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Make interface of linear_sieve generic #1

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Make interface of linear_sieve generic #1

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cf98424
Make interface of linear_sieve based on output iterator.
jeremy-murphy Sep 8, 2020
29cf8f4
Simplify logic of linear_sieve slightly.
jeremy-murphy Sep 9, 2020
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74 changes: 50 additions & 24 deletions include/boost/math/special_functions/prime_sieve.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -21,30 +21,58 @@
#include <algorithm>
#include <execution>

namespace boost::math { namespace detail

namespace boost::math {

template <typename Integer>
Integer upper_bound_prime_count(Integer x)
{
using std::floor;
using std::log;
constexpr
auto c = 30 * log(113) / 113; // Magic numbers from Wikipedia.
return floor(c * x / log(x));
}

namespace detail
{
// https://mathworld.wolfram.com/SieveofEratosthenes.html
// https://www.cs.utexas.edu/users/misra/scannedPdf.dir/linearSieve.pdf
template<class Integer, class Container>
void linear_sieve(Integer upper_bound, Container &resultant_primes)
template<class Integer, class OutputIterator>
OutputIterator linear_sieve(Integer upper_bound, OutputIterator resultant_primes)
{
std::size_t least_divisors_size{static_cast<std::size_t>(upper_bound + 1)};
auto const least_divisors_size = upper_bound + 1;
std::unique_ptr<Integer[]> least_divisors{new Integer[least_divisors_size]{0}};

for (std::size_t i{2}; i < upper_bound; ++i)
for (Integer i{2}; i < upper_bound; ++i)
{
if (least_divisors[i] == 0)
{
least_divisors[i] = i;
resultant_primes.emplace_back(i);
*resultant_primes++ = i;
}

for (std::size_t j{}; j < resultant_primes.size() && i * resultant_primes[j] <= upper_bound &&
resultant_primes[j] <= least_divisors[i] && j < least_divisors_size; ++j)
for (Integer j = 0; j < i - 1
&& i * resultant_primes[j] <= upper_bound
&& resultant_primes[j] <= least_divisors[i]
&& j < least_divisors_size; ++j)
{
least_divisors[i * static_cast<std::size_t>(resultant_primes[j])] = resultant_primes[j];
least_divisors[i * resultant_primes[j]] = resultant_primes[j];
}
}

return resultant_primes;
}

// This wrapper function could possibly drop the _container suffix with the
// judicious use of SFINAE.
template<class Integer, class Container>
void linear_sieve_container(Integer upper_bound, Container &resultant_primes)
{
resultant_primes.resize(upper_bound_prime_count(upper_bound));
auto const first = std::begin(resultant_primes);
auto const last = linear_sieve(upper_bound, first);
resultant_primes.resize(last - first);
}

// 4096 is where benchmarked performance of linear_sieve begins to diverge
Expand Down Expand Up @@ -95,10 +123,9 @@ template<class Integer, class Container>
void mask_sieve(Integer lower_bound, Integer upper_bound, Container &resultant_primes)
{
auto limit{std::floor(std::sqrt(static_cast<double>(upper_bound))) + 1};
std::vector<Integer> primes {};
primes.reserve(limit / std::log(limit));
std::vector<Integer> primes;

boost::math::detail::linear_sieve(limit, primes);
boost::math::detail::linear_sieve_container(limit, primes);

boost::math::detail::mask_sieve(lower_bound, upper_bound, primes, resultant_primes);
}
Expand Down Expand Up @@ -187,12 +214,12 @@ void segmented_sieve(Integer lower_bound, Integer upper_bound, Container &result
// Prepare for max value so you do not have to calculate this again
if(limit < linear_sieve_limit<Integer>)
{
boost::math::detail::linear_sieve(static_cast<Integer>(limit), primes);
boost::math::detail::linear_sieve_container(static_cast<Integer>(limit), primes);
}

else
{
boost::math::detail::linear_sieve(linear_sieve_limit<Integer>, primes);
boost::math::detail::linear_sieve_container(linear_sieve_limit<Integer>, primes);
boost::math::detail::segmented_sieve(linear_sieve_limit<Integer>, limit, primes, primes);
}

