Undefined behavior (UB) in C and C++ is a clear and present danger to developers, especially when they are writing code that will execute near a trust boundary. A less well-known kind of undefined behavior exists in the intermediate representation (IR) for most optimizing, ahead-of-time compilers. For example, LLVM IR has undef and poison in addition to true explodes-in-your-face C-style UB. When people become aware of this, a typical reaction is: “Ugh, why? LLVM IR is just as bad as C!” This piece explains why that is not the correct reaction.

Undefined behavior is the result of a design decision: the refusal to systematically trap program errors at one particular level of a system. The responsibility for avoiding these errors is delegated to a higher level of abstraction. For example, it is obvious that a safe programming language can be compiled to machine code, and it is also obvious that the unsafety of machine code in no way compromises the high-level guarantees made by the language implementation. Swift and Rust are compiled to LLVM IR; some of their safety guarantees are enforced by dynamic checks in the emitted code, other guarantees are made through type checking and have no representation at the LLVM level. Either way, UB at the LLVM level is not a problem for, and cannot be detected by, code in the safe subsets of Swift and Rust. Even C can be used safely if some tool in the development environment ensures that it will not execute UB. The L4.verified project does exactly this.

The essence of undefined behavior is the freedom to avoid a forced coupling between error checks and unsafe operations. The checks, once decoupled, can be optimized, for example by being hoisted out of loops or eliminated outright. The remaining unsafe operations can be — in a well-designed IR — mapped onto basic processor operations with little or no overhead. As a concrete example, consider this Swift code:

func add(a : Int, b : Int)->Int {
  return (a & 0xffff) + (b & 0xffff);
}

Although a Swift implementation must trap on integer overflow, the compiler observes that overflow is impossible and emits this LLVM IR:

define i64 @add(i64 %a, i64 %b) {
  %0 = and i64 %a, 65535
  %1 = and i64 %b, 65535
  %2 = add nuw nsw i64 %0, %1
  ret i64 %2
}

Not only has the checked addition operation been lowered to an unchecked one, but also the add instruction has been marked with LLVM’s nsw and nuw attributes, indicating that both signed and unsigned overflow are undefined. In isolation these attributes provide no benefit, but they may enable additional optimizations after this function is inlined. When the Swift benchmark suite is compiled to LLVM, about one in eight addition instructions has an attribute indicating that integer overflow is undefined.

In this particular example the nsw and nuw attributes are redundant since an optimization pass could re-derive the fact that the add cannot overflow. However, in general these attributes and others like them add real value by avoiding the need for potentially expensive static analyses to rediscover known program facts. Also, some facts cannot be rediscovered later, even in principle, since information is lost at some compilation steps.

In summary, undefined behavior in programmer-visible abstractions represents an aggressive and dangerous tradeoff: it sacrifices program correctness in favor of performance and compiler simplicity. On the other hand, UB at lower levels of the system, such as machine code or a compiler IR, is an internal design choice that needn’t have any effect on the programmer-facing parts of the system. This kind of UB simply requires us to accept that safety checks can be usefully factored out of their corresponding unsafe operations to afford efficient execution.

Type-based alias analysis, where pointers to different types are assumed to point to distinct objects, gives compilers a simple and effective way to disambiguate memory references in order to generate better code. Unfortunately, C and C++ make it easy for programmers to violate the assumptions upon which type-based alias analysis is built. “Strict aliasing” refers to a collection of rules in the C and C++ standards that restrict the ways in which you are allowed to modify and look at memory objects, in order to make type-based alias analysis work in these weakly-typed languages. The problem is that the strict aliasing rules contain tricky and confusing corner cases and also that they rule out many idioms that have historically worked, such as using a pointer type cast to view a float as an unsigned, in order to inspect its bits. Such tricks are undefined behavior. See the first part of this post for more of an introduction to these issues.

The purpose of this piece is to call your attention to a new paper, Detecting Strict Aliasing Violations in the Wild, by Pascal Cuoq and his colleagues. C and C++ programmers should read it. Sections 1 and 2 introduce strict aliasing, they’re quick and easy.

Section 3 shows what compilers think about strict aliasing problems by looking at how a number of C functions get translated to x86-64 assembly. This material requires perseverance but it is worth taking the time to understand the examples in detail, because compilers apply the same thinking to real programs that they apply to tiny litmus tests.

