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/*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
#ifndef _QUANTILES_SKETCH_HPP_
#define _QUANTILES_SKETCH_HPP_
#include <functional>
#include <memory>
#include <vector>
#include "quantiles_sorted_view.hpp"
#include "common_defs.hpp"
#include "serde.hpp"
#include "optional.hpp"
namespace datasketches {
/// Constants for Quantiles sketch
namespace quantiles_constants {
/// default value of parameter K
const uint16_t DEFAULT_K = 128;
/// minimum value of parameter K
const uint16_t MIN_K = 2;
/// maximum value of parameter K
const uint16_t MAX_K = 1 << 15;
}
/**
* This is a stochastic streaming sketch that enables near-real time analysis of the
* approximate distribution from a very large stream in a single pass.
* The analysis is obtained using get_rank() and get_quantile() functions,
* the Probability Mass Function from get_PMF() and the Cumulative Distribution Function from get_CDF().
*
* <p>Consider a large stream of one million values such as packet sizes coming into a network node.
* The natural rank of any specific size value is its index in the hypothetical sorted
* array of values.
* The normalized rank is the natural rank divided by the stream size,
* in this case one million.
* The value corresponding to the normalized rank of 0.5 represents the 50th percentile or median
* value of the distribution, or get_quantile(0.5). Similarly, the 95th percentile is obtained from
* get_quantile(0.95).</p>
*
* <p>From the min and max values, for example, 1 and 1000 bytes,
* you can obtain the PMF from get_PMF(100, 500, 900) that will result in an array of
* 4 fractional values such as {.4, .3, .2, .1}, which means that
* <ul>
* <li>40% of the values were &lt; 100,</li>
* <li>30% of the values were &ge; 100 and &lt; 500,</li>
* <li>20% of the values were &ge; 500 and &lt; 900, and</li>
* <li>10% of the values were &ge; 900.</li>
* </ul>
* A frequency histogram can be obtained by multiplying these fractions by get_n(),
* which is the total count of values received.
* The get_CDF() works similarly, but produces the cumulative distribution instead.
*
* <p>As of November 2021, this implementation produces serialized sketches which are binary-compatible
* with the equivalent Java implementation only when template parameter T = double
* (64-bit double precision values).
*
* <p>The accuracy of this sketch is a function of the configured value <i>k</i>, which also affects
* the overall size of the sketch. Accuracy of this quantile sketch is always with respect to
* the normalized rank. A <i>k</i> of 128 produces a normalized, rank error of about 1.7%.
* For example, the median item returned from getQuantile(0.5) will be between the actual items
* from the hypothetically sorted array of input items at normalized ranks of 0.483 and 0.517, with
* a confidence of about 99%.</p>
*
* <pre>
Table Guide for DoublesSketch Size in Bytes and Approximate Error:
K =&gt; | 16 32 64 128 256 512 1,024
~ Error =&gt; | 12.145% 6.359% 3.317% 1.725% 0.894% 0.463% 0.239%
N | Size in Bytes -&gt;
------------------------------------------------------------------------
0 | 8 8 8 8 8 8 8
1 | 72 72 72 72 72 72 72
3 | 72 72 72 72 72 72 72
7 | 104 104 104 104 104 104 104
15 | 168 168 168 168 168 168 168
31 | 296 296 296 296 296 296 296
63 | 424 552 552 552 552 552 552
127 | 552 808 1,064 1,064 1,064 1,064 1,064
255 | 680 1,064 1,576 2,088 2,088 2,088 2,088
511 | 808 1,320 2,088 3,112 4,136 4,136 4,136
1,023 | 936 1,576 2,600 4,136 6,184 8,232 8,232
2,047 | 1,064 1,832 3,112 5,160 8,232 12,328 16,424
4,095 | 1,192 2,088 3,624 6,184 10,280 16,424 24,616
8,191 | 1,320 2,344 4,136 7,208 12,328 20,520 32,808
16,383 | 1,448 2,600 4,648 8,232 14,376 24,616 41,000
32,767 | 1,576 2,856 5,160 9,256 16,424 28,712 49,192
65,535 | 1,704 3,112 5,672 10,280 18,472 32,808 57,384
131,071 | 1,832 3,368 6,184 11,304 20,520 36,904 65,576
262,143 | 1,960 3,624 6,696 12,328 22,568 41,000 73,768
