ClickHouse/dbms/src/AggregateFunctions/UniquesHashSet.h

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#pragma once
#include <math.h>
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#include <common/Types.h>
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#include <IO/WriteBuffer.h>
#include <IO/WriteHelpers.h>
#include <IO/ReadBuffer.h>
#include <IO/ReadHelpers.h>
#include <IO/VarInt.h>
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#include <Common/HashTable/HashTableAllocator.h>
#include <Common/HashTable/Hash.h>
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/** Approximate calculation of anything, as usual, is constructed according to the following scheme:
* - some data structure is used to calculate the value of X;
* - Not all values are added to the data structure, but only selected ones (according to some selectivity criteria);
* - after processing all elements, the data structure is in some state S;
* - as an approximate value of X, the value calculated according to the maximum likelihood principle is returned:
* at what real value X, the probability of finding the data structure in the obtained state S is maximal.
*/
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/** In particular, what is described below can be found by the name of the BJKST algorithm.
*/
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/** Very simple hash-set for approximate number of unique values.
* Works like this:
* - you can insert UInt64;
* - before insertion, first the hash function UInt64 -> UInt32 is calculated;
* - the original value is not saved (lost);
* - further all operations are made with these hashes;
* - hash table is constructed according to the scheme:
* - open addressing (one buffer, position in buffer is calculated by taking remainder of division by its size);
* - linear probing (if the cell already has a value, then the cell following it is taken, etc.);
* - the missing value is zero-encoded; to remember presence of zero in set, separate variable of type bool is used;
* - buffer growth by 2 times when filling more than 50%;
* - if the set has more UNIQUES_HASH_MAX_SIZE elements, then all the elements are removed from the set,
* not divisible by 2, and then all elements that do not divide by 2 are not inserted into the set;
* - if the situation repeats, then only elements dividing by 4, etc., are taken.
* - the size() method returns an approximate number of elements that have been inserted into the set;
* - there are methods for quick reading and writing in binary and text form.
*/
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/// The maximum degree of buffer size before the values are discarded
#define UNIQUES_HASH_MAX_SIZE_DEGREE 17
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/// The maximum number of elements before the values are discarded
#define UNIQUES_HASH_MAX_SIZE (1ULL << (UNIQUES_HASH_MAX_SIZE_DEGREE - 1))
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/** The number of least significant bits used for thinning. The remaining high-order bits are used to determine the position in the hash table.
* (high-order bits are taken because the younger bits will be constant after dropping some of the values)
*/
#define UNIQUES_HASH_BITS_FOR_SKIP (32 - UNIQUES_HASH_MAX_SIZE_DEGREE)
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/// Initial buffer size degree
#define UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE 4
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/** This hash function is not the most optimal, but UniquesHashSet states counted with it,
* stored in many places on disks (in the Yandex.Metrika), so it continues to be used.
*/
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struct UniquesHashSetDefaultHash
{
size_t operator() (UInt64 x) const
{
return intHash32<0>(x);
}
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};
template <typename Hash = UniquesHashSetDefaultHash>
class UniquesHashSet : private HashTableAllocatorWithStackMemory<(1ULL << UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE) * sizeof(UInt32)>
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{
private:
using Value = UInt64;
using HashValue = UInt32;
using Allocator = HashTableAllocatorWithStackMemory<(1ULL << UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE) * sizeof(UInt32)>;
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UInt32 m_size; /// Number of elements
UInt8 size_degree; /// The size of the table as a power of 2
UInt8 skip_degree; /// Skip elements not divisible by 2 ^ skip_degree
bool has_zero; /// The hash table contains an element with a hash value of 0.
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HashValue * buf;
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#ifdef UNIQUES_HASH_SET_COUNT_COLLISIONS
/// For profiling.
mutable size_t collisions;
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#endif
void alloc(UInt8 new_size_degree)
{
buf = reinterpret_cast<HashValue *>(Allocator::alloc((1ULL << new_size_degree) * sizeof(buf[0])));
size_degree = new_size_degree;
}
void free()
{
if (buf)
{
Allocator::free(buf, buf_size() * sizeof(buf[0]));
buf = nullptr;
}
}
inline size_t buf_size() const { return 1ULL << size_degree; }
inline size_t max_fill() const { return 1ULL << (size_degree - 1); }
inline size_t mask() const { return buf_size() - 1; }
inline size_t place(HashValue x) const { return (x >> UNIQUES_HASH_BITS_FOR_SKIP) & mask(); }
/// The value is divided by 2 ^ skip_degree
inline bool good(HashValue hash) const
{
return hash == ((hash >> skip_degree) << skip_degree);
}
HashValue hash(Value key) const
{
return Hash()(key);
}
/// Delete all values whose hashes do not divide by 2 ^ skip_degree
void rehash()
{
for (size_t i = 0; i < buf_size(); ++i)
{
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if (buf[i])
{
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if (!good(buf[i]))
{
buf[i] = 0;
--m_size;
}
/** After removing the elements, there may have been room for items,
* which were placed further than necessary, due to a collision.
* You need to move them.
