P2664R8
Extend std::simd with permutation API

1. Motivation

ISO/IEC 19570:2018 introduced data-parallel types to the C++ Extensions for Parallelism TS. [P1915R0] asked for feedback on std::simd in Parallelism TS 2. [P1928R4] aims to make that a part of C++ IS. Intel supports the concept of a standard interface to SIMD instruction capabilities and has made further suggestions for other APIs and facilities for std::simd in document [P2638R0].

One of the extra features we suggested was the ability to be able to permute elements across or within SIMD values. These operations are critical for supporting formatting of data in preparation for other operations (e.g., transpose, strided operations, interleaving, and many more), but are relatively poorly supported in the current std::simd proposal. Many modern SIMD processors include sophisticated support for permutation instructions so in this document we shall propose a set of API functions which make those underlying instructions accessible in a generic way.

In this document we shall start with some background into the current std::simd proposal and extensions, describe the state of the art on other simd libraries, and then describe a proposal for some new API functions to add to std::simd.

2. Revision History

R7 => R8

• Added parameter to gather_from to be consistent with the API proposed for load_from in [P3299R0], and in particular, to allow element type conversions as part of the gather operation.

R6 => R7

• Changed default behaviour of out-of-range gather/scatter to UB to be consistent with [P3299R0].

R5 => R6

• Removed section on named permutation generator functions. These will be put into their own paper.

• Modified gather_from and scatter_to to use ranges instead of iterators. Added more details about their behaviour and our implementation experience.

• Removed section on using [DNMSO]. This will be revisited if that paper makes further progress.

R4 => R5

• Renamed gather and scatter to gather_from and scatter_to.

• Made masking overloads for gather_from and scatter_to part of the proposal rather than a design option.

• Added Flags to gather_from and scatter_to to control memory behaviour.

• Added a design option discussing the merits of making gather_from and scatter_to member functions.

• Switched to using new names for functions like simd_split and simd_cat.

R3 => R4

• Renamed simd/simd_mask to basic_simd/basic_simd_mask to match [P1928R4].

• Replaced deduced masks with nested typedefs (i.e., use basic_simd<T, ABI>::mask_type instead of basic_simd_mask<T, MaskABI>).

• Replaced fixed_size types with their new counterparts (e.g., fixed_size_simd<T, 5> would now be simd<T, 5>).

• Removed design option to allow compress and expand to take simd value parameters which are different sizes. This would always lead to some silent loss of data (either the mask or the values being compressed).

• Reordered mask parameter position (it now matches simd_select, copy_to, etc., by having the mask appear first).

R2 => R3

• Added more detail about compiler’s ability to optimise a generated sequence

• Made memory operations (gather/scatter) a class of its own, rather than trying to make them appear like special forms of the other types of permute.

• Moved special indexes and generator size parameter description into main body of text rather than being a design option.

• Added fill value parameters for compress and expand functions.

• Improved wording and examples for memory permutations (gather/scatter).

• Added wording for static permute, dynamic permute, mask permute and gather/scatter.

R1 => R2

• Rewrite to bikeshed

• Add more content for proposal overview.

R0 => R1

• Add polls from Kona SG1 2022

3. Background

In ISO/IEC 19570:2018 there were only a few functions which could be used to achieve any sort of element permutation across or within simd<> values. Those functions were relatively modest in scope and they built upon the ability to split and concatenate simd values at compile-time. For example, a simd value containing 5 elements could be split into two smaller pieces of sizes 2 and 3 respectively:

simd<float, 5> x;
…
const auto [piece0, piece1] = simd_split<3>(x);

Those smaller pieces could be acted on using any of the std::simd features, and then later recombined using simd_cat, possibly in a different order or with duplication:

const auto output = simd_cat(piece1, piece1, piece0);

The simd_split and simd_cat functions can be used to achieve several permutation effects, but they are unwieldy for anything complicated, and since they are also compile-time they preclude any dynamic runtime permutation.

In [P2638R0] Intel suggested extra operations to insert and extract SIMD values to and from other SIMD containers:

const auto t = extract<2, 5>(v); // Read out 3 SIMD values, starting from position 2
insert<5>(v, t); // Put the 3 previously read values back into the container at position 5 

These are convenient, but they still don’t allow arbitrary or expressive permute operations.

