integer_sort.hpp
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// Details for templated Spreadsort-based integer_sort.
// Copyright Steven J. Ross 2001 - 2014.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// See http://www.boost.org/libs/sort for library home page.
/*
Some improvements suggested by:
Phil Endecott and Frank Gennari
*/
#ifndef BOOST_SORT_SPREADSORT_DETAIL_INTEGER_SORT_HPP
#define BOOST_SORT_SPREADSORT_DETAIL_INTEGER_SORT_HPP
#include <algorithm>
#include <vector>
#include <limits>
#include <functional>
#include <boost/static_assert.hpp>
#include <boost/serialization/static_warning.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/sort/spreadsort/detail/constants.hpp>
#include <boost/sort/spreadsort/detail/spreadsort_common.hpp>
#include <boost/cstdint.hpp>
//! \cond DETAIL
namespace boost {
namespace sort {
namespace detail {
// Return true if the list is sorted. Otherwise, find the minimum and
// maximum using <.
template <class RandomAccessIter>
inline bool
is_sorted_or_find_extremes(RandomAccessIter current, RandomAccessIter last,
RandomAccessIter & max, RandomAccessIter & min)
{
min = max = current;
//This assumes we have more than 1 element based on prior checks.
while (!(*(current + 1) < *current)) {
//If everything is in sorted order, return
if (++current == last - 1)
return true;
}
//The maximum is the last sorted element
max = current;
//Start from the first unsorted element
while (++current < last) {
if (*max < *current)
max = current;
else if (*current < *min)
min = current;
}
return false;
}
// Return true if the list is sorted. Otherwise, find the minimum and
// maximum.
// Use a user-defined comparison operator
template <class RandomAccessIter, class Compare>
inline bool
is_sorted_or_find_extremes(RandomAccessIter current, RandomAccessIter last,
RandomAccessIter & max, RandomAccessIter & min, Compare comp)
{
min = max = current;
while (!comp(*(current + 1), *current)) {
//If everything is in sorted order, return
if (++current == last - 1)
return true;
}
//The maximum is the last sorted element
max = current;
while (++current < last) {
if (comp(*max, *current))
max = current;
else if (comp(*current, *min))
min = current;
}
return false;
}
//Gets a non-negative right bit shift to operate as a logarithmic divisor
template<unsigned log_mean_bin_size>
inline int
get_log_divisor(size_t count, int log_range)
{
int log_divisor;
//If we can finish in one iteration without exceeding either
//(2 to the max_finishing_splits) or n bins, do so
if ((log_divisor = log_range - rough_log_2_size(count)) <= 0 &&
log_range <= max_finishing_splits)
log_divisor = 0;
else {
//otherwise divide the data into an optimized number of pieces
log_divisor += log_mean_bin_size;
//Cannot exceed max_splits or cache misses slow down bin lookups
if ((log_range - log_divisor) > max_splits)
log_divisor = log_range - max_splits;
}
return log_divisor;
}
//Implementation for recursive integer sorting
template <class RandomAccessIter, class Div_type, class Size_type>
inline void
spreadsort_rec(RandomAccessIter first, RandomAccessIter last,
std::vector<RandomAccessIter> &bin_cache, unsigned cache_offset
, size_t *bin_sizes)
{
//This step is roughly 10% of runtime, but it helps avoid worst-case
//behavior and improve behavior with real data
//If you know the maximum and minimum ahead of time, you can pass those
//values in and skip this step for the first iteration
RandomAccessIter max, min;
if (is_sorted_or_find_extremes(first, last, max, min))
return;
RandomAccessIter * target_bin;
unsigned log_divisor = get_log_divisor<int_log_mean_bin_size>(
last - first, rough_log_2_size(Size_type((*max >> 0) - (*min >> 0))));
