Sunday, July 6, 2025

Maps on chains

(From a conversation with Vassil Vassilev.) Suppose we want to have a C++ map where the keys are disjoint, integer intervals of the form [a, b]:

struct interval
{
  int min, max;
};

std::map<interval, std::string> m;

m[{0, 9}] = "ABC";
m[{10, 19}] = "DEF";

This looks easy enough, we just have to write the proper comparison operator for intervals, right?

bool operator<(const interval& x, const interval& y)
{
  return x.max < y.min;
}

But what happens if we try to insert an interval which is not disjoint with those already in the map?

m[{5, 14}] = "GHI"; // intersects both {0, 9} and {10, 19}

The short answer is that this is undefined behavior, but let's try to undertand why. C++ associative containers depend on the comparison function (typically, std::less<Key>) inducing a so-called strict weak ordering on elements of Key. In layman terms, a strict weak order < behaves as the "less than" relationship does for numbers, except that there may be incomparable elements x, y such that xy and y ≮ x; for numbers, this only happens if x = y, but in the case of a general SWO we allow for distinct, incomparable elements as long as they form equivalence classes. A convenient way to rephrase this condition is to require that incomparable elements are totally equivalent in how they compare to the rest of the elements, that is, they're truly indistinguishable from the point of view of the SWO. Getting back to our interval scenario, we have three possible cases when comparing [a, b] and [c, d]:

  • If b < c, the intervals don't overlap and [a, b] < [c, d].
  • If d < a, the intervals don't overlap and [c, d] < [a, b].
  • Otherwise, the intervals are incomparable. This can happen when [a, b] and [c, d] overlap partially or when they are exactly the same interval.

What we have described is a well known relationship called interval order. The problem is that the interval order is not a strict weak order. Let's depict a Hasse diagram for the interval order on integer intervals [a,b] between 0 and 4:

A Hasse diagram works like this: given two elements x and y, x < y iff there is a path going upwards that connects x to y. For instance, the fact that [1, 1] < [3, 4] is confirmed by the path [1, 1] → [2, 2] → [3, 4]. But the diagram also serves to show why this relationship is not a strict weak order: for it to be so, incomparable elements (those not connected) should be indistinguishable in that they are connected upwards and downwards with the same elements, and this is clearly not the case (in fact, it is not the case for any pair of incomparable elements). In mathematical terms, our relationship is of a more general type called a strict partial order.

Going back to C++, associative containers assume that the elements inserted form a linear arrangement with respect to <: when we try to insert a new element y that is incomparable with some previously inserted element x, the properties of strict weak orders allows us to determine that x and y are equivalent, so nothing breaks up (the insertion fails as a duplicate for a std::map, or y is added next to x for a std::multimap).

There's a way to accommodate our interval scenario with std::map, though. As long as the elements we are inserting belong to the same connecting path or chainstd::map can't possibly "know" if our relationship is a strict weak order or not: it certainly looks like one for the limited subset of elements it has seen so far. Implementation-wise, we just have to make sure we're not comparing partially overlapping intervals:

struct interval_overlap: std::runtime_error
{
  interval_overlap(): std::runtime_error("interval overlap"){}
};

bool operator<(const interval& x, const interval& y)
{
  if(x.min == y.min) {
    if(x.max != y.max) throw interval_overlap();
    return false;
  }
  else if(x.min < y.min) {
    if(x.max >= y.min) throw interval_overlap();
    return true;
  }
  else /* x.min > y.min */
  {
    if(x.min <= y.max) throw interval_overlap();
    return false;
  }
}

std::map<interval, std::string> m;

m[{0, 9}] = "ABC";
m[{10, 19}] = "DEF";
m[{5, 14}] = "GHI"; // throws interval_overlap

So, when we try to insert an element that would violate the strict weak ordering constraints (that is, it lies outside the chain connecting the intervals inserted so far), an exception is thrown and no undefined behavior is hit. A strict reading of the standard would not allow this workaround, as it is required that the comparison object for the map induce a strict weak ordering for all possible values of Key, not only those in the container (or that is my interpretation, at least): for all practical purposes, though, this works and will foreseeably continue to work for all future revisions of the standard.

Bonus point. Thanks to heterogeneous lookup, we can extend our use case to support lookup for integers inside the intervals:

struct less_interval
{
  using is_transparent = void;

  bool operator()(const interval& x, const interval& y) const
  {
    // as operator< before
  }

  bool operator()(int x, const interval& y) const
  {
    return x < y.min;
  }
  
  bool operator()(const interval& x, int y) const
  {
    return x.max < y; 
  }    
};

std::map<interval, std::string, less_interval> m;
  
m[{0, 9}] = "ABC";
m[{10, 19}] = "DEF";

std::cout << m.find(5)->second << "\n"; // prints "ABC"

Exercise for the reader: Can you formally prove that this works? (Hint: define a strict weak order on ℕ I, where ℕ is the set of natural numbers and I is a collection of disjoint integer intervals.)

Thursday, May 23, 2024

WG21, Boost, and the ways of standardization

Goals of standardization

Standardization, in a form resembling our contemporary practices, began in the Industrial Revolution as a means to harmonize incipient mass production and their associated supply chains through the concept of interchangeability of parts. Some early technical standards are the Gribeauval system (1765, artillery pieces) and the British Standard Whitworth (1841, screw threads). Taylorism expanded standardization efforts from machinery to assembly processes themselves with the goal of increasing productivity (and, it could be said, achieving interchangeability of workers). Standards for metric systems, such as that of Revolutionary France (1791) were deemed "scientific" (as befitted the enlightenment spirit of the era) in that they were defined by exact, reproducible methods, but their main motivation was to facilitate local and international trade rather than support the advancement of science. We see a common theme here: standardization normalizes or leverages technology to favor industry and trade, that is, technology precedes standards.

