Sort Operations¶
RAJA provides portable parallel sort operations, which are described in this section.
A few important notes:
Note
All RAJA sort operations are in the namespace
RAJA
.Each RAJA sort operation is a template on an execution policy parameter. The same policy types used for
RAJA::forall
methods may be used for RAJA sorts. Please see Policies for more information.RAJA sort operations accept an optional comparator argument so users can perform different types of sort operations. If no operator is given, the default is a less than operation and the result is a sequence sorted in non-decreasing order.
Also:
Note
For sorts using the CUDA or HIP back-end, RAJA implementation uses
the NVIDIA CUB library or AMD rocPRIM library, respectively.
Typically, the CMake variable CUB_DIR
or ROCPRIM_DIR
will
be automatically set to the location of the CUB or rocPRIM library
for the CUDA or rocPRIM installation specified when either back-end
is enabled. More details for configuring the CUB or rocPRIM library
for a RAJA build can be found Dependencies.
Please see the following tutorial sections for detailed examples that use RAJA scan operations:
Sort Operations¶
In general, a sort operation takes a sequence of numbers ‘x’ and a binary comparison operator ‘op’ to form a strict weak ordering of elements in input sequence ‘x’ and produce a sequence of numbers ‘y’ as output. The output sequence is a permutation of the input sequence where each pair of elements ‘a’ and ‘b’, where ‘a’ is before ‘b’ in the output sequence, satisfies ‘!(b op a)’. Sorts are stable if they always preserve the order of equivalent elements, where equivalent means ‘!(a op b) && !(b op a)’ is true.
A stable sort takes an input sequence ‘x’ where ai appears before aj if i < j when ai and aj are equivalent for any i != j.
x = { a0, b0, a1, … }
and calculates the stably sorted output sequence ‘y’ that preserves the order of equivalent elements. That is, the sorted sequence where element ai appears before the equivalent element aj if i < j:
y = { a0, a1, b0, … }
An unstable sort may not preserve the order of equivalent elements and may produce either of the following output sequences:
y = { a0, a1, b0, … }
or
y = { a1, a0, b0, … }
RAJA Unstable Sorts¶
RAJA unstable sort operations look like the following:
RAJA::sort< exec_policy >(container)
RAJA::sort< exec_policy >(container, comparator)
For example, sorting an integer array with this sequence of values:
6 7 2 1 0 9 4 8 5 3 4 9 6 3 7 0 1 8 2 5
with a sequential unstable sort operation:
std::copy_n(in, N, out);
RAJA::sort<RAJA::seq_exec>(RAJA::make_span(out, N));
produces the out
array with this sequence of values:
0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9
Note that the syntax is essentially the same as Scan Operations.
Here, container
is a random access range of elements. container
provides
access to the input sequence and contains the output sequence at the end of
sort. The sort operation listed above will be a non-decreasing sort
since there is no comparator argument given; i.e., the sequences will be
reordered in-place using the default RAJA less-than comparator.
Equivalently, the RAJA::operators::less
comparator operator could be
passed as the second argument to the sort routine to produce the same result:
RAJA::sort<RAJA::seq_exec>(RAJA::make_span(out, N),
RAJA::operators::less<int>{});
Note that container arguments can be generated from iterators using
RAJA::make_span(out, N)
, where we pass the base pointer for the array
and its length.
RAJA also provides sort operations that operate on key-value pairs stored separately:
RAJA::sort_pairs< exec_policy >(keys_container, vals_container)
RAJA::sort_pairs< exec_policy >(keys_container, vals_container, comparator)
RAJA::sort_pairs
methods generate the same output sequence of keys in
keys_container
as RAJA::sort
does in container
and reorders the
sequence of values in vals_container
by permuting the sequence of values in
the same manner as the sequence of keys; i.e. the sequence of pairs is sorted
based on comparing their keys. Detailed examples are provided in
Parallel Sort Operations.
Note
The comparator used in RAJA::sort_pairs
only compares keys.
RAJA Stable Sorts¶
RAJA stable sort operations are used essentially the same as unstable sorts:
RAJA::stable_sort< exec_policy >(container)
RAJA::stable_sort< exec_policy >(container, comparator)
RAJA also provides stable sort pairs that operate on key-value pairs stored separately:
RAJA::stable_sort_pairs< exec_policy >(keys_container, vals_container)
RAJA::stable_sort_pairs< exec_policy >(keys_container, vals_container, comparator)
RAJA Comparison Operators¶
RAJA provides two operators that can be used to produce different ordered sorts:
RAJA::operators::less<T>
RAJA::operators::greater<T>
Note
All RAJA comparison operators are in the namespace RAJA::operators
.