Two suggestions were made in [P0918R1]: add an arbitrary compile-time shuffle function, and add a specific type of permutation called an interleave. The compile-time shuffle can be used as follows:

const auto p = shuffle<3, 4, 1, 1, 2, 3>(x);
// p::value_type will be the same as x::value_type
// p::size will be 6

The indexes can be arbitrary, and therefore allow any duplication and reordering of elements. The output std::simd object will have the same number of elements as there are supplied indexes, and the type of the SIMD output will be that of the input. It is noted also in the shuffle API that this function can be applied to basic_simd_mask values too, and that shuffling across multiple SIMD values can be achieved by first concatenating the values into a single larger SIMD:

const auto p = shuffle<10, 9, 0, 1>(simd_cat(x, y));

In addition to the shuffle function, [P0918R1] also proposes a function called interleave which accepts two SIMD values and interleaves respective elements into a new SIMD value which is twice the size. For example, given inputs [a0 a1 a2] and [b0 b1 b2], the output would be [a0 b0 a1 b1 a2 b2]. Interleaving is a common operation and is often directly supported by processors with explicit instructions (e.g., Intel’s punpcklwd), so as in [P0918R1] and also in other simd libraries there will be named functions which expose that instruction. There will be other common permutation operations which also have specialist hardware support and it is common for them to be exposed in named functions also. For example, [Highway] provides DupOdd, DupEven, ReverseBlocks, Shuffle0231, and so on, which map efficiently to underlying instructions. While this can ensure that good code is generated for specific function, it does mean that:

• the set of named functions can only include those features available on all potential targets

• portability is reduced by exposing functions only on those targets which support them.

Neither of these is desirable, and in our suggestions below we provide an alternative.

4. Extending std::simd to support permutations

There are four classes of permutation which could be supported by std::simd;

• using compile-time computed indexes

• using another SIMD as a dynamic index

• using a bit-mask for selecting active elements

• permuting memory (gather and scatter)

Modern processor instruction sets typically support all 4 of these classes of instruction. In the following sections we shall examine in more detail each of these classes and the potential APIs needed to expose those features to the user. We shall also examine what it means to permute memory, and whether named functions should be provided for common permutation patterns.

std::simd could be modified to allow permutations either by adding to the base definition of std::simd itself (specifically, to include a new simd::operator[] or simd_mask::operator[]), or by introducing overloaded free functions which extend std::simd. We shall consider both options below.

Note that a basic_simd_mask is a special case of a type of SIMD and can therefore be permuted in the same way as a conventional SIMD. In our discussions below we assume that the permutations would apply equally to a basic_simd_mask unless we note otherwise.

4.1. Using compile-time computed indexes

The first proposal is to provide a permute function which accepts a compile-time function which is used to generate the indexes to use in the permutation. This is a very powerful concept: firstly, it allows the task of computing the indexes to be offloaded to the compiler using an index-generating function, and secondly it works on simd<> values of arbitrary size. It’s definition would be something like:

template<std::size_t SizeSelector = 0, typename T, typename Abi, typename PermuteGenerator>
constexpr simd<T, output-size>
permute(const basic_simd<T, Abi>& v, PermuteGenerator&& fn)

It can be used as in the following example:

const auto dupEvenIndex = [](size_t idx) -> size_t { return (idx / 2) * 2; };
const auto de = permute(values, dupEvenIndex);

Note that the permutation function maps from the index of each output element to the index which should be used as the source for that position. So, for example, the dupEvenIndex function would map the output indexes [0, 1, 2...) to the source indexes [0 0 2 2 4 4…). This example permutation is common enough that it has hardware support in Intel processors, and the compiler can map the above function directly to the corresponding instruction:

vmovsldup ymm0, ymm0

By default, the permute function will generate as many elements in the output simd as there were input values, but the output size can be explicitly specified if it cannot be inferred or it needs to be modified. For example, the following permute generates 4 values with a stride of 3 (i.e., indexes [0, 3, 6, 9]).

const auto stride3 = permute<4>(values, [](size_t idx) -> size_t { return idx * 3; });

4.1.1. Special generator indexes

The obvious index representation to return from each generator invocation is to return an integral value in the range [0...size). The compiler can enforce at compile-time that the index is in the valid range and dynamic indexes would not be permitted. In addition, there are three other types of index value which can be returned which give the compiler even more flexibility.

