Restrict Access Property for mdspan and span

Published Proposal,

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


This paper proposes a semantic for the use of the property customization point on span and mdspan to express non-aliasing semantics analogous to those of the ISO-C keyword restrict. Reconceptualizing non-aliasing semantics as a customization point on a library feature addresses many of the previous ambiguities in non-aliasing semantics for C++, and the implications of this new approach are discussed.

1. Revision History

1.1. P0856r0

Address 2017-11-Albuquerque LEWG feedback to generate paper for restrict_access property for mdspan and span.

2. Motivation

The restrict (non-aliasing) property is a widely useful mechanism to enable array access optimization. This functionality is part of the C standard, several C++ compilers' extensions, and native to FORTRAN array semantics.

While the utility of non-aliasing type annotations is well-established in the literature, it is useful to reproduce several common motivating examples here to illustrate the utility in the context of span and mdspan.

Linear algebra produces one of the most compelling needs for non-aliasing semantics. Even the simplest operations, such as vector addition, suffer noticable degredation in the absense of a non-aliasing guarantee:

// Performce element-wise dest = a + b 
template <typename T>
void element_product(span<const T> a, span<const T> b, span<T> dest) {
  assert(a.size() == b.size() && b.size() == c.size());
  for(typename span<T>::size_type i = 0; i < a.size(); ++i) {
    dest[i] = a[i] + b[i];

Without restrict annotations, the compiler cannot vectorize this code, since a or b could point to the same memory as dest. With dest being changed every iteration, the compiler needs to preform fresh loads a[i] and b[i] every iteration in case, for instance, they point to dest[i-1].

Reordering for the purposes of optimizing memory operations is another example of an optimization that restrict enables. Consider the (albeit naïve) implementation of a function that initializes two arrays at the start of some user’s program:

void initialize_data(span<int> v0, span<int> v1) {
  for(typename span<int>::size_type i = 0; i < v0.size(); ++i) {
      v0[i] = 0;
      v1[i] = 1;

In the absence of restrict information, the compiler cannot tell at what point, if any, the statement v1[i] = 1 starts to overwrite the effects of previous statements on v0 (or vice versa). With non-aliasing information provided, however, the compiler can transform this function into two calls to memset, which would be much more efficient on most architectures. (It’s clear to most people in this example that the user should have made this transformation to begin with, but with intervening work in between the two assignments, or other increased complexity, this may not be as clear).

We propose to add the restrict_access property to the set of admissible properties of mdspan and span.

This paper does not propose a strategy for subsequent extensibility. We identify open questions that must be addressed in the design of such a strategy. P0900 addresses the design of the customization point utilized here in a more generic context.

3. Background and Precedent

[N3538], [N3635], and [N3988] previously proposed restrict-like semantics as a language feature rather than a library feature. A discussion of how presenting restrict semantics as a library feature addresses many of the concerns previously raised about these papers is given below in §5.1 Why a library feature?

3.1. ISO C Language Standard

The C language standard provides the restrict keyword in 6.7.3 of the WG14 document [WG14-N1570]. An informal definition is given in paragraph 8 of 6.7.3:

An object that is accessed through a restrict-qualified pointer has a special association with that pointer. This association, defined in below, requires that all accesses to that object use, directly or indirectly, the value of that particular pointer. The intended use of the restrict qualifier (like the register storage class) is to promote optimization, and deleting all instances of the qualifier from all preprocessing translation units composing a conforming program does not change its meaning (i.e., observable behavior).

A formal definition of restrict follows in of [WG14-N1570]:

Let D be a declaration of an ordinary identifier that provides a means of designating an object P as a restrict-qualified pointer to type T.

If D appears inside a block and does not have storage class extern, let B denote the block. If D appears in the list of parameter declarations of a function definition, let B denote the associated block. Otherwise, let B denote the block of main (or the block of whatever function is called at program startup in a freestanding environment).

In what follows, a pointer expression E is said to be based on object P if (at some sequence point in the execution of B prior to the evaluation of E) modifying P to point to a copy of the array object into which it formerly pointed would change the value of E. Note that "based" is defined only for expressions with pointer types.