This approach is embraced by 20th century standards organizations (DIN 1917, ANSI 1918, ISO 1947) through the advent of electronics, telecommunications and IT, and up to our days. Technological advancement, or, more generally, innovation (a concept coined around 1940 and ubiquitous today) is not seen as the focus of standardization, even though standards can promote innovation by consolidating advancements and best practices upon which further cycles of innovation can be built —and potentially be standardized in their turn. This interplay between standardization and innovation has been discussed extensively within standards organizations and outside. The old term "interchangeability of parts" has been replaced today by the more abstract concepts of compatibility, interoperability and (within the realm of IT) portability.

Standardizing programming languages

Most programming languages are not officially standardized, but some are. As of today, these are the ISO-standardized languages actively maintained by dedicated working groups within the ISO/IEC JTC1/SC22 subcommittee for programming languages:

  • COBOL (WG4)
  • Fortran (WG5)
  • Ada (WG9)
  • C (WG14)
  • Prolog (WG17)
  • C++ (WG21)

What's the purpose of standardizing a programming language? JC22 has a sort of foundational paper which centers on the benefits of portability, understood as both portability across systems/environments and portability of people (a rather blunt allusion to old-school Taylorism). The paper does not mention the subject of implementation certification, which can play a significant role for languages such as Ada that are used in heavily regulated sectors. More importantly to our discussion, it does not either mention what position SC22 holds with respect to innovation: regardless, we will see that innovation does indeed happen within SC22 workgroups, in what represents a radical departure from classical standardization practices.

WG21

C++ was mostly a one man's effort since its inception in the early 80s until the publication of The Annotated C++ Reference Manual (ARM, 1990), which served as the basis for the creation of an ANSI/ISO standardization committee that would eventually release its first C++ standard in 1998. Bjarne Stroustrup cited avoidance of compiler vendor lock-in (a variant of portability) as a major reason for having the language standardized —a concern that made much sense in a scene then dominated by company-owned languages such as Java.

Innovation was seen as WG21's business from its very beginning: some features of the core language, such as templates and exceptions, were labeled as experimental in the ARM, and the first version of the standard library, notably including Alexander Stepanov's STL, was introduced by the committee in the 1990-1998 period with little or no field experience. After a minor update to C++98 in 2003, the innovation pace picked up again in subsequent revisions of the standard (2011, 2014, 2017, 2020, 2023), and the current innovation backlog does not seem to falter; if anything, we could say that the main blocker for innovation within the standard is lack of human resources in WG21 rather than lack of proposals.

Innovation vs. adoption

Not all new features in the C++ standard have originated within WG21. We must distinguish here between the core language and the standard library:

  • External innovation in the core language is generally hard as it requires writing or modifying a C++ compiler, a task outside the capabilities of many even though this has been made much more accessible with the emergence of open-source, extensible compiler frameworks such as LLVM. As a result, most innovation activity here happens within WG21, with some notable exceptions like Circle and Cpp2. Others have chosen to depart from the C++ language completely (Carbon, Hylo), so their potential impact on C++ standardization is remote at best.
  • As for the standard library, the situation is more varied. These are some examples:
In general, the trend for the evolution of the standard library seems to be towards proposing new components straight into the standard with very little field experience.

Pros and cons of standardization

The history of C++ standardization has met with some resounding successes (STL, templates, concurrency, most vocabulary types) as well as failures (exported templates, GC support, exception specifications, std::auto_ptr)  and in-between scenarios (std::regexranges).

Focusing on the standard library, we can identify benefits of standardization vs. having a separate, non-standard component:

  • The level of exposure to C++ users increases dramatically. Some companies have bans on the usage of external libraries, and even if no bans are in place, consuming the standard library is much more convenient than having to manage external dependencies —though this is changing.
  • Standardization ensures a high level of (system) portability, potentially beyond the reach of external library authors without access to exotic environments.
  • For components with high interoperability potential (think vocabulary types), having them in the standard library guarantees that they become the tool of choice for API-level module integration.

But there are drawbacks as well that must be taken into consideration:

  • The evolution of a library halts or reduces significantly once it is standardized. One major factor for this is WG21's self-imposed restriction to preserve backwards compatibility, and in particular ABI compatibility. For example:
Another factor contributing to library freeze may be the lack of motivation from the authors once they succeed in getting their proposals accepted, as the process involved is very demanding and can last for years.
  • Some libraries cover specialized domains that standard library implementors cannot be expected to master. Some cases in point:
    • Current implementations of std::regex are notoriously slower than Boost.Regex, a situation aggravated by the need to keep ABI compatibility.
    • Correct and efficient implementations of mathematical special functions require ample expertise in the area of numerical computation. As a result, Microsoft standard library implements these as mere wrappers over Boost.Math, and libc++ seems to be following suit. This is technically valid, but begs the question of what the standardization of these functions was useful for to begin with.
  • Additions to the upcoming standard (as of this writing, C++26) don't benefit users immediately because the community typically lags behind by two or three revisions of the language.

So, standardizing a library component is not always the best course of action for the benefit of current and future users of that component. Back in 2001, Stroustrup remarked that "[p]eople sometime forget that a library doesn't have to be part of the standard to be useful", but, to this day, WG21 does not seem to have formal guidelines as to what constitutes a worthy addition to the standard, or how to engage with the community in a world of ever-expanding and more accessible external libraries. We would like to contribute some modest ideas in that direction.

An assessment model for library standardization

Going back to the basic principles of standards, the main benefits to be derived from standardizing a technology (in our case, a C++ library) are connected to higher compatibility and interoperability as a means to increase overall productivity (assumedly correlated to the level of usage of the library within the community). Leaving aside for the moment the size of the potential target audience, we identify two characteristics of a given library that make it suitable for standardization:

  • Its portability requirements, defined as the level of coupling that an optimal implementation has with the underlying OS, CPU architecture, etc. The higher these requirements the more sense it makes to include the library as a mandatory part of the standard.
  • Its interoperability potential, that is, how much the library is expected to be used as part of public APIs interconnecting different program modules vs. as a private implementation detail. A library with high interoperability potential is maximally useful when included in the common software "stack" shared by the community.