*/
else if (i != place(buf[i]))
{
HashValue x = buf[i];
buf[i] = 0;
reinsertImpl(x);
}
}
}
/** We must process first collision resolution chain once again.
* Look at the comment in "resize" function.
*/
for (size_t i = 0; i < buf_size() && buf[i]; ++i)
{
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if (i != place(buf[i]))
{
HashValue x = buf[i];
buf[i] = 0;
reinsertImpl(x);
}
}
}
/// Increase the size of the buffer 2 times or up to new_size_degree, if it is non-zero.
void resize(size_t new_size_degree = 0)
{
size_t old_size = buf_size();
if (!new_size_degree)
new_size_degree = size_degree + 1;
/// Expand the space.
buf = reinterpret_cast<HashValue *>(Allocator::realloc(buf, old_size * sizeof(buf[0]), (1ULL << new_size_degree) * sizeof(buf[0])));
size_degree = new_size_degree;
/** Now some items may need to be moved to a new location.
* The element can stay in place, or move to a new location "on the right",
* or move to the left of the collision resolution chain, because the elements to the left of it have been moved to the new "right" location.
* There is also a special case
* if the element was to be at the end of the old buffer, [ x]
* but is at the beginning because of the collision resolution chain, [o x]
* then after resizing, it will first be out of place again, [ xo ]
* and in order to transfer it to where you need it,
* will have to be after transferring all elements from the old half [ o x ]
* process another tail from the collision resolution chain immediately after it [ o x ]
* This is why || buf[i] below.
*/
for (size_t i = 0; i < old_size || buf[i]; ++i)
{
HashValue x = buf[i];
if (!x)
continue;
size_t place_value = place(x);
/// The element is in its place.
if (place_value == i)
continue;
while (buf[place_value] && buf[place_value] != x)
{
++place_value;
place_value &= mask();
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#ifdef UNIQUES_HASH_SET_COUNT_COLLISIONS
++collisions;
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#endif
}
/// The element remained in its place.
if (buf[place_value] == x)
continue;
buf[place_value] = x;
buf[i] = 0;
}
}
/// Insert a value.
void insertImpl(HashValue x)
{
if (x == 0)
{
m_size += !has_zero;
has_zero = true;
return;
}
size_t place_value = place(x);
while (buf[place_value] && buf[place_value] != x)
{
++place_value;
place_value &= mask();
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#ifdef UNIQUES_HASH_SET_COUNT_COLLISIONS
++collisions;
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#endif
}
if (buf[place_value] == x)
return;
buf[place_value] = x;
++m_size;
}
/** Insert a value into the new buffer that was in the old buffer.
* Used when increasing the size of the buffer, as well as when reading from a file.
*/
void reinsertImpl(HashValue x)
{
size_t place_value = place(x);
while (buf[place_value])
{
++place_value;
place_value &= mask();
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#ifdef UNIQUES_HASH_SET_COUNT_COLLISIONS
++collisions;
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#endif
}
buf[place_value] = x;
}
/** If the hash table is full enough, then do resize.
* If there are too many items, then throw half the pieces until they are small enough.
*/
void shrinkIfNeed()
{
if (unlikely(m_size > max_fill()))
{
if (m_size > UNIQUES_HASH_MAX_SIZE)
{
while (m_size > UNIQUES_HASH_MAX_SIZE)
{
++skip_degree;
rehash();
}
}
else
resize();
}
}
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public:
using value_type = Value;
UniquesHashSet() :
m_size(0),
skip_degree(0),
has_zero(false)
{
alloc(UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE);
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#ifdef UNIQUES_HASH_SET_COUNT_COLLISIONS
collisions = 0;
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#endif
}
UniquesHashSet(const UniquesHashSet & rhs)
: m_size(rhs.m_size), skip_degree(rhs.skip_degree), has_zero(rhs.has_zero)
{
alloc(rhs.size_degree);
memcpy(buf, rhs.buf, buf_size() * sizeof(buf[0]));
}
UniquesHashSet & operator= (const UniquesHashSet & rhs)
{
if (size_degree != rhs.size_degree)
{
free();
alloc(rhs.size_degree);
}
m_size = rhs.m_size;
skip_degree = rhs.skip_degree;
has_zero = rhs.has_zero;
memcpy(buf, rhs.buf, buf_size() * sizeof(buf[0]));
return *this;
}
~UniquesHashSet()
{
free();
}
void insert(Value x)
{
HashValue hash_value = hash(x);
if (!good(hash_value))
return;
insertImpl(hash_value);
shrinkIfNeed();
}
size_t size() const
{
if (0 == skip_degree)
return m_size;
size_t res = m_size * (1ULL << skip_degree);
/** Pseudo-random remainder - in order to be not visible,
* that the number is divided by the power of two.
*/
res += (intHashCRC32(m_size) & ((1ULL << skip_degree) - 1));
/** Correction of a systematic error due to collisions during hashing in UInt32.
* `fixed_res(res)` formula
* - with how many different elements of fixed_res,
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* when randomly scattered across 2^32 buckets,
* filled buckets with average of res is obtained.
