radix_sort_by_key Function Templates

The radix_sort_by_key function sorts keys using the radix sort algorithm, applying the same order to the corresponding values. 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 sequences.

The functions implement a Onesweep* ¹ algorithm variant.

A synopsis of the radix_sort_by_key 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 Iterator1, typename Iterator2>
sycl::event
radix_sort_by_key (sycl::queue q, Iterator1 keys_first, Iterator1 keys_last,
                   Iterator2 values_first, KernelParam param); // (1)

template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename KeysRng, typename ValuesRng>
sycl::event
radix_sort_by_key (sycl::queue q, KeysRng&& keys,
                   ValuesRng&& values, KernelParam param); // (2)


// Sort out-of-place
template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename KeysIterator1,
          typename ValuesIterator1, typename KeysIterator2,
          typename ValuesIterator2>
sycl::event
radix_sort_by_key (sycl::queue q, KeysIterator1 keys_first,
                   KeysIterator1 keys_last, ValuesIterator1 values_first,
                   KeysIterator2 keys_out_first, ValuesIterator2 values_out_first,
                   KernelParam param); // (3)

template <bool IsAscending = true, std::uint8_t RadixBits = 8,
          typename KernelParam, typename KeysRng1, typename ValuesRng1,
          typename KeysRng2, typename ValuesRng2>
sycl::event
radix_sort_by_key (sycl::queue q, KeysRng1&& keys, ValuesRng1&& values,
                   KeysRng2&& keys_out, ValuesRng2&& values_out,
                   KernelParam param); // (4)
}

Template Parameters

Parameters

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.

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_by_key.cpp -o radix_sort_by_key -I /path/to/oneDPL/include && ./radix_sort_by_key

#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};
   sycl::buffer<std::uint32_t> keys{sycl::range<1>(n)};
   sycl::buffer<char> values{sycl::range<1>(n)};

   // initialize
   {
      sycl::host_accessor k_acc{keys, sycl::write_only};
      k_acc[0] = 3, k_acc[1] = 2, k_acc[2] = 1, k_acc[3] = 5, k_acc[4] = 3, k_acc[5] = 3;

      sycl::host_accessor v_acc{values, sycl::write_only};
      v_acc[0] = 'r', v_acc[1] = 'o', v_acc[2] = 's', v_acc[3] = 'd', v_acc[4] = 't', v_acc[5] = 'e';
   }

   // sort
   auto e = kt::gpu::esimd::radix_sort_by_key<true, 8>(q, keys, values, kt::kernel_param<96, 64>{}); // (2)
   e.wait();

   // print
   {
      sycl::host_accessor k_acc{keys, sycl::read_only};
      for(std::size_t i = 0; i < n; ++i)
            std::cout << k_acc[i] << ' ';
      std::cout << '\n';

      sycl::host_accessor v_acc{values, sycl::read_only};
      for(std::size_t i = 0; i < n; ++i)
            std::cout << v_acc[i] << ' ';
      std::cout << '\n';
   }

   return 0;
}

Output:

1 2 3 3 3 5
s o r t e d

Out-of-Place Example

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

#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};
   sycl::buffer<std::uint32_t> keys{sycl::range<1>(n)};
   sycl::buffer<std::uint32_t> keys_out{sycl::range<1>(n)};
   sycl::buffer<char> values{sycl::range<1>(n)};
   sycl::buffer<char> values_out{sycl::range<1>(n)};


   // initialize
   {
      sycl::host_accessor k_acc{keys, sycl::write_only};
      k_acc[0] = 3, k_acc[1] = 2, k_acc[2] = 1, k_acc[3] = 5, k_acc[4] = 3, k_acc[5] = 3;

      sycl::host_accessor v_acc{values, sycl::write_only};
      v_acc[0] = 'r', v_acc[1] = 'o', v_acc[2] = 's', v_acc[3] = 'd', v_acc[4] = 't', v_acc[5] = 'e';
   }

   // sort
   auto e = kt::gpu::esimd::radix_sort_by_key<true, 8>(q, keys, values, keys_out, values_out,
                                                       kt::kernel_param<96, 64>{}); // (4)
   e.wait();

   // print
   {
      sycl::host_accessor k_acc{keys, sycl::read_only};
      for(std::size_t i = 0; i < n; ++i)
            std::cout << k_acc[i] << ' ';
      std::cout << '\n';

      sycl::host_accessor v_acc{values, sycl::read_only};
      for(std::size_t i = 0; i < n; ++i)
            std::cout << v_acc[i] << ' ';
      std::cout << "\n\n";

      sycl::host_accessor k_out_acc{keys_out, sycl::read_only};
      for(std::size_t i = 0; i < n; ++i)
            std::cout << k_out_acc[i] << ' ';
      std::cout << '\n';

      sycl::host_accessor v_out_acc{values_out, sycl::read_only};
      for(std::size_t i = 0; i < n; ++i)
            std::cout << v_out_acc[i] << ' ';
      std::cout << '\n';
   }

   return 0;
}

Output:

3 2 1 5 3 3
r o s d t e

1 2 3 3 3 5
s o r t e d

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:

N_keys + N_values + C * N_keys

where the sequence with keys takes N_keys space, the sequence with values takes N_values space, and the additional space is C * N_keys.

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.

Local Memory Requirements

Local memory is used for reordering key-value pairs 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:

N_{keys_per_workgroup} + N_{values_per_workgroup} + C

where N_{keys_per_workgroup} and N_{values_per_workgroup} are the amounts of memory to store keys and values, respectively. C is some additional space for storing internal data.

N_{keys_per_workgroup} equals to sizeof(key_type) * param.data_per_workitem * param.workgroup_size, N_{values_per_workgroup} equals to sizeof(value_type) * param.data_per_workitem * param.workgroup_size, C does not exceed 4KB.

Recommended Settings for Best Performance

The general advice is to choose kernel parameters based on performance measurements and profiling information. The initial configuration may be selected according to these high-level guidelines:

• When the number of elements to sort N is less than 1M, utilizing all available compute cores is key for better performance. Allow creating enough work chunks to feed all X^e-cores ² on a GPU: param.data_per_workitem * param.workgroup_size ≈ N / xe_core_count.

• When the number of elements to sort is large (more than ~1M), maximizing the number of elements processed by a work-group, which equals to param.data_per_workitem * param.workgroup_size, reduces synchronization overheads between work-groups and usually benefits the overall performance.

[1]

Andy Adinets and Duane Merrill (2022). Onesweep: A Faster Least Significant Digit Radix Sort for GPUs. https://arxiv.org/abs/2206.01784.

[2]

The X^e-core term is described in the oneAPI GPU Optimization Guide. Check the number of cores in the device specification, such as Intel® Data Center GPU Max specification.