So, the baseline standardization value of a library, denoted V0, can be modeled as:

V0 = aP + bI,

where P denotes the library's portability requirements and I its interoperability potential. The figure shows the baseline standardization value of some library domains within the P-I plane. The color red indicates that this value is low, green that it is high.

A low baseline standardization value for a library does not mean that the library is not useful, but rather that there is little gain to be obtained from standardizing it as opposed to making it available externally. The locations of the exemplified domains in the P-I plane reflect the author's estimation and may differ from that of the reader.

Now, we have seen that the adoption of a library requires some prior field experience, defined as

E = T·U,

where T is the age of the library and U is average number of users.

  • When E is very low, the library is not mature enough and standardizing it can result in a defective design that will be much harder to fix within the standard going forward; this effectively decreases the net value of standardization.
  • On the contrary, if E is very high, which is correlated to the library having already reached its maximum target audience, the benefits of standardization are vanishingly small: most people are already using the library and including it into the official standard has little value added —the library has become a de facto standard.

So, we may expect to attain an optimum standardization opportunity S between the extremes E = 0 and Emax.

Finally, the net standardization value of a library is defined as

V = V0·S·Umax,

where Umax is the library's maximum target audience. Being a conceptual model, the purpose of this framework is not so much to establish a precise evaluation formula as to help stakeholders raise the right questions when considering a library for standardization:

  • How high are the library's portability requirements?
  • How high its interoperability potential?
  • Is it too immature yet? Does it have actual field experience?
  • Or, on the contrary, has it already reached its maximum target audience?
  • How big is this audience?

Boost, the standard and beyond

Boost was launched in 1998 upon the idea that "[a] world-wide web site containing a repository of free C++ class libraries would be of great benefit to the C++ community". Serving as a venue for future standardization was mentioned only as a secondary goal, yet very soon many saw the project as a launching pad towards the standard library, a perception that has changed since. We analyze the different stages of this 25+-year-old project in connection with its contributions to the standard and to the community.

Golden era: 1998-2011

In its first 14 years of existence, the project grew from 0 to 113 libraries, for a total uncompressed size of 324 MB. Out of these 113 libraries, 12 would later be included in C++11, typically with modifications (Array, Bind, Chrono, EnableIf, Function, Random, Ref, Regex, SmartPtr, Thread, Tuple, TypeTraits); it may be noted that, even at this initial stage, most Boost libraries were not standardized or meant for standardization. From the point of view of the C++ standard library, however, Boost was the first contributor by far. We may venture some reasons for this success:

  • There was much low-hanging fruit in the form of small vocabulary types and obvious utilities.
  • Maybe due to a combination of scarce competition and sheer luck, Boost positioned itself very quickly as the go-to place for contributing and consuming high-quality C++ libraries. This ensured a great deal of field experience with the project.
  • Many of the authors of the most relevant libraries were also prominent figures within the C++ community and WG21.

Middle-age issues: 2012-2020

By 2020, Boost had reached 164 libraries totaling 717 MB in uncompressed size (so, the size of the average library, including source, tests and documentation, grew by 1.5 with respect to 2011). Five Boost libraries were standardized between C++14 and C++20 (Any, Filesystem, Math/Special Functions, Optional, Variant): all of these, however, were already in existence before 2012, so the rate of successful new contributions from Boost to the standard decreased effectively to zero in this period. There were some additional unsuccessful proposals (Mp11).

The transition of Boost from the initial ramp-up to a more mature stage met with several scale problems that impacted negatively the public perception of the project (and, to some extent that we haven't able to determine, its level of usage). Of particular interest is a public discussion that took place in 2022 on Reddit and touched on several issues more or less recognized within the community of Boost authors:

  • The default/advertised way to consume Boost as a monolithic download introduces a bulky, hard to manage dependency on projects.
  • B2, Boost's native build technology, is unfamiliar to users more accustomed to widespread tools such as CMake.
  • Individual Boost libraries are perceived as bloated in terms of size, internal dependences and compile times. Alternative competing libraries are self-contained, easier to install and smaller as they rely on newer versions of the C++ standard.
  • Many useful components are already provided by the standard library.
  • There are great differences between libraries in terms of their quality; some libraries are all but abandoned.
  • Documentation is not good enough, in particular if compared to cppreference.com, which is regarded as the golden standard in this area.

A deeper analysis reveals some root causes for this state of affairs:

  • Overall, the Boost project is very conservative and strives not to break users' code on each version upgrade (even though, unlike the standard, backwards API/ABI compatibility is not guaranteed). In particular, many Boost authors are reluctant to increase the minimum C++ standard version required for their libraries. Also, there is no mechanism in place to retire libraries from the project.
  • Supporting older versions of the C++ standard locks in some libraries with suboptimal internal dependencies, the most infamous being Boost.MPL, which many identify (with or without reason) as responsible for long compile times and cryptic error messages.
  • Boost's distribution and build mechanisms were invented in an era where package managers and build systems were not prevalent. This works well for smaller footprints but presents scaling problems that were not foreseen at the beginning of the project.
  • Ultimately, Boost is a federation of libraries with different authors and sensibilities. This fact accounts for the various levels of documentation quality, user support, maintenance, etc.

Some of these characteristics are not negative per se, and have in fact resulted in an extremely durable and available service to the C++ community that some may mistakenly take for granted. Supporting "legacy C++" users is, by definition, neglected by WG21, and maintaining libraries that were already standardized is of great value to those who don't live on the edge (and, in the case of the std::regex fiasco, those who do). Confronted with the choice of serving the community today vs. tomorrow (via standardization proposals), the Boost project took, perhaps unplannedly, the first option. This is not to say that all is good with the Boost project, as many of the problems found in 2012-2020 are strictly operational.

Evolution: 2021-2024 and the future

Boost 1.85 (April 2024) contains 176 libraries (7% increase with respect to 2020) and has a size of 731 MB (2% increase). Only one Boost component has partially contributed to the C++23 standard library (boost::container::flat_map), though there has been some unsuccessful proposals (the most notable being Boost.Asio).