Section 4 is about a new tool, built as part of Trust-in-Soft’s static analyzer, that can diagnose violations of the strict aliasing rules in C code. As the paper says, “it works best when applied on definite inputs,” meaning that the tool should be used as an extended checker for tis-interpreter. Pascal tells me that a release containing the strict aliasing checker is planned, but the time frame is not definite. In any case, readers interested in strict aliasing, but not specifically in tools for dealing with it, can skip this section.

Section 5 applies the strict aliasing checker to open source software. This is good reading because it describes problems that are very common in the wild today. Finding a bug in zlib was a nice touch: zlib is small and has already been looked at closely. Some programs mitigate these bugs by asking the compiler to avoid enforcing the strict aliasing rules: LLVM, GCC, and Intel CC all take a -fno-strict-aliasing flag and MSVC doesn’t implement type-based alias analysis at all. Many other programs contain time bombs: latent UB bugs that don’t happen to be exploited now, that might be exploited later when the compiler becomes a bit brighter.

Also see libcrunch and its paper and a paper about SafeType.

[This piece is loosely a followup to this one.]

Background

Once a piece of software reaches a certain size, it is guaranteed to be loosely specified and not completely understood by any individual. It gets committed to many times per day by people who are only loosely aware of each others’ work. It has many dependencies including the compiler, operating system, and libraries, all of which are buggy in their own special ways, and all of which are updated from time to time. Moreover, it usually has to run atop several different platforms, each one individually quirky. Given the massive number of possibilities for flaky behavior, why should we expect our large piece of software to work as expected? One of the most important reasons is testing. That is, we routinely ensure that it works as intended in every important configuration and on every important platform, and when it doesn’t work we have smart people tracking down and fixing the issues.

Today we’re talking about testing LLVM. In some ways, a compiler makes a very friendly target for testing:

• The input format (source code) and output format (assembly code) are well-understood and have independent specifications.
• Many compilers have an intermediate representation (IR) that has its own documented semantics and can be dumped and parsed, making it easier (though not always easy) to test internals.
• It is often the case that a compiler is one of several independent implementations of a given specification, such as the C++ standard, enabling differential testing. Even when multiple implementations are unavailable, we can often test a compiler against itself by comparing the output of different backends or different optimization modes.
• Compilers are usually not networked, concurrent, or timing-dependent, and overall interact with the outside world only in very constrained ways. Moreover, compilers are generally intended to be deterministic.
• Compilers usually don’t run for very long, so they don’t have to worry too much about resource leaks or recovering gracefully from error conditions.

But in other ways, compilers are not so easy to test:

• Production compilers are supposed to be fast, so they are often written in an unsafe language and may skimp on assertions. They use caching and lazy evaluation when possible, adding complexity. Furthermore, splitting compiler functionality into lots of clean, independent little passes leads to slow compilers, so there tends to be some glomming together of unrelated or not-too-closely-related functionality, making it more difficult to understand, test, and maintain the resulting code.
• The invariants on compiler-internal data structures can be hellish and are often not documented completely.
• Some compiler algorithms are difficult, and it is almost never the case that a compiler implements a textbook algorithm exactly, but rather a close or distant relative of it.
• Compiler optimizations interact in difficult ways.
• Compilers for unsafe languages do not have lots of obligations when compiling undefined behaviors, placing the responsibility for avoiding UB outside of the compiler (and on the person creating test cases for the compiler). This complicates differential testing.
• The standards for compiler correctness are high since miscompilations are tough to debug and also they can quietly introduce security vulnerabilities in any code that they compile.

So, with that background out of the way, how is LLVM tested?

Unit Tests and Regression Tests

LLVM’s first line of defense against bugs is a collection of tests that get run when a developer builds the check target. All of these tests should pass before a developer commits a patch to LLVM (and of course many patches should include some new tests). I have a fairly fast desktop machine that runs 19,267 tests in 96 seconds. The number of tests that run depends on what auxiliary LLVM projects you have downloaded (compiler-rt, libcxx, etc.) and, to a lesser extent, on what other software gets autodetected on your machine (e.g. the OCaml bindings don’t get tested unless you have OCaml installed). These tests need to be fast so developers can run them often, as mentioned here. Additional tests get run by some alternate build targets such as check-all and check-clang.