During each execution of B, let L be any lvalue that has &L based on P. If L is used to access the value of the object X that it designates, and X is also modified (by any means), then the following requirements apply: T shall not be const-qualified. Every other lvalue used to access the value of X shall also have its address based on P. Every access that modifies X shall be considered also to modify P, for the purposes of this subclause. If P is assigned the value of a pointer expression E that is based on another restricted pointer object P2, associated with block B2, then either the execution of B2 shall begin before the execution of B, or the execution of B2 shall end prior to the assignment. If these requirements are not met, then the behavior is undefined.

Here an execution of B means that portion of the execution of the program that would correspond to the lifetime of an object with scalar type and automatic storage duration associated with B.

A translator is free to ignore any or all aliasing implications of uses of restrict.

3.1.1. Dependence of N4700 on ISO C restrict

Note that [N4700] already references the ISO C restrict keyword in paragraph 2 of [library.c], implying that C++ implementations should already be aware of its semantics (though, as stated in [WG14-N1570], conforming implementations can completely ignore restrict):

The descriptions of many library functions rely on the C standard library for the semantics of those functions. In some cases, the signatures specified in this document may be different from the signatures in the C standard library, and additional overloads may be declared in this document, but the behavior and the preconditions (including any preconditions implied by the use of an ISO C restrict qualifier) are the same unless otherwise stated.

3.2. GCC’s __restrict__

GCC implements restricted access in C++ via the __restrict__ (or __restrict) compiler-specific extension. The compiler documentation [GCCRestrictDoc] provides the following description:

In addition to allowing restricted pointers, you can specify restricted references, which indicate that the reference is not aliased in the local context.

void fn (int *__restrict__ rptr, int &__restrict__ rref)
  /* … */

In the body of fn, rptr points to an unaliased integer and rref refers to a (different) unaliased integer.

You may also specify whether a member function’s this pointer is unaliased by using __restrict__ as a member function qualifier.

void T::fn () __restrict__
  /* … */

Within the body of T::fn, this has the effective definition T *__restrict__ const this. Notice that the interpretation of a __restrict__ member function qualifier is different to that of const or volatile qualifier, in that it is applied to the pointer rather than the object. This is consistent with other compilers that implement restricted pointers.

As with all outermost parameter qualifiers, __restrict__ is ignored in function definition matching. This means you only need to specify __restrict__ in a function definition, rather than in a function prototype as well.

It is clear that GCC’s implementation of this extension would be sufficient to implement the proposed feature trivially. Tests with gcc 7.3 and subsequent analysis of the machine code produced during compilation indicates that the existing extension would support the semantics proposed herein and perform the expected optimizations consistent with analogous non-aliasing information on raw pointers.

3.3. MSVC’s __declspec(restrict)

MSVC provides a couple of similar compiler-specific extensions via the syntaxes __declspec(restrict) and __restrict. The compiler documentation [MSVCRestrictDoc] gives the following description of __declspec(restrict):

Applied to a function declaration or definition that returns a pointer type and tells the compiler that the function returns an object that will not be aliased with any other pointers.

The compiler documentation’s description for __restrict indicates that it is similar to __declspec(restrict), and, indeed, to ISO C restrict:

__restrict is similar to restrict from the C99 spec, but __restrict can be used in C++ or C programs.

3.4. Clang++ and the noalias Metadata in LLVM IR

LLVM’s internal representation (IR) includes a rich set of memory aliasing metadata annotations [LLVMIRDoc], including the noalias metadata that expresses restrict-like semantics for function parameters (among other uses). Clang++ supports the __restrict and __restrict__ extensions from GCC both in the Clang++ frontend and through these metadata attributes. The presence of these attributes in the LLVM IR means that other frontends that translate into LLVM IR will also have the ability to express these semantics.

3.5. IBM XL C++

The documentation for IBM XL C++ [XLCRestrictDoc] indicates that it supports ISO C restrict semantics in C++ via the __restrict or __restrict__ extensions.

