GPU Multimerge Sorting Algorithm
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Multiway mergesort for GPUs

Developed and implemented by the Algorithms and Parallel Computing (AlgoPARC) research group at the University of Hawai'i at Manoa.

This is an implementaton of the sorting algorithm described in the paper:

B. Karsin, V. Weichert, H. Casanova, J. Iacono, and N. Sitchinava. Analysis-driven Engineering of Comparison-based Sorting Algorithms on GPUs. In Proceedings of the 32nd International Conference on Supercomputing (ICS), 2018, to appear.

More details are available in chapter 7 (case study: sorting) of Ben Karsin's dissertation:


src/ provides an example of how to call GPU-MMS to sort a given input. To use GPU-MMS in your own code, include "src/multimergesort.hxx" and call the sorting function by:

multimergesort<T,cmp>(input, output, host_array, threadBlocks, N);

With the following parameters:

  • T: datatype of input being sorted
  • cmp: comparison function used to sort by
  • input: input array (defined as memory on the GPU)
  • output: output array (defined as memory on the GPU)
  • host_array: array defined as host memory (used for debugging/correctness verification)
  • threadBlocks: number of GPU thread blocks to use
  • N: size of array being sorted

In addition to these parameters, a series of parameters that dictate how the GPU-MMS algorithm runs are defined in "src/params.h". These parameters can be left as-is, or can be changed for users who want to further customize GPU-MMS operation.

  • K: Branching factor of GPU-MMS (number of lists merged into one per round)
  • PL: Log of K
  • PIPELINE: Flag to enable pipelining of merges in the blockHeap
  • RANGE: Range of values for randomly generated integer input

Code Organization

The code is organized as follows:

  • src/ is a test harness that builds random input sets and calls multimergesort to sort them.
  • src/Makefile builds the executable testMM
  • src/multimergesort.hxx contains the main sorting method that uses methods from the following files:
  • src/basecase/ contains all of the files for the 1024 base case sort.
  • src/warp-partition.hxx contains the code used to find partitions among merge lists for each warp to work on.
  • src/io-merge.hxx contains methods to merge K lists using the minBlockHeap data structure.
  • src/params.h contains definitions of all constants used by the sorting algorithm, including input size, K, number of blocks, etc.
  • src/cmp.hxx contains the definition of the comparision function and datatypes used to sort. The default < comparator to sort integer datatypes is enabled by default.
  • scripts/ contains several scripts used to run performance benchmarks of GPU-MMS

Limitations and future improvements

Current limitations of this implementation include:

  • Only input sizes that are M*(K^i) work, where M is the base case size (1024) and K is the chosen merge factor (defined in params.h).
  • As-is, base case can only be used to sort groups of 1024 elements. Code is available to sort 2048 or 4096 as well, but it is commented out.
  • There is an issue with certain values of P and THREADS not working properly, depending on the input size. Seems to be an issue with merging and needs to be debugged.