如何将指向 boost::multi_array 中元素的指针转换为其索引？

【问题标题】：How to convert a pointer to an element in boost::multi_array into its indices?如何将指向 boost::multi_array 中元素的指针转换为其索引？
【发布时间】：2021-05-14 11:02:42
【问题描述】：

在我的程序中，我使用 boost::multi_array ，有时将指向容器内元素的指针转换为其索引很重要，例如，检查该元素是否在任何维度上都不在数组的边界上. 这是过度简化的代码，只是为了解释其含义：

    boost::multi_array<int, 2> arr2d(boost::extents[10][10]);
    const auto data = arr2d.data();
    const auto end = data + arr2d.num_elements();

    for ( auto it = data; it != end; ++it )
    {
        [[maybe_unused]] int v = *it;
        // how to convert it into x and y indices in arr2d?
    }

在 boost::multi_array 中是否有任何内置的有效方法用于指针到索引的转换？或者唯一的可能性是手动分割相对于数据开始的偏移量？

【问题讨论】：

  • 获取两个指针（都指向同一个数组）之间的元素数量的正常方法是减去它们。要获取索引，其中一个指针应该是指向第一个元素的指针。我不知道这如何转化为boost::multi_array。

标签： c++ boost boost-multi-array


【解决方案1】：

图书馆里好像没有这个设施。这有点可惜，但从库的接口/用例来看是有道理的。

我想出了这个解决方案，它考虑了所有存储顺序/方向和基本索引：

template <typename MultiArray,
          typename Element = typename MultiArray::element_type>
auto get_coords(Element const* el, MultiArray const& arr)
{
    using index            = typename MultiArray::index;
    using size_type        = typename MultiArray::size_type;
    auto constexpr NumDims = MultiArray::dimensionality;

    auto raw_index = std::distance(arr.data(), el);
    assert(raw_index >= 0 && size_t(raw_index) < arr.num_elements());

    std::array<index, NumDims> coord {0};
    auto shape    = arr.shape();
    auto strides  = arr.strides();
    auto bases    = arr.index_bases();
    auto& storage = arr.storage_order();

    for (size_type n = 0; n < NumDims; ++n) {
        auto dim = storage.ordering(NumDims - 1 - n); // reverse order
        //fmt::print("dim: {} stride: {}\n", dim, strides[dim]);
        coord[dim] = raw_index / strides[dim];
        raw_index -= coord[dim] * strides[dim];
    }

    for (size_type dim = 0; dim < NumDims; ++dim) {
        coord[dim] += bases[dim];
        if (!storage.ascending(dim))
            coord[dim] += shape[dim] - 1;
    }

    return coord;
}

因为这太逻辑了，所以不测试它我想出了一个严格的测试：

void test(auto arr) {
    iota_n(arr.data(), 1, arr.num_elements());
    fmt::print("\n{} -> {}\n", arr, map(arr));
    check_all(arr);
}

这会导致按内存顺序为每个元素打印映射坐标：

template <typename MultiArray> auto map(MultiArray const& arr)
{
    using Coord =
        std::array<typename MultiArray::index, MultiArray::dimensionality>;

    std::vector<Coord> v;
    for (size_t n = 0; n<arr.num_elements(); ++n) {
        v.push_back(get_coords(arr.data() + n, arr));
    }

    return v;
}

并且还检查所有元素：

void check_element(auto const& el, auto& arr) {
    auto coord = get_coords(&el, arr);
    //fmt::print("{} at {}\n", el, coord);

    // assert same value at same address
    auto& check = deref(arr, coord);
    assert(el == check);
    assert(&el == &check);
    s_elements_checked += 1;
}

void check_all(int    const& el, auto& arr) { check_element(el, arr); }
void check_all(double const& el, auto& arr) { check_element(el, arr); }

void check_all(auto const& rank, auto& arr) {
    for (auto&& rank_or_val : rank) check_all(rank_or_val, arr);
}
void check_all(auto const& arr) {
    for (auto&& rank : arr) check_all(rank, arr);
}

