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prime_sieve.cpp
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142 lines (128 loc) · 3.69 KB
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#include <symengine/prime_sieve.h>
#if __cplusplus <= 201703L
#include <ciso646>
#else
#include <version>
#endif
#include <cmath>
#include <valarray>
#include <algorithm>
#include <vector>
#include <iterator>
#ifdef HAVE_SYMENGINE_PRIMESIEVE
#include <primesieve.hpp>
#endif
namespace SymEngine
{
static std::vector<unsigned> &sieve_primes()
{
static std::vector<unsigned> primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
return primes;
}
bool Sieve::_clear = true;
unsigned Sieve::_sieve_size = 32 * 1024 * 8; // 32K in bits
void Sieve::set_clear(bool clear)
{
_clear = clear;
}
void Sieve::clear()
{
std::vector<unsigned> &_primes = sieve_primes();
_primes.erase(_primes.begin() + 10, _primes.end());
}
void Sieve::set_sieve_size(unsigned size)
{
#ifdef HAVE_SYMENGINE_PRIMESIEVE
primesieve::set_sieve_size(size);
#else
_sieve_size = size * 1024 * 8; // size in bits
#endif
}
void Sieve::_extend(unsigned limit)
{
std::vector<unsigned> &_primes = sieve_primes();
#ifdef HAVE_SYMENGINE_PRIMESIEVE
if (_primes.back() < limit)
primesieve::generate_primes(_primes.back() + 1, limit, &_primes);
#else
const unsigned sqrt_limit
= static_cast<unsigned>(std::floor(std::sqrt(limit)));
unsigned start = _primes.back() + 1;
if (limit <= start)
return;
if (sqrt_limit >= start) {
_extend(sqrt_limit);
start = _primes.back() + 1;
}
unsigned segment = _sieve_size;
std::valarray<bool> is_prime(segment);
for (; start <= limit; start += 2 * segment) {
unsigned finish = std::min(start + segment * 2 + 1, limit);
is_prime[std::slice(0, segment, 1)] = true;
// considering only odd integers. An odd number n corresponds to
// n-start/2 in the array.
for (unsigned index = 1; index < _primes.size()
and _primes[index] * _primes[index] <= finish;
++index) {
unsigned n = _primes[index];
unsigned multiple = (start / n + 1) * n;
if (multiple % 2 == 0)
multiple += n;
if (multiple > finish)
continue;
std::slice sl = std::slice((multiple - start) / 2,
1 + (finish - multiple) / (2 * n), n);
// starting from n*n, all the odd multiples of n are marked not
// prime.
is_prime[sl] = false;
}
for (unsigned n = start + 1; n <= finish; n += 2) {
if (is_prime[(n - start) / 2])
_primes.push_back(n);
}
}
#endif
}
void Sieve::generate_primes(std::vector<unsigned> &primes, unsigned limit)
{
_extend(limit);
std::vector<unsigned> &_primes = sieve_primes();
auto it = std::upper_bound(_primes.begin(), _primes.end(), limit);
// find the first position greater than limit and reserve space for the
// primes
primes.reserve(it - _primes.begin());
std::copy(_primes.begin(), it, std::back_inserter(primes));
if (_clear)
clear();
}
Sieve::iterator::iterator(unsigned max)
{
_limit = max;
_index = 0;
}
Sieve::iterator::iterator()
{
_limit = 0;
_index = 0;
}
Sieve::iterator::~iterator()
{
if (_clear)
Sieve::clear();
}
unsigned Sieve::iterator::next_prime()
{
std::vector<unsigned> &_primes = sieve_primes();
if (_index >= _primes.size()) {
unsigned extend_to = _primes[_index - 1] * 2;
if (_limit > 0 and _limit < extend_to) {
extend_to = _limit;
}
_extend(extend_to);
if (_index >= _primes.size()) { // the next prime is greater than _limit
return _limit + 1;
}
}
return _primes[_index++];
}
}; // namespace SymEngine