Some of the unit/regression tests are at the API level, these use Google Test, a lightweight framework that provides C++ macros for hooking into the test framework. Here’s a test:

TEST_F(MatchSelectPatternTest, FMinConstantZero) {
  parseAssembly(
      "define float @test(float %a) {\n"
      "  %1 = fcmp ole float %a, 0.0\n"
      "  %A = select i1 %1, float %a, float 0.0\n"
      "  ret float %A\n"
      "}\n");
  // This shouldn't be matched, as %a could be -0.0.
  expectPattern({SPF_UNKNOWN, SPNB_NA, false});
}

The first argument to the TEST_F macro indicates the name of the test case (a collection of tests) and the second names the actual test shown here. The parseAssembly() and expectPattern() methods respectively call into an LLVM API and then check that this had the expected result. This example is from ValueTrackingTest.cpp. Many tests can be put into a single file, keeping things fast by avoiding forks/execs.

The other infrastructure used by LLVM’s fast test suite is lit, the LLVM Integrated Tester. lit is shell-based: it executes commands found in a test case, and considers the test to have been successful if all of its sub-commands succeed.

Here’s a test case for lit (I grabbed the top of this file, which contains additional tests that don’t matter to us right now):

; RUN: opt < %s -instcombine -S | FileCheck %s

define i64 @test1(i64 %A, i32 %B) {
        %tmp12 = zext i32 %B to i64
        %tmp3 = shl i64 %tmp12, 32
        %tmp5 = add i64 %tmp3, %A
        %tmp6 = and i64 %tmp5, 123
        ret i64 %tmp6
; CHECK-LABEL: @test1(
; CHECK-NEXT: and i64 %A, 123
; CHECK-NEXT: ret i64
}

This test case is making sure that InstCombine, the LLVM-level peephole optimization pass, is able to notice some useless instructions: the zext, shl, and add are not needed here. The CHECK-LABEL line looks for the line of optimized code that begins the function, the first CHECK-NEXT makes sure that the and instruction is on the next line, and the second CHECK-NEXT makes sure the ret instruction is on the line following the and (thanks Michael Kuperstein for correcting an earlier explanation of this test).

To run this test case, the file is interpreted three times. First, lit scans it looking for lines containing RUN: and executes each associated command. Second, the file is interpreted by opt, the standalone optimizer for LLVM IR; this happens because lit replaces the %s variable with the name of the file being processed. Since comments in textual LLVM IR are preceded by a semicolon, the lit directives are ignored by opt. The output of opt is piped to the FileCheck utility which parses the file yet again, looking for commands such as CHECK and CHECK-NEXT; these tell it to look for strings in its stdin, and to return a non-zero status code if any of the specified strings isn't found. (CHECK-LABEL is used to divide up a file into a collection of logically separate tests.)

An important part of a long-term testing campaign is using coverage tools to find parts of the code base that aren't being tested. Here's a recent LLVM coverage report based on running the unit/regression tests. This data is pretty interesting to poke around in. Let's take a quick look at coverage of InstCombine, which is generally very good. An interesting project for someone wanting to get started with LLVM would be to write and submit test cases that cover untested parts of InstCombine. For example, here's the first uncovered code (colored red) in InstCombineAndOrXor.cpp:

The comment tells us what the transformation is looking for, it should be fairly easy to target this code with a test case. Code that can't be covered is dead; some dead code wants to be removed, other code such as this example (from the same file) is a bug if it isn't dead:

Trying to cover these lines is a good idea, but in that case you're trying to find bugs in LLVM, as opposed to trying to improve the test suite. It would probably be good to teach the coverage tool to not tell us about lines that are marked unreachable.

The LLVM Test Suite

In contrast with the regression/unit tests, which are part of the main LLVM repository and can be run quickly, the test suite is external and takes longer to run. It is not expected that developers will run these tests prior to committing; rather, these tests get run automatically and often, on the side, by LNT (see the next section). The LLVM test suite contains entire programs that are compiled and run; it isn't intended to look for specific optimizations, but rather to help ascertain the quality and correctness of the generated code overall.

For each benchmark, the test suite contains test inputs and their corresponding expected outputs. Some parts of the test suite are external, meaning that there is support for invoking the tests, but the tests themselves are not part of the test suite and must be downloaded separately, typically because the software being compiled is not free.

LNT

LNT (LLVM Nightly Test) doesn't contain any test cases; it is a tool for aggregating and analyzing test results, focusing on monitoring the quality of the compiler's generated code. It consists of local utilities for running tests and submitting results, and then there's a server side database and web frontend that makes it easy to look through results. The NTS (Nightly Test Suite) results are here.