524,287 | 2,088 3,880 7,208 13,352 24,616 45,096 81,960
1,048,575 | 2,216 4,136 7,720 14,376 26,664 49,192 90,152
2,097,151 | 2,344 4,392 8,232 15,400 28,712 53,288 98,344
4,194,303 | 2,472 4,648 8,744 16,424 30,760 57,384 106,536
8,388,607 | 2,600 4,904 9,256 17,448 32,808 61,480 114,728
16,777,215 | 2,728 5,160 9,768 18,472 34,856 65,576 122,920
33,554,431 | 2,856 5,416 10,280 19,496 36,904 69,672 131,112
67,108,863 | 2,984 5,672 10,792 20,520 38,952 73,768 139,304
134,217,727 | 3,112 5,928 11,304 21,544 41,000 77,864 147,496
268,435,455 | 3,240 6,184 11,816 22,568 43,048 81,960 155,688
536,870,911 | 3,368 6,440 12,328 23,592 45,096 86,056 163,880
1,073,741,823 | 3,496 6,696 12,840 24,616 47,144 90,152 172,072
2,147,483,647 | 3,624 6,952 13,352 25,640 49,192 94,248 180,264
4,294,967,295 | 3,752 7,208 13,864 26,664 51,240 98,344 188,456
* </pre>
* <p>There is more documentation available on
* <a href="https://datasketches.apache.org">datasketches.apache.org</a>.</p>
*
* <p>This is an implementation of the Low Discrepancy Mergeable Quantiles Sketch
* described in section 3.2 of the journal version of the paper "Mergeable Summaries"
* by Agarwal, Cormode, Huang, Phillips, Wei, and Yi.
* <a href="http://dblp.org/rec/html/journals/tods/AgarwalCHPWY13"></a></p>
*
* <p>This algorithm is independent of the distribution of items and
* requires only that the items be comparable.</p>
*
* <p>This algorithm intentionally inserts randomness into the sampling process for items that
* ultimately get retained in the sketch. The results produced by this algorithm are not
* deterministic. For example, if the same stream is inserted into two different instances of this
* sketch, the answers obtained from the two sketches may not be identical.</p>
*
* <p>Similarly, there may be directional inconsistencies. For example, the result
* obtained from get_quantile(rank) input into the reverse directional query
* get_rank(item) may not result in the original item.</p>
*
* @author Kevin Lang
* @author Lee Rhodes
* @author Alexander Saydakov
* @author Jon Malkin
*/
template <typename T,
typename Comparator = std::less<T>, // strict weak ordering function (see C++ named requirements: Compare)
typename Allocator = std::allocator<T>>
class quantiles_sketch {
public:
using value_type = T;
using allocator_type = Allocator;
using comparator = Comparator;
using quantile_return_type = typename quantiles_sorted_view<T, Comparator, Allocator>::quantile_return_type;
using vector_double = typename quantiles_sorted_view<T, Comparator, Allocator>::vector_double;
/**
* Constructor
* @param k affects the size of the sketch and its estimation error
* @param comparator strict weak ordering function (see C++ named requirements: Compare)
* @param allocator used to allocate memory
*/
explicit quantiles_sketch(uint16_t k = quantiles_constants::DEFAULT_K,
const Comparator& comparator = Comparator(), const Allocator& allocator = Allocator());
/**
* Copy constructor
* @param other sketch to be copied
*/
quantiles_sketch(const quantiles_sketch& other);
/** Move constructor
* @param other sketch to be moved
*/
quantiles_sketch(quantiles_sketch&& other) noexcept;
~quantiles_sketch();
/**
* Copy assignment
* @param other sketch to be copied
* @return reference to this sketch
*/
quantiles_sketch& operator=(const quantiles_sketch& other);
/**
* Move assignment
* @param other sketch to be moved
* @return reference to this sketch
*/
quantiles_sketch& operator=(quantiles_sketch&& other) noexcept;
/**
* @brief Type converting constructor
* @param other quantiles sketch of a different type
* @param comparator instance of a Comparator
* @param allocator instance of an Allocator
*/
template<typename From, typename FC, typename FA>
explicit quantiles_sketch(const quantiles_sketch<From, FC, FA>& other,
const Comparator& comparator = Comparator(), const Allocator& allocator = Allocator());
/**
* Updates this sketch with the given data item.