In response to the operational problems we have described before, some authors have embarked on a number of improvement and modernization tasks:

  • Beginning in Boost 1.82 (Apr 2023), some core libraries announced the upcoming abandonment of C++03 support as part of a plan to reduce code base sizes, maintenance costs, and internal dependencies on "polyfill" components. This initiative has a cascading effect on dependent libraries that is still ongoing.
  • Alongside C++03 support drop, many libraries have been updated to reduce the number of internal dependencies (that even were, in some cases, cyclic). The figure shows the cumulative histograms of the number of dependencies for Boost libraries in versions 1.66 (2017), 1.75 (2020) and 1.85 (2024):
  • Official CMake support for the entire Boost project was announced in Oct 2023. This support also allows for downloading and building of individual libraries (and their dependencies).
  • On the same front of modular consumption, there is work in progress to modularize B2-based library builds, which will enable package managers such as Conan to offer Boost libraries individually. vcpkg already offers this option.
  • Starting in July 2023, boost.org includes a search widget indexing the documentation of all libraries. The ongoing MrDocs project seeks to provide a Doxygen-like tool for automatic C++ documentation generation that could eventually support Boost authors  —library docs are currently written more or less manually in a plethora of languages such as raw HTML, Quickbook, Asciidoc, etc. There is a new Boost website in the works scheduled for launch during mid-2024.

Where is Boost headed? It must be stressed again that the project is a federation of authors without a central governing authority in strategic matters, so the following should be taken as an interpretation of detected current trends:

  • Most of the recently added libraries cover relatively specific application-level domains (networking/database protocols, parsing) or else provide utilities likely to be superseded by future C++ standards, as is the case with reflection (Describe, PFR). One library is a direct backport of a C++17 standard library component (Charconv). Boost.JSON provides yet another solution in an area already rich with alternatives external to the standard library. Boost.LEAF proposes an approach to error handling radically different to that of the latest standard (std::expected). Boost.Scope implements and augment a WG21 proposal currently on hold (<experimental/scope>).
  • In some cases, standard compatibility has been abandoned to provide faster performance or richer functionality (Container, Unordered, Variant2).
  • No new library supports C++03, which reduces drastically their number of internal dependencies (except in the case of networking libraries depending on Boost.Asio).
  • On the other hand, most new libraries are still conservative in that they only require C++11/14, with some exceptions (Parser and Redis require C++17, Cobalt requires C++20).
  • There are some experimental initiatives like the proposal to serve Boost libraries as C++ modules, which has been met with much interest and support from the Visual Studio team. An important appeal of this idea is that it will allow compiler vendors and the committee to obtain field experience from a large, non-trivial codebase.

The current focus of Boost seems then to have shifted from standards-bound innovation to higher-level and domain-specific libraries directly available to users of C++11/14 and later. More stress is increasingly being put on maintenance, reduced internal dependencies and modular availability, which further cements the thesis that Boost authors are more concerned about serving the C++ community from Boost itself than eventually migrating to the standard. There is still a flow of ideas from Boost to WG21, but they do not represent the bulk of the project activity.

Conclusions

Traditionally, the role of standardization has been to consolidate previous innovations that have reached maturity so as to maximize their potential for industry vendors and users. In the very specific case of programming languages, and WG21/LEWG in particular, the standards committee has taken on the role of innovator and is pushing the industry rather than adopting external advancements or coexisting with them. This presents some problems related to lack of field experience, limitations to internal evolution imposed by backwards compatibility and an associated workload that may exceed the capacity of the committee. Thanks to open developer platforms (GitHub, GitLab), widespread build systems (CMake) and package managers (Conan, vcpkg), the world of C++ libraries is richer and more available than ever. WG21 could reconsider its role as part of an ecosystem that thrives outside and alongside its own activity. We have proposed a conceptual evaluation model for standardization of C++ libraries that may help in the conversations around these issues. Boost has shifted its focus from being a primary venue for standardization to serving the C++ community (including users of previous versions of the language) through increasingly modular, high level and domain-specific libraries. Hopefully, the availability and reach of the Boost project will help gain much needed field experience that could eventually lead to further collaborations with and contributions to WG21 in a non-preordained way.

Thursday, April 4, 2024

A case in API ergonomics for ordered containers

Suppose we have a std::set<int> and would like to retrieve the elements between values a and b, both inclusive. This task is served by operations std::set::lower_bound and std::set::upper_bound:

std::set<int> x=...;

// elements in [a,b]
auto first = x.lower_bound(a);
auto last = x.upper_bound(b);

while(first != last) std::cout<< *first++ <<" ";

Why do we use lower_bound for the first iterator and upper_bound for the second? The well-known STL convention is that a range of elements is determined by two iterators first and last, where first points to the first element of the range and last points to the position right after the last element. This is done so that empty ranges can be handled without special provisions (first == last).

Now, with this convention in mind and considering that

  • lower_bound(a) returns an iterator to the first element not less than a,
  • upper_bound(b) returns an iterator to the first element greater than b,

we can convince ourselves that the code above is indeed correct. The situations where one or both of the interval endpoints are not inclusive can also be handled:

// elements in [a,b)
auto first = x.lower_bound(a);
auto last  = x.lower_bound(b);

// elements in (a,b]
auto first = x.upper_bound(a);
auto last  = x.upper_bound(b);

// elements in (a,b)
auto first = x.upper_bound(a);
auto last  = x.lower_bound(b);

but getting them right requires some thinking.

