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// Copyright (c) 2016 Jeremy Rubin
// Distributed under the MIT software license, see the accompanying
// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef STARWELS_CUCKOOCACHE_H
#define STARWELS_CUCKOOCACHE_H
#include <array>
#include <algorithm>
#include <atomic>
#include <cstring>
#include <cmath>
#include <memory>
#include <vector>
/** namespace CuckooCache provides high performance cache primitives
*
* Summary:
*
* 1) bit_packed_atomic_flags is bit-packed atomic flags for garbage collection
*
* 2) cache is a cache which is performant in memory usage and lookup speed. It
* is lockfree for erase operations. Elements are lazily erased on the next
* insert.
*/
namespace CuckooCache
{
/** bit_packed_atomic_flags implements a container for garbage collection flags
* that is only thread unsafe on calls to setup. This class bit-packs collection
* flags for memory efficiency.
*
* All operations are std::memory_order_relaxed so external mechanisms must
* ensure that writes and reads are properly synchronized.
*
* On setup(n), all bits up to n are marked as collected.
*
* Under the hood, because it is an 8-bit type, it makes sense to use a multiple
* of 8 for setup, but it will be safe if that is not the case as well.
*
*/
class bit_packed_atomic_flags
{
std::unique_ptr<std::atomic<uint8_t>[]> mem;
public:
/** No default constructor as there must be some size */
bit_packed_atomic_flags() = delete;
/**
* bit_packed_atomic_flags constructor creates memory to sufficiently
* keep track of garbage collection information for size entries.
*
* @param size the number of elements to allocate space for
*
* @post bit_set, bit_unset, and bit_is_set function properly forall x. x <
* size
* @post All calls to bit_is_set (without subsequent bit_unset) will return
* true.
*/
explicit bit_packed_atomic_flags(uint32_t size)
{
// pad out the size if needed
size = (size + 7) / 8;
mem.reset(new std::atomic<uint8_t>[size]);
for (uint32_t i = 0; i < size; ++i)
mem[i].store(0xFF);
};
/** setup marks all entries and ensures that bit_packed_atomic_flags can store
* at least size entries
*
* @param b the number of elements to allocate space for
* @post bit_set, bit_unset, and bit_is_set function properly forall x. x <
* b
* @post All calls to bit_is_set (without subsequent bit_unset) will return
* true.
*/
inline void setup(uint32_t b)
{
bit_packed_atomic_flags d(b);
std::swap(mem, d.mem);
}
/** bit_set sets an entry as discardable.
*
* @param s the index of the entry to bit_set.
* @post immediately subsequent call (assuming proper external memory
* ordering) to bit_is_set(s) == true.
*
*/
inline void bit_set(uint32_t s)
{
mem[s >> 3].fetch_or(1 << (s & 7), std::memory_order_relaxed);
}
/** bit_unset marks an entry as something that should not be overwritten
*
* @param s the index of the entry to bit_unset.
* @post immediately subsequent call (assuming proper external memory
* ordering) to bit_is_set(s) == false.
*/
inline void bit_unset(uint32_t s)
{
mem[s >> 3].fetch_and(~(1 << (s & 7)), std::memory_order_relaxed);
}
/** bit_is_set queries the table for discardability at s
*
* @param s the index of the entry to read.
* @returns if the bit at index s was set.
* */
inline bool bit_is_set(uint32_t s) const
{
return (1 << (s & 7)) & mem[s >> 3].load(std::memory_order_relaxed);
}
};
/** cache implements a cache with properties similar to a cuckoo-set
*
* The cache is able to hold up to (~(uint32_t)0) - 1 elements.
*
* Read Operations:
* - contains(*, false)
*
* Read+Erase Operations:
* - contains(*, true)
*
* Erase Operations:
* - allow_erase()
*
* Write Operations:
* - setup()
* - setup_bytes()
* - insert()
* - please_keep()
*
* Synchronization Free Operations:
* - invalid()
* - compute_hashes()
*
* User Must Guarantee:
*
* 1) Write Requires synchronized access (e.g., a lock)
* 2) Read Requires no concurrent Write, synchronized with the last insert.