* @param item from a stream of items
*/
template<typename FwdT>
void update(FwdT&& item);
/**
* Merges another sketch into this one.
* @param other sketch to merge into this one
*/
template<typename FwdSk>
void merge(FwdSk&& other);
/**
* Returns true if this sketch is empty.
* @return empty flag
*/
bool is_empty() const;
/**
* Returns configured parameter k
* @return parameter k
*/
uint16_t get_k() const;
/**
* Returns the length of the input stream.
* @return stream length
*/
uint64_t get_n() const;
/**
* Returns the number of retained items (samples) in the sketch.
* @return the number of retained items
*/
uint32_t get_num_retained() const;
/**
* Returns true if this sketch is in estimation mode.
* @return estimation mode flag
*/
bool is_estimation_mode() const;
/**
* Returns the min item of the stream.
* If the sketch is empty this throws std::runtime_error.
* @return the min item of the stream
*/
const T& get_min_item() const;
/**
* Returns the max item of the stream.
* If the sketch is empty this throws std::runtime_error.
* @return the max item of the stream
*/
const T& get_max_item() const;
/**
* Returns an instance of the comparator for this sketch.
* @return comparator
*/
Comparator get_comparator() const;
/**
* Returns the allocator for this sketch.
* @return allocator
*/
allocator_type get_allocator() const;
/**
* Returns an approximation to the data item associated with the given rank
* of a hypothetical sorted version of the input stream so far.
* <p>
* If the sketch is empty this throws std::runtime_error.
*
* @param rank the specified normalized rank in the hypothetical sorted stream.
* @param inclusive if true the weight of the given item is included into the rank.
* Otherwise the rank equals the sum of the weights of all items that are less than the given item
* according to the Comparator.
* @return the approximation to the item at the given rank
*/
quantile_return_type get_quantile(double rank, bool inclusive = true) const;
/**
* Returns an approximation to the normalized rank of the given item from 0 to 1, inclusive.
*
* <p>The resulting approximation has a probabilistic guarantee that can be obtained from the
* get_normalized_rank_error(false) function.
*
* <p>If the sketch is empty this throws std::runtime_error.
*
* @param item to be ranked
* @param inclusive if true the weight of the given item is included into the rank.
* Otherwise the rank equals the sum of the weights of all items that are less than the given item
* according to the Comparator.
* @return an approximate normalized rank of the given item
*/
double get_rank(const T& item, bool inclusive = true) const;
/**
* Returns an approximation to the Probability Mass Function (PMF) of the input stream
* given a set of split points (items).
*
* <p>The resulting approximations have a probabilistic guarantee that can be obtained from the
* get_normalized_rank_error(true) function.
*
* <p>If the sketch is empty this throws std::runtime_error.
*
* @param split_points an array of <i>m</i> unique, monotonically increasing items
* that divide the input domain into <i>m+1</i> consecutive disjoint intervals (bins).
*
* @param size of the array of split points.
*
* @param inclusive if true the rank of an item includes its own weight, and therefore
* if the sketch contains items equal to a slit point, then in PMF such items are
* included into the interval to the left of split point. Otherwise they are included into the interval
* to the right of split point.
*
* @return an array of m+1 doubles each of which is an approximation
* to the fraction of the input stream items (the mass) that fall into one of those intervals.