Boost.MultiIndex introduces the operation range to handle this type of queries:

template<typename LowerBounder,typename UpperBounder>
std::pair<iterator,iterator>
range(LowerBounder lower, UpperBounder upper);

lower and upper are user-provided predicates that determine whether an element is not to the left and not to the right of the considered interval, respectively. The formal specification of LowerBounder and UpperBounder is quite impenetrable, but using this facility, in particular in combination with Boost.Lambda2, is actually straightforward:

// equivalent to std::set<int>
boost::multi_index_container<int> x=...;

using namespace boost::lambda2;

// [a,b] auto [first, last] = x.range(_1 >= a, _1 <= b);
// [a,b) auto [first, last] = x.range(_1 >= a, _1 < b); // (a,b] auto [first, last] = x.range(_1 > a, _1 <= b); // (a,b) auto [first, last] = x.range(_1 > a, _1 < b);

The resulting code is much easier to read and to get right in the first place, and is also more efficient than two separate calls to [lower|upper]_bound   (because the two internal rb-tree top-to-bottom traversals can be partially joined in the implementation of range). Just as importantly, range handles situations such as this:

int a = 5;
int b = 2; // note a > b

// elements in [a,b]
auto first = x.lower_bound(a);
auto last = x.upper_bound(b);

// undefined behavior
while(first != last) std::cout<< *first++ <<" ";

When a > b, first may be strictly to the right of last, and consequently the while loop will crash or never terminate. range, on the other hand, handles the situation gracefully and returns an empty range.

We have seen an example of how API design can help reduce programming errors and increase efficiency by providing higher-level facilities that model and encapsulate scenarios otherwise served by a combination of lower-level operations. It may be interesting to have range-like operations introduced for standard associative containers.

Friday, October 20, 2023

Bulk visitation in boost::concurrent_flat_map

Introduction

boost::concurrent_flat_map and its boost::concurrent_flat_set counterpart are Boost.Unordered's associative containers for high-performance concurrent scenarios. These containers dispense with iterators in favor of a visitation-based interface:

boost::concurrent_flat_map<int, int> m;
...
// find the element with key k and increment its associated value
m.visit(k, [](auto& x) {
  ++x.second;
});

This design choice was made because visitation is not affected by some inherent problems afflicting iterators in multithreaded environments.

Starting in Boost 1.84, code like the following:

std::array<int, N> keys;
...
for(const auto& key: keys) {
  m.visit(key, [](auto& x) { ++x.second; });
}

can be written more succintly via the so-called bulk visitation API:

m.visit(keys.begin(), keys.end(), [](auto& x) { ++x.second; });

As it happens, bulk visitation is not provided merely for syntactic convenience: this operation is internally optimized so that it performs significantly faster than the original for-loop. We discuss here the key ideas behind bulk visitation internal design and analyze its performance.

Prior art

In their paper "DRAMHiT: A Hash Table Architected for the Speed of DRAM", Narayanan et al. explore some optimization techniques from the domain of distributed system as translated to concurrent hash tables running on modern multi-core architectures with hierarchical caches. In particular, they note that cache misses can be avoided by batching requests to the hash table, prefetching the memory positions required by those requests and then completing the operations asynchronously when enough time has passed for the data to be effectively retrieved. Our bulk visitation implementation draws inspiration from this technique, although in our case visitation is fully synchronous and in-order, and it is the responsibility of the user to batch keys before calling the bulk overload of boost::concurrent_flat_map::visit.

Bulk visitation design

As discussed in a previous article, boost::concurrent_flat_map uses an open-addressing data structure comprising:

  • A bucket array split into 2n groups of N = 15 slots.
  • A metadata array associating a 16-byte metadata word to each slot group, used for SIMD-based reduced-hash matching.
  • An access array with a spinlock (and some additional information) for locked access to each group.

The happy path for successful visitation looks like this:

  1. The hash value for the looked-up key and its mapped group position are calculated.
  2. The metadata for the group is retrieved and matched against the hash value.
  3. If the match is positive (which is the case for the happy path), the group is locked for access and the element indicated by the matching mask is retrieved and compared with the key. Again, in the happy path this comparison is positive (the element is found); in the unhappy path, more elements (within this group or beyond) need be checked.

(Note that happy unsuccessful visitation simply terminates at step 2, so we focus our analysis on successful visitation.) As the diagram shows, the CPU has to wait for memory retrieval between steps 1 and 2 and between steps 2 and 3 (in the latter case, retrievals of mutex and element are parallelized through manual prefetching). A key insight is that, under normal circumstances, these memory accesses will almost always be cache misses: successive visitation operations, unless for the very same key, won't have any cache locality. In bulk visitation, the stages of the algorithm are pipelined as follows (the diagram shows the case of three operations in the bulk batch):

The data required at step N+1 is prefetched at the end of step N. Now, if a sufficiently large number of operations are pipelined, we can effectively eliminate cache miss stalls: all memory addresses will be already cached by the time they are used.

The operation visit(first, last, f) internally splits [first, last) into chunks of bulk_visit_size elements that are then processed as described above. This chunk size has to be sufficiently large to give time for memory to be actually cached at the point of usage. On the upper side, the chunk size is limited by the number of outstanding memory requests that the CPU can handle at a time: in Intel architectures, this is limited by the size of the line fill buffer, typically 10-12. We have empirically confirmed that bulk visitation maxes at around bulk_visit_size = 16, and stabilizes beyond that.

Performance analysis

For our study of bulk visitation performance, we have used a computer with a Skylake-based Intel Core i5-8265U CPU:


Size/core Latency [ns]
L1 data cache 32 KB 3.13
L2 cache 256 KB 6.88
L3 cache 6 MB 25.00
DDR4 RAM
77.25

We measure the throughput in Mops/sec of single-threaded lookup (50/50 successful/unsuccessful) for both regular and bulk visitation on a boost::concurrent_flat_map<int, int> with sizes N = 3k, 25k, 600k, and 10M: for the three first values, the container fits entirely into L1, L2 and L3, respectively. The test program has been compiled with clang-cl for Visual Studio 2022 in release mode.

As expected, the relative performance of bulk vs. regular visitation grows as data is fetched from a slower cache (or RAM in the latter case). The theoretical throughput achievable by bulk visitation has been estimated from regular visitation by subtracting memory retrieval times as calculated with the following model:

  • If the container fits in Ln (L4 = RAM), Ln−1 is entirely occupied by metadata and access objects (and some of this data spills over to Ln).
  • Mutex and element retrieval times (which only apply to successful visitation) are dominated by the latter.