BuildBot

The Linux/Windows BuiltBot and the Darwin one (I don't know why there are two) are used to make sure LLVM configures, builds, and passes its unit/regression tests on a wide variety of platforms and in a variety of configurations. The BuildBot has some blame support to help find problematic commits and will send mail to their authors.

Eclectic Testing Efforts

Some testing efforts originate outside of the core LLVM community and aren't as systematic in terms of which versions of LLVM get tested. These tests represent efforts by individuals who usually have some specific tool or technique to try out. For example, for a long time my group tested Clang+LLVM using Csmith and reported the resulting bugs. (See the high-level writeup.) Sam Liedes applied afl-fuzz to the Clang test suite. Zhendong Su and his group have been finding a very impressive number of bugs. Nuno Lopes has done some awesome formal-methods-based testing of optimization passes that he'll hopefully write about soon.

A testing effort that needs to be done is repeatedly generating a random (but valid) IR function, running a few randomly-chosen optimization passes on it, and then making sure the optimized function refines the original one (the desired relationship is refinement, rather than equivalence, because optimizations are free to make the domain of definedness of a function larger). This needs to be done in a way that is sensitive to LLVM-level undefined behavior. I've heard that something like this is being worked on, but don't have details.

Testing in the Wild

The final level of testing is, of course, carried out by LLVM's users, who occasionally run into crashes and miscompiles that have escaped other testing methods. I've often wanted to better understand the incidence of compiler bugs in the wild. For crashes this could be done by putting a bit of telemetry into the compiler, though few would use this if opt-in, and many would (legitimately) object if opt-out. Miscompiles in the wild are very hard to quantify. My hypothesis is that most miscompiles go unreported since reducing their triggers is so difficult. Rather, as people make pseudorandom code changes during debugging, they eventually work around the problem by luck and then promptly forget about it.

A big innovation would be to ship LLVM with a translation validation scheme that would optionally use an SMT solver to prove that the compiler's output refines its input. There are all sorts of challenges including undefined behavior and the fact that it's probably very difficult to scale translation validation up to the large functions that seem to be the ones that trigger miscompilations in practice.

Alternate Test Oracles

A "test oracle" is a way to decide whether a test passes or fails. Easy oracles include "compiler terminates with exit code 0" and "compiled benchmark produces the expected output." But these miss lots of interesting bugs, such as a use-after-free that doesn't happen to trigger a crash or an integer overflow (see page 7 of this paper for an example from GCC). Bug detectors like ASan, UBSan, and Valgrind can instrument a program with oracles derived from the C and C++ language standards, providing lots of useful bug-finding power. To run LLVM under Valgrind when executing it on its test suite, pass -DLLVM_LIT_ARGS="-v --vg" to CMake, but be warned that Valgrind will give some false positives that seem to be difficult to eliminate. To instrument LLVM using UBSan, pass -DLLVM_USE_SANITIZER=Undefined to CMake. This is all great but there's more work left to do since UBSan/ASan/MSan don't yet catch all undefined behaviors and also there are defined-but-buggy behaviors, such as the unsigned integer overflow in GCC mentioned above, that we'd like to flag when they are unintentional.

What Happens When a Test Fails?

A broken commit can cause test failure at any level. The offending commit is then either amended (if easy to fix) or backed out (if it turns out to be deeply flawed or otherwise undesirable in light of the new information supplied by failing tests). These things happen reasonably often, as they do in any project that is rapidly pushing changes into a big, complicated code base with many real-world users.

When a test fails in a way that is hard to fix right now, but that will get fixed eventually (for example when some new feature gets finished), the test can be marked XFAIL, or "expected failure." These are counted and reported separately by the testing tool and they do not count towards the test failures that must be fixed before a patch becomes acceptable.

Conclusions

Testing a large, portable, widely-used software system is hard; there are a lot of moving parts and a lot of ongoing work is needed if we want to prevent LLVM's users from being exposed to bugs. Of course there are other super-important things that have to happen to maintain high-quality code: good design, code reviews, tight semantics on the internal representation, static analysis, and periodic reworking of problematic areas.

I’ve had a post with this title on the back burner for years but I was never quite convinced that it would say anything I haven’t said before. Last night I watched Chandler Carruth’s talk about undefined behavior at CppCon 2016 and it is good material and he says it better than I think I would have, and I wanted to chat about it a bit.

First off, this is a compiler implementor’s point of view. Other smart people, such as Dan Bernstein, have a very different point of view (but also keep in mind that Dan doesn’t believe compiler optimization is useful).

