Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton-Raphson Corrections
Cezary J Walczyk1, Leonid V Moroz2, Jan L Cieśliński1
1Wydział Fizyki, Uniwersytet w Białymstoku, ul. Ciołkowskiego 1L, 15-245 Białystok, Poland.
Entropy (Basel, Switzerland)
|January 13, 2021
Summary
This study introduces improved, low-complexity algorithms for fast inverse square root calculations. These new methods enhance accuracy significantly while maintaining efficient computational costs for floating-point numbers.
Area of Science:
- Computer Science
- Numerical Analysis
- Algorithm Optimization
Background:
- Direct computation of functions is crucial for hardware constraints and data storage challenges.
- Efficient algorithms are needed for processing large datasets and complex calculations.
- The fast inverse square root algorithm is a key function in many computational systems.
Purpose of the Study:
- To develop improved algorithms for the fast calculation of the inverse square root function.
- To enhance accuracy for single-precision and double-precision floating-point numbers.
- To explore higher precision calculations for the inverse square root.
Main Methods:
- Minimizing maximal errors through the optimization of magic constants.
- Modifying Newton-Raphson coefficients for improved accuracy.
- Developing low-complexity algorithms for direct function computation.
Main Results:
- Achieved significantly higher accuracy compared to the original fast inverse square root algorithm.
- Maintained very low computational costs, similar to the original algorithm.
- Demonstrated improved performance for both single-precision and double-precision floating-point numbers.
Conclusions:
- The developed algorithms offer a superior balance of accuracy and computational efficiency.
- These algorithms are suitable for applications with hardware or storage limitations.
- Further exploration into higher precision inverse square root calculations is warranted.
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