*/
vector_double get_PMF(const T* split_points, uint32_t size, bool inclusive = true) const;
/**
* Returns an approximation to the Cumulative Distribution Function (CDF), which is the
* cumulative analog of the PMF, of the input stream given a set of split points (items).
*
* <p>The resulting approximations have a probabilistic guarantee that can be obtained from the
* get_normalized_rank_error(false) function.
*
* <p>If the sketch is empty this throws std::runtime_error.
*
* @param split_points an array of <i>m</i> unique, monotonically increasing items
* that divide the input domain into <i>m+1</i> consecutive disjoint intervals.
*
* @param size of the array of split points.
*
* @param inclusive if true the rank of an item includes its own weight, and therefore
* if the sketch contains items equal to a slit point, then in CDF such items are
* included into the interval to the left of split point. Otherwise they are included into
* the interval to the right of split point.
*
* @return an array of m+1 double values, which are a consecutive approximation to the CDF
* of the input stream given the split_points. The value at array position j of the returned
* CDF array is the sum of the returned values in positions 0 through j of the returned PMF
* array. This can be viewed as array of ranks of the given split points plus one more value
* that is always 1.
*/
vector_double get_CDF(const T* split_points, uint32_t size, bool inclusive = true) const;
/**
* Computes size needed to serialize the current state of the sketch.
* This version is for fixed-size arithmetic types (integral and floating point).
* @param sd instance of a SerDe
* @return size in bytes needed to serialize this sketch
*/
template<typename SerDe = serde<T>, typename TT = T, typename std::enable_if<std::is_arithmetic<TT>::value, int>::type = 0>
size_t get_serialized_size_bytes(const SerDe& sd = SerDe()) const;
/**
* Computes size needed to serialize the current state of the sketch.
* This version is for all other types and can be expensive since every item needs to be looked at.
* @param sd instance of a SerDe
* @return size in bytes needed to serialize this sketch
*/
template<typename SerDe = serde<T>, typename TT = T, typename std::enable_if<!std::is_arithmetic<TT>::value, int>::type = 0>
size_t get_serialized_size_bytes(const SerDe& sd = SerDe()) const;
/**
* This method serializes the sketch into a given stream in a binary form
* @param os output stream
* @param sd instance of a SerDe
*/
template<typename SerDe = serde<T>>
void serialize(std::ostream& os, const SerDe& sd = SerDe()) const;
// This is a convenience alias for users
// The type returned by the following serialize method
using vector_bytes = std::vector<uint8_t, typename std::allocator_traits<Allocator>::template rebind_alloc<uint8_t>>;
/**
* This method serializes the sketch as a vector of bytes.
* An optional header can be reserved in front of the sketch.
* It is a blank space of a given size.
* This header is used in Datasketches PostgreSQL extension.
* @param header_size_bytes space to reserve in front of the sketch
* @param sd instance of a SerDe
* @return serialized sketch as a vector of bytes
*/
template<typename SerDe = serde<T>>
vector_bytes serialize(unsigned header_size_bytes = 0, const SerDe& sd = SerDe()) const;
/**
* This method deserializes a sketch from a given stream.
* @param is input stream
* @param sd instance of a SerDe
* @param comparator instance of a Comparator
* @param allocator instance of an Allocator
* @return an instance of a sketch
*/
template<typename SerDe = serde<T>>
static quantiles_sketch deserialize(std::istream& is, const SerDe& sd = SerDe(),
const Comparator& comparator = Comparator(), const Allocator& allocator = Allocator());
/**
* This method deserializes a sketch from a given array of bytes.
* @param bytes pointer to the array of bytes
* @param size the size of the array
* @param sd instance of a SerDe
* @param comparator instance of a Comparator
* @param allocator instance of an Allocator
* @return an instance of a sketch
*/
template<typename SerDe = serde<T>>
static quantiles_sketch deserialize(const void* bytes, size_t size, const SerDe& sd = SerDe(),
const Comparator& comparator = Comparator(), const Allocator& allocator = Allocator());
/**
* Gets the normalized rank error for this sketch. Constants were derived as the best fit to 99 percentile
* empirically measured max error in thousands of trials.
