ClickHouse/dbms/src/AggregateFunctions/QuantileTDigest.h
Evgenii Pravda 91ccf2ab20 Fixes
2019-04-27 20:52:43 +03:00

345 lines
11 KiB
C++

#pragma once
#include <cmath>
#include <Common/RadixSort.h>
#include <Common/PODArray.h>
#include <IO/WriteBuffer.h>
#include <IO/ReadBuffer.h>
#include <IO/VarInt.h>
namespace DB
{
namespace ErrorCodes
{
extern const int TOO_LARGE_ARRAY_SIZE;
}
/** The algorithm was implemented by Alexei Borzenkov https://github.com/snaury
* He owns the authorship of the code and half the comments in this namespace,
* except for merging, serialization, and sorting, as well as selecting types and other changes.
* We thank Alexei Borzenkov for writing the original code.
*/
/** Implementation of t-digest algorithm (https://github.com/tdunning/t-digest).
* This option is very similar to MergingDigest on java, however the decision about
* the union is accepted based on the original condition from the article
* (via a size constraint, using the approximation of the quantile of each
* centroid, not the distance on the curve of the position of their boundaries). MergingDigest
* on java gives significantly fewer centroids than this variant, that
* negatively affects accuracy with the same compression factor, but gives
* size guarantees. The author himself on the proposal for this variant said that
* the size of the digest grows like O(log(n)), while the version on java
* does not depend on the expected number of points. Also an variant on java
* uses asin, which slows down the algorithm a bit.
*/
template <typename T>
class QuantileTDigest
{
using Value = Float32;
using Count = Float32;
/** The centroid stores the weight of points around their mean value
*/
struct Centroid
{
Value mean;
Count count;
Centroid() = default;
explicit Centroid(Value mean, Count count)
: mean(mean)
, count(count)
{}
Centroid & operator+=(const Centroid & other)
{
count += other.count;
mean += other.count * (other.mean - mean) / count;
return *this;
}
bool operator<(const Centroid & other) const
{
return mean < other.mean;
}
};
/** :param epsilon: value \delta from the article - error in the range
* quantile 0.5 (default is 0.01, i.e. 1%)
* :param max_unmerged: when accumulating count of new points beyond this
* value centroid compression is triggered
* (default is 2048, the higher the value - the
* more memory is required, but amortization of execution time increases)
*/
struct Params
{
Value epsilon = 0.01;
size_t max_unmerged = 2048;
};
Params params;
/// The memory will be allocated to several elements at once, so that the state occupies 64 bytes.
static constexpr size_t bytes_in_arena = 128 - sizeof(PODArray<Centroid>) - sizeof(Count) - sizeof(UInt32);
using Summary = PODArray<Centroid, bytes_in_arena / sizeof(Centroid), AllocatorWithStackMemory<Allocator<false>, bytes_in_arena>>;
Summary summary;
Count count = 0;
UInt32 unmerged = 0;
/** Linear interpolation at the point x on the line (x1, y1)..(x2, y2)
*/
static Value interpolate(Value x, Value x1, Value y1, Value x2, Value y2)
{
double k = (x - x1) / (x2 - x1);
return y1 + k * (y2 - y1);
}
struct RadixSortTraits
{
using Element = Centroid;
using Key = Value;
using CountType = UInt32;
using KeyBits = UInt32;
static constexpr size_t PART_SIZE_BITS = 8;
using Transform = RadixSortFloatTransform<KeyBits>;
using Allocator = RadixSortMallocAllocator;
/// The function to get the key from an array element.
static Key & extractKey(Element & elem) { return elem.mean; }
};
/** Adds a centroid `c` to the digest
*/
void addCentroid(const Centroid & c)
{
summary.push_back(c);
count += c.count;
++unmerged;
if (unmerged >= params.max_unmerged)
compress();
}
/** Performs compression of accumulated centroids
* When merging, the invariant is retained to the maximum size of each
* centroid that does not exceed `4 q (1 - q) \ delta N`.
*/
void compress()
{
if (unmerged > 0)
{
RadixSort<RadixSortTraits>::executeLSD(summary.data(), summary.size());
if (summary.size() > 3)
{
/// A pair of consecutive bars of the histogram.
auto l = summary.begin();
auto r = std::next(l);
Count sum = 0;
while (r != summary.end())
{
// we use quantile which gives us the smallest error
/// The ratio of the part of the histogram to l, including the half l to the entire histogram. That is, what level quantile in position l.
Value ql = (sum + l->count * 0.5) / count;
Value err = ql * (1 - ql);
/// The ratio of the portion of the histogram to l, including l and half r to the entire histogram. That is, what level is the quantile in position r.
