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Design of variable precision transcendental function automatic generator

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Abstract

The performance of transcendental functions is important to high-performance applications. Various customized implementations of transcendental functions in practice to obtain better performance for some particular applications, but specializing the transcendental functions for each individual application cannot scale with the increase and diversity of the latter. It is thus of vital importance to design and implement an automatic generator for transcendental functions. This article implements an automatic generator TGen (transcendental function generator) for variable precision transcendental functions. Given a specific computation interval, TGen can automatically generate independent implementations with different precisions for a transcendental function, and select the most suitable version for the target by means of a code filtering strategy. Our generator can now support the automatic generation of 18 representative transcendental functions. The experimental results show that TGen can generate code with the unfixed accuracy, and the performance of the generated code is superior to that of the code generated by metalibm. More specifically, when compiled with the GCC compiler, the code generated by TGen can provide a mean speedup of 1.84\(\times\) over that of a metalibm’s version, while the speedup of TGen’s code over that of the metalibm is 1.27\(\times\) when compiled with the SW5CC compiler.

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Notes

  1. https://www.gnu.org/software/libc/.

  2. https://software.intel.com/content/www/us/en/develop/articles/intel-math-kernel-library-intel-mkl-2020-system-requirements.html.

  3. http://www.netlib.org/fdlibm/.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China—Precision analysis and optimization of basic mathematical functions on domestic processors (No. 61802434).

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Authors and Affiliations

  1. State Key Laboratory of Mathematical Engineering and Advanced Computing, No. 62 Science Avenue, High-Tech Zone, Zhengzhou, Henan, 450001, China

    Jiangwei Hao, Jinchen Xu, Shaozhong Guo & YuanYuan Xia

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  1. Jiangwei Hao
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Correspondence to Jinchen Xu.

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Hao, J., Xu, J., Guo, S. et al. Design of variable precision transcendental function automatic generator. J Supercomput 78, 2196–2218 (2022). https://doi.org/10.1007/s11227-021-03937-8

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