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Numerical behavior of NVIDIA tensor cores.

Massimiliano Fasi1, Nicholas J Higham2, Mantas Mikaitis2

  • 1School of Science and Technology, Örebro University, Örebro, Sweden.

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|April 5, 2021
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Summary
This summary is machine-generated.

NVIDIA tensor cores

Keywords:
Binary16Dot productFloating-point arithmeticHalf precisionIEEE 754 arithmeticMatrix multiply-accumulateNVIDIA A100 GPUNVIDIA T4 GPUNVIDIA V100 GPUTensor core

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Area of Science:

  • Computer Engineering
  • Numerical Analysis

Background:

  • NVIDIA tensor cores accelerate mixed-precision matrix multiplication.
  • Their precise floating-point arithmetic is undocumented by NVIDIA.

Purpose of the Study:

  • To investigate the undocumented floating-point arithmetic of NVIDIA tensor cores.
  • To provide insights for accurate simulation, result comparison, and custom hardware design.

Main Methods:

  • Designed numerical experiments on NVIDIA Volta, Turing, and Ampere GPUs.
  • Analyzed intermediate precision, subnormal number support, rounding modes, operation order, and normalization.

Main Results:

  • Determined undocumented floating-point arithmetic details of NVIDIA tensor cores.
  • Identified a non-monotonicity issue in floating-point adders without intermediate normalization.
  • Developed a test suite for tensor core arithmetic analysis.

Conclusions:

  • Understanding tensor core arithmetic is crucial for accurate simulation and hardware design.
  • The developed test suite aids in evaluating current and future accelerators.