然后我在各种测试矩阵上运行它：

int main() {
    // default
    test(boost::multi_array<int, 2>{boost::extents[3][2], boost::c_storage_order()});
    // FORTRAN
    test(boost::multi_array<int, 2>{boost::extents[3][2], boost::fortran_storage_order()});

    {
        boost::multi_array<int, 3> based{boost::extents[3][2][3], boost::fortran_storage_order()};
        // using standard bases (0)
        test(based);

        // using non-standard bases
        based.reindex(std::array<int, 3> {50,-20,100});
        test(based);
    }

    {
        // with custom storage ordering of dimensions, including descending
        std::array<int, 3> order{2, 0, 1};
        std::array<bool, 3> ascending {false,true,true};
        boost::multi_array<int, 3> custom{
            boost::extents[3][2][4],
            boost::general_storage_order<3>(order.data(), ascending.data())};
        custom.reindex(std::array<int, 3> {100,100,100});
        test(custom);
    }

    fmt::print("Checked a total of {} elements, verified ok\n", s_elements_checked);
}

打印出来

{{1, 2}, {3, 4}, {5, 6}} -> {{0, 0}, {0, 1}, {1, 0}, {1, 1}, { 2, 0}, {2, 1}}

{{1, 4}, {2, 5}, {3, 6}} -> {{0, 0}, {1, 0}, {2, 0}, {0, 1}, { 1, 1}, {2, 1}}

{{{1, 7, 13}, {4, 10, 16}}, {{2, 8, 14}, {5, 11, 17}}, {{3, 9, 15}, {6, 12, 18}}} -> {{0, 0, 0}, {1, 0, 0}, {2, 0, 0}, {0, 1, 0}, {1, 1, 0}, {2, 1, 0}, {0, 0, 1}, {1, 0, 1}, {2, 0, 1}, {0, 1, 1}, {1, 1, 1} , {2, 1, 1}, {0, 0, 2}, {1, 0, 2}, {2, 0, 2}, {0, 1, 2}, {1, 1, 2}, {2 , 1, 2}}

{{{1, 7, 13}, {4, 10, 16}}, {{2, 8, 14}, {5, 11, 17}}, {{3, 9, 15}, {6, 12, 18}}} -> {{50, -20, 100}, {51, -20, 100}, {52, -20, 100}, {50, -19, 100}, {51, -19, 100}, {52, -19, 100}, {50, -20, 101}, {51, -20, 101}, {52, -20, 101} , {50, -19, 101}, {51, -19, 101}, {52, -19, 101}, {50, -20, 102}, {51, -20, 102}, {52, -20, 102}, {50, -19, 102}, {51, -19, 102}, {52, -19, 102}}

{{{9, 10, 11, 12}, {21, 22, 23, 24}}, {{5, 6, 7, 8}, {17, 18, 19, 20}}, {{1, 2, 3, 4}, {13, 14, 15, 16}}} -> {{102, 100, 100}, {102, 100, 101}, {102, 100, 102}, {102, 100, 103}, {101, 100, 100}, {101, 100, 101}, {101, 100, 102}, {101, 100, 103}, {100, 100, 100}, {100, 100, 101}, {100, 100, 102}, {100, 100, 103}, {102, 101, 100}, {102, 101, 101}, {102, 101, 102}, {102, 101, 103}, {101, 101, 100}, {101, 101, 101}, {101, 101, 102}, {101, 101, 103}, {100, 101, 100}, {100, 101, 101}, {100, 101, 102}, {100, 101, 103}} 共查了72 元素，验证正常

