Sunday, October 2, 2022

Deferred argument evaluation

Suppose our program deals with heavy entities of some type object which are uniquely identified by an integer ID. The following is a possible implementation of a function that controls ID-constrained creation of such objects:

object* retrieve_or_create(int id)
{
  static std::unordered_map<int, std::unique_ptr<object>> m;

  // see if the object is already in the map
auto [it,b] = m.emplace(id, nullptr);
// create it otherwise if(b) it->second = std::make_unique<object>(id); return it->second.get(); }

Note that the code is careful not to create a spurious object if an equivalent one already exists; but in doing so, we have introduced a potentially inconsistency in the internal map if object creation throws:

// fixed version

object* retrieve_or_create(int id)
{
  static std::unordered_map<int, std::unique_ptr<object>> m;

  // see if the object is already in the map
auto [it,b] = m.emplace(id, nullptr); // create it otherwise
if(b){ try{ it->second = std::make_unique<object>(id); } catch(...){
// we can get here when running out of memory, for instance m.erase(it); throw; } } return it->second.get(); }

This fixed version is a little cumbersome, to say the least. Starting in C++17, we can use try_emplace to rewrite retrieve_or_create as follows:

object* retrieve_or_create(int id)
{
  static std::unordered_map<int, std::unique_ptr<object>> m;

  auto [it,b] = m.try_emplace(id, std::make_unique<object>(id));
  return it->second.get();
}

But then we've introduced the problem of spurious object creation we strived to avoid. Ideally, we'd like for try_emplace to not create the object except when really needed. What we're effectively asking for is some sort of technique for deferred argument evaluation. As it happens, it is very easy to devise our own:

template<typename F>
struct deferred_call
{
  using result_type=decltype(std::declval<const F>()());
  operator result_type() const { return f(); }

  F f;
};

object* retrieve_or_create(int id)
{
  static std::unordered_map<int, std::unique_ptr<object>> m;

  auto [it,b] = m.try_emplace(
    id,
    deferred_call([&]{ return std::make_unique<object>(id); }));
  return it->second.get();
}

deferred_call is a small utlity that computes a value upon request of conversion to deferred_call::result_type. In the example, such conversion will only happen if try_emplace really needs to create a std::pair<const int, std::unique_ptr<object>>, that is, if no equivalent object was already present in the map.

In a general setting, for deferred_call to work as expected, that is, to delay producing the value until the point of actual usage, the following conditions must be met:

  1. The deferred_call object is passed to function/constructor template accepting generic, unconstrained parameters.
  2. All internal intermediate interfaces are also generic.
  3. The final function/constructor where actual usage happens asks exactly for a deferred_call::result_type value or reference.

It is the last condition that can be the most problematic:

void f(std::string);
    
// error: deferred_call not convertible to std::string
f(deferred_call([]{ return "hello"; }));

C++ rules for conversion alows just one user-defined conversion to take place at most, and here we are calling for the sequence deferred_callconst char*std::string. In this case, however, the fix is trivial:

void f(std::string);

f(deferred_call([]{ return std::string("hello"); })); 

Update Oct 4

Jessy De Lannoit proposes a variation on deferred_call that solves the problem of producing a value that is one user-defined conversion away from the target type:

template<typename F>
struct deferred_call
{
using result_type=decltype(std::declval<const F>()());
operator result_type() const { return f(); }

template<typename T>
requires (std::is_constructible_v<T, result_type>)
constexpr operator T() const { return {f()}; }

F f;
};

void f(std::string); // works ok: deferred_call converts to std::string
f(deferred_call([]{ return "hello"; }));

This version of deferred_call has an eager conversion operator producing any requested value as long  as it is constructible from deferred_call::result_type. The solution comes with a different set of problems, though:

void f(std::string);
void f(const char*); // ambiguous call to f
f(deferred_call([]{ return "hello"; }));
There is probably little more we can do without language support. One can imagine some sort of "silent" conversion operator that does not add to the cap on user-defined conversions allowed by the rules of C++:
template<typename F>
struct deferred_call
{
using result_type=decltype(std::declval<const F>()());
operator result_type() const { return f(); }

// "silent" conversion operator marked with ~explicit
// (not actual C++)
template<typename T>
requires (std::is_constructible_v<T, result_type>)
~explicit constexpr operator T() const { return {f()}; }

F f;
};

Saturday, June 18, 2022

Advancing the state of the art for std::unordered_map implementations

Introduction

Several Boost authors have embarked on a project to improve the performance of Boost.Unordered's implementation of std::unordered_map (and multimap, set and multiset variants), and to extend its portfolio of available containers to offer faster, non-standard alternatives based on open addressing.

