40 research outputs found
Accelerating 128-bit Floating-Point Matrix Multiplication on FPGAs
General Matrix Multiplication (GEMM) is a fundamental operation widely used
in scientific computations. Its performance and accuracy significantly impact
the performance and accuracy of applications that depend on it. One such
application is semidefinite programming (SDP), and it often requires binary128
or higher precision arithmetic to solve problems involving SDP stably. However,
only some processors support binary128 arithmetic, which makes SDP solvers
generally slow. In this study, we focused on accelerating GEMM with binary128
arithmetic on field-programmable gate arrays (FPGAs) to enable the flexible
design of accelerators for the desired computations. Our binary128 GEMM designs
on a recent high-performance FPGA achieved approximately 90GFlops, 147x faster
than the computation executed on a recent CPU with 20 threads for large
matrices. Using our binary128 GEMM design on the FPGA, we successfully
accelerated two numerical applications: LU decomposition and SDP problems, for
the first time.Comment: 12 pages, 8 figure
Numerical Simulations of Globular Cluster Formation
We examine various physical processes associated with the formation of
globular clusters by using the three-dimensional Smoothed Particle
Hydrodynamics (SPH) code. Our code includes radiative cooling of gases, star
formation, energy feedback from stars including stellar winds and supernovae,
and chemical enrichment by stars. We assume that, in the collapsing galaxy,
isothermal cold clouds form through thermal condensations and become
proto-globular clouds. We calculate the size of proto-globular clouds by
solving the linearized equations for perturbation. We compute the evolution of
the inner region of the proto-cloud with our SPH code for various initial
radius and initial composition of gases. When the initial gases contain no
heavy elements, the evolution of proto-clouds sensitively depends on the
initial radius. For a smaller initial radius, the initial star burst is so
intense that the subsequent star formation occurs in the central regions to
form a dense star cluster as massive as the globular cluster. When the initial
gases contain some heavy elements, the metallicity of gases affects the
evolution and the final stellar mass. If the initial radius of the
proto-globular clouds was relatively large, the formation of a star cluster as
massive as the globular clusters requires the initial metallicity as high as
[Fe/H] . The self-enrichment of heavy elements in the star cluster
does not occur in all cases.Comment: Accpeted for publication in the ApJ. Correctiong errors in Table