Expand Down Expand Up @@ -251,22 +278,21 @@ void prime_sieve(ExecutionPolicy&& policy, Integer upper_bound, Container &prime

if(upper_bound <= linear_sieve_limit<Integer>)
{
boost::math::detail::linear_sieve(static_cast<Integer>(upper_bound), primes);
boost::math::detail::linear_sieve_container(static_cast<Integer>(upper_bound), primes);
}

else if(typeid(policy) == typeid(std::execution::seq))
{
boost::math::detail::linear_sieve(linear_sieve_limit<Integer>, primes);
boost::math::detail::linear_sieve_container(linear_sieve_limit<Integer>, primes);
boost::math::detail::sequential_segmented_sieve(linear_sieve_limit<Integer>, upper_bound, primes);
}

else
{
std::vector<Integer> small_primes {};
small_primes.reserve(1028);
std::vector<Integer> small_primes;

std::thread t1([&small_primes] {
boost::math::detail::linear_sieve(static_cast<Integer>(linear_sieve_limit<Integer> * 2), small_primes);
boost::math::detail::linear_sieve_container(static_cast<Integer>(linear_sieve_limit<Integer> * 2), small_primes);
});
std::thread t2([upper_bound, &primes] {
boost::math::detail::segmented_sieve(static_cast<Integer>(linear_sieve_limit<Integer> * 2), upper_bound, primes);
Expand Down Expand Up @@ -298,14 +324,14 @@ void prime_range(ExecutionPolicy&& policy, Integer lower_bound, Integer upper_bo

if(upper_bound <= linear_sieve_limit<Integer>)
{
boost::math::detail::linear_sieve(static_cast<Integer>(upper_bound), primes);
boost::math::detail::linear_sieve_container(static_cast<Integer>(upper_bound), primes);
}

else if(typeid(policy) == typeid(std::execution::seq))
{
if(limit <= linear_sieve_limit<Integer>)
{
boost::math::detail::linear_sieve(limit, primes);
boost::math::detail::linear_sieve_container(limit, primes);

if(lower_bound <= limit)
{
Expand All @@ -320,7 +346,7 @@ void prime_range(ExecutionPolicy&& policy, Integer lower_bound, Integer upper_bo

else
{
boost::math::detail::linear_sieve(linear_sieve_limit<Integer>, primes);
boost::math::detail::linear_sieve_container(linear_sieve_limit<Integer>, primes);
boost::math::detail::sequential_segmented_sieve(linear_sieve_limit<Integer>, limit, primes);
boost::math::detail::sequential_segmented_sieve(lower_bound, upper_bound, primes);
}
Expand All @@ -335,7 +361,7 @@ void prime_range(ExecutionPolicy&& policy, Integer lower_bound, Integer upper_bo
small_primes.reserve(1028);

std::thread t1([limit, &small_primes] {
boost::math::detail::linear_sieve(limit, small_primes);
boost::math::detail::linear_sieve_container(limit, small_primes);
});

std::thread t2([lower_bound, limit, upper_bound, &primes] {
Expand All @@ -361,7 +387,7 @@ void prime_range(ExecutionPolicy&& policy, Integer lower_bound, Integer upper_bo
boost::math::prime_reserve(limit, small_primes);

std::thread t1([&small_primes] {
boost::math::detail::linear_sieve(static_cast<Integer>(linear_sieve_limit<Integer> * 2), small_primes);
boost::math::detail::linear_sieve_container(static_cast<Integer>(linear_sieve_limit<Integer> * 2), small_primes);
});

std::thread t2([limit, &primes] {
Expand Down
14 changes: 4 additions & 10 deletions reporting/performance/prime_sieve_performance.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -74,22 +74,16 @@ void interval_sieve(benchmark::State& state)
state.SetComplexityN(state.range(0));
}

// Complete Implementations
template<class ExecuitionPolicy, class Integer, class Container>
inline auto prime_sieve_helper(ExecuitionPolicy policy, Integer upper, Container primes)
{
boost::math::prime_sieve(policy, upper, primes);
return primes;
}

template <class Integer>
void prime_sieve(benchmark::State& state)
{
Integer upper = static_cast<Integer>(state.range(0));
std::vector<Integer> primes;

for(auto _ : state)
{
std::vector<Integer> primes;
benchmark::DoNotOptimize(prime_sieve_helper(std::execution::par, upper, primes));
primes.clear();
boost::math::prime_sieve(std::execution::par, upper, primes);
}
state.SetComplexityN(state.range(0));
}
Expand Down