  Data movement is the dominating factor affecting performance and energy in
modern computing systems. Consequently, many algorithms have been developed to
minimize the number of I/O operations for common computing patterns. Matrix
multiplication is no exception, and lower bounds have been proven and
implemented both for shared and distributed memory systems. Reconfigurable
hardware platforms are a lucrative target for I/O minimizing algorithms, as
they offer full control of memory accesses to the programmer. While bounds
developed in the context of fixed architectures still apply to these platforms,
the spatially distributed nature of their computational and memory resources
requires a decentralized approach to optimize algorithms for maximum hardware
utilization. We present a model to optimize matrix multiplication for FPGA
platforms, simultaneously targeting maximum performance and minimum off-chip
data movement, within constraints set by the hardware. We map the model to a
concrete architecture using a high-level synthesis tool, maintaining a high
level of abstraction, allowing us to support arbitrary data types, and enables
maintainability and portability across FPGA devices. Kernels generated from our
architecture are shown to offer competitive performance in practice, scaling
with both compute and memory resources. We offer our design as an open source
project to encourage the open development of linear algebra and I/O minimizing
algorithms on reconfigurable hardware platforms.