Div_type div_min = *min >> log_divisor;
Div_type div_max = *max >> log_divisor;
unsigned bin_count = unsigned(div_max - div_min) + 1;
unsigned cache_end;
RandomAccessIter * bins =
size_bins(bin_sizes, bin_cache, cache_offset, cache_end, bin_count);
//Calculating the size of each bin; this takes roughly 10% of runtime
for (RandomAccessIter current = first; current != last;)
bin_sizes[size_t((*(current++) >> log_divisor) - div_min)]++;
//Assign the bin positions
bins[0] = first;
for (unsigned u = 0; u < bin_count - 1; u++)
bins[u + 1] = bins[u] + bin_sizes[u];
RandomAccessIter nextbinstart = first;
//Swap into place
//This dominates runtime, mostly in the swap and bin lookups
for (unsigned u = 0; u < bin_count - 1; ++u) {
RandomAccessIter * local_bin = bins + u;
nextbinstart += bin_sizes[u];
//Iterating over each element in this bin
for (RandomAccessIter current = *local_bin; current < nextbinstart;
++current) {
//Swapping elements in current into place until the correct
//element has been swapped in
for (target_bin = (bins + ((*current >> log_divisor) - div_min));
target_bin != local_bin;
target_bin = bins + ((*current >> log_divisor) - div_min)) {
//3-way swap; this is about 1% faster than a 2-way swap
//The main advantage is less copies are involved per item
//put in the correct place
typename std::iterator_traits<RandomAccessIter>::value_type tmp;
RandomAccessIter b = (*target_bin)++;
RandomAccessIter * b_bin = bins + ((*b >> log_divisor) - div_min);
if (b_bin != local_bin) {
RandomAccessIter c = (*b_bin)++;
tmp = *c;
*c = *b;
}
else
tmp = *b;
*b = *current;
*current = tmp;
}
}
*local_bin = nextbinstart;
}
bins[bin_count - 1] = last;
//If we've bucketsorted, the array is sorted and we should skip recursion
if (!log_divisor)
return;
//log_divisor is the remaining range; calculating the comparison threshold
size_t max_count =
get_min_count<int_log_mean_bin_size, int_log_min_split_count,
int_log_finishing_count>(log_divisor);
//Recursing
RandomAccessIter lastPos = first;
for (unsigned u = cache_offset; u < cache_end; lastPos = bin_cache[u],
++u) {
Size_type count = bin_cache[u] - lastPos;
//don't sort unless there are at least two items to Compare
if (count < 2)
continue;
//using std::sort if its worst-case is better
if (count < max_count)
std::sort(lastPos, bin_cache[u]);
else
spreadsort_rec<RandomAccessIter, Div_type, Size_type>(lastPos,
bin_cache[u],
bin_cache,
cache_end,
bin_sizes);
}
}
//Generic bitshift-based 3-way swapping code
template <class RandomAccessIter, class Div_type, class Right_shift>
inline void inner_swap_loop(RandomAccessIter * bins,
const RandomAccessIter & next_bin_start, unsigned ii, Right_shift &rshift
, const unsigned log_divisor, const Div_type div_min)
{
RandomAccessIter * local_bin = bins + ii;
for (RandomAccessIter current = *local_bin; current < next_bin_start;
++current) {
for (RandomAccessIter * target_bin =
(bins + (rshift(*current, log_divisor) - div_min));
target_bin != local_bin;
target_bin = bins + (rshift(*current, log_divisor) - div_min)) {
typename std::iterator_traits<RandomAccessIter>::value_type tmp;
RandomAccessIter b = (*target_bin)++;
RandomAccessIter * b_bin =
bins + (rshift(*b, log_divisor) - div_min);
//Three-way swap; if the item to be swapped doesn't belong
//in the current bin, swap it to where it belongs
if (b_bin != local_bin) {
RandomAccessIter c = (*b_bin)++;
tmp = *c;
*c = *b;
}
//Note: we could increment current once the swap is done in this case
//but that seems to impair performance
else
tmp = *b;
*b = *current;
*current = tmp;
}
}
*local_bin = next_bin_start;
}
//Standard swapping wrapper for ascending values