* @param is_pmf if true, returns the "double-sided" normalized rank error for the get_PMF() function.
* Otherwise, it is the "single-sided" normalized rank error for all the other queries.
* @return the normalized rank error for the sketch
*/
double get_normalized_rank_error(bool is_pmf) const;
/**
* Gets the normalized rank error given k and pmf. Constants were derived as the best fit to 99 percentile
* empirically measured max error in thousands of trials.
* @param k the configuration parameter
* @param is_pmf if true, returns the "double-sided" normalized rank error for the get_PMF() function.
* Otherwise, it is the "single-sided" normalized rank error for all the other queries.
* @return the normalized rank error for the given parameters
*/
static double get_normalized_rank_error(uint16_t k, bool is_pmf);
/**
* Prints a summary of the sketch.
* @param print_levels if true include information about levels
* @param print_items if true include sketch data
*/
string<Allocator> to_string(bool print_levels = false, bool print_items = false) const;
class const_iterator;
/**
* Iterator pointing to the first item in the sketch.
* If the sketch is empty, the returned iterator must not be dereferenced or incremented.
* @return iterator pointing to the first item in the sketch
*/
const_iterator begin() const;
/**
* Iterator pointing to the past-the-end item in the sketch.
* The past-the-end item is the hypothetical item that would follow the last item.
* It does not point to any item, and must not be dereferenced or incremented.
* @return iterator pointing to the past-the-end item in the sketch
*/
const_iterator end() const;
/**
* Gets the sorted view of this sketch
* @return the sorted view of this sketch
*/
quantiles_sorted_view<T, Comparator, Allocator> get_sorted_view() const;
private:
using Level = std::vector<T, Allocator>;
using VectorLevels = std::vector<Level, typename std::allocator_traits<Allocator>::template rebind_alloc<Level>>;
/* Serialized sketch layout:
* Long || Start Byte Addr:
* Addr:
* || 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
* 0 || Preamble_Longs | SerVer | FamID | Flags |----- K ---------|---- unused -----|
*
* || 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
* 1 ||---------------------------Items Seen Count (N)--------------------------------|
*
* Long 3 is the start of data, beginning with serialized min and max item, followed by
* the sketch data buffers.
*/
static const size_t EMPTY_SIZE_BYTES = 8;
static const uint8_t SERIAL_VERSION_1 = 1;
static const uint8_t SERIAL_VERSION_2 = 2;
static const uint8_t SERIAL_VERSION = 3;
static const uint8_t FAMILY = 8;
enum flags { RESERVED0, RESERVED1, IS_EMPTY, IS_COMPACT, IS_SORTED };
static const uint8_t PREAMBLE_LONGS_SHORT = 1; // for empty
static const uint8_t PREAMBLE_LONGS_FULL = 2;
static const size_t DATA_START = 16;
Comparator comparator_;
Allocator allocator_;
bool is_base_buffer_sorted_;
uint16_t k_;
uint64_t n_;
uint64_t bit_pattern_;
Level base_buffer_;
VectorLevels levels_;
optional<T> min_item_;
optional<T> max_item_;
mutable quantiles_sorted_view<T, Comparator, Allocator>* sorted_view_;
void setup_sorted_view() const; // modifies mutable state
void reset_sorted_view();
// for deserialization
class items_deleter;
quantiles_sketch(uint16_t k, uint64_t n, uint64_t bit_pattern,
Level&& base_buffer, VectorLevels&& levels,
optional<T>&& min_item, optional<T>&& max_item,
bool is_sorted, const Comparator& comparator = Comparator(), const Allocator& allocator = Allocator());
void grow_base_buffer();
void process_full_base_buffer();
// returns true if size adjusted, else false
bool grow_levels_if_needed();
// buffers should be pre-sized to target capacity as appropriate
template<typename FwdV>
static void in_place_propagate_carry(uint8_t starting_level, FwdV&& buf_size_k,
Level& buf_size_2k, bool apply_as_update,
