KAVEESHA K30 v1.0: A 38-Cycle, 1.14e-17 Error Elliptic Integral Formula Surpassing Boost.Math
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| Format: | Recurso digital |
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2026
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| _version_ | 1866901515825840128 |
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| author | Dombagahawaththa, Kaveesha Methsara Dombagahawaththa |
| author_facet | Dombagahawaththa, Kaveesha Methsara Dombagahawaththa |
| contents | <p>This work introduces KAVEESHA K30 v1.0, a sqrt-free rational minimax approximation for the complete elliptic integral E(k). The formula achieves 1.143e-17 peak error vs Mathematica with 38 CPU cycles, 0 sqrt, 0 branches, and 0 pow, outperforming Boost.Math 1.88 by 5.8x speedup and 4.3x accuracy. Full C99 implementation, 64-bit coefficients, and Mathematica verification code included. Attribution required to ORCID 0009-0004-2223-5377 under MIT License.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20210567 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | KAVEESHA K30 v1.0: A 38-Cycle, 1.14e-17 Error Elliptic Integral Formula Surpassing Boost.Math Dombagahawaththa, Kaveesha Methsara Dombagahawaththa minimax polynomial sqrt-free elliptic integrals Boost.Math KAVEESHA K30 numerical methods Horana HPC Sri Lanka FMA Horner <p>This work introduces KAVEESHA K30 v1.0, a sqrt-free rational minimax approximation for the complete elliptic integral E(k). The formula achieves 1.143e-17 peak error vs Mathematica with 38 CPU cycles, 0 sqrt, 0 branches, and 0 pow, outperforming Boost.Math 1.88 by 5.8x speedup and 4.3x accuracy. Full C99 implementation, 64-bit coefficients, and Mathematica verification code included. Attribution required to ORCID 0009-0004-2223-5377 under MIT License.</p> |
| title | KAVEESHA K30 v1.0: A 38-Cycle, 1.14e-17 Error Elliptic Integral Formula Surpassing Boost.Math |
| topic | minimax polynomial sqrt-free elliptic integrals Boost.Math KAVEESHA K30 numerical methods Horana HPC Sri Lanka FMA Horner |
| url | https://doi.org/10.5281/zenodo.20210567 |