The first goal of the project has been completed in time for Boost 1.80 (due August 2022). We describe here the technical innovations introduced in boost::unordered_map that makes it the fastest implementation of std::unordered_map on the market.

Closed vs. open addressing

On a first approximation, hash table implementations fall on either of two general classes:

  • Closed addressing (also known as separate chaining) relies on an array of buckets, each of which points to a list of elements belonging to it. When a new element goes to an already occupied bucket, it is simply linked to the associated element list. The figure depicts what we call the textbook implementation of closed addressing, arguably the simplest layout, and among the fastest, for this type of hash tables.
textbook layout
  • Open addressing (or closed hashing) stores at most one element in each bucket (sometimes called a slot). When an element goes to an already occupied slot, some probing mechanism is used to locate an available slot, preferrably close to the original one.

Recent, high-performance hash tables use open addressing and leverage on its inherently better cache locality and on widely available SIMD operations. Closed addressing provides some functional advantages, though, and remains relevant as the required foundation for the implementation of std::unodered_map.

Restrictions on the implementation of std::unordered_map

The standardization of C++ unordered associative containers is based on Matt Austern's 2003 N1456 paper. Back in the day, open-addressing approaches were not regarded as sufficiently mature, so closed addressing was taken as the safe implementation of choice. Even though the C++ standard does not explicitly require that closed addressing must be used, the assumption that this is the case leaks through the public interface of std::unordered_map:

  • A bucket API is provided.
  • Pointer stability implies that the container is node-based. In C++17, this implication was made explicit with the introduction of extract capabilities.
  • Users can control the container load factor.
  • Requirements on the hash function are very lax (open addressing depends on high-quality hash functions with the ability to spread keys widely across the space of std::size_t values.)

As a result, all standard library implementations use some form of closed addressing for the internal structure of their std::unordered_map (and related containers).

Coming as an additional difficulty, there are two complexity requirements:

  • iterator increment must be (amortized) constant time,
  • erase must be constant time on average,

that rule out the textbook implementation of closed addressing (see N2023 for details). To cope with this problem, standard libraries depart from the textbook layout in ways that introduce speed and memory penalties: this is, for instance, how libstdc++-v3 and libc++ layouts look like:

libstdc++-v3/libc++ layout

To provide constant iterator increment, all nodes are linked together, which in its turn forces two adjustments to the data structure:

  • Buckets point to the node before the first one in the bucket so as to preserve constant-time erasure.
  • To detect the end of a bucket, the element hash value is added as a data member of the node itself (libstdc++-v3 opts for on-the-fly hash calculation under some circumstances).

Visual Studio standard library (formerly from Dinkumware) uses an entirely different approach to circumvent the problem, but the general outcome is that resulting data structures perform significantly worse than the textbook layout in terms of speed, memory consumption, or both.

Boost.Unordered 1.80 data layout

The new data layout used by Boost.Unordered goes back to the textbook approach:

Boost.Unordered layout

Unlike the rest of standard library implementations, nodes are not linked across the container but only within each bucket. This makes constant-time erase trivially implementable, but leaves unsolved the problem of constant-time iterator increment: to achieve it, we introduce so-called bucket groups (top of the diagram). Each bucket group consists of a 32/64-bit bucket occupancy mask plus next and prev pointers linking non-empty bucket groups together. Iteration across buckets resorts to a combination of bit manipulation operations on the bitmasks plus group traversal through next pointers, which is not only constant time but also very lightweight in terms of execution time and of memory overhead (4 bits per bucket).

Fast modulo

When inserting or looking for an element, hash table implementations need to map the element hash value into the array of buckets (or slots in the open-addressing case). There are two general approaches in common use:

  • Bucket array sizes follow a sequence of prime numbers p, and mapping is of the form hh mod p.
  • Bucket array sizes follow a power-of-two sequence 2n, and mapping takes n bits from h. Typically it is the n least significant bits that are used, but in some cases, like when h is postprocessed to improve its uniformity via multiplication by a well-chosen constant m (such as defined by Fibonacci hashing), it is best to take the n most significant bits, that is, h → (h × m) >> (Nn), where N is the bitwidth of std::size_t and >> is the usual C++ right shift operation.