Actual and theoretical figures match quite well, which sugggests that the algorithmic overhead imposed by bulk visitation is negligible.

We have also run benchmarks under conditions more similar to real-life for boost::concurrent_flat_map, with and without bulk visitation, and other concurrent containers, using different compilers and architectures. As an example, these are the results for a workload of 50M insert/lookup mixed operations distributed across several concurrent threads for different data distributions with Clang 12 on an ARM64 computer:

5M updates, 45M lookups
skew=0.01
5M updates, 45M lookups
skew=0.5
5M updates, 45M lookups
skew=0.99

Again, bulk visitation increases performance noticeably. Please refer to the benchmark site for further information and results.

Conclusions and next steps

Bulk visitation is an addition to the interface of boost::concurrent_flat_map and boost::concurrent_flat_set that improves lookup performance by pipelining the internal visitation operations for chunked groups of keys. The tradeoff for this increased throughput is higher latency, as keys need to be batched by the user code before issuing the visit operation.

The insights we have gained with bulk visitation for concurrent containers can be leveraged for future Boost.Unordered features:

  • In principle, insertion can also be made to operate in bulk mode, although the resulting pipelined algorithm is likely more complex than in the visitation case, and thus performance increases are expected to be lower.
  • Bulk visitation (and insertion) is directly applicable to non-concurrent containers such as boost::unordered_flat_map: the main problem for this is one of interface design because we are not using visitation here as the default lookup API (classical iterator-based lookup is provided instead). Some possible options are:
    1. Use visitation as in the concurrent case.
    2. Use an iterator-based lookup API that outputs the resulting iterators to some user-provided buffer (probably modelled as an output "meta" iterator taking container iterators).

Bulk visitation will be officially shipping in Boost 1.84 (December 2023) but is already available by checking out the Boost.Unordered repo. If you are interested in this feature, please try it and report your local results and suggestions for improvement. Your feedback on our current and future work is much welcome.

Friday, August 18, 2023

User-defined class qualifiers in C++23

It is generally known that type qualifiers (such as const and volatile in C++) can be regarded as a form of subtyping: for instance, const T is a supertype of T because the interface (available operations) of T are strictly wider than those of const T. Foster et al. call a qualifier q positive if q T is a supertype of T, and negative it if is the other way around. Without real loss of generality, in what follows we only consider negative qualifiers, where q T is a subtype of (extends the interface of) T.

C++23 explicit object parameters (coloquially known as "deducing this") allow for a particularly concise and effective realization of user-defined qualifiers for class types beyond what the language provides natively. For instance, this is a syntactically complete implementation of qualifier mut, the dual/inverse of const (not to be confused with mutable):

template<typename T>
struct mut: T
{
using T::T;
};

template<typename T>
T& as_const(T& x) { return x;}

template<typename T>
T& as_const(mut<T>& x) { return x;}

struct X
{
void foo() {}
void bar(this mut<X>&) {}
};

int main()
{
mut<X> x;
x.foo();
x.bar();

auto& y = as_const(x);
y.foo();
y.bar(); // error: cannot convert argument 1 from 'X' to 'mut<X> &'

X& z = x;
z.foo();
z.bar(); // error: cannot convert argument 1 from 'X' to 'mut<X> &'
}

The class X has a regular (generally accessible) member function foo and then bar, which is only accessible to instances of the form mut<X>. Access checking and implicit and explicit conversion between subtype mut<X> and mut<X> work as expected.

With some help fom Boost.Mp11, the idiom can be generalized to the case of several qualifiers:

#include <boost/mp11/algorithm.hpp>
#include <boost/mp11/list.hpp>
#include <type_traits>

template<typename T,typename... Qualifiers>
struct access: T
{
using qualifier_list=boost::mp11::mp_list<Qualifiers...>;

using T::T;
};

template<typename T, typename... Qualifiers>
concept qualified =
(boost::mp11::mp_contains<
typename std::remove_cvref_t<T>::qualifier_list,
Qualifiers>::value && ...);

// some qualifiers
struct mut;
struct synchronized;

template<typename T>
concept is_mut = qualified<T, mut>;

template<typename T>
concept is_synchronized = qualified<T, synchronized>;

struct X
{
void foo() {}

template<is_mut Self>
void bar(this Self&&) {}

template<is_synchronized Self>
void baz(this Self&&) {}

template<typename Self>
void qux(this Self&&)
requires qualified<Self, mut, synchronized>
{}
};

int main()
{
access<X, mut> x;

x.foo();
x.bar();
x.baz(); // error: associated constraints are not satisfied
x.qux(); // error: associated constraints are not satisfied

X y;
x.foo();
y.bar(); // error: associated constraints are not satisfied

access<X, mut, synchronized> z;
z.bar();
z.baz();
z.qux();
}
One difficulty remains, though:
int main()
{
access<X, mut, synchronized> z;
//...
access<X, mut>& w=z; // error: cannot convert from
// 'access<X,mut,synchronized>'
// to 'access<X,mut> &'

}
access<T,Qualifiers...>& converts to T&, but not to access<T,Qualifiers2...>&  where Qualifiers2 is a subset of  Qualifiers (for the mathematically inclined, qualifiers q1, ... , qN over a type T induce a lattice of subtypes Q T, Q ⊆ {q1, ... , qN}, ordered by qualifier inclusion). Incurring undefined behavior, we could do the following:
template<typename T,typename... Qualifiers>
struct access: T
{
using qualifier_list=boost::mp11::mp_list<Qualifiers...>;

using T::T;

template<typename... Qualifiers2>
operator access<T, Qualifiers2...>&()
requires qualified<access, Qualifiers2...>
{
return reinterpret_cast<access<T, Qualifiers2...>&>(*this);
}
};
A more interesting challenge is the following: As laid out, this technique implements syntactic qualifier subtyping, but does not do anything towards enforcing the semantics associated to each qualifier: for instance, synchronized should lock a mutex automatically, and a qualifier associated to some particular invariant should assert it after each invocation to a qualifier-constraied member function. I don't know if this functionality can be more or less easily integrated into the presented framework: feedback on the matter is much welcome.

