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///
/// @file SegmentedPiTable.hpp
/// @brief The A and C formulas in Xavier Gourdon's prime counting
/// algorithm require looking up PrimePi[x] values with
/// x < x^(1/2). Since a PrimePi[x] lookup table of size x^(1/2)
/// would use too much memory we need a segmented PrimePi[x]
/// lookup table that uses only O(x^(1/4)) memory.
///
/// The SegmentedPiTable 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.
///
/// The algorithm of the easy special leaves and the usage of
/// the SegmentedPiTable are described in more detail in:
/// https://github.com/kimwalisch/primecount/blob/master/doc/Easy-Special-Leaves.md
///
/// Copyright (C) 2022 Kim Walisch, <kim.walisch@gmail.com>
///
/// This file is distributed under the BSD License. See the COPYING
/// file in the top level directory.
///
#ifndef SEGMENTEDPITABLE_HPP
#define SEGMENTEDPITABLE_HPP
#include <BitSieve240.hpp>
#include <macros.hpp>
#include <pod_vector.hpp>
#include <popcnt.hpp>
#include <stdint.h>
#include <algorithm>
namespace primecount {
class SegmentedPiTable : public BitSieve240
{
public:
void init(uint64_t low, uint64_t high);
int64_t low() const
{
return low_;
}
int64_t high() const
{
return high_;
}
static constexpr int64_t numbers_per_byte()
{
return 240 / sizeof(pi_t);
}
/// Make sure size % 240 == 0
static int64_t get_segment_size(uint64_t size)
{
size = std::max<uint64_t>(240, size);
if (size % 240)
size += 240 - size % 240;
return size;
}
/// Get number of primes <= x
ALWAYS_INLINE int64_t operator[](uint64_t x) const
{
ASSERT(x >= low_);
ASSERT(x < high_);
if_unlikely(x < pi_tiny_.size())
return pi_tiny_[x];
x -= low_;
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);
}
private:
void init_bits();
void init_count(uint64_t pi_low);
struct pi_t
{
uint64_t count;
uint64_t bits;
};
pod_vector<pi_t> pi_;
uint64_t low_ = 0;
uint64_t high_ = 0;
};
} // namespace
#endif
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