Presentation
(PhD02) Mixed precision multi-level approach for FFTs
SessionPhD Forum
Event Type
PhD Forum
HPC Accelerators
Heterogeneous Systems
Parallel Algorithms
Parallel Applications
TimeMonday, June 25th1:09pm - 1:13pm
LocationAnalog 1, 2
DescriptionFast Fourier Transform (FFT) is a common tool for spectral analysis of
PDEs. Applications such as medical image registration in brain tumor
research involve many large FFTs dominating the overall runtime. For
this research, efficiently solving the forward and backward Poisson
equation and computing derivatives in the spectral space on
heterogeneous hardware platforms with native FP16 support is the main
objective.
For large three dimensional FFTs on distributed architectures the
runtime is dominated by the communication, since the data need to be
transposed several times. To decrease the communication volume and
improve the computational throughput low precision floating-point
numbers can be used. However, restricting the accuracy not only
influences stability, but also raises numerical problems due to the
limited dynamic range of floating-point numbers.
To overcome these issues, our aim is to develop a mixed precision
multi-level approach for FFTs. The basic idea is to split a given high
precision data on a fine grid into a coarser grid of same accuracy and
a fine grid with lower accuracy. The coarse grid has less
computational volume and the remaining low precision data on the fine
grid stays within the dynamic range, as high frequency modes of
typical application data decay fast. One of the core issues of this
study is the error analysis of this mixed precision splitting approach.
PDEs. Applications such as medical image registration in brain tumor
research involve many large FFTs dominating the overall runtime. For
this research, efficiently solving the forward and backward Poisson
equation and computing derivatives in the spectral space on
heterogeneous hardware platforms with native FP16 support is the main
objective.
For large three dimensional FFTs on distributed architectures the
runtime is dominated by the communication, since the data need to be
transposed several times. To decrease the communication volume and
improve the computational throughput low precision floating-point
numbers can be used. However, restricting the accuracy not only
influences stability, but also raises numerical problems due to the
limited dynamic range of floating-point numbers.
To overcome these issues, our aim is to develop a mixed precision
multi-level approach for FFTs. The basic idea is to split a given high
precision data on a fine grid into a coarser grid of same accuracy and
a fine grid with lower accuracy. The coarse grid has less
computational volume and the remaining low precision data on the fine
grid stays within the dynamic range, as high frequency modes of
typical application data decay fast. One of the core issues of this
study is the error analysis of this mixed precision splitting approach.
Poster PDF
