sort.h

// Copyright (C) 2021-2025 Igor Baratta and Paul T. Kühner
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier:    LGPL-3.0-or-later
 
#pragma once
 
#include <algorithm>
#include <bit>
#include <cassert>
#include <concepts>
#include <cstdint>
#include <functional>
#include <iterator>
#include <limits>
#include <numeric>
#include <span>
#include <type_traits>
#include <utility>
#include <vector>
 
namespace dolfinx
{
 
struct __unsigned_projection
{
  // Transforms the projected value to an unsigned int (if signed), while
  // maintaining relative order by
  //    x ↦ x + |std::numeric_limits<I>::min()|
  template <std::signed_integral T>
  constexpr std::make_unsigned_t<T> operator()(T e) const noexcept
  {
    using uT = std::make_unsigned_t<T>;
 
    // Assert binary structure for bit shift
    static_assert(static_cast<uT>(std::numeric_limits<T>::min())
                      + static_cast<uT>(std::numeric_limits<T>::max())
                  == static_cast<uT>(T(-1)));
    static_assert(std::numeric_limits<uT>::digits
                  == std::numeric_limits<T>::digits + 1);
    static_assert(std::bit_cast<uT>(std::numeric_limits<T>::min())
                  == (uT(1) << (sizeof(T) * 8 - 1)));
 
    return std::bit_cast<uT>(std::forward<T>(e))
           ^ (uT(1) << (sizeof(T) * 8 - 1));
  }
};

inline constexpr __unsigned_projection unsigned_projection{};
 
struct __radix_sort
{
  template <std::ranges::random_access_range R, typename P = std::identity,
            std::make_unsigned_t<std::remove_cvref_t<
                std::invoke_result_t<P, std::iter_value_t<R>>>>
                BITS
            = 8>
    requires std::integral<decltype(BITS)>
  constexpr void operator()(R&& range, P proj = {}) const
  {
    // value type
    using T = std::iter_value_t<R>;
 
    // index type (if no projection is provided it holds I == T)
    using I = std::remove_cvref_t<std::invoke_result_t<P, T>>;
    using uI = std::make_unsigned_t<I>;
 
    if constexpr (!std::is_same_v<uI, I>)
    {
      __radix_sort()(std::forward<R>(range), [&](const T& e) -> uI
                     { return unsigned_projection(proj(e)); });
      return;
    }
 
    if (range.size() <= 1)
      return;
 
    uI max_value = proj(*std::ranges::max_element(range, std::less{}, proj));
 
    // Sort N bits at a time
    constexpr uI bucket_size = 1 << BITS;
    uI mask = (uI(1) << BITS) - 1;
 
    // Compute number of iterations, most significant digit (N bits) of
    // maxvalue
    I its = 0;
 
    // optimize for case where all first bits are set - then order will not
    // depend on it
    bool all_first_bit = std::ranges::all_of(
        range, [&](const auto& e)
        { return proj(e) & (uI(1) << (sizeof(uI) * 8 - 1)); });
    if (all_first_bit)
      max_value = max_value & ~(uI(1) << (sizeof(uI) * 8 - 1));
 
    while (max_value)
    {
      max_value >>= BITS;
      its++;
    }
 
    // Adjacency list arrays for computing insertion position
    std::array<I, bucket_size> counter;
    std::array<I, bucket_size + 1> offset;
 
    uI mask_offset = 0;
    std::vector<T> buffer(range.size());
    std::span<T> current_perm = range;
    std::span<T> next_perm = buffer;
    for (I i = 0; i < its; i++)
    {
      // Zero counter array
      std::ranges::fill(counter, 0);
 
      // Count number of elements per bucket
      for (const auto& c : current_perm)
        counter[(proj(c) & mask) >> mask_offset]++;
 
      // Prefix sum to get the inserting position
      offset[0] = 0;
      std::partial_sum(counter.begin(), counter.end(),
                       std::next(offset.begin()));
      for (const auto& c : current_perm)
      {
        uI bucket = (proj(c) & mask) >> mask_offset;
        uI new_pos = offset[bucket + 1] - counter[bucket];
        next_perm[new_pos] = c;
        counter[bucket]--;
      }
 
      mask = mask << BITS;
      mask_offset += BITS;
 
      std::swap(current_perm, next_perm);
    }
 
    // Copy data back to array
    if (its % 2 != 0)
      std::ranges::copy(buffer, range.begin());
  }
};

inline constexpr __radix_sort radix_sort{};

template <typename T, int BITS = 16>
std::vector<std::int32_t> sort_by_perm(std::span<const T> x, std::size_t shape1)
{
  static_assert(std::is_integral_v<T>, "Integral required.");
 
  if (x.empty())
    return std::vector<std::int32_t>{};
 
  assert(shape1 > 0);
  assert(x.size() % shape1 == 0);
  const std::size_t shape0 = x.size() / shape1;
  std::vector<std::int32_t> perm(shape0);
  std::iota(perm.begin(), perm.end(), 0);
 
  // Sort by each column, right to left. Col 0 has the most significant
  // "digit".
  std::vector<T> column(shape0);
  for (std::size_t i = 0; i < shape1; ++i)
  {
    std::size_t col = shape1 - 1 - i;
    for (std::size_t j = 0; j < shape0; ++j)
      column[j] = x[j * shape1 + col];
 
    radix_sort(perm, [&column](auto index) { return column[index]; });
  }
 
  return perm;
}
 
} // namespace dolfinx