  The massive quantities of genomic data being made available through gene
sequencing techniques are enabling breakthroughs in genomic science in many
areas such as medical advances in the diagnosis and treatment of diseases.
Analyzing this data, however, is a computational challenge insofar as the
computational costs of the relevant algorithms can grow with quadratic, cubic
or higher complexity-leading to the need for leadership scale computing. In
this paper we describe a new approach to calculations of the Custom Correlation
Coefficient (CCC) between Single Nucleotide Polymorphisms (SNPs) across a
population, suitable for parallel systems equipped with graphics processing
units (GPUs) or Intel Xeon Phi processors. We describe the mapping of the
algorithms to accelerated processors, techniques used for eliminating redundant
calculations due to symmetries, and strategies for efficient mapping of the
calculations to many-node parallel systems. Results are presented demonstrating
high per-node performance and near-ideal parallel scalability with rates of
more than nine quadrillion elementwise comparisons achieved per second with the
latest optimized code on the ORNL Titan system, this being orders of magnitude
faster than rates achieved using other codes and platforms as reported in the
literature. Also it is estimated that as many as 90 quadrillion comparisons per
second may be achievable on the upcoming ORNL Summit system, an additional 10X
performance increase. In a companion paper we describe corresponding techniques
applied to calculations of the Proportional Similarity metric for comparative
genomics applications.
