include/ceres/internal/integer_sequence_algorithm.h

// Ceres Solver - A fast non-linear least squares minimizer
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// http://ceres-solver.org/
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// Author: jodebo_beck@gmx.de (Johannes Beck)
//
// Algorithms to be used together with integer_sequence, like computing the sum
// or the exclusive scan (sometimes called exclusive prefix sum) at compile
// time.

#ifndef CERES_PUBLIC_INTERNAL_INTEGER_SEQUENCE_ALGORITHM_H_
#define CERES_PUBLIC_INTERNAL_INTEGER_SEQUENCE_ALGORITHM_H_

#include <utility>

namespace ceres {
namespace internal {

// Implementation of calculating the sum of an integer sequence.
// Recursively instantiate SumImpl and calculate the sum of the N first
// numbers. This reduces the number of instantiations and speeds up
// compilation.
//
// Examples:
// 1) integer_sequence<int, 5>:
//   Value = 5
//
// 2) integer_sequence<int, 4, 2>:
//   Value = 4 + 2 + SumImpl<integer_sequence<int>>::Value
//   Value = 4 + 2 + 0
//
// 3) integer_sequence<int, 2, 1, 4>:
//   Value = 2 + 1 + SumImpl<integer_sequence<int, 4>>::Value
//   Value = 2 + 1 + 4
template <typename Seq>
struct SumImpl;

// Strip of and sum the first number.
template <typename T, T N, T... Ns>
struct SumImpl<std::integer_sequence<T, N, Ns...>> {
  static constexpr T Value =
      N + SumImpl<std::integer_sequence<T, Ns...>>::Value;
};

// Strip of and sum the first two numbers.
template <typename T, T N1, T N2, T... Ns>
struct SumImpl<std::integer_sequence<T, N1, N2, Ns...>> {
  static constexpr T Value =
      N1 + N2 + SumImpl<std::integer_sequence<T, Ns...>>::Value;
};

// Strip of and sum the first four numbers.
template <typename T, T N1, T N2, T N3, T N4, T... Ns>
struct SumImpl<std::integer_sequence<T, N1, N2, N3, N4, Ns...>> {
  static constexpr T Value =
      N1 + N2 + N3 + N4 + SumImpl<std::integer_sequence<T, Ns...>>::Value;
};

// Only one number is left. 'Value' is just that number ('recursion' ends).
template <typename T, T N>
struct SumImpl<std::integer_sequence<T, N>> {
  static constexpr T Value = N;
};

// No number is left. 'Value' is the identity element (for sum this is zero).
template <typename T>
struct SumImpl<std::integer_sequence<T>> {
  static constexpr T Value = T(0);
};

// Calculate the sum of an integer sequence. The resulting sum will be stored in
// 'Value'.
template <typename Seq>
class Sum {
  using T = typename Seq::value_type;

 public:
  static constexpr T Value = SumImpl<Seq>::Value;
};

// Implementation of calculating an exclusive scan (exclusive prefix sum) of an
// integer sequence. Exclusive means that the i-th input element is not included
// in the i-th sum. Calculating the exclusive scan for an input array I results
// in the following output R:
//
// R[0] = 0
// R[1] = I[0];
// R[2] = I[0] + I[1];
// R[3] = I[0] + I[1] + I[2];
// ...
//
// In C++17 std::exclusive_scan does the same operation at runtime (but
// cannot be used to calculate the prefix sum at compile time). See
// https://en.cppreference.com/w/cpp/algorithm/exclusive_scan for a more
// detailed description.
//
// Example for integer_sequence<int, 1, 4, 3> (seq := integer_sequence):
//                   T  , Sum,          Ns...   ,          Rs...
// ExclusiveScanImpl<int,   0, seq<int, 1, 4, 3>, seq<int         >>
// ExclusiveScanImpl<int,   1, seq<int,    4, 3>, seq<int, 0      >>
// ExclusiveScanImpl<int,   5, seq<int,       3>, seq<int, 0, 1   >>
// ExclusiveScanImpl<int,   8, seq<int         >, seq<int, 0, 1, 5>>
//                                                ^^^^^^^^^^^^^^^^^
//                                                resulting sequence
template <typename T, T Sum, typename SeqIn, typename SeqOut>
struct ExclusiveScanImpl;

template <typename T, T Sum, T N, T... Ns, T... Rs>
struct ExclusiveScanImpl<T,
                         Sum,
                         std::integer_sequence<T, N, Ns...>,
                         std::integer_sequence<T, Rs...>> {
  using Type =
      typename ExclusiveScanImpl<T,
                                 Sum + N,
                                 std::integer_sequence<T, Ns...>,
                                 std::integer_sequence<T, Rs..., Sum>>::Type;
};

// End of 'recursion'. The resulting type is SeqOut.
template <typename T, T Sum, typename SeqOut>
struct ExclusiveScanImpl<T, Sum, std::integer_sequence<T>, SeqOut> {
  using Type = SeqOut;
};

// Calculates the exclusive scan of the specified integer sequence. The last
// element (the total) is not included in the resulting sequence so they have
// same length. This means the exclusive scan of integer_sequence<int, 1, 2, 3>
// will be integer_sequence<int, 0, 1, 3>.
template <typename Seq>
class ExclusiveScanT {
  using T = typename Seq::value_type;

 public:
  using Type =
      typename ExclusiveScanImpl<T, T(0), Seq, std::integer_sequence<T>>::Type;
};

// Helper to use exclusive scan without typename.
template <typename Seq>
using ExclusiveScan = typename ExclusiveScanT<Seq>::Type;

}  // namespace internal
}  // namespace ceres

#endif  // CERES_PUBLIC_INTERNAL_INTEGER_SEQUENCE_ALGORITHM_H_