Value qr = (sum + l->count + r->count * 0.5) / count;
Value err2 = qr * (1 - qr);
if (err > err2)
err = err2;
Value k = 4 * count * err * params.epsilon;
/** The ratio of the weight of the glued column pair to all values is not greater,
* than epsilon multiply by a certain quadratic coefficient, which in the median is 1 (4 * 1/2 * 1/2),
* and at the edges decreases and is approximately equal to the distance to the edge * 4.
*/
if (l->count + r->count <= k)
{
// it is possible to merge left and right
/// The left column "eats" the right.
*l += *r;
}
else
{
// not enough capacity, check the next pair
sum += l->count;
++l;
/// We skip all the values "eaten" earlier.
if (l != r)
*l = *r;
}
++r;
}
/// At the end of the loop, all values to the right of l were "eaten".
summary.resize(l - summary.begin() + 1);
}
unmerged = 0;
}
}
public:
/** Adds to the digest a change in `x` with a weight of `cnt` (default 1)
*/
void add(T x, UInt64 cnt = 1)
{
addCentroid(Centroid(Value(x), Count(cnt)));
}
void merge(const QuantileTDigest & other)
{
for (const auto & c : other.summary)
addCentroid(c);
}
void serialize(WriteBuffer & buf)
{
compress();
writeVarUInt(summary.size(), buf);
buf.write(reinterpret_cast<const char *>(summary.data()), summary.size() * sizeof(summary[0]));
}
void deserialize(ReadBuffer & buf)
{
size_t size = 0;
readVarUInt(size, buf);
if (size > params.max_unmerged)
throw Exception("Too large t-digest summary size", ErrorCodes::TOO_LARGE_ARRAY_SIZE);
summary.resize(size);
buf.read(reinterpret_cast<char *>(summary.data()), size * sizeof(summary[0]));
count = 0;
for (const auto & c : summary)
count += c.count;
}
/** Calculates the quantile q [0, 1] based on the digest.
* For an empty digest returns NaN.
*/
template <typename ResultType>
ResultType getImpl(Float64 level)
{
if (summary.empty())
return std::is_floating_point_v<ResultType> ? NAN : 0;
compress();
if (summary.size() == 1)
return summary.front().mean;
Float64 x = level * count;
Float64 prev_x = 0;
Count sum = 0;
Value prev_mean = summary.front().mean;
for (const auto & c : summary)
{
Float64 current_x = sum + c.count * 0.5;
if (current_x >= x)
return interpolate(x, prev_x, prev_mean, current_x, c.mean);
sum += c.count;
prev_mean = c.mean;
prev_x = current_x;
}
return summary.back().mean;
}
/** Get multiple quantiles (`size` parts).
* levels - an array of levels of the desired quantiles. They are in a random order.
* levels_permutation - array-permutation levels. The i-th position will be the index of the i-th ascending level in the `levels` array.
* result - the array where the results are added, in order of `levels`,
*/
template <typename ResultType>
void getManyImpl(const Float64 * levels, const size_t * levels_permutation, size_t size, ResultType * result)
{
if (summary.empty())
{
for (size_t result_num = 0; result_num < size; ++result_num)
result[result_num] = std::is_floating_point_v<ResultType> ? NAN : 0;
return;
}
compress();
if (summary.size() == 1)
{
for (size_t result_num = 0; result_num < size; ++result_num)
result[result_num] = summary.front().mean;
return;
}
Float64 x = levels[levels_permutation[0]] * count;
Float64 prev_x = 0;
Count sum = 0;
Value prev_mean = summary.front().mean;
size_t result_num = 0;
for (const auto & c : summary)
{
Float64 current_x = sum + c.count * 0.5;
while (current_x >= x)
{
result[levels_permutation[result_num]] = interpolate(x, prev_x, prev_mean, current_x, c.mean);
++result_num;
if (result_num >= size)
return;
x = levels[levels_permutation[result_num]] * count;
}
sum += c.count;
prev_mean = c.mean;
prev_x = current_x;
}
auto rest_of_results = summary.back().mean;
for (; result_num < size; ++result_num)
result[levels_permutation[result_num]] = rest_of_results;
}
T get(Float64 level)
{
return getImpl<T>(level);
}
Float32 getFloat(Float64 level)
{
return getImpl<Float32>(level);
}
void getMany(const Float64 * levels, const size_t * indices, size_t size, T * result)
{
getManyImpl(levels, indices, size, result);
}
void getManyFloat(const Float64 * levels, const size_t * indices, size_t size, Float32 * result)
{
getManyImpl(levels, indices, size, result);
}
};
}