*/
size_t p32 = 1ULL << 32;
size_t fixed_res = round(p32 * (log(p32) - log(p32 - res)));
return fixed_res;
}
void merge(const UniquesHashSet & rhs)
{
if (rhs.skip_degree > skip_degree)
{
skip_degree = rhs.skip_degree;
rehash();
}
if (!has_zero && rhs.has_zero)
{
has_zero = true;
++m_size;
shrinkIfNeed();
}
for (size_t i = 0; i < rhs.buf_size(); ++i)
{
if (rhs.buf[i] && good(rhs.buf[i]))
{
insertImpl(rhs.buf[i]);
shrinkIfNeed();
}
}
}
void write(DB::WriteBuffer & wb) const
{
if (m_size > UNIQUES_HASH_MAX_SIZE)
throw Poco::Exception("Cannot write UniquesHashSet: too large size_degree.");
DB::writeIntBinary(skip_degree, wb);
DB::writeVarUInt(m_size, wb);
if (has_zero)
{
HashValue x = 0;
DB::writeIntBinary(x, wb);
}
for (size_t i = 0; i < buf_size(); ++i)
if (buf[i])
DB::writeIntBinary(buf[i], wb);
}
void read(DB::ReadBuffer & rb)
{
has_zero = false;
DB::readIntBinary(skip_degree, rb);
DB::readVarUInt(m_size, rb);
if (m_size > UNIQUES_HASH_MAX_SIZE)
throw Poco::Exception("Cannot read UniquesHashSet: too large size_degree.");
free();
UInt8 new_size_degree = m_size <= 1
? UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE
: std::max(UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE, static_cast<int>(log2(m_size - 1)) + 2);
alloc(new_size_degree);
for (size_t i = 0; i < m_size; ++i)
{
HashValue x = 0;
DB::readIntBinary(x, rb);
if (x == 0)
has_zero = true;
else
reinsertImpl(x);
}
}
void readAndMerge(DB::ReadBuffer & rb)
{
UInt8 rhs_skip_degree = 0;
DB::readIntBinary(rhs_skip_degree, rb);
if (rhs_skip_degree > skip_degree)
{
skip_degree = rhs_skip_degree;
rehash();
}
size_t rhs_size = 0;
DB::readVarUInt(rhs_size, rb);
if (rhs_size > UNIQUES_HASH_MAX_SIZE)
throw Poco::Exception("Cannot read UniquesHashSet: too large size_degree.");
if ((1ULL << size_degree) < rhs_size)
{
UInt8 new_size_degree = std::max(UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE, static_cast<int>(log2(rhs_size - 1)) + 2);
resize(new_size_degree);
}
for (size_t i = 0; i < rhs_size; ++i)
{
HashValue x = 0;
DB::readIntBinary(x, rb);
insertHash(x);
}
}
static void skip(DB::ReadBuffer & rb)
{
size_t size = 0;
rb.ignore();
DB::readVarUInt(size, rb);
if (size > UNIQUES_HASH_MAX_SIZE)
throw Poco::Exception("Cannot read UniquesHashSet: too large size_degree.");
rb.ignore(sizeof(HashValue) * size);
}
void writeText(DB::WriteBuffer & wb) const
{
if (m_size > UNIQUES_HASH_MAX_SIZE)
throw Poco::Exception("Cannot write UniquesHashSet: too large size_degree.");
DB::writeIntText(skip_degree, wb);
wb.write(",", 1);
DB::writeIntText(m_size, wb);
if (has_zero)
wb.write(",0", 2);
for (size_t i = 0; i < buf_size(); ++i)
{
if (buf[i])
{
wb.write(",", 1);
DB::writeIntText(buf[i], wb);
}
}
}
void readText(DB::ReadBuffer & rb)
{
has_zero = false;
DB::readIntText(skip_degree, rb);
DB::assertChar(',', rb);
DB::readIntText(m_size, rb);
if (m_size > UNIQUES_HASH_MAX_SIZE)
throw Poco::Exception("Cannot read UniquesHashSet: too large size_degree.");
free();
UInt8 new_size_degree = m_size <= 1
? UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE
: std::max(UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE, static_cast<int>(log2(m_size - 1)) + 2);
alloc(new_size_degree);
for (size_t i = 0; i < m_size; ++i)
{
HashValue x = 0;
DB::assertChar(',', rb);
DB::readIntText(x, rb);
if (x == 0)
has_zero = true;
else
reinsertImpl(x);
}
}
void insertHash(HashValue hash_value)
{
if (!good(hash_value))
return;
insertImpl(hash_value);
shrinkIfNeed();
}
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#ifdef UNIQUES_HASH_SET_COUNT_COLLISIONS
size_t getCollisions() const
{
return collisions;
}
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#endif
};
#undef UNIQUES_HASH_MAX_SIZE_DEGREE
#undef UNIQUES_HASH_MAX_SIZE
#undef UNIQUES_HASH_BITS_FOR_SKIP
#undef UNIQUES_HASH_SET_INITIAL_SIZE_DEGREE