ANALYTICALLY CONTINUOUS FUNCTIONS FOR COMPUTING THE ARGUMENT OF A COMPLEX NUMBER
DOI:
https://doi.org/10.30890/2567-5273.2025-41-01-023Keywords:
argument computation, atan2, Atan4, inverse trigonometric functions, symbolic computation, phase analysis, branchless algorithms, SIMD vectorization.Abstract
Computing the argument of a complex number is fundamental to signal processing, navigation, and computational geometry. The standard atan2 function, while numerically efficient, produces cumbersome piecewise expressions in symbolic computation systems, coReferences
IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2019, