Tearable Atomics

Published Proposal,

This version:
ISO JTC1/SC22/WG21: Programming Language C++


Atomics which can tear—which are more relaxed than relaxed—seem useless. This paper shows otherwise.

1. Edit History

1.1. r0 → r1

In Toronto, SG1 discussed [p0690r0], the different approaches that it proposed, and didn’t really conclude anything. This update proposes a single one among all approaches that were proposed in r0.

2. Background

Is it useful for C++ to support "tearable" atomic memory ordering, where the access participates in atomic ordering as strongly as memory_order_relaxed accesses, but where the memory is allowed to tear (i.e. isn’t single-copy atomic). In C++ standards speak: particular atomic object are not indivisible with respect to all other atomic accesses to that object.

Indeed, advanced concurrency and parallelism users will sometimes find a need for objects which are accessed by multiple threads, yet either:

  1. Rely on separate atomic objects to provide inter-thread observability guarantees; or

  2. Use lock-free accesses on a memory locations on which they would also like to speculate.

What we describe often amounts to a data race:

Data races are undefined behavior, and it is often said that there is no such thing as a "benign" data race [benign]. Issues that arise when mixing atomic and non-atomic accesses have been discussed before in the context of the C language’s memory model [n4136].

Reconciling these types of issue is discussed in the concurrency and parallelism group from time to time, and so far only one-off solutions have been proposed to the Committee, or the problem has been punted. We believe that this proposal can fix this interesting problem once and for all by looking at how other areas have solved this issue.

After all, this has been solved in non-C++ contexts. To assembly programmers, or to those used to memory models such as Linux’s memory model [p0124r2], the distinctions the Standard makes seems overly complex. Their code simply defines atomicity as a property or code rather than C++'s definition of atomicity as a property of particular memory locations during an object’s lifetime. Indeed, in assembly a memory location can be concurrently accessed with a regular non-atomic memory instruction as well as an atomic memory instruction.

3. Usecases

Sample usecases include:

  1. Speculative load before a compare-and-exchange instruction

  2. Sequence locks

  3. Work-stealing deque

Others exist, but we will focus on these three.

3.1. Speculative Load

Consider the following code:

struct alignas(sizeof(intptr_t) * 2) Node {
    intptr_t l, r;

Node action(const Node& old);

void do_action(std::atomic<Node> *n) {
    Node old = n->load(std::memory_order_relaxed); // Relaxed loads can’t tear.
    while (!n->compare_exchange_weak(old, action(old), std::memory_order_release,

In this example, all lock-free operations (including load / store) must be implemented as a compare-and-exchange or load-linked / store-conditional:

The relaxed memory access could instead speculate by using a tearable load / store, potentially cheaper than a compare-and-exchange or load-link / store-conditional, as long as a compare-and-exchange retry loop follows it to handle races. If tearing occurs then the compare-and-exchange does the right thing.

3.2. Seqlock

In the case of sequence locks, the data being protected can be accessed non-atomically and is known to be race-free if the sequence number hasn’t changed before and after the data was retrieved, and if it isn’t "tagged" as being modified (below, by being odd):

template<typename T>
struct Data {
  std::atomic<unsigned> sequence_number = 0;
  std::atomic<T> value0;
  std::atomic<T> value1;

std::tuple<T, T> reader(const Data& data) {
  T value0, value1;
  unsigned sequence_before, sequence_after;
  do {
    sequence_before = data.sequence_number.load(std::memory_order_acquire);
    value0 = data.value0.load(std::memory_order_relaxed);
    value1 = data.value1.load(std::memory_order_relaxed);
    sequence_after = data.sequence_number.load(std::memory_order_relaxed);
  } while (sequence_before != sequence_after || sequence_before & 1);
  return {value0, value1};

void writer(Data& data, T value0, T value1) {
  auto sequence_start = data.sequence_number.load(std::memory_order_relaxed);
  data.sequence_number.store(sequence_start + 1, std::memory_order_relaxed);
  data.value0.store(value0, std::memory_order_release);
  data.value1.store(value1, std::memory_order_release);
  data.sequence_number.store(sequence_start + 2, std::memory_order_release);

Notice that in C++ the values being protected must be atomic because this algorithm doesn’t use more common acquire / release patterns which C++ encourages. Doing otherwise would be a data race according to the memory model. One would need to add fences for non-atomic accesses to not be racy.

A more in-depth discussion of seqlock [seqlock] is available.

For the purpose of our discussion, it is especially interesting to considers value types T which are never lock-free.

3.3. Work-Stealing Deque

It appears intended that implementations of the parallelism TS [N4578] back scheduling of partitioned work using an ABP work-stealing scheduler, originally described in [ThreadSched].

Under this model, each thread has a local deque of work where it can access the "bottom" of the deque without any synchronization overhead, but other threads can concurrently remove work from the "top". A similar data structure was presented implementable on hardware without double-wide CAS instructions in [WSDeque].

In the Chase-Lev deque, the "top" counter is used to track concurrent access to the top of the deque; and access to the actual elements in the top of the deque is unsynchronized. From the original paper:

public Object steal() {
    long t = this.top;
    long b = this.bottom;
    CircularArray a = this.activeArray;
    long size = b - t;
    if (size <= 0) return Empty;
    Object o = a.get(t);
    if (! casTop(t, t+1))
        return Abort;
    return o;

or translated to C++:

variant<empty_t, abort_t, T> steal() {
    int64_t t = top.load();
    int64_t b = bottom.load();
    T * a = activeArray.load();
    int64_t size = b - t;
    if (size <= 0) return empty_t{};
    T o = a[t % aSize];
    if (! top.compare_exchange_strong(t, t+1))
        return abort_t{};
    return o;

If the deque contains only one element, this causes undefined behavior in C++'s memory model, because the element accessed on line 16 may be concurrently written by the owning thread of the deque. However, if a data race occurs, the CAS on line 17 fails, and the result of this speculative read is never observed. Only one thread can win the CAS race to increment top.

Of note, imposing that T be an atomic type in this instance defeats the entire purpose of using the work-stealing deque, as it would require the owning "bottom" thread to use synchronized access to read from the bottom (including potentially taking a lock of T is large; egregious for a data structure whose purpose is to be lock-free) in the uncontended cases, even though the correctness of the algorithm is maintained by discarding any potentially torn results.

4. Further Considerations

Extrapolating from the above examples, it is also useful to consider a few extra usecases where:

5. Proposal

A previous version of this paper [p0690r0] considered several possible solutions for making the above examples well-formed. Here we select one based on SG1 feedback. (We would like to emphasize that none of the authors are deeply invested in this particular solution, but all of us would like to make progress towards C++ supporting our use cases somehow; if a different solution would be much more acceptable, that is excellent feedback.) We give strawman wording for our definitions, but with no expectation at all that it is final.

In particular our solution is an adaption of [p0603r0]. We define two new member functions for std::atomic:

T std::atomic<T>::nonatomic_load(
    memory_order order = memory_order_seq_cst) const noexcept;

Effects: equivalent to load(order), but if there exists a potentially concurrent conflicting action X (i.e. a modification to A) which neither happens before nor happens after this call, this call returns an indeterminate value. If this occurs, this call is considered to "read the value written by X" as described in [atomics.fences].

Remarks: Lock free, regardless of the values of is_lock_free() and is_always_lock_free().

We would also require wording changes to [dcl.init.12]'s definition of indeterminate values, allowing expressions like

auto a = atomic_var.nonatomic_load();

to produce indeterminate values without invoking undefined behavior. (We don’t provide such wording here.)

This function allows a simple and correct §3.2 Seqlock and §3.3 Work-Stealing Deque but does not fix §3.1 Speculative Load without some additional work. Even with a relaxation of [dcl.init], an indeterminately-valued Node is unsafe to use in action(). Clearly the intention of that code is that any sequence of arbitrary bytes is well-defined as a Node, but more wording work would be required to allow this.

(Note that race_or<T> as proposed in [n3710] does no better, as the speculatively loaded Node must be realized from its race_or holder, even when the value is in fact racy; this was defined in that paper as undefined behavior).

We also have the matching write variant:

void std::atomic<T>::nonatomic_store(
    T desired, memory_order order = memory_order_seq_cst) const noexcept;

Requires: The order argument shall not be memory_order_consume, memory_order_acquire, nor memory_order_acq_rel.

Effects: Replaces (non-atomically) the value of this with the value of desired, affecting memory according to the value of order. If there exists a potentially concurrent conflicting action X, which neither happens before nor happens after this call, then:

If no such action X exists, then this call is exactly equivalent to store(desired, order).

Remarks: Lock free, regardless of the values of is_lock_free() and is_always_lock_free().

This function optimizes the write-side of a seqlock or deque, but isn’t strictly necessary for its correctness. (In the seqlock case the performance advantage is minor; in the deque case, this is more likely to be significant.) One difficulty here is that we’d need even more extensions to the indeterminate value changes, since we can effectively "poison" a std::atomic<T> with an indeterminate value in the case of two racy writes.


Informative References

Hans-J. Boehm. How to miscompile programs with “benign” data races. May 2011. URL: http://hboehm.info/boehm-hotpar11.pdf
H. Boehm, et al.. Specifying the absence of "out of thin air" results (LWG2265). URL: https://wg21.link/n3710
M. Batty, P. Sewell, et al.. C Concurrency Challenges Draft. 13 October 2014. URL: https://wg21.link/n4136
Jared Hoberock. Working Draft, Technical Specification for C++ Extensions for Parallelism Version 2. 22 February 2016. URL: https://wg21.link/n4578
Paul E. McKenney, Ulrich Weigand, Andrea Parri, Boqun Feng. Linux-Kernel Memory Model. 26 June 2016. URL: https://wg21.link/p0124r2
JF Bastien, Michael Spencer. The Curious Case of Padding Bits, Featuring Atomic Compare-and-Exchange. 12 November 2016. URL: https://wg21.link/p0528r0
JF Bastien; Michael Spencer. The Curious Case of Padding Bits, Featuring Atomic Compare-and-Exchange. 6 February 2018. URL: https://wg21.link/p0528r1
Andrew Hunter. safe memcpy: A simpler implementation primitive for seqlock and friends. URL: https://wg21.link/p0603r0
JF Bastien, Billy Robert O'Neal III. Tearable Atomics. URL: https://wg21.link/p0690r0
Hans-J. Boehm. Can Seqlocks Get Along with Programming Language Memory Models?. 16 June 2012. URL: http://safari.ece.cmu.edu/MSPC2012/slides_posters/boehm-slides.pdf
Nimar S. Arora; Robert D. Blumofe; C. Greg Plaxton. Thread Scheduling for Multiprogrammed Microprocessors. June 1998. URL: https://www.eecis.udel.edu/~cavazos/cisc879-spring2008/papers/arora98thread.pdf
David Chase; Yossi Lev. Dynamic Circular Work-Stealing Deque. July 2005. URL: http://citeseerx.ist.psu.edu/viewdoc/download?doi=