Undergrad Research Project - Emulating higher precision for numerical computations

Spring 2018

Kashish Garg
Franz Franchetti
Project description

Most numerical computations today are performed on CPU/GPU architectures with 64-bit precision for doubles. While this level of precision is appropriate for smaller problem sizes, a greater level of precision is required for many numerical simulations (e.g. cosmology, earthquake simulations and molecular simulations) that have larger problem sizes. For example, many of these simulations use the Fast Fourier Transform, which involves multiplication with roots of unity. Since the level of precision is limited to 64-bits, in large problem sizes, the accuracy of the computation is affected. One solution to this problem that I will explore in my research is using software to emulate higher precision. Indeed, a consequence of this would be that each computation would take more operations to perform. For example, adding two numbers with extended precision may require up to five 64-bit additions. The main goal is to create the wrappers for extended precision that can be used to provide a higher level of accuracy for Fast Fourier Transforms and/or other linear algebra operations on modern-day 64-bit CPU/GPU architectures.

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