# Iteration Spaces: Segments and IndexSets¶

This section contains an exercise file RAJA/exercises/segment-indexset-basics.cpp for you to work through if you wish to get some practice with RAJA. The file RAJA/exercises/segment-indexset-basics_solution.cpp contains complete working code for the examples discussed in this section. You can use the solution file to check your work and for guidance if you get stuck. To build the exercises execute make segment-indexset-basics and make segment-indexset-basics_solution from the build directory.

Key RAJA features shown in this example are:

• RAJA::forall loop execution template
• RAJA::TypedRangeSegment, RAJA::TypedRangeStrideSegment, and RAJA::TypedListSegment iteration space constructs
• RAJA::TypedIndexSet container and associated execution policies

The concepts of iteration spaces and associated Loop variables are central to writing kernels in RAJA. RAJA provides basic iteration space types that serve as flexible building blocks that can be used to form a variety of loop iteration patterns. These types can be used to define a particular order for loop iterates, aggregate and partition iterates, as well as other configurations.

The examples in this section focus on how to use RAJA index sets and iteration space segments, such as index ranges and lists of indices. Lists of indices are important for algorithms that use indirection arrays for irregular array accesses. Combining different segment types, such as ranges and lists in an index set allows a user to launch different iteration patterns in a single loop execution construct (i.e., one kernel). This is something that is not supported by other programming models and abstractions and is unique to RAJA. Applying these concepts judiciously can help improve performance by allowing compilers to optimize for specific segment types (e.g., SIMD for range segments) while providing the flexibility of indirection arrays for general indexing patterns.

Although the constructs described in the section are useful in numerical computations and parallel execution, the examples only contain print statements and sequential execution. The goal is to show you how to use RAJA iteration space constructs.

## RAJA Segments¶

A RAJA Segment represents a set of indices that one wants to execute as a unit for a kernel. RAJA provides the following Segment types:

• RAJA::TypedRangeSegment represents a stride-1 range
• RAJA::TypedRangeStrideSegment represents a (non-unit) stride range
• RAJA::TypedListSegment represents an arbitrary set of indices

These segment types are used in RAJA::forall and other RAJA kernel execution mechanisms to define the iteration space for a kernel.

After we briefly introduce these types, we will present several examples using them.

### TypedRangeSegment¶

A RAJA::TypedRangeSegment is the fundamental type for defining a stride-1 (i.e., contiguous) range of indices. This is illustrated in the figure below.

One creates a range segment object as follows:

// A stride-1 index range [beg, end) using type int.
RAJA::TypedRangeSegment<int> my_range(beg, end);


Any integral type can be given as the template parameter.

Note

When using a RAJA range segment, no loop iterations will be run when begin >= end.

### TypedRangeStrideSegment¶

A RAJA::TypedRangeStrideSegment defines a range with a constant stride, including negative stride values if needed. This is illustrated in the figure below.

One creates a range stride segment object as follows:

// A stride-3 index range [beg, end) using type int.
RAJA::TypedRangeStrideSegment<int> my_stride2_range(beg, end, 3);

// A index range with -1 stride [0, N-1) using type int
RAJA::TypedRangeStrideSegment<int> my_neg1_range( N-1, -1, -1);


Any integral type can be given as the template parameter.

When the negative-stride segment above is passed to a RAJA::forall method, for example, the loop will run in reverse order with iterates:

N-1  N-2  N-3 ... 1 0


Note

When using a RAJA strided range, no loop iterations will be run under the following conditions:

• Stride > 0 and begin > end
• Stride < 0 and begin < end
• Stride == 0

### TypedListSegment¶

A RAJA::TypedListSegment is used to define an arbitrary set of indices, akin to an indirection array. This is illustrated in the figure below.

One creates a list segment object by passing a container of integral values to a list segment constructor. For example:

// Create a vector holding some integer index values
std::vector<int> idx = {0, 2, 3, 4, 7, 8, 9, 53};

// Create list segment with these indices where the indices are
// stored in the CUDA device memory space
camp::resources::Resource cuda_res{camp::resources::Cuda()};
RAJA::TypedListSegment<int> idx_list( idx[0], cuda_res );

// Alternatively
RAJA::TypedListSegment<int> idx_list( &idx[0], idx.size(),
cuda_res );


When the list segment above is passed to a RAJA::forall method, for example, the kernel will execute with iterates:

0 2 3 4 7 8 9 53


Note that a RAJA::TypedListSegment constructor can take a pointer to an array of indices and an array length. If the indices are in a container, such as std::vector that provides begin(), end(), and size() methods, the container can be passed to the constructor and the length argument is not required.

Note

Currently, a camp resource object must be passed to a list segment constructor to copy the indices in the indices into the proper memory space for a kernel to execute (as shown above). In the future, this will change and the user will be responsible for providing the indices in the proper memory space.

## IndexSets¶

A RAJA::TypedIndexSet is a container that can hold an arbitrary collection of segment objects. The following figure shows an index set with two contiguous ranges and an irregularly-spaced list of indices.

We can create such an index set as follows:

// Create an index set that can hold range and list segments with
// int index value type
RAJA::TypedIndexSet< RAJA::TypedRangeSegment<int>,
RAJA::TypedListSegment<int> > iset;

// Add two range segments and one list segment to the index set
iset.push_back( RAJA::TypedRangeSegment<int>( ... ) );
iset.push_back( RAJA::TypedListSegment<int>(...) );
iset.push_back( RAJA::TypedRangeSegment<int>( ... ) );


A RAJA::TypedIndexSet object can be passed to a RAJA kernel execution method, such as RAJA::forall to execute all segments in the index set with one method call. We will show this in detail in the examples below.

Note

It is the responsibility of the user to ensure that segments are defined properly when using RAJA index sets. For example, if the same index appears in multiple segments, the corresponding loop iteration will be run multiple times.

## Segment and IndexSet Examples¶

The examples in this section illustrate how the segment types that RAJA provides can be used to define kernel iteration spaces. We use the following type aliases to make the code more compact:

using IdxType = int;
using RangeSegType = RAJA::TypedRangeSegment<IdxType>;
using RangeStrideSegType = RAJA::TypedRangeStrideSegment<IdxType>;
using ListSegType = RAJA::TypedListSegment<IdxType>;
using IndexSetType = RAJA::TypedIndexSet< RangeSegType, ListSegType >;


### Stride-1 Indexing¶

Consider a simple C-style kernel that prints a contiguous sequence of values:

  for (IdxType i = 0; i < 20; i++) {
std::cout << i << "  ";
}


When run, the kernel prints the following sequence, as expected:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19


Three RAJA variants of the kernel using a RAJA::TypedRangeSegment, a RAJA::TypedRangeStrideSegment, and a RAJA::TypedListSegment are:

  RAJA::forall<RAJA::seq_exec>(RangeSegType(0, 20), [=] (IdxType i) {
std::cout << i << "  ";
});

  RAJA::forall<RAJA::seq_exec>(RangeStrideSegType(0, 20, 1), [=] (IdxType i) {
std::cout << i << "  ";
});

  //
// Collect indices in a vector to create list segment
//
std::vector<IdxType> idx;
for (IdxType i = 0; i < 20; ++i) {
idx.push_back(i);
}

ListSegType idx_list1( idx, host_res );

RAJA::forall<RAJA::seq_exec>(idx_list1, [=] (IdxType i) {
std::cout << i << "  ";
});


Each of these variants prints the same integer sequence shown above.

One interesting thing to note is that with RAJA::TypedListSegment and RAJA::forall, the actual iteration value is passed to the lambda loop body. So the indirection array concept is not visible. In contrast, in C-style code, one has to manually retrieve the index value from the indirection array to achieve the desired result. For example:

  IdxType iis = static_cast<IdxType>(idx.size());  // to avoid compiler warning
for (IdxType ii = 0; ii < iis; ++ii) {
std::cout << idx[ ii ] << "  ";
}


### Non-unit Stride Indexing¶

Consider the following C-style kernel that prints the integer sequence discussed earlier in reverse order:

  for (IdxType i = 19; i > -1; i--) {
std::cout << i << "  ";
}


We can accomplish the same result using a RAJA::TypedRangeStrideSegment:

  RAJA::forall<RAJA::seq_exec>(RangeStrideSegType(19, -1, -1), [=] (IdxType i) {
std::cout << i << "  ";
});


Alternatively, we can use a RAJA::TypedListSegment, where we reverse the index array we used earlier to define the appropriate list segment:

  //
// Reverse the order of indices in the vector
//
std::reverse( idx.begin(), idx.end() );
ListSegType idx_list1_reverse( &idx[0], idx.size(), host_res );

RAJA::forall<RAJA::seq_exec>(idx_list1_reverse, [=] (IdxType i) {
std::cout << i << "  ";
});


The more common use of the RAJA::TypedRangeStrideSegment type is to run constant strided loops with a positive non-unit stride. For example:

  RAJA::forall<RAJA::seq_exec>(RangeStrideSegType(0, 20, 2), [=] (IdxType i) {
std::cout << i << "  ";
});


The C-style equivalent of this is:

  for (IdxType i = 0; i < 20; i += 2) {
std::cout << i << "  ";
}


### IndexSets: Complex Iteration Spaces¶

We noted earlier that RAJA::TypedIndexSet objects can be used to partition iteration spaces into disjoint parts. Among other things, this can be useful to expose parallelism in algorithms that would otherwise require significant code transformation to do so. Please see Iteration Space Coloring: Mesh Vertex Sum for discussion of an example that illustrates this.

Here is an example that uses two RAJA::TypedRangeSegment objects in an index set to represent an iteration space broken into two disjoint contiguous intervals:

  using SEQ_ISET_EXECPOL = RAJA::ExecPolicy<RAJA::seq_segit,
RAJA::seq_exec>;

IndexSetType is2;
is2.push_back( RangeSegType(0, 10) );
is2.push_back( RangeSegType(15, 20) );

RAJA::forall<SEQ_ISET_EXECPOL>(is2, [=] (IdxType i) {
std::cout << i << "  ";
});


The integer sequence that is printed is:

0  1  2  3  4  5  6  7  8  9  15  16  17  18  19


as we expect.

The execution policy type when using a RAJA index set is a two-level policy. The first level specifies how to iterate over the segments in the index set, such as sequentially or in parallel using OpenMP. The second level is the execution policy used to execute each segment.

Note

Iterating over the indices of all segments in a RAJA index set requires a two-level execution policy, with two template parameters, as shown above. The first parameter specifies how to iterate over the segments. The second parameter specifies how the kernel will execute each segment over each segment. See RAJA IndexSet Execution Policies for more information about RAJA index set execution policies.

It is worth noting that a C-style version of this kernel requires either an indirection array to run in one loop or two for-loops. For example:

  for (IdxType i = 0; i < 10; ++i) {
std::cout << i << "  ";
}
for (IdxType i = 15; i < 20; ++i) {
std::cout << i << "  ";
}


Finally, we show an example that uses an index set holding two range segments and one list segment to partition an iteration space into three parts:

  IndexSetType is3;

is3.push_back( RangeSegType(0, 8) );

IdxType indx[ ] = {10, 11, 14, 20, 22};
ListSegType list2( indx, 5, host_res );
is3.push_back( list2 );

is3.push_back( RangeSegType(24, 28) );

RAJA::forall<SEQ_ISET_EXECPOL>(is3, [=] (IdxType i) {
std::cout << i << "  ";
});


The integer sequence that is printed is:

0  1  2  3  4  5  6  7  10  11  14  20  22  24  25  26  27