Get linear index for multidimensional access - c++

Question

I'm trying to implement a multidimensional std::array, which hold a contigous array of memory of size Dim-n-1 * Dim-n-2 * ... * Dim-1. For that, i use private inheritance from std::array :
constexpr std::size_t factorise(std::size_t value)
{
return value;
}
template<typename... Ts>
constexpr std::size_t factorise(std::size_t value, Ts... values)
{
return value * factorise(values...);
}
template<typename T, std::size_t... Dims>
class multi_array : std::array<T, factorise(Dims...)>
{
// using directive and some stuff here ...
template<typename... Indexes>
reference operator() (Indexes... indexes)
{
return base_type::operator[] (linearise(std::make_integer_sequence<Dims...>(), indexes...)); // Not legal, just to explain the need.
}
}
For instance, multi_array<5, 2, 8, 12> arr; arr(2, 1, 4, 3) = 12; will access to the linear index idx = 2*(5*2*8) + 1*(2*8) + 4*(8) + 3.
I suppose that i've to use std::integer_sequence, passing an integer sequence to the linearise function and the list of the indexes, but i don't know how to do it. What i want is something like :
template<template... Dims, std::size_t... Indexes>
auto linearise(std::integer_sequence<int, Dims...> dims, Indexes... indexes)
{
return (index * multiply_but_last(dims)) + ...;
}
With multiply_but_last multiplying all remaining dimension but the last (i see how to implement with a constexpr variadic template function such as for factorise, but i don't understand if it is possible with std::integer_sequence).
I'm a novice in variadic template manipulation and std::integer_sequence and I think that I'm missing something. Is it possible to get the linear index computation without overhead (i.e. like if the operation has been hand-writtent) ?
Thanks you very much for your help.

Answer 1

Following might help:
#include <array>
#include <cassert>
#include <iostream>
template <std::size_t, typename T> using alwaysT_t = T;
template<typename T, std::size_t ... Dims>
class MultiArray
{
public:
const T& operator() (alwaysT_t<Dims, std::size_t>... indexes) const
{
return values[computeIndex(indexes...)];
}
T& operator() (alwaysT_t<Dims, std::size_t>... indexes)
{
return values[computeIndex(indexes...)];
}
private:
size_t computeIndex(alwaysT_t<Dims, std::size_t>... indexes_args) const
{
constexpr std::size_t dimensions[] = {Dims...};
std::size_t indexes[] = {indexes_args...};
size_t index = 0;
size_t mul = 1;
for (size_t i = 0; i != sizeof...(Dims); ++i) {
assert(indexes[i] < dimensions[i]);
index += indexes[i] * mul;
mul *= dimensions[i];
}
assert(index < (Dims * ...));
return index;
}
private:
std::array<T, (Dims * ...)> values;
};
Demo
I replaced your factorize by fold expression (C++17).

Answer 2

I have a very simple function that converts multi-dimensional index to 1D index.
#include <initializer_list>
template<typename ...Args>
inline constexpr size_t IDX(const Args... params) {
constexpr size_t NDIMS = sizeof...(params) / 2 + 1;
std::initializer_list<int> args{params...};
auto ibegin = args.begin();
auto sbegin = ibegin + NDIMS;
size_t res = 0;
for (int dim = 0; dim < NDIMS; ++dim) {
size_t factor = dim > 0 ? sbegin[dim - 1] : 0;
res = res * factor + ibegin[dim];
}
return res;
}
You may need to add "-Wno-c++11-narrowing" flag to your compiler if you see a warning like non-constant-expression cannot be narrowed from type 'int'.
Example usage:
2D array
int array2D[rows*cols];
// Usually, you need to access the element at (i,j) like this:
int elem = array2D[i * cols + j]; // = array2D[i,j]
// Now, you can do it like this:
int elem = array2D[IDX(i,j,cols)]; // = array2D[i,j]
3D array
int array3D[rows*cols*depth];
// Usually, you need to access the element at (i,j,k) like this:
int elem = array3D[(i * cols + j) * depth + k]; // = array3D[i,j,k]
// Now, you can do it like this:
int elem = array3D[IDX(i,j,k,cols,depth)]; // = array3D[i,j,k]
ND array
// shapes = {s1,s2,...,sn}
T arrayND[s1*s2*...*sn]
// indices = {e1,e2,...,en}
T elem = arrayND[IDX(e1,e2,...,en,s2,...,sn)] // = arrayND[e1,e2,...,en]
Note that the shape parameters passed to IDX(...) begins at the second shape, which is s2 in this case.
BTW: This implementation requires C++ 14.