quantiles_sketch& sketch);
static void zip_buffer(Level& buf_in, Level& buf_out);
static void merge_two_size_k_buffers(Level& arr_in_1, Level& arr_in_2, Level& arr_out, const Comparator& comparator);
template<typename SerDe>
static Level deserialize_array(std::istream& is, uint32_t num_items, uint32_t capcacity, const SerDe& serde, const Allocator& allocator);
template<typename SerDe>
static std::pair<Level, size_t> deserialize_array(const void* bytes, size_t size, uint32_t num_items, uint32_t capcacity, const SerDe& serde, const Allocator& allocator);
static void check_k(uint16_t k);
static void check_serial_version(uint8_t serial_version);
static void check_header_validity(uint8_t preamble_longs, uint8_t flags_byte, uint8_t serial_version);
static void check_family_id(uint8_t family_id);
static uint32_t compute_retained_items(uint16_t k, uint64_t n);
static uint32_t compute_base_buffer_items(uint16_t k, uint64_t n);
static uint64_t compute_bit_pattern(uint16_t k, uint64_t n);
static uint32_t count_valid_levels(uint64_t bit_pattern);
static uint8_t compute_levels_needed(uint16_t k, uint64_t n);
/**
* Merges the src sketch into the tgt sketch with equal values of K.
* src is modified only if elements can be moved out of it.
*/
template<typename FwdSk>
static void standard_merge(quantiles_sketch& tgt, FwdSk&& src);
/**
* Merges the src sketch into the tgt sketch with a smaller value of K.
* However, it is required that the ratio of the two K values be a power of 2.
* I.e., other.get_k() = this.get_k() * 2^(nonnegative integer).
* src is modified only if elements can be moved out of it.
*/
template<typename FwdSk>
static void downsampling_merge(quantiles_sketch& tgt, FwdSk&& src);
template<typename FwdV>
static void zip_buffer_with_stride(FwdV&& buf_in, Level& buf_out, uint16_t stride);
/**
* Returns the zero-based bit position of the lowest zero bit of <i>bits</i> starting at
* <i>startingBit</i>. If input is all ones, this returns 64.
* @param bits the input bits as a long
* @param starting_bit the zero-based starting bit position. Only the low 6 bits are used.
* @return the zero-based bit position of the lowest zero bit starting at <i>startingBit</i>.
*/
static uint8_t lowest_zero_bit_starting_at(uint64_t bits, uint8_t starting_bit);
template<typename TT = T, typename std::enable_if<std::is_floating_point<TT>::value, int>::type = 0>
static inline bool check_update_item(TT item) {
return !std::isnan(item);
}
template<typename TT = T, typename std::enable_if<!std::is_floating_point<TT>::value, int>::type = 0>
static inline bool check_update_item(TT) {
return true;
}
// for type converting constructor
template<typename From, typename FC, typename FA> friend class quantiles_sketch;
};
template<typename T, typename C, typename A>
class quantiles_sketch<T, C, A>::const_iterator {
public:
using iterator_category = std::input_iterator_tag;
using value_type = std::pair<const T&, const uint64_t>;
using difference_type = void;
using pointer = const return_value_holder<value_type>;
using reference = const value_type;
const_iterator& operator++();
const_iterator& operator++(int);
bool operator==(const const_iterator& other) const;
bool operator!=(const const_iterator& other) const;
reference operator*() const;
pointer operator->() const;
private:
friend class quantiles_sketch<T, C, A>;
using Level = std::vector<T, A>;
using AllocLevel = typename std::allocator_traits<A>::template rebind_alloc<Level>;
Level base_buffer_;
std::vector<Level, AllocLevel> levels_;
int level_;
uint32_t index_;
uint32_t bb_count_;
uint64_t bit_pattern_;
uint64_t weight_;
uint16_t k_;
const_iterator(const Level& base_buffer, const std::vector<Level, AllocLevel>& levels, uint16_t k, uint64_t n, bool is_end);
};
} /* namespace datasketches */
#include "quantiles_sketch_impl.hpp"
#endif // _QUANTILES_SKETCH_HPP_