• Negative indexes represent reverse indexes, which are intepreted as indexes taken from the end of the simd instead of the beginning. So -1 would be the last element, -2 the penultimate element, and so on.

• The special index named simd_zero_element will instead a zero value at the indicated element position, rather than copying a value from the input simd.

• The special index named simd_uninit_element will indicate to the compiler that the element at the indicated position can be left in an uninitialized state. This gives an opportunity for more efficient code generation where the programmer knows that an element is unused.

Here is an example where zeros are inserted into the even-indexed output positions of a SIMD value while the odd-indexed values are copied directly from the input.

permute(v, [](auto idx) { (idx % 2) ? simd_zero_element : idx; });

4.1.2. Generator function size argument

It can be useful to create libraries of common permutation generator functions to handle common use cases, but such functions need to be able to know the extent of the indexes that they are allowed to permute. The generator function is allowed to accept an optional std::size_t argument giving the size of the SIMD value being permuted. For example, the following generator extracts elements of a SIMD starting at the half-way point:

auto topHalf = [](std::integral auto idx, std::size_t simd_size) {
  return (simd_size / 2) + idx;
};

4.1.3. Design option - more special constants

There are other possible special constants that could be given special status in the compile-time permute, including the ability to insert NaN, +ve infinity, -ve infinite, max_value, min_value, and so on. Should these be adopted too?

4.1.4. Implementation experience

In other simd or vector libraries which provide named specific permute functions, the reason often given is that it allows specific hardware instructions to be used to efficiently implement those permutes. For example, Intel has the vmovsldup instruction as noted above, so some libraries provide functions in their API with names which reflect this (e.g., such a function might be called DupLow). The disadvantages are that it hinders portability, and only allows access to the hardware features that the authors of the library have chosen to expose.

Using the generator-based approach makes it easier to access a wide range of underlying special purpose instructions, or to fall back to equivalent instructions sequences where they are not available, but it is desirable that such behavior should be efficient. To judge whether the generator-based permutation API was efficient and useful we implemented the extensions in the Intel std::simd library and looked at the performance of different compile-time patterns and their generated instruction sequences. We found that GCC and LLVM were able to determine the correct hardware instructions to use for a variety of common permutation patterns, and in some cases the compiler was even able to use the side-effects of other instructions to effect permutations in ways that human programmers had overlooked. In all cases, where the pattern was too complicated to map to native hardware features the compiler fell back to using general purpose permutation patterns, such as Intel’s permutex2var family of instructions.

The generator function works by creating a list of compile-time constants which are used to perform the permutation. Because the list is compile-time it can be generated using completely arbitrary (and potentially very inefficient) code, but the outcome will always be a list of constants. Therefore the compiler’s ability to generate a permutation is dependent upon how well it can convert a list of constants into a permutation, not how well the programmer is at writing clear permute functions.

As a small illustration of the compiler’s ability, the following table shows some compile-time function permute calls and the code that the LLVM 14.0.0 compiler has generated for each:

In each case the compiler has accepted the compile-time index constants and converted them into an instruction which efficiently implements the desired permutation. We can safely leave the compiler to determine the best instruction from an arbitrary compile-time function.

4.2. Using another SIMD as the dynamic index

The second proposal for the permute API is to allow the required indexes to be passed in using a second SIMD value containing the run-time indexes:

template<typename T, typename AbiT, std::integral Idx, typename AbiIdx>
constexpr simd<T, basic_simd<Idx, AbiIdx>::size()>
permute(const basic_simd<T, AbiT>& v, const basic_simd<Idx, AbiIdx>& indexes)

This can be used as in the following example:

simd<unsigned, 8> indexes = getIndexes();
simd<float, 5> values = getValues();
...
const auto result = permute(values, indexes);
// result::value_type is float
// result::size is 8

The permute function will return a new SIMD value which has the same element type as the input value being permuted, and the same number of elements as the indexing SIMD (i.e., float and 8 in the example above). The permute may duplicate or arbitrarily reorder the values. The index values must be of integral type, with no implicit conversions from other types permitted. The behavior is undefined if any index is outside the valid index range. Dynamic permutes across multiple input values are handled by concatenating the input values together. The indexes in the selector will only be treated as indexes, and will never have special properties as described above (e.g., no zero element selection)

In addition to the function called permute, a subscript operator will also be provided:

template <std::integral Idx, typename AbiIdx>
constexpr simd<T, basic_simd<Idx, AbiIdx>::size()>
simd::operator[](const basic_simd<Idx, AbiIdx> &indexes) const;

Here is an example of how this could be used:

simd<int, 8> indexes = getIndexes();
simd<float, 5> values = getValues();
...
const auto result = values[indexes];
// result::value_type is float
// result::size is 8

4.2.1. Design option - C++23 multi-index subscript

Sometimes the subscripts to use in a permute might be known at compile time, but to use them in a permutation requires them to be put into an index simd first:

constexpr simd<int> indexes = {3, 6, 1, 6}; // Note - assumes initialiser list from P2876R0.
auto output = values[indexes];

In C++23 multi-subscript operator was introduced and this could be used to allow a more compact representation:

auto output = values[3, 6, 1, 6];
// output::value_type is values::value_type
// output::size is 4

It would be good if it could also appear on the left-hand-side;

output_simd[2, 5, 6] = x; // Overwrite selected elements with a single value.

Should non-constant indexes be allowed too? Our experience with GCC and LLVM suggests that work would be needed on their code generation for non-constant variable indexes to be improved though, as they are both currently poor at this.

Should operator[] be reserved for slicing or sub-ranges?

4.2.2. Implementation experience

We implemented the runtime-indexed permute API in Intel’s example std::simd implementation. Small index operations (e.g., indexing one native sized simd by another) were mapped directly onto the underlying native instruction and so were as efficient as calling an intrinsic. More complicated cases for permutation, such as where either the index or data SIMD parameters were bigger than a native register are also handled with comparable efficiency to hand-written intrinsic code.

4.3. Permutation using simd masks (compress/expand)

A third variant of permutation is where a basic_simd_mask is used as a proxy for an index sequence instead. The presence or absence of an element in the basic_simd_mask will cause the element to be used or not. The following diagrams illustrate this:

On the left the values in the SIMD are compressed; only those elements which have their respective basic_simd_mask element set will be copied into the next available space in the output SIMD. Their relative order will be maintained, and the selected elements will be stored contiguously in the output. The output value will have the same number of elements as the input value, with any unused elements being left in a valid but unspecified state. The behavior of the function is similar to std::copy_if, although other simd libraries may call this function compression or compaction instead. The expansion function on the right of the diagram has the opposite effect, copying values from a contiguous region to potentially non-contiguous positions indicated by a mask bit. The two functions have prototypes as follows:

template<typename T, typename Abi>
constexpr basic_simd<T, Abi>
compress(const typename basic_simd<T, Abi>::mask_type& mask, const basic_simd<T, Abi>& value);

template<typename T, typename Abi>
constexpr basic_simd<T, Abi>
compress(const typename basic_simd<T, Abi>::mask_type& mask,
         const basic_simd<T, Abi>& value, T fill_value);

template<typename T, typename Abi>
constexpr basic_simd<T, Abi>
expand(const typename basic_simd<T, Abi>::mask_type& mask,
       const basic_simd<T, Abi>& value, const simd<T, Abi>& original);

In both functions all basic_simd or basic_simd_mask values must have the same value_type and size.

A compression operation is typically used to throw away unwanted values (i.e., values which do not satisfy the mask condition). Unwanted positions in the output will be left unspecified, unless the user supplies a third parameter specifying the value which should be used to fill those unwanted positions.

An expansion operation is typically used to overwrite selected elements of some existing SIMD value with new values taken from the contiguous beginning of another SIMD value. The expansion operation therefore has a slightly different meaning for its fill value.

4.3.1. Unused value element initialisation

In the design shown above the compress function comes in two variants, the first of which leaves unused values in the output in an unitialised but valid state, and the second function provides a default value to use for the initialisation. Is is worth looking at this in more detail to understand why there isn’t a single function which always initializes its unused elements. Consider a compression operation:

simd<int, 6> values = ...;
simd_mask<int, 6> mask = ...;

auto compressed = compress(values, mask);
// compressed::value_type is int
// compressed::size is 6

The output value has the same size as the mask selector, but the actual mask bits won’t be known until run-time. This raises the question of what values should be put into the unused output elements.

The current proposal would leave the unused elements in a valid but unspecified state. This is comparable to functions like std::shift_left and std::shift_right. The alternative is for the compress function to leave the unused values in a value-initialized state.

The advantage of an unspecified state is that the code doesn’t need to make a special effort to insert values which might not be used anyway, but has the disadvantage that the unspecified state might catch out the unwary user. Using a value initialized state helps the unwary user by providing a default state which is sane and repeatable, but may come with a performance cost.

Intel have an example implementation of std::simd, and our experience with that demonstrates that when native support is available (e.g., with AVX-512 ISA) it makes no difference to performance whether the unused values are initialising to specific value or left uninitialized, since the instruction itself inserts the values into unused positions as an integrated part of its operation. However, a synthesized code sequence is more expensive when setting the elements to a specific value since it is necessary to also compute the population count of the mask, turn that into a mask and then arrange for the unused values to be overwritten with something else using that mask.

Given that the compress function is essentially only extracting valid values from the input SIMD and discarding the others, and that there is a potential performance penalty that comes from initialising unused values, then we think that the default should be to leave unused elements in unspecified states.

Related to this is what to do when a programmer does want to initialize unused values to a known value. With the proposed interface the programmer would be required to compute a new partial mask from their original selection mask (i.e., compute the population count of the original mask, and then turn that into a mask of the lower elements), and then use that to conditionally blend in their desired value. This can be inefficient, and for targets like Intel AVX-512, it doesn’t exploit the hardware’s ability to automatically insert a value anyway. For this reason we propose that an overload of compress is provided that accepts a third parameter giving a value to insert into unused elements:

template<typename T, typename Abi>
basic_simd<T, Abi>
compress(const basic_simd<T, Abi>& value,
         const typename basic_simd<T, Abi>::mask_type& mask,
         T default_value);

This makes the programmer’s intent explicit in the code, it simplifies the code, and it allows those targets which support automatic insertion of a value to efficiently make use of that feature.

4.3.2. Implementation experience

In Intel’s example implementation of std::simd we have implemented permute-by-mask. On modern processors which support AVX-512 or VBMI2 we found the mapping from compress or operator[] to be efficient, and allowed a natural representation of this compaction operation where needed. Implementing permute-by-mask on older processors which lacked native support was a little harder, but could still be implemented as efficiently as an experienced programmer could achieve using hand-written intrinsics. Determining the most efficient implementation under all conditions however showed that less experienced programmers would struggle to implement this feature. Therefore, making this feature available in std::simd itself removed any non-portable calls to native compression/expansion instructions, and also allowed the library implementer to use efficient sequences for different scenarios.

4.4. Memory-based permutes

When permuting values which are stored in memory, the operations are normally called gather (reading data from memory), or scatter (writing values to memory). We propose that four functions are provided which implement these two operations, each provided in masked and unmasked forms.

4.4.1. Range-based gather function

The gather function is defined as follows:

template<typename ReturnType = void,
         typename Range, std::integral Idx, typename AbiIdx, typename... Flags>
    requires std::ranges::sized_range<Range> && std::ranges::contiguous_range<Range>
constexpr (see later)
gather_from(const Range&& in, const simd<Idx, AbiIdx>& indexes, simd_flags<Flags...> f = {});

template<typename ReturnType = void,
         typename Range, std::integral Idx, typename AbiIdx, typename... Flags>
constexpr (see later)
gather_from(Range&& in, const typename simd<Idx, AbiIdx>::mask_type& mask,
            const simd<Idx, AbiIdx>& indexes, simd_flags<Flags...> f = {});

The gather operation loads values from within a constrained contiguous finite range. By default it returns a new simd whose type is deduced from the input parameters: it will have the same element type as the input range elements and the same number of elements as the supplied index simd. Alternatively, the user may provide an template parameter specifying the return type, either as a basic_simd or as a scalar type. That enables the user to perform a conversion as part of the gather operation. The return template parameter matches the proposal for load_from in [P3299R0].

If an index is supplied which is outside the valid input range then we have two options for how the implementation should behave. The first option is to make this undefined behaviour, while the second option is to make the gather safe by replacing invalid indexes by some default value. The extra code introduced in the second option may reduce performance. In common with our reasoning in [P3299R0] (Range constuctors), we think that std::simd is a low-level library which should place performance above safety, and we propose that gather operations will give undefined behaviour if an invalid index is used.

In the masked overload the mask’s parameter type matches that of the supplied indexes since it is effectively turning indexes on and off. Any values which are unmasked will be value initialized in the result.

Both overloads accept a flags parameter which will mirror any control over the memory operations provided by copy_from, and the memory-loading constructors (e.g., cache bypass, prefetching). In addition, the flag called simd_default_init introduced in [P3299R0] can also be used, and will prevent any out-of-bounds accesses to the input range, and will insert a default-initialised value for the corresponding element.

The default gather_from function could be used as follows:

int array[1024];
simd<unsigned> indexes = GetIndexes();
...
const auto r1 = gather_from(array, indexes);

By specifying a return type parameter a conversion can be implemented as part of the gather:

int array[1024];
simd<unsigned> indexes = GetIndexes();
...
const auto r1 = gather_from<float>(array, indexes);

Or the return type can be a compelte simd type which specifies both the element type and the required ABI:

int array[1024];
simd<unsigned> indexes = GetIndexes();
using OutType = simd<float, simd<unsigned>::size>;
...
const auto r1 = gather_from<OutType>(array, indexes);

4.4.2. Range-based scatter function

The scatter function is defined as:

template<typename Range,
         typename T, typename TAbi,
         std::integral Idx, typename IdxAbi, typename... Flags>
constexpr void
scatter_to(const simd<T, TAbi>& values, Range&& out,
           const simd<Idx, IdxAbi>& indexes, simd_flags<Flags...> f = {});

template<std::contiguous_iterator Iter,
         typename T, typename TAbi,
         std::integral Idx, typename IdxAbi, typename... Flags>
constexpr void
scatter_to(const simd<T, TAbi>& values, Range&& out,
           const typename simd<Idx, AbiIdx>::mask_type& mask,
           const simd<Idx, IdxAbi>& indexes,
           simd_flags<Flags...> f = {});

The scatter function will write each input value to the respective indexed position of the output range. The output range must be contiguous and finite. If an index falls outside the valid input range then this is Undefined Behaviour, and the programmer is responsible for ensuring that the indexes are valid.

In the masked overload, the mask parameter type has been chosen to match the index type to be consistent with the gather_from function. The values written to memory will be of the range’s value type, with a conversion from the input type taking place if they are different. The conversion to the range value type must be value preserving, unless simd_flags_convert is passed as an option.

The scatter_to function should accept any flags similar to those found in copy_to, allowing control over effects such memory caching, write-through, and so on. An extra flag called simd_flag_checked will be introduced to provide dynamic range checking of the indexes to suppress writes outside the valid range. The use of this flag will generate extra runtime code which may degrade execution performance, but will improve memory safety.

The memory writes performed by scatter_to are unsequenced. The programmer cannot rely on the values being written to the output range in any order.

The scatter could be used as follows:

int array[1024];
simd<int> values = ...;
simd<int> indexes = ...;
simd<int>::mask_type mask = ...;
...
scatter_to(values, array, mask, indexes);

4.4.3. A note on iterator-based gather and scatter

In early revisions of this paper there was a proposal to make gather_from and scatter_to accept contiguous iterators to indicate where to gather and scatter to memory. Although these functions directly mirrored common hardware instructions, which also accept a pointer and a vector of indexes, the functions are potentially very dangerous. Given a pointer, and a large enough index element type, any part of the execution space can be read or written, with writes being particularly catastrophic if mis-handled. In common with the direction being taken in [P3299R0] to make other memory-related operations range-safe, we have replaced the iterator-based gather and scatter operations with range-based operations.