* 3) Erase requires no concurrent Write, synchronized with last insert.
* 4) An Erase caller must release all memory before allowing a new Writer.
*
*
* Note on function names:
* - The name "allow_erase" is used because the real discard happens later.
* - The name "please_keep" is used because elements may be erased anyways on insert.
*
* @tparam Element should be a movable and copyable type
* @tparam Hash should be a function/callable which takes a template parameter
* hash_select and an Element and extracts a hash from it. Should return
* high-entropy uint32_t hashes for `Hash h; h<0>(e) ... h<7>(e)`.
*/
template <typename Element, typename Hash>
class cache
{
private:
/** table stores all the elements */
std::vector<Element> table;
/** size stores the total available slots in the hash table */
uint32_t size;
/** The bit_packed_atomic_flags array is marked mutable because we want
* garbage collection to be allowed to occur from const methods */
mutable bit_packed_atomic_flags collection_flags;
/** epoch_flags tracks how recently an element was inserted into
* the cache. true denotes recent, false denotes not-recent. See insert()
* method for full semantics.
*/
mutable std::vector<bool> epoch_flags;
/** epoch_heuristic_counter is used to determine when an epoch might be aged
* & an expensive scan should be done. epoch_heuristic_counter is
* decremented on insert and reset to the new number of inserts which would
* cause the epoch to reach epoch_size when it reaches zero.
*/
uint32_t epoch_heuristic_counter;
/** epoch_size is set to be the number of elements supposed to be in a
* epoch. When the number of non-erased elements in an epoch
* exceeds epoch_size, a new epoch should be started and all
* current entries demoted. epoch_size is set to be 45% of size because
* we want to keep load around 90%, and we support 3 epochs at once --
* one "dead" which has been erased, one "dying" which has been marked to be
* erased next, and one "living" which new inserts add to.
*/
uint32_t epoch_size;
/** depth_limit determines how many elements insert should try to replace.
* Should be set to log2(n)*/
uint8_t depth_limit;
/** hash_function is a const instance of the hash function. It cannot be
* static or initialized at call time as it may have internal state (such as
* a nonce).
* */
const Hash hash_function;
/** compute_hashes is convenience for not having to write out this
* expression everywhere we use the hash values of an Element.
*
* We need to map the 32-bit input hash onto a hash bucket in a range [0, size) in a
* manner which preserves as much of the hash's uniformity as possible. Ideally
* this would be done by bitmasking but the size is usually not a power of two.
*
* The naive approach would be to use a mod -- which isn't perfectly uniform but so
* long as the hash is much larger than size it is not that bad. Unfortunately,
* mod/division is fairly slow on ordinary microprocessors (e.g. 90-ish cycles on
* haswell, ARM doesn't even have an instruction for it.); when the divisor is a
* constant the compiler will do clever tricks to turn it into a multiply+add+shift,
* but size is a run-time value so the compiler can't do that here.
*
* One option would be to implement the same trick the compiler uses and compute the
* constants for exact division based on the size, as described in "{N}-bit Unsigned
* Division via {N}-bit Multiply-Add" by Arch D. Robison in 2005. But that code is
* somewhat complicated and the result is still slower than other options:
*
* Instead we treat the 32-bit random number as a Q32 fixed-point number in the range
* [0,1) and simply multiply it by the size. Then we just shift the result down by
* 32-bits to get our bucket number. The results has non-uniformity the same as a
* mod, but it is much faster to compute. More about this technique can be found at
* http://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/
*
* The resulting non-uniformity is also more equally distributed which would be
* advantageous for something like linear probing, though it shouldn't matter
* one way or the other for a cuckoo table.