template <class RandomAccessIter, class Div_type, class Right_shift>
inline void swap_loop(RandomAccessIter * bins,
RandomAccessIter & next_bin_start, unsigned ii, Right_shift &rshift
, const size_t *bin_sizes
, const unsigned log_divisor, const Div_type div_min)
{
next_bin_start += bin_sizes[ii];
inner_swap_loop<RandomAccessIter, Div_type, Right_shift>(bins,
next_bin_start, ii, rshift, log_divisor, div_min);
}
//Functor implementation for recursive sorting
template <class RandomAccessIter, class Div_type, class Right_shift,
class Compare, class Size_type, unsigned log_mean_bin_size,
unsigned log_min_split_count, unsigned log_finishing_count>
inline void
spreadsort_rec(RandomAccessIter first, RandomAccessIter last,
std::vector<RandomAccessIter> &bin_cache, unsigned cache_offset
, size_t *bin_sizes, Right_shift rshift, Compare comp)
{
RandomAccessIter max, min;
if (is_sorted_or_find_extremes(first, last, max, min, comp))
return;
unsigned log_divisor = get_log_divisor<log_mean_bin_size>(last - first,
rough_log_2_size(Size_type(rshift(*max, 0) - rshift(*min, 0))));
Div_type div_min = rshift(*min, log_divisor);
Div_type div_max = rshift(*max, log_divisor);
unsigned bin_count = unsigned(div_max - div_min) + 1;
unsigned cache_end;
RandomAccessIter * bins = size_bins(bin_sizes, bin_cache, cache_offset,
cache_end, bin_count);
//Calculating the size of each bin
for (RandomAccessIter current = first; current != last;)
bin_sizes[unsigned(rshift(*(current++), log_divisor) - div_min)]++;
bins[0] = first;
for (unsigned u = 0; u < bin_count - 1; u++)
bins[u + 1] = bins[u] + bin_sizes[u];
//Swap into place
RandomAccessIter next_bin_start = first;
for (unsigned u = 0; u < bin_count - 1; ++u)
swap_loop<RandomAccessIter, Div_type, Right_shift>(bins, next_bin_start,
u, rshift, bin_sizes, log_divisor, div_min);
bins[bin_count - 1] = last;
//If we've bucketsorted, the array is sorted
if (!log_divisor)
return;
//Recursing
size_t max_count = get_min_count<log_mean_bin_size, log_min_split_count,
log_finishing_count>(log_divisor);
RandomAccessIter lastPos = first;
for (unsigned u = cache_offset; u < cache_end; lastPos = bin_cache[u],
++u) {
size_t count = bin_cache[u] - lastPos;
if (count < 2)
continue;
if (count < max_count)
std::sort(lastPos, bin_cache[u], comp);
else
spreadsort_rec<RandomAccessIter, Div_type, Right_shift, Compare,
Size_type, log_mean_bin_size, log_min_split_count, log_finishing_count>
(lastPos, bin_cache[u], bin_cache, cache_end, bin_sizes, rshift, comp);
}
}
//Functor implementation for recursive sorting with only Shift overridden
template <class RandomAccessIter, class Div_type, class Right_shift,
class Size_type, unsigned log_mean_bin_size,
unsigned log_min_split_count, unsigned log_finishing_count>
inline void
spreadsort_rec(RandomAccessIter first, RandomAccessIter last,
std::vector<RandomAccessIter> &bin_cache, unsigned cache_offset
, size_t *bin_sizes, Right_shift rshift)
{
RandomAccessIter max, min;
if (is_sorted_or_find_extremes(first, last, max, min))
return;
unsigned log_divisor = get_log_divisor<log_mean_bin_size>(last - first,
rough_log_2_size(Size_type(rshift(*max, 0) - rshift(*min, 0))));
Div_type div_min = rshift(*min, log_divisor);
Div_type div_max = rshift(*max, log_divisor);
unsigned bin_count = unsigned(div_max - div_min) + 1;
unsigned cache_end;
RandomAccessIter * bins = size_bins(bin_sizes, bin_cache, cache_offset,
cache_end, bin_count);
//Calculating the size of each bin
for (RandomAccessIter current = first; current != last;)
bin_sizes[unsigned(rshift(*(current++), log_divisor) - div_min)]++;
bins[0] = first;
for (unsigned u = 0; u < bin_count - 1; u++)