Chandler is not a fan of the term nasal demons, which he says is misleadingly hyperbolic, since the compiler isn’t going to maliciously turn undefined behavior (UB) into code for erasing your files or whatever. This is true, but Chandler leaves out the fact that our 28-year-long computer security train wreck (the Morris Worm seems like as good a starting point as any) has been fueled to a large extent by undefined behavior in C and (later) C++ code. In other words, while the compiler won’t emit system calls for erasing your files, a memory-related UB in your program will permit a random person on the Internet to insert instructions into your process that issue system calls doing precisely that. From this slightly broader point of view, nasal demons are less of a caricature.

The first main idea in Chandler’s talk is that we should view UB at the PL level as being analogous to narrow contracts on APIs. Let’s look at this in more detail. An API with a wide contract is one where you can issue calls in any order, and you can pass any arguments to API calls, and expect predictable behavior. One simple way that an API can have a wider contract is by quietly initializing library state upon the first call into the library, as opposed to requiring an explicit call to an init() function. Some libraries do this, but many libraries don’t. For example, an OpenSSL man page says “SSL_library_init() must be called before any other action takes place.” This kind of wording indicates that a severe obligation is being placed on users of the OpenSSL API, and failing to respect it would generally be expected to result in unpredictable behavior. Chandler’s goal in this first part of the talk is to establish the analogy between UB and narrow API contracts and convince us that not all APIs want to be maximally wide. In other words, narrow APIs may be acceptable when their risks are offset by, for example, performance advantages.

Coming back to programming languages (PL), we can look at something like the signed left shift operator as exposing an API. The signed left shift API in C and C++ is particularly narrow and while many people have by now internalized that it can trigger UB based on the shift exponent (e.g., 1 << -1 is undefined), fewer developers have come to terms with restrictions on the left hand argument (e.g., 0 << 31 is defined but 1 << 31 is not). Can we design a wide API for signed left shift? Of course! We might specify, for example, that the result is zero when the shift exponent is too large or is negative, and that otherwise the result is the same as if the signed left-hand argument was interpreted as unsigned, shifted in the obvious way, and then reinterpreted as signed.

At this point in the talk, we should understand that “UB is bad” is an oversimplification, that there is a large design space relating to narrow vs. wide APIs for libraries and programming language features, and that finding the best point in this design space is not straightforward since it depends on performance requirements, on the target platform, on developers’ expectations, and more. C and C++, as low-level, performance-oriented languages, are famously narrow in their choice of contracts for core language features such as pointer and integer operations. The particular choices made by these languages have caused enormous problems and reevaluation is necessary and ongoing. The next part of Chandler’s talk provides a framework for deciding whether a particular narrow contract is a good idea or not.

Chandler provides these four principles for narrow language contracts:

1. Checkable (probabilistically) at runtime
2. Provide significant value: bug finding, simplification, and/or optimization
3. Easily explained and taught to programmers
4. Not widely violated by existing code that works correctly and as intended

The first criterion, runtime checkability, is crucial and unarguable: without it, we get latent errors of the kind that continue to contribute to insecurity and that have been subject to creeping exploitation by compiler optimizations. Checking tools such as ASan, UBSan, and tis-interpreter reduce the problem of finding these errors to the problem of software testing, which is very difficult, but which we need to deal with anyhow since there’s more to programming than eliminating undefined behaviors. Of course, any property that can be checked at runtime can also be checked without running the code. Sound static analysis avoids the need for test inputs but is otherwise much more difficult to usefully implement than runtime checking.

Principle 2 tends to cause energetic discussions, with (typically) compiler developers strongly arguing that UB is crucial for high-quality code generation and compiler users equally strongly arguing for defined semantics. I find the bug-finding arguments to be the most interesting ones: do we prefer Java-style two’s complement integers or would we rather retain maximum performance as in C and C++ or mandatory traps as in Swift or a hybrid model as in Rust? Discussions of this principle tend to center around examples, which is mostly good, but is bad in that any particular example excludes a lot of other use cases and other compilers and other targets that are also important.

Principle 3 is an important one that tends to get neglected in discussions of UB. The intersection of HCI and PL is not incredibly crowded with results, as far as I know, though many of us have some informal experience with this topic because we teach people to program. Chandler’s talk contains a section on explaining signed left shift that’s quite nice.

Finally, Principle 4 seems pretty obvious.