If a programmer only has an iterator referencing the region from which to gather or scatter, then they must convert that iterator to a suitable range. For example, if there exists a pointer to a lookup table, and it is known that the lookup table can only contain N entries, then the programmer could implement that as follows:

const uint16_t* ptr = ...;
const simd<unsigned> indexes = ...;
...
auto v = gather_from(std::span(ptr, N), indexes);

Using a raw iterator and converting it to a span or range should be only a stop-gap measure, and ideally the code should be refactored to allow the appropriate input range to be used directly. Therefore to encourage good use of ranges no iterator-based overloads for gather_from and scatter_to are provided.

4.4.4. Implementation experience

Intel’s example implementation of std::simd has been modified to include both iterator-based and range-based versions of gather_from and scatter_to, with and without runtime checking. The code has been evaluated for performance.

Our benchmarking showed that the addition of range checking, value-initialization, and write suppression for invalid indexes did not significantly degrade execution performance on modern machines running AVX-512. In fact, we found that the choice of index values (i.e., what happens if the indexes are in the same cache line, adjacent cache lines, consecutive, reversed, etc.) had a much greater impact on execution performance than whether the range check was present or not.

When rewriting older iterator-based code in terms of the range-based API, we could implement the code as follows:

const uint16_t* ptr = ...;
const simd<unsigned> indexes = ...;

// Original iterator-based API
auto v_old = gather_from(ptr, indexes);

// New API
auto v_new = gather_from(std::span(ptr, N), indexes);

The generated code for these two uses is identical, so the performance levels of the original API can be achieved while using an API which encourages the programmer to think about the ranges that they are using for scatter and gather.

4.4.5. A note on proposing that gather_from and scatter_to should be member functions

At Varna 2023 there was a suggestion to make gather_from and scatter_to become member functions. Reasons for this included:

• to match copy_from and copy_to, which are the closest equivalents to these memory operations that already exist, and which are already members (though they are the only ones).

• to allow gather_from to perform a conversion from the iterator type to the object’s own element type. Note that scatter_to already accepts an iterator of one type and a value simd of another element type, so scatter-conversion is already supported.

• to allow a masked gather_from to partially overwrite an existing simd value (i.e., masked gather_from currently has no way of specifying what value should be used for unused elements and uses value initialization).

Since that meeting [P3299R0] (range-based constructors) has been suggested. In particular non-member load_from and store_to replace member copy_from and copy_to respectively, with improved memory safety, and with conversion capabilities. LEWG gave strong direction to pursue the ideas of [P3299R0] and we have incorporated the mechanisms into this proposal, and we will abandon any further exploration of gather/scatter member functions.

5. Summary

In this document we have described four styles of interface for handling permutes: compile-time generated, simd-indexed, mask-indexed, and memory based. In combination, these interfaces allow all types of common permute to be expressed in a way which is clean, concise, and efficient for the compiler to implement.

6. Wording

6.1. Modify [simd.flags]

Add the following:

Note: simd_flag_default_init is also specified in [P3299R0].

6.2. Add new section [simd.static_permute]

6.3. Add new section [simd.dynamic_permute]

6.4. Add new section [simd.mask_permute]

6.5. Add new section [simd.memory_permute]

7. Acknowledgments

Thank you to Matthias Kretz for useful offline discussions regarding the behaviour and contents of the permutation API.

8. Polls

8.1. Varna Meeting - 16th May 2023

POLL: SIMD permute should not support negative indices

POLL: SIMD permute should always pass both an index and a size to the invocable.

POLL: Rename gather to gather_from and scatter to scatter_to and make them member functions that do conversion and take simd_flags<...> (like copy_to/copy_from).

8.2. Telecon Meeting - 2nd May 2023

Poll: We should promise more committee time to pursuing P2664R2 (Proposal to extend std::simd with permutation API), knowing that our time is scarce and this will leave less time for other work.

Poll: Pursue extended indices in the permute callable (e.g., negative indices, special values for zero element, etc.).

Poll: Pursue multi-index subscripting for dynamic permutations in the initial revision.

Poll : Pursue operator[](simd) subscripting for dynamic permutations in the initial revision.

Poll: Pursue operator[](simd_mask) subscripting for dynamic expand (output[] = input) in the initial revision.