Friday, July 7, 2023

Inside boost::concurrent_flat_map

Introduction

Starting in Boost 1.83, Boost.Unordered provides boost::concurrent_flat_map, an associative container suitable for high-load parallel scenarios. boost::concurrent_flat_map leverages much of the work done for boost::unordered_flat_map, but also introduces innovations, particularly in the areas of low-contention operation and API design, that we find worth discussing.

State of the art

The space of C++ concurrent hashmaps spans a diversity of competing techniques, from traditional ones such as lock-based structures or sharding, to very specialized approaches relying on CAS instructions, hazard pointers, Read-Copy-Update (RCU), etc. We list some prominent examples:

  • tbb::concurrent_hash_map uses closed addressing combined with bucket-level read-write locking. The bucket array is split in a number of segments to allow for incremental rehashing without locking the entire table. Concurrent insertion, lookup and erasure are supported, but iterators are not thread safe. Locked access to elements is done via so-called accessors.
  • tbb::concurrent_unordered_map also uses closed addressing, but buckets are organized into lock-free split-ordered lists. Concurrent insertion, lookup, and traversal are supported, whereas erasure is not thread safe. Element access via iterators is not protected against data races.
  • Sharding consists in dividing the hashmap into a fixed number N of submaps indexed by hash (typically, the element x goes into the submap with index hash(x) mod N). Sharding is extremely easy to implement starting from a non-concurrent hashmap and provides incremental rehashing, but the degree of concurrency is limited by N. As an example, gtl::parallel_flat_hash_map uses sharding with submaps essentially derived from absl::flat_hash_map, and inherits the excellent performance of this base container.
  • libcuckoo::cuckoohash_map adds efficient thread safety to classical cuckoo hashing by means of a number of carefully engineered techniques including fine-grained locking of slot groups or "strips" (of size 4 by default), optimistic insertion and data prefetching.
  • Meta's folly::ConcurrentHashMap combines closed addressing, sharding and hazard pointers to elements to achieve lock-free lookup (modifying operations such as insertion and erasure lock the affected shard). Iterators, which internally hold a hazard pointer to the element, can be validly dereferenced even after the element has been erased from the map; access, on the other hand, is constant and elements are basically treated as immutable.
  • folly::AtomicHashMap is a very specialized hashmap that imposes severe usage restrictions in exchange for very high time and space performance. Keys must be trivially copyable and 32 or 64 bits in size so that they can be handled internally by means of atomic instructions; also, some key values must be reserved to mark empty slots, tombstones and locked elements, so that no extra memory is required for bookkeeping information and locks. The internal data structure is based on open addressing with linear probing. Non-modifying operations are lock-free. Rehashing is not provided: instead, extra bucket arrays are appended when the map becomes full, the expectation being that the user provide the estimated final size at construction time to avoid this rather inefficient growth mechanism. Element access is not protected against data races.
  • On a more experimental/academic note, we can mention initiatives such as Junction, Folklore and DRAMHiT. In general, these do not provide industry-grade container implementations but explore interesting ideas that could eventually be adopted by mainstream libraries, such as RCU-based data structures, lock-free algorithms relying on CAS and/or transactional memory, parallel rehashing and operation batching.
Design principles

Unlike non-concurrent C++ containers, where the STL acts as a sort of reference interface, concurrent hashmaps in the market differ wildly in terms of requirements, API and provided functionality. When designing boost::concurrent_flat_map, we have aimed for a general-purpose container

  • with no special restrictions on key and mapped types,
  • providing full thread safety without external synchronization mechanisms,
  • and disrupting as little as possible the conceptual and operational model of "traditional" containers.

These principles rule out some scenarios such as requiring that keys be of an integral type or putting an extra burden on the user in terms of access synchronization or active garbage collection. They also inform concrete design decisions:

  • boost::concurrent_flat_map<Key, T, Hash, Pred, Allocator> must be a valid instantiation in all practical cases where boost::unordered_flat_map<Key, T, Hash, Pred, Allocator> is.
  • Thread-safe value semantics are provided (including copy construction, assignment, swap, etc.)
  • All member functions in boost::unordered_flat_map are provided by boost::concurrent_flat_map except if there's a fundamental reason why they can't work safely or efficiently in a concurrent setting.

The last guideline has the most impact on API design. In particular, we have decided not to provide iterators, either blocking or not: if not-blocking, they're unsafe, and if blocking they increase contention when not properly used, and can very easily lead to deadlocks:

// Thread 1
map_type::iterator it1=map.find(x1), it2=map.find(x2);

// Thread 2
map_type::iterator it2=map.find(x2), it1=map.find(x1);

In place of iterators, boost::concurrent_flat_map offers an access API based on internal visitation, as described in a later section.

Data structure

boost::concurrent_flat_map uses the same open-addressing layout as boost::unordered_flat_map, where the bucket array is split into 2n groups of N = 15 slots and each group has an associated 16-byte metadata word for SIMD-based reduced-hash matching and insertion overflow control.

On top of this layout, two synchronization levels are added:

  • Container level: A read-write mutex is used to control access from any operation to the container. This access is always requested in read mode (i.e. shared) except for operations that require that the whole bucket array be replaced, like rehashing, swapping, assignment, etc. This means that, in practice, this level of synchronization does not cause any contention at all, even for modifying operations like insertion and erasure. To reduce cache coherence traffic, the mutex is implemented as an array of read-write spinlocks occupying separate cache lines, and each thread is assigned one spinlock in a round-robin fashion at thread_local construction time: read/shared access does only involve the assigned spinlock, whereas write/exclusive access, which is comparatively much rarer, requires that all spinlocks be locked.
  • Group level: Each group has a dedicated read-write spinlock to control access to its slots, plus an atomic insertion counter used for transactional optimistic insertion as described below.
Algorithms

The core algorithms of boost::concurrent_flat_map are variations of those of boost::unordered_flat_map with minimal changes to prevent data races while keeping group-level contention to a minimum.

