Radix Sort#

radix_sort Function Templates#

The radix_sort function sorts data using the radix sort algorithm. The sorting is stable, preserving the relative order of elements with equal keys. Both in-place and out-of-place overloads are provided. Out-of-place overloads do not alter the input sequence.

The functions implement a Onesweep* 1 algorithm variant.

A synopsis of the radix_sort function is provided below:

// defined in <oneapi/dpl/experimental/kernel_templates>

namespace oneapi::dpl::experimental::kt::gpu::esimd {

// Sort in-place
template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename Iterator>
sycl::event
radix_sort (sycl::queue q, Iterator first, Iterator last,
            KernelParam param); // (1)

template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename Range>
sycl::event
radix_sort (sycl::queue q, Range&& r, KernelParam param); // (2)


// Sort out-of-place
template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename Iterator1,
          typename Iterator2>
sycl::event
radix_sort (sycl::queue q, Iterator1 first, Iterator1 last,
            Iterator2 first_out, KernelParam param); // (3)

template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename Range1, typename Range2>
sycl::event
radix_sort (sycl::queue q, Range1&& r, Range2&& r_out,
            KernelParam param); // (4)
}

Note

The radix_sort is currently available only for Intel® Data Center GPU Max Series, and requires Intel® oneAPI DPC++/C++ Compiler 2023.2 or newer.

Template Parameters#

Name

Description

bool IsAscending

The sort order. Ascending: true; Descending: false.

std::uint8_t RadixBits

The number of bits to sort for each radix sort algorithm pass.

Parameters#

Name

Description

q

The SYCL* queue where kernels are submitted.

  • first, last (1),

  • r (2),

  • first, last, first_out (3),

  • r, r_out (4).

The sequences to apply the algorithm to. Supported sequence types:

param

A kernel_param object. Its data_per_workitem must be a positive multiple of 32.

Type Requirements:

  • The element type of sequence(s) to sort must be a C++ integral or floating-point type other than bool with a width of up to 64 bits.

Note

Current limitations:

  • Number of elements to sort must not exceed 2^30.

  • RadixBits can only be 8.

  • param.workgroup_size can only be 64.

Return Value#

A sycl::event object representing the status of the algorithm execution.

Usage Examples#

In-Place Example#

// possible build and run commands:
//    icpx -fsycl radix_sort.cpp -o radix_sort -I /path/to/oneDPL/include && ./radix_sort

#include <cstdint>
#include <iostream>
#include <sycl/sycl.hpp>

#include <oneapi/dpl/experimental/kernel_templates>

namespace kt = oneapi::dpl::experimental::kt;

int main()
{
   std::size_t n = 6;
   sycl::queue q{sycl::gpu_selector_v};
   std::uint32_t* keys = sycl::malloc_shared<std::uint32_t>(n, q);

   // initialize
   keys[0] = 3, keys[1] = 2, keys[2] = 1, keys[3] = 5, keys[4] = 3, keys[5] = 3;

   // sort
   auto e = kt::gpu::esimd::radix_sort<false, 8>(q, keys, keys + n, kt::kernel_param<416, 64>{}); // (1)
   e.wait();

   // print
   for(std::size_t i = 0; i < n; ++i)
      std::cout << keys[i] << ' ';
   std::cout << '\n';

   sycl::free(keys, q);
   return 0;
}

Output:

5 3 3 3 2 1

Out-of-Place Example#

// possible build and run commands:
//    icpx -fsycl radix_sort.cpp -o radix_sort -I /path/to/oneDPL/include && ./radix_sort

#include <cstdint>
#include <iostream>
#include <sycl/sycl.hpp>

#include <oneapi/dpl/experimental/kernel_templates>

namespace kt = oneapi::dpl::experimental::kt;

int main()
{
   std::size_t n = 6;
   sycl::queue q{sycl::gpu_selector_v};
   std::uint32_t* keys = sycl::malloc_shared<std::uint32_t>(n, q);
   std::uint32_t* keys_out = sycl::malloc_shared<std::uint32_t>(n, q);

   // initialize
   keys[0] = 3, keys[1] = 2, keys[2] = 1, keys[3] = 5, keys[4] = 3, keys[5] = 3;

   // sort
   auto e = kt::gpu::esimd::radix_sort<false, 8>(q, keys, keys + n, keys_out, kt::kernel_param<416, 64>{}); // (3)
   e.wait();

   // print
   for(std::size_t i = 0; i < n; ++i)
      std::cout << keys[i] << ' ';
   std::cout << '\n';
   for(std::size_t i = 0; i < n; ++i)
      std::cout << keys_out[i] << ' ';
   std::cout << '\n';

   sycl::free(keys, q);
   sycl::free(keys_out, q);
   return 0;
}

Output:

3 2 1 5 3 3
5 3 3 3 2 1

Memory Requirements#

The algorithm uses global and local device memory (see SYCL 2020 Specification) for intermediate data storage. For the algorithm to operate correctly, there must be enough memory on the device. If there is not enough global device memory, a std::bad_alloc exception is thrown. The behavior is undefined if there is not enough local memory. The amount of memory that is required depends on input data and configuration parameters, as described below.

Global Memory Requirements#

Global memory is used for copying the input sequence(s) and storing internal data such as radix value counters. The used amount depends on many parameters; below is an upper bound approximation:

Nkeys + C * Nkeys

where the sequence with keys takes Nkeys space, and the additional space is C * Nkeys.

The value of C depends on param.data_per_workitem, param.workgroup_size, and RadixBits. For param.data_per_workitem set to 32, param.workgroup_size to 64, and RadixBits to 8, C approximately equals to 1. Incrementing RadixBits increases C up to twice, while doubling either param.data_per_workitem or param.workgroup_size leads to a halving of C.

Note

If the number of elements to sort does not exceed param.data_per_workitem * param.workgroup_size, radix_sort is executed by a single work-group and does not use any global memory.

Local Memory Requirements#

Local memory is used for reordering keys within a work-group, and for storing internal data such as radix value counters. The used amount depends on many parameters; below is an upper bound approximation:

Nkeys_per_workgroup + C

where Nkeys_per_workgroup is the amount of memory to store keys. C is some additional space for storing internal data.

Nkeys_per_workgroup equals to sizeof(key_type) * param.data_per_workitem * param.workgroup_size, C does not exceed 4KB.