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///
/// @file PiTable.hpp
/// @brief The PiTable class is a compressed lookup table of prime
/// counts. Each bit of the lookup table corresponds to an
/// integer that is not divisible by 2, 3 and 5. The 8 bits of
/// each byte correspond to the offsets { 1, 7, 11, 13, 17, 19,
/// 23, 29 }. Since our lookup table uses the uint64_t data
/// type, one array element (8 bytes) corresponds to an
/// interval of size 30 * 8 = 240.
///
/// Copyright (C) 2024 Kim Walisch, <kim.walisch@gmail.com>
///
/// This file is distributed under the BSD License. See the COPYING
/// file in the top level directory.
///
#ifndef PITABLE_HPP
#define PITABLE_HPP
#include <BitSieve240.hpp>
#include <popcnt.hpp>
#include <macros.hpp>
#include <Vector.hpp>
#include <stdint.h>
namespace primecount {
class PiTable : public BitSieve240
{
public:
PiTable(uint64_t max_x, int threads);
uint64_t size() const
{
return max_x_ + 1;
}
static int64_t max_cached()
{
return pi_cache_.size() * 240 - 1;
}
/// Get number of primes <= x
ALWAYS_INLINE int64_t operator[](uint64_t x) const
{
ASSERT(x <= max_x_);
if (x < pi_tiny_.size())
return pi_tiny_[x];
uint64_t count = pi_[x / 240].count;
uint64_t bits = pi_[x / 240].bits;
uint64_t bitmask = unset_larger_[x % 240];
return count + popcnt64(bits & bitmask);
}
/// Get number of primes <= x
static int64_t pi_cache(uint64_t x)
{
if (x < pi_tiny_.size())
return pi_tiny_[x];
uint64_t count = pi_cache_[x / 240].count;
uint64_t bits = pi_cache_[x / 240].bits;
uint64_t bitmask = unset_larger_[x % 240];
return count + popcnt64(bits & bitmask);
}
private:
struct pi_t
{
uint64_t count;
uint64_t bits;
};
void init(uint64_t limit, uint64_t cache_limit, int threads);
void init_bits(uint64_t low, uint64_t high, uint64_t thread_num);
void init_count(uint64_t low, uint64_t high, uint64_t thread_num);
static const Array<pi_t, 128> pi_cache_;
Vector<pi_t> pi_;
Vector<uint64_t> counts_;
uint64_t max_x_;
};
} // namespace
#endif
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