In the following diagrams, white boxes represent lock-free steps, while gray boxes are executed within the scope of a group lock. Metadata is handled atomically both in locked and lock-free scenarios.

Most steps of the lookup algorithm (hash calculation, probing, element pre-checking via SIMD matching with the value's reduced hash) are lock-free and do not synchronize with any operation on the metadata. When SIMD matching detects a potential candidate, double-checking for slot occupancy and the actual comparison with the element are done within the group lock; note that the occupancy double check is necessary precisely because SIMD matching is lock-free and the status of the identified slot may have changed before group locking.

Insertion

The main challenge of any concurrent insertion algorithm is to prevent an element x from being inserted twice by different threads running at the same time. As open-addressing probing starts at a position p0 univocally determined by the hash value of x, a naïve (and flawed) approach is to lock p0 for the entire duration of the insertion procedure: this leads to deadlocking if the probing sequences of two different elements intersect.

We have implemented the following transactional optimistic insertion algorithm: At the beginning of insertion, the value of the insertion counter for the group at position p0 is saved locally and insertion proceeds normally, first checking that an element equivalent to x does not exist and then looking for available slots starting at p0 and locking only one group of the probing sequence at a time; when an available slot is found, the associated metadata is updated, the insertion counter at p0 is incremented, and:

  • If no other thread got in the way (i.e. if the pre-increment value of the counter coincides with the local value stored at the beginning), then the transaction is successful and insertion can be finished by storing the element into the slot before releasing the group lock.
  • Otherwise, metadata changes are rolled back and the entire insertion process is started over.

Our measurements indicate that, even under adversarial situations, the ratio of start-overs to successful insertions ranges in the parts per million.

Visitation API

From an operational point of view, container iterators serve two main purposes: combining lookup/insertion with further access to the relevant element:

auto it = m.find(k);
if (it != m.end()) {
  it->second = 0;
}

and container traversal:

// iterators used internally by range-for
for(auto& x: m) {
  x.second = 0;
}

Having decided that boost::concurrent_flat_map not rely on iterators due to their inherent concurrency problems, a design alternative is to move element access into the container operations themselves, where it can be done in a thread-safe manner. This is just a form of the familiar visitation pattern:

m.visit(k, [](auto& x) {
  x.second = 0;
});

m.visit_all([](auto& x) {
  x.second = 0;
});

boost::concurrent_flat_map provides visitation-enabled variations of classical map operations wherever it makes sense:

  • visit, cvisit (in place of find)
  • visit_all, cvisit_all (as a substitute of container traversal)
  • emplace_or_visit, emplace_or_cvisit
  • insert_or_visit, insert_or_cvisit
  • try_emplace_or_visit, try_emplace_or_cvisit

cvisit stands for constant visitation, that is, the visitation function is granted read-only access to the element, which has less contention than write access.

Traversal functions [c]visit_all and erase_if have also parallel versions:

m.visit_all(std::execution::par, [](auto& x) {
  x.second = 0;
});
Benchmarks

We've tested boost::concurrent_flat_map against tbb::concurrent_hash_map and gtl::parallel_flat_hash_map for the following synthetic scenario: T threads concurrently perform N operations update, successful lookup and unsuccessful lookup, randomly chosen with probabilities 10%, 45% and 45%, respectively, on a concurrent map of (int, int) pairs. The keys used by all operations are also random, where update and successful lookup follow a Zipf distribution over [1, N/10] with skew exponent s, and unsuccessful lookup follows a Zip distribution with the same skew s over an interval not overlapping with the former.

We provide the full benchmark code and results for different 64- and 32-bit architectures in a dedicated repository; here, we just show as an example the plots for Visual Studio 2022 in x64 mode on an AMD Ryzen 5 3600 6-Core @ 3.60 GHz without hyperthreading and 64 GB of RAM.

500k updates, 4.5M lookups
skew=0.01
500k updates, 4.5M lookups
skew=0.5
500k updates, 4.5M lookups
skew=0.99
5M updates, 45M lookups
skew=0.01
5M updates, 45M lookups
skew=0.5
5M updates, 45M lookups
skew=0.99

Note that, for the scenario with 500k updates, boost::concurrent_flat_map continues to improve after the number of threads exceed the number of cores (6), a phenomenon for which we don't have a readily explanation —we could hypothesize that execution is limited by memory latency, but the behavior does not reproduce in the scenario with 5M updates, where the cache miss ratio is necessarily higher. Note also that gtl::parallel_flat_hash_map performs comparatively worse for high-skew scenarios where the load is concentrated on a very small number of keys: this may be due to gtl::parallel_flat_hash_map having a much coarser lock granularity (256 shards in the configuration used) than the other two containers.

In general, results are very dependent on the particular CPU and memory system used; you are welcome to try out the benchmark in your architecture of interest and report back.

Conclusions and next steps

boost::concurrent_flat_map is a new, general-purpose concurrent hashmap that leverages the very performant open-addressing techniques of boost::unordered_flat_map and provides a fully thread-safe, iterator-free API we hope future users will find flexible and convenient.

We are considering a number of new functionalities for upcoming releases:

  • As boost::concurrent_flat_map and boost::unordered_flat_map basically share the same data layout, it's possible to efficiently implement move construction from one to another by simply transferring the internal structure. There are scenarios where this feature can lead to more performant execution, like, for instance, multithreaded population of a boost::concurrent_flat_map followed by single- or multithreaded read-only lookup on a boost::unordered_flat_map move-constructed from the former.
  • DRAMHiT shows that pipelining/batching several map operations on the same thread in combination with heavy memory prefetching can reduce or eliminate waiting CPU cycles. We have conducted some preliminary experiments using this idea for a feature we dubbed bulk lookup (providing an array of keys to look for at once), with promising results.

We're launching this new container with trepidation: we cannot possibly try the vast array of different CPU architectures and scenarios where concurrent hashmaps are used, and we don't have yet field data on the suitability of the novel API we're proposing for boost::concurrent_flat_map. For these reasons, your feedback and proposals for improvement are most welcome.