*
* The primary disadvantage of this approach is increased intermediate precision is
* required but for a 32-bit random number we only need the high 32 bits of a
* 32*32->64 multiply, which means the operation is reasonably fast even on a
* typical 32-bit processor.
*
* @param e the element whose hashes will be returned
* @returns std::array<uint32_t, 8> of deterministic hashes derived from e
*/
inline std::array<uint32_t, 8> compute_hashes(const Element& e) const
{
return {{(uint32_t)((hash_function.template operator()<0>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<1>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<2>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<3>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<4>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<5>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<6>(e) * (uint64_t)size) >> 32),
(uint32_t)((hash_function.template operator()<7>(e) * (uint64_t)size) >> 32)}};
}
/* end
* @returns a constexpr index that can never be inserted to */
constexpr uint32_t invalid() const
{
return ~(uint32_t)0;
}
/** allow_erase marks the element at index n as discardable. Threadsafe
* without any concurrent insert.
* @param n the index to allow erasure of
*/
inline void allow_erase(uint32_t n) const
{
collection_flags.bit_set(n);
}
/** please_keep marks the element at index n as an entry that should be kept.
* Threadsafe without any concurrent insert.
* @param n the index to prioritize keeping
*/
inline void please_keep(uint32_t n) const
{
collection_flags.bit_unset(n);
}
/** epoch_check handles the changing of epochs for elements stored in the
* cache. epoch_check should be run before every insert.
*
* First, epoch_check decrements and checks the cheap heuristic, and then does
* a more expensive scan if the cheap heuristic runs out. If the expensive
* scan succeeds, the epochs are aged and old elements are allow_erased. The
* cheap heuristic is reset to retrigger after the worst case growth of the
* current epoch's elements would exceed the epoch_size.
*/
void epoch_check()
{
if (epoch_heuristic_counter != 0) {
--epoch_heuristic_counter;
return;
}
// count the number of elements from the latest epoch which
// have not been erased.
uint32_t epoch_unused_count = 0;
for (uint32_t i = 0; i < size; ++i)
epoch_unused_count += epoch_flags[i] &&
!collection_flags.bit_is_set(i);
// If there are more non-deleted entries in the current epoch than the
// epoch size, then allow_erase on all elements in the old epoch (marked
// false) and move all elements in the current epoch to the old epoch
// but do not call allow_erase on their indices.
if (epoch_unused_count >= epoch_size) {
for (uint32_t i = 0; i < size; ++i)
if (epoch_flags[i])
epoch_flags[i] = false;
else
allow_erase(i);
epoch_heuristic_counter = epoch_size;
} else
// reset the epoch_heuristic_counter to next do a scan when worst
// case behavior (no intermittent erases) would exceed epoch size,
// with a reasonable minimum scan size.
// Ordinarily, we would have to sanity check std::min(epoch_size,
// epoch_unused_count), but we already know that `epoch_unused_count
// < epoch_size` in this branch
epoch_heuristic_counter = std::max(1u, std::max(epoch_size / 16,
epoch_size - epoch_unused_count));
}
public:
/** You must always construct a cache with some elements via a subsequent
* call to setup or setup_bytes, otherwise operations may segfault.
*/
cache() : table(), size(), collection_flags(0), epoch_flags(),
epoch_heuristic_counter(), epoch_size(), depth_limit(0), hash_function()
{
}
/** setup initializes the container to store no more than new_size
* elements.
*
* setup should only be called once.
