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Adding integer sequence and algorithms
This PR adds integer sequence and two algorithms (sum and exclusive scan). Those will be needed to implement a sized cost function using variadic templates. Change-Id: I8e98d7c11fac94286fe9c364633406e59438f059
This commit is contained in:
Johannes Beck
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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2018 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: jodebo_beck@gmx.de (Johannes Beck)
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//
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// Algorithms to be used together with integer_sequence, like computing the sum
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// or the exclusive scan (sometimes called exclusive prefix sum) at compile
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// time.
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#ifndef CERES_PUBLIC_INTERNAL_INTEGER_SEQUENCE_ALGORITHM_H_
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#define CERES_PUBLIC_INTERNAL_INTEGER_SEQUENCE_ALGORITHM_H_
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#include "integer_sequence.h"
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namespace ceres {
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namespace internal {
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// Implementation of calculating the sum of an integer sequence.
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// Recursively instantiate SumImpl and calculate the sum of the N first
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// numbers. This reduces the number of instantiations and speeds up
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// compilation.
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//
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// Examples:
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// 1) integer_sequence<int, 5>:
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// Value = 5
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//
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// 2) integer_sequence<int, 4, 2>:
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// Value = 4 + 2 + SumImpl<integer_sequence<int>>::Value
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// Value = 4 + 2 + 0
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//
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// 3) integer_sequence<int, 2, 1, 4>:
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// Value = 2 + 1 + SumImpl<integer_sequence<int, 4>>::Value
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// Value = 2 + 1 + 4
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template <typename Seq>
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struct SumImpl;
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// Strip of and sum the first number.
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template <typename T, T N, T... Ns>
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struct SumImpl<integer_sequence<T, N, Ns...>> {
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static constexpr T Value = N + SumImpl<integer_sequence<T, Ns...>>::Value;
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};
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// Strip of and sum the first two numbers.
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template <typename T, T N1, T N2, T... Ns>
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struct SumImpl<integer_sequence<T, N1, N2, Ns...>> {
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static constexpr T Value =
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N1 + N2 + SumImpl<integer_sequence<T, Ns...>>::Value;
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};
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// Strip of and sum the first four numbers.
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template <typename T, T N1, T N2, T N3, T N4, T... Ns>
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struct SumImpl<integer_sequence<T, N1, N2, N3, N4, Ns...>> {
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static constexpr T Value =
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N1 + N2 + N3 + N4 + SumImpl<integer_sequence<T, Ns...>>::Value;
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};
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// Only one number is left. 'Value' is just that number ('recursion' ends).
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template <typename T, T N>
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struct SumImpl<integer_sequence<T, N>> {
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static constexpr T Value = N;
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};
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// No number is left. 'Value' is the identity element (for sum this is zero).
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template <typename T>
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struct SumImpl<integer_sequence<T>> {
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static constexpr T Value = T(0);
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};
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// Calculate the sum of an integer sequence. The resulting sum will be stored in
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// 'Value'.
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template <typename Seq>
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class Sum {
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using T = typename Seq::value_type;
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public:
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static constexpr T Value = SumImpl<Seq>::Value;
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};
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// Implementation of calculating an exclusive scan (exclusive prefix sum) of an
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// integer sequence. Exclusive means that the i-th input element is not included
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// in the i-th sum. Calculating the exclusive scan for an input array I results
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// in the following output R:
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//
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// R[0] = 0
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// R[1] = I[0];
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// R[2] = I[0] + I[1];
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// R[3] = I[0] + I[1] + I[2];
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// ...
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//
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// In C++17 std::exclusive_scan does the same operation at runtime (but
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// cannot be used to calculate the prefix sum at compile time). See
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// https://en.cppreference.com/w/cpp/algorithm/exclusive_scan for a more
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// detailed description.
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//
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// Example for integer_sequence<int, 1, 4, 3> (seq := integer_sequence):
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// T , Sum, Ns... , Rs...
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// ExclusiveScanImpl<int, 0, seq<int, 1, 4, 3>, seq<int >>
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// ExclusiveScanImpl<int, 1, seq<int, 4, 3>, seq<int, 0 >>
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// ExclusiveScanImpl<int, 5, seq<int, 3>, seq<int, 0, 1 >>
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// ExclusiveScanImpl<int, 8, seq<int >, seq<int, 0, 1, 5>>
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// ^^^^^^^^^^^^^^^^^
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// resulting sequence
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template <typename T, T Sum, typename SeqIn, typename SeqOut>
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struct ExclusiveScanImpl;
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template <typename T, T Sum, T N, T... Ns, T... Rs>
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struct ExclusiveScanImpl<T, Sum, integer_sequence<T, N, Ns...>,
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integer_sequence<T, Rs...>> {
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using Type =
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typename ExclusiveScanImpl<T, Sum + N, integer_sequence<T, Ns...>,
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integer_sequence<T, Rs..., Sum>>::Type;
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};
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// End of 'recursion'. The resulting type is SeqOut.
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template <typename T, T Sum, typename SeqOut>
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struct ExclusiveScanImpl<T, Sum, integer_sequence<T>, SeqOut> {
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using Type = SeqOut;
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};
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// Calculates the exclusive scan of the specified integer sequence. The last
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// element (the total) is not included in the resulting sequence so they have
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// same length. This means the exclusive scan of integer_sequence<int, 1, 2, 3>
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// will be integer_sequence<int, 0, 1, 3>.
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template <typename Seq>
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class ExclusiveScanT {
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using T = typename Seq::value_type;
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public:
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using Type =
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typename ExclusiveScanImpl<T, T(0), Seq, integer_sequence<T>>::Type;
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};
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// Helper to use exclusive scan without typename.
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template <typename Seq>
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using ExclusiveScan = typename ExclusiveScanT<Seq>::Type;
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} // namespace internal
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} // namespace ceres
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#endif // CERES_PUBLIC_INTERNAL_INTEGER_SEQUENCE_ALGORITHM_H_
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