bins[u + 1] = bins[u] + bin_sizes[u];
//Swap into place
RandomAccessIter nextbinstart = first;
for (unsigned ii = 0; ii < bin_count - 1; ++ii)
swap_loop<RandomAccessIter, Div_type, Right_shift>(bins, nextbinstart,
ii, rshift, bin_sizes, log_divisor, div_min);
bins[bin_count - 1] = last;
//If we've bucketsorted, the array is sorted
if (!log_divisor)
return;
//Recursing
size_t max_count = get_min_count<log_mean_bin_size, log_min_split_count,
log_finishing_count>(log_divisor);
RandomAccessIter lastPos = first;
for (unsigned u = cache_offset; u < cache_end; lastPos = bin_cache[u],
++u) {
size_t count = bin_cache[u] - lastPos;
if (count < 2)
continue;
if (count < max_count)
std::sort(lastPos, bin_cache[u]);
else
spreadsort_rec<RandomAccessIter, Div_type, Right_shift, Size_type,
log_mean_bin_size, log_min_split_count, log_finishing_count>(lastPos,
bin_cache[u], bin_cache, cache_end, bin_sizes, rshift);
}
}
//Holds the bin vector and makes the initial recursive call
template <class RandomAccessIter, class Div_type>
//Only use spreadsort if the integer can fit in a size_t
inline typename boost::enable_if_c< sizeof(Div_type) <= sizeof(size_t),
void >::type
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type)
{
size_t bin_sizes[1 << max_finishing_splits];
std::vector<RandomAccessIter> bin_cache;
spreadsort_rec<RandomAccessIter, Div_type, size_t>(first, last,
bin_cache, 0, bin_sizes);
}
//Holds the bin vector and makes the initial recursive call
template <class RandomAccessIter, class Div_type>
//Only use spreadsort if the integer can fit in a uintmax_t
inline typename boost::enable_if_c< (sizeof(Div_type) > sizeof(size_t))
&& sizeof(Div_type) <= sizeof(boost::uintmax_t), void >::type
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type)
{
size_t bin_sizes[1 << max_finishing_splits];
std::vector<RandomAccessIter> bin_cache;
spreadsort_rec<RandomAccessIter, Div_type, boost::uintmax_t>(first,
last, bin_cache, 0, bin_sizes);
}
template <class RandomAccessIter, class Div_type>
inline typename boost::disable_if_c< sizeof(Div_type) <= sizeof(size_t)
|| sizeof(Div_type) <= sizeof(boost::uintmax_t), void >::type
//defaulting to std::sort when integer_sort won't work
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type)
{
//Warning that we're using std::sort, even though integer_sort was called
BOOST_STATIC_WARNING( sizeof(Div_type) <= sizeof(size_t) );
std::sort(first, last);
}
//Same for the full functor version
template <class RandomAccessIter, class Div_type, class Right_shift,
class Compare>
//Only use spreadsort if the integer can fit in a size_t
inline typename boost::enable_if_c< sizeof(Div_type) <= sizeof(size_t),
void >::type
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type,
Right_shift shift, Compare comp)
{
size_t bin_sizes[1 << max_finishing_splits];
std::vector<RandomAccessIter> bin_cache;
spreadsort_rec<RandomAccessIter, Div_type, Right_shift, Compare,
size_t, int_log_mean_bin_size, int_log_min_split_count,
int_log_finishing_count>
(first, last, bin_cache, 0, bin_sizes, shift, comp);
}
template <class RandomAccessIter, class Div_type, class Right_shift,
class Compare>
//Only use spreadsort if the integer can fit in a uintmax_t
inline typename boost::enable_if_c< (sizeof(Div_type) > sizeof(size_t))
&& sizeof(Div_type) <= sizeof(boost::uintmax_t), void >::type
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type,
Right_shift shift, Compare comp)
{
size_t bin_sizes[1 << max_finishing_splits];
std::vector<RandomAccessIter> bin_cache;
spreadsort_rec<RandomAccessIter, Div_type, Right_shift, Compare,
boost::uintmax_t, int_log_mean_bin_size,
int_log_min_split_count, int_log_finishing_count>