3.6. NVIDIA’s nvcc

The nvcc compiler supports the __restrict or __restrict__ extensions for the GPU and (as long as the underlying CPU compiler supports it) the CPU. [NVCCRestrict]

4. Proposal

We propose utilitzing the customization point explored in P0900 to express the restrict_access property:

namespace std {
namespace experimental {
inline namespace fundamentals_v3 {

  // Trait common to all span and mdspan property proposals, as given in e.g., P0009r4
  template< class T, class P >
  struct has_property;

  // Variable template for has_property
  template< class T, class P >
  inline constexpr bool has_property_v = has_property<T, P>::value ;

  // Tag class for indicating restrict access
  struct restrict_access ;

  // Specialization of has_property for restrict_access
  template< class T >
  struct has_property<T, restrict_access> {
    inline constexpr bool value = /* see below */;


4.1. has_property<T, restrict_access>::value

Evaluates to true if T is instantiation of span or mdspan and the Properties... parameter pack of T contains restrict_access.

4.2. Application of the Restriction to span

Working relative to [P0122r5], a preliminary attempt at wording the restriction proposed herein is as follows (in addition to the changes proposed by [P0546r1]): [span.restrict]

Let S be an instantiation of span such that has_property<S,restrict_access>::value is true, and let s be an instance of S. Let p be an object of type S::pointer and sz be an object of type S::index_type. The restricted lifetime of s with respect to { p, sz } is defined such that it either:

and has the property that p == s.data() and sz == s.size(). We abbreviate the "restricted lifetime of s with respect to { p, sz } with the notation L{s, p, sz}. The lifetime of s thus consists of a disjoint set of restricted lifetimes L_1{s, p_1, sz_1}, ..., L_n{s, p_n, sz_n}. The truth of has_property<S,restrict_access>::value implies that during any given restricted lifetime L_i{s, p_i, sz_i} of an instance s of S, no value of a pointer or address of a reference may be used to form a glvalue expression that modifies an object with an address in the range [p_i, p_i + sz_i) except for those derived from:

These restrictions apply to any modifying accesses indeterminately sequenced with the beginning or end of the given restricted lifetime L_i. Any other accesses that modify the referenced memory through any other means result in undefined behavior. Additionally, accessing any object not in the range [p_i, p_i + sz_i) via a pointer or reference derived from any of the above sources results in undefined behavior.

Formal wording for the application of the restriction to mdspan will follow discussion of the content in the current paper, but it likely to be similar to the wording for span above.

5. Discussion

5.1. Why a library feature?

From [N3988] itself and from the on-the-record discussion of it at the Rapperswil meeting in 2014, here are some of the objections raised about restrict-like semantics in C++:

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Informative References

Restricted Pointer Aliasing. URL: https://gcc.gnu.org/onlinedocs/gcc/Restricted-Pointers.html
LLVM Language Reference Manual. URL: https://llvm.org/docs/LangRef.html
restrict. URL: https://docs.microsoft.com/en-us/cpp/cpp/restrict
Lawrence Crowl. Pass by Const Reference or Value. 6 March 2013. URL: https://wg21.link/n3538
M. Wong, R. Silvera, R. Mak, C. Cambly, et al.. Towards restrict-like semantics for C++. 29 April 2013. URL: https://wg21.link/n3635
H. Finkel, H. Tong, et al.. Towards restrict-like aliasing semantics for C++. 23 May 2014. URL: https://wg21.link/n3988
Richard Smith. Working Draft, Standard for Programming Language C++ Note:. URL: https://wg21.link/n4700
Jeremy Appleyard. CUDA Pro Tip: Optimize for Pointer Aliasing. URL: https://devblogs.nvidia.com/parallelforall/cuda-pro-tip-optimize-pointer-aliasing/
Neil MacIntosh. span: bounds-safe views for sequences of objects. URL: https://wg21.link/p0122r5
Carter Edwards, Bryce Lelbach. Span - foundation for the future. URL: https://wg21.link/p0546r1
Committee Draft, Programming Languages — C. URL: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1570.pdf
The restrict type qualifier. URL: https://www.ibm.com/support/knowledgecenter/en/SS2LWA_12.1.0/com.ibm.xlcpp121.bg.doc/language_ref/restrict_type_qualifier.html