One small problem you might have noticed is that there are undefined behaviors that fail one or more of Chandler’s criteria, that many C and C++ compiler developers will defend to their dying breath. I’m talking about things like strict aliasing and termination of infinite loops that violate (at least) principles 1 and 3.

In summary, the list of principles proposed by Chandler is excellent and, looking forward, it would be great to use it as a standard set of questions to ask about any narrow contract, preferably before deploying it. Even if we disagree about the details, framing the discussion is super helpful.

Humans are typically not very good at reasoning about integers with limited range, whereas computers fundamentally work with limited-range numbers. This impedance mismatch has been the source of a lot of bugs over the last 50 years. The solution comes in multiple parts.

In most programming languages, the default integer type should be a bignum: an arbitrary-precision integer that allocates more space when needed. Efficient bignum libraries exist and most integers never end up needing more than one machine word anyway, except in domains like crypto. As far as I’m concerned, for ~95% of programming tasks integer overflow is a solved problem: it should never happen. The solution isn’t yet implemented widely enough, but happily there are plenty of languages such as Python that give bignums by default.

When performance and/or predictability is a major consideration, bignums won’t work and we’re stuck with fixed-width integers that wrap, trap, saturate, or trigger undefined behavior upon overflow. Saturation is a niche solution that we won’t discuss further. Undefined behavior is bad but at least it enables a few loop optimizations and also permits trapping implementations. Although wrapping is an extremely poor default, there are a few good things to say about it: wrapping is efficient, people have come to expect it, and it is a good match for a handful of application domains.

Swift is a modern programming language that traps instead of providing bignums, this is also a generally sensible behavior. Why not bignums? The About Swift web page says that Swift gives “the developer the control needed in a true systems programming language,” so perhaps the designers were worried about unpredictable allocations. I’d love to see a study of the performance of best-of-breed trapping and bignum implementations on important modern applications.

The Rust developers have adopted a hybrid solution where integer overflows trap in debug builds and wrap in optimized builds. This is pragmatic, especially since integer overflows do not compromise Rust’s memory safety guarantees. On the other hand, perhaps as MIR matures, Rust will gravitate towards checking in optimized builds.

For safety-critical programs, the solution to integer overflow is to prove that it cannot happen using some combination of manual reasoning, testing, and formal verification. SPARK Ada and the TrustInSoft analyzer are suitable for proving that integer overflows won’t occur. More work is needed to make this sort of verification scalable and less expert-intensive.

Systems programming tasks, such as building operating systems, language runtimes, and web browsers, are caught in the middle. Wrapping sucks, bignums and trapping are slow or at least perceived as slow (and you do not want to trap or allocate while handling a hardware interrupt anyway), and the codes are too large for formal verification and thorough testing. One answer is to work hard on making trapping fast. For example, Swift has a high-level optimization pass specifically for removing integer overflow checks, and then the LLVM optimization passes do more of this, and then the LLVM backends can lower checked math operations to efficient condition code checks, and then modern Intel processors fuse the resulting branch-on-overflow instructions away.

In summary, bignums should be the default whenever this is feasible, and trapping on overflow should be the backup default behavior. Continued work on the compilers and processors will ensure that the overhead of trapping overflow checks is down in the noise. Java-style wrapping integers should never be the default, this is arguably even worse than C and C++’s UB-on-overflow which at least permits an implementation to trap. In domains where wrapping, trapping, and allocation are all unacceptable, we need to be able to prove that overflow does not occur.

I’ll end up with a few random observations:

• Dan Luu wrote a piece on the overhead of overflow checking.
• Arbitrary (fixed) width bitvectors are a handy datatype and I wish more languages supported them. These can overflow but it’s not as big of a deal since we choose the number of bits.
• Explicitly ranged integers as seen in Ada are also very nice, there’s no reason that traps should only occur at the 32-bit or 64-bit boundaries.
• The formal verification community ignored integer overflow for far too long, there’s a long history of assuming that program integers behave like mathematical integers. Things are finally better though.

UPDATE: I didn’t want this piece to be about C and C++ but I should have clarified that it is only signed overflow in these languages that is undefined behavior; unsigned overflow is defined to be two’s complement wraparound. While it is possible to trap on unsigned overflow — UBSan has a flag that turns on these traps — this behavior does not conform to the standards. Even so, trapping unsigned wraparounds can — in some circumstances — be useful for finding software defects. The question is whether the wraparound was intentional or not.