(first, last, bin_cache, 0, bin_sizes, shift, comp);
}
template <class RandomAccessIter, class Div_type, class Right_shift,
class Compare>
inline typename boost::disable_if_c< sizeof(Div_type) <= sizeof(size_t)
|| sizeof(Div_type) <= sizeof(boost::uintmax_t), void >::type
//defaulting to std::sort when integer_sort won't work
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type,
Right_shift shift, Compare comp)
{
//Warning that we're using std::sort, even though integer_sort was called
BOOST_STATIC_WARNING( sizeof(Div_type) <= sizeof(size_t) );
std::sort(first, last, comp);
}
//Same for the right shift version
template <class RandomAccessIter, class Div_type, class Right_shift>
//Only use spreadsort if the integer can fit in a size_t
inline typename boost::enable_if_c< sizeof(Div_type) <= sizeof(size_t),
void >::type
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type,
Right_shift shift)
{
size_t bin_sizes[1 << max_finishing_splits];
std::vector<RandomAccessIter> bin_cache;
spreadsort_rec<RandomAccessIter, Div_type, Right_shift, size_t,
int_log_mean_bin_size, int_log_min_split_count,
int_log_finishing_count>
(first, last, bin_cache, 0, bin_sizes, shift);
}
template <class RandomAccessIter, class Div_type, class Right_shift>
//Only use spreadsort if the integer can fit in a uintmax_t
inline typename boost::enable_if_c< (sizeof(Div_type) > sizeof(size_t))
&& sizeof(Div_type) <= sizeof(boost::uintmax_t), void >::type
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type,
Right_shift shift)
{
size_t bin_sizes[1 << max_finishing_splits];
std::vector<RandomAccessIter> bin_cache;
spreadsort_rec<RandomAccessIter, Div_type, Right_shift,
boost::uintmax_t, int_log_mean_bin_size,
int_log_min_split_count, int_log_finishing_count>
(first, last, bin_cache, 0, bin_sizes, shift);
}
template <class RandomAccessIter, class Div_type, class Right_shift>
inline typename boost::disable_if_c< sizeof(Div_type) <= sizeof(size_t)
|| sizeof(Div_type) <= sizeof(boost::uintmax_t), void >::type
//defaulting to std::sort when integer_sort won't work
integer_sort(RandomAccessIter first, RandomAccessIter last, Div_type,
Right_shift shift)
{
//Warning that we're using std::sort, even though integer_sort was called
BOOST_STATIC_WARNING( sizeof(Div_type) <= sizeof(size_t) );
std::sort(first, last);
}
}
}
}
//! \endcond
#endif
boost::sort::integer_sort
void integer_sort(RandomAccessIter first, RandomAccessIter last)
Integer sort algorithm using random access iterators. (All variants fall back to std::sort if the dat...
Definition: integer_sort.hpp:78
boost
Definition: constants.hpp:11
boost::sort::detail::int_log_finishing_count
Definition: constants.hpp:30
boost::sort::detail::max_finishing_splits
Definition: constants.hpp:22
boost::sort::detail::get_min_count
size_t get_min_count(unsigned log_range)
Definition: spreadsort_common.hpp:51
boost::sort::detail::int_log_min_split_count
Definition: constants.hpp:27
boost::sort::detail::max_splits
Definition: constants.hpp:19
spreadsort_common.hpp
boost::sort::detail::rough_log_2_size
unsigned rough_log_2_size(const T &input)
Definition: spreadsort_common.hpp:34
boost::sort::detail::is_sorted_or_find_extremes
bool is_sorted_or_find_extremes(RandomAccessIter current, RandomAccessIter last, Div_type &max, Div_type &min, Right_shift rshift)
Definition: float_sort.hpp:54
constants.hpp
boost::sort::detail::size_bins
RandomAccessIter * size_bins(size_t *bin_sizes, std::vector< RandomAccessIter > &bin_cache, unsigned cache_offset, unsigned &cache_end, unsigned bin_count)
Definition: spreadsort_common.hpp:106
boost::sort::detail::int_log_mean_bin_size
Definition: constants.hpp:24