequence<sizeof...(P)>{});
}
template <typename T, typename F, std::size_t MaxArity, typename ...P>
auto tabulate_impl(T q, F &&f)
{
if constexpr (!std::is_invocable_v<F, P...>)
{
static_assert(sizeof...(P) < MaxArity, "Invalid function.");
return tabulate_impl<T, F, MaxArity, P..., T>(q, std::forward<F>(f));
}
else
{
using return_type = std::invoke_result_t<F, P...>;
std::vector<return_type> vec;
std::tuple<P...> params{};
do
{
vec.push_back(std::apply(f, params));
}
while (increment_tuple(q, params));
return vec;
}
}
template <typename T, typename F>
auto tabulate(T q, F &&f)
{
constexpr int max_arity = 8;
return tabulate_impl<T, F, max_arity, T>(q, std::forward<F>(f));
}
int main()
{
auto v = tabulate(3, [](int x, int y){return x*10 + y;});
// Prints `0 10 20 1 11 21 2 12 22`.
for (auto x : v)
std::cout << x << ' ';
}
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