*
* @param new_size the desired number of elements to store
* @returns the maximum number of elements storable
**/
uint32_t setup(uint32_t new_size)
{
// depth_limit must be at least one otherwise errors can occur.
depth_limit = static_cast<uint8_t>(std::log2(static_cast<float>(std::max((uint32_t)2, new_size))));
size = std::max<uint32_t>(2, new_size);
table.resize(size);
collection_flags.setup(size);
epoch_flags.resize(size);
// Set to 45% as described above
epoch_size = std::max((uint32_t)1, (45 * size) / 100);
// Initially set to wait for a whole epoch
epoch_heuristic_counter = epoch_size;
return size;
}
/** setup_bytes is a convenience function which accounts for internal memory
* usage when deciding how many elements to store. It isn't perfect because
* it doesn't account for any overhead (struct size, MallocUsage, collection
* and epoch flags). This was done to simplify selecting a power of two
* size. In the expected use case, an extra two bits per entry should be
* negligible compared to the size of the elements.
*
* @param bytes the approximate number of bytes to use for this data
* structure.
* @returns the maximum number of elements storable (see setup()
* documentation for more detail)
*/
uint32_t setup_bytes(size_t bytes)
{
return setup(bytes/sizeof(Element));
}
/** insert loops at most depth_limit times trying to insert a hash
* at various locations in the table via a variant of the Cuckoo Algorithm
* with eight hash locations.
*
* It drops the last tried element if it runs out of depth before
* encountering an open slot.
*
* Thus
*
* insert(x);
* return contains(x, false);
*
* is not guaranteed to return true.
*
* @param e the element to insert
* @post one of the following: All previously inserted elements and e are
* now in the table, one previously inserted element is evicted from the
* table, the entry attempted to be inserted is evicted.
*
*/
inline void insert(Element e)
{
epoch_check();
uint32_t last_loc = invalid();
bool last_epoch = true;
std::array<uint32_t, 8> locs = compute_hashes(e);
// Make sure we have not already inserted this element
// If we have, make sure that it does not get deleted
for (uint32_t loc : locs)
if (table[loc] == e) {
please_keep(loc);
epoch_flags[loc] = last_epoch;
return;
}
for (uint8_t depth = 0; depth < depth_limit; ++depth) {
// First try to insert to an empty slot, if one exists
for (uint32_t loc : locs) {
if (!collection_flags.bit_is_set(loc))
continue;
table[loc] = std::move(e);
please_keep(loc);
epoch_flags[loc] = last_epoch;
return;
}
/** Swap with the element at the location that was
* not the last one looked at. Example:
*
* 1) On first iteration, last_loc == invalid(), find returns last, so
* last_loc defaults to locs[0].
* 2) On further iterations, where last_loc == locs[k], last_loc will
* go to locs[k+1 % 8], i.e., next of the 8 indices wrapping around
* to 0 if needed.
*
* This prevents moving the element we just put in.
*
* The swap is not a move -- we must switch onto the evicted element
* for the next iteration.
*/
last_loc = locs[(1 + (std::find(locs.begin(), locs.end(), last_loc) - locs.begin())) & 7];
std::swap(table[last_loc], e);
// Can't std::swap a std::vector<bool>::reference and a bool&.
bool epoch = last_epoch;
last_epoch = epoch_flags[last_loc];
epoch_flags[last_loc] = epoch;
// Recompute the locs -- unfortunately happens one too many times!
locs = compute_hashes(e);
}
}
/* contains iterates through the hash locations for a given element
* and checks to see if it is present.
*
* contains does not check garbage collected state (in other words,
* garbage is only collected when the space is needed), so:
*
* insert(x);
* if (contains(x, true))
* return contains(x, false);
* else
* return true;
*
* executed on a single thread will always return true!
*
* This is a great property for re-org performance for example.
*
* contains returns a bool set true if the element was found.
*
* @param e the element to check
* @param erase
*
* @post if erase is true and the element is found, then the garbage collect
* flag is set
* @returns true if the element is found, false otherwise
*/
inline bool contains(const Element& e, const bool erase) const
{
std::array<uint32_t, 8> locs = compute_hashes(e);
for (uint32_t loc : locs)
if (table[loc] == e) {
if (erase)
allow_erase(loc);
return true;
}
return false;
}
};
} // namespace CuckooCache
#endif // STARWELS_CUCKOOCACHE_H