完整列表

Live On Compiler Explorer

#include <boost/multi_array.hpp>
#include <fmt/ranges.h>

template <typename MultiArray,
        typename Element = typename MultiArray::element_type>
auto get_coords(Element const* el, MultiArray const& arr)
{
    using index            = typename MultiArray::index;
    using size_type        = typename MultiArray::size_type;
    auto constexpr NumDims = MultiArray::dimensionality;

    auto raw_index = std::distance(arr.data(), el);
    assert(raw_index >= 0 && size_t(raw_index) < arr.num_elements());

    std::array<index, NumDims> coord {0};
    auto shape    = arr.shape();
    auto strides  = arr.strides();
    auto bases    = arr.index_bases();
    auto& storage = arr.storage_order();

    for (size_type n = 0; n < NumDims; ++n) {
        auto dim = storage.ordering(NumDims - 1 - n); // reverse order
        //fmt::print("dim: {} stride: {}\n", dim, strides[dim]);
        coord[dim] = raw_index / strides[dim];
        raw_index -= coord[dim] * strides[dim];
    }

    for (size_type dim = 0; dim < NumDims; ++dim) {
        coord[dim] += bases[dim];
        if (!storage.ascending(dim))
            coord[dim] += shape[dim] - 1;
    }

    return coord;
}

template <typename MultiArray> auto map(MultiArray const& arr)
{
    using Coord =
        std::array<typename MultiArray::index, MultiArray::dimensionality>;

    std::vector<Coord> v;
    for (size_t n = 0; n<arr.num_elements(); ++n) {
        v.push_back(get_coords(arr.data() + n, arr));
    }

    return v;
}

#include <boost/algorithm/cxx11/iota.hpp>
using boost::algorithm::iota_n;

auto& deref(auto const& arr, std::array<long, 1> coord) { return arr[coord[0]]; }
auto& deref(auto const& arr, std::array<long, 2> coord) { return arr[coord[0]][coord[1]]; }
auto& deref(auto const& arr, std::array<long, 3> coord) { return arr[coord[0]][coord[1]][coord[2]]; }
auto& deref(auto const& arr, std::array<long, 4> coord) { return arr[coord[0]][coord[1]][coord[2]][coord[3]]; }

static int s_elements_checked = 0;

void check_element(auto const& el, auto& arr) {
    auto coord = get_coords(&el, arr);
    //fmt::print("{} at {}\n", el, coord);

    // assert same value at same address
    auto& check = deref(arr, coord);
    assert(el == check);
    assert(&el == &check);
    s_elements_checked += 1;
}

void check_all(int    const& el, auto& arr) { check_element(el, arr); }
void check_all(double const& el, auto& arr) { check_element(el, arr); }

void check_all(auto const& rank, auto& arr) {
    for (auto&& rank_or_val : rank) check_all(rank_or_val, arr);
}
void check_all(auto const& arr) {
    for (auto&& rank : arr) check_all(rank, arr);
}

void test(auto arr) {
    iota_n(arr.data(), 1, arr.num_elements());
    fmt::print("\n{} -> {}\n", arr, map(arr));
    check_all(arr);
}

int main() {
    // default
    test(boost::multi_array<int, 2>{boost::extents[3][2], boost::c_storage_order()});
    // FORTRAN
    test(boost::multi_array<int, 2>{boost::extents[3][2], boost::fortran_storage_order()});

    {
        boost::multi_array<int, 3> based{boost::extents[3][2][3], boost::fortran_storage_order()};
        // using standard bases (0)
        test(based);

        // using non-standard bases
        based.reindex(std::array<int, 3> {50,-20,100});
        test(based);
    }

    {
        // with custom storage ordering of dimensions, including descending
        std::array<int, 3> order{2, 0, 1};
        std::array<bool, 3> ascending {false,true,true};
        boost::multi_array<int, 3> custom{
            boost::extents[3][2][4],
            boost::general_storage_order<3>(order.data(), ascending.data())};
        custom.reindex(std::array<int, 3> {100,100,100});
        test(custom);
    }

    fmt::print("Checked a total of {} elements, verified ok\n", s_elements_checked);
}

【讨论】：

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