We use the modulo by a prime approach because it produces very good spreading even if hash values are not uniformly distributed. In modern CPUs, however, modulo is an expensive operation involving integer division; compilers, on the other hand, know how to perform modulo by a constant much more efficiently, so one possible optimization is to keep a table of pointers to functions fp : hh mod p. This technique replaces expensive modulo calculation with a table jump plus a modulo-by-a-constant operation.

In Boost.Unordered 1.80, we have gone a step further. Daniel Lemire et al. show how to calculate h mod p as an operation involving some shifts and multiplications by p and a pre-computed c value acting as a sort of reciprocal of p. We have used this work to implement hash mapping as h → fastmod(h, p, c) (some details omitted). Note that, even though fastmod is generally faster than modulo by a constant, most performance gains actually come from the fact that we are eliminating the table jump needed to select fp, which prevented code inlining.

Time and memory performance of Boost 1.80 boost::unordered_map

We are providing some benchmark results of the boost::unordered_map against libstdc++-v3, libc++ and Visual Studio standard library for insertion, lookup and erasure scenarios. boost::unordered_map is mostly faster across the board, and in some cases significantly so. There are three factors contributing to this performance advantage:

  • the very reduced memory footprint improves cache utilization,
  • fast modulo is used,
  • the new layout incurs one less pointer indirection than libstdc++-v3 and libc++ to access the elements of a bucket.

As for memory consumption, let N be the number of elements in a container with B buckets: the memory overheads (that is, memory allocated minus memory used strictly for the elements themselves) of the different implementations on 64-bit architectures are:

Implementation Memory overhead (bytes)
libstdc++-v3 16 N + 8 B (hash caching)
8 N + 8 B (no hash caching)
libc++ 16 N + 8 B
Visual Studio (Dinkumware) 16 N + 16 B
Boost.Unordered 8 N + 8.5 B
 

Which hash container to choose

Opting for closed-addressing (which, in the realm of C++, is almost synonymous with using an implementation of std::unordered_map) or choosing a speed-oriented, open-addressing container is in practice not a clear-cut decision. Some factors favoring one or the other option are listed:

  • std::unordered_map
    • The code uses some specific parts of its API like node extraction, the bucket interface or the ability to set the maximum load factor, which are generally not available in open-addressing containers.
    • Pointer stability and/or non-moveability of values required (though some open-addressing alternatives support these at the expense of reduced performance).
    • Constant-time iterator increment required.
    • Hash functions used are only mid-quality (open addressing requires that the hash function have very good key-spreading properties).
    • Equivalent key support, ie. unordered_multimap/unordered_multiset required. We do not know of any open-addressing container supporting equivalent keys.
  • Open-addressing containers
    • Performance is the main concern.
    • Existing code can be adapted to a basically more stringent API and more demanding requirements on the element type (like moveability).
    • Hash functions are of good quality (or the default ones from the container provider are used).

If you decide to use std::unordered_map, Boost.Unordered 1.80 now gives you the fastest, fully-conformant implementation on the market.

Next steps

There are some further areas of improvement to boost::unordered_map that we will investigate post Boost 1.80:

  • Reduce the memory overhead of the new layout from 4 bits to 3 bits per bucket.
  • Speed up performance for equivalent key variants (unordered_multimap/unordered_multiset).

In parallel, we are working on the future boost::unordered_flat_map, our proposal for a top-speed, open-addressing container beyond the limitations imposed by std::unordered_map interface. Your feedback on our current and future work is much welcome.

Thursday, March 10, 2022

Emulating template named arguments in C++20

std::unordered_map is a highly configurable class template with five parameters:

template<
    class Key,
    class Value,
    class Hash = std::hash<Key>,
    class KeyEqual = std::equal_to<Key>,
    class Allocator = std::allocator< std::pair<const Key, Value> >
> class unordered_map;

Typical usage depends on default values for most of these parameters:

using my_map=std::unordered_map<int,std::string>;

but things get cumbersome when we want to specify one of the usually defaulted types:

using my_allocator = ...;
using my_map=std::unordered_map<
int, std::string,
std::hash<int>, std::equal_to<int>,
my_allocator< std::pair<const int, std::string> >
>;

In the example, we are forced to specify the hash and equality predicate with their default value types just to get to the allocator, which is the parameter we really wanted to specify. Ideally we would like to have a syntax like this:

// this is not actual C++
using my_map = std::unordered_map<
Key=int, Value=std::string,
Allocator=my_allocator< std::pair<const int, std::string> >
>;

Turns out we can emulate this by resorting to designated initializers, introduced in C++20:

template<
typename Key, typename Value,
typename Hash = std::hash<Key>,
typename Equal = std::equal_to<Key>,
typename Allocator = std::allocator< std::pair<const Key,Value> >
>
struct unordered_map_config
{
Key *key = nullptr;
Value *value = nullptr;
Hash *hash = nullptr;
Equal *equal = nullptr;
Allocator *allocator = nullptr;

using type = std::unordered_map<Key,Value,Hash,Equal,Allocator>;
};

template<typename T>
constexpr T *type = nullptr;

template<unordered_map_config Cfg>
using unordered_map = typename decltype(Cfg)::type;

...

using my_map = unordered_map<{
.key = type<int>, .value = type<std::string>,
.allocator = type< my_allocator< std::pair<const int, std::string > > >
}>;

The approach taken by the simulation is to use designated initializers to create an aggregate object consisting of dummy null pointers: the values of the pointers do not matter, but their types are captured via CTAD and used to synthesize the associated std::unordered_map instantiation. Two more C++20 features this technique depends on are:

  • Non-type template parameters have been extended to accept literal types (which include aggregate types such as unordered_map_config instantiations).
  • The class template unordered_map_config can be specified as a non-type template parameter of unordered_map. In C++17, we would have had to define unordered_map as
    template<auto Cfg>
    using unordered_map = typename decltype(Cfg)::type;
    which would force the user to explicit name unordered_map_config in
    using my_map = unordered_map<unordered_map_config{...}>;

There is still the unavoidable noise of having to use the type template alias since, of course, aggregate initialization is about values rather than types.

Another limitation of this simulation is that we cannot mix named and unnamed parameters:

// compiler error: either all initializer clauses should be designated
// or none of them should be
using my_map = unordered_map<{
type<int>, type<std::string>,
.allocator = type< my_allocator< std::pair<const int, std::string > > >
}>;

C++20 designated parameters are more restrictive than their C99 counterpart; some of the constraints (initializers cannot be specified out of order) are totally valid in the context of C++, but I personally fail to see why mixing named and unnamed parameters would pose any problem.

Monday, January 17, 2022

Start Wordle with TARES

There have been some discussions on what the best first guess is for the game Wordle, but none, to the best of my knowledge, has used the following approach. After each guess, the game answers back with a matching result like these:

■■■■■ (all letters wrong), 

■■ (two letters right, one mispositioned),

■■■■■ (all letters right).

There are 35=243 possible answers. From an information-theoretic point of view, the word we are trying to guess is a random variable (selected from a predefined dictionary), and the information we are obtaining by submitting our query is measured by the entropy formula

H(guess) = pi log2 pi bits,

where pi is the probability that the game returns the i-th answer (i = 1, ... , 243) for our particular guess. So, the best first guess is the one for which we get the most information, that is, the associated entropy is maximum. Intuitively speaking, we are going for the guess that yields the most balanced partition of the dictionary words as grouped by their matching result: entropy is maximum when all pi are equal (this is impossible for our problem, but gives an upper bound on the attainable entropy of log2(243) = 7.93 bits).

Let's compute then the best guesses. Wordle uses a dictionary of 2,315 entries which is unfortunately not disclosed; in its place we will resort to Stanford GraphBase list. I wrote a trivial C++17 program that goes through each of the 5,757 words of Stanford's list and computes its associated entropy as a first guess (see it running online). The resulting top 10 best words, along with their entropies are:

TARES    6.20918
RATES    6.11622
TALES    6.09823
TEARS    6.05801
NARES    6.01579
TIRES    6.01493
REALS    6.00117
DARES    5.99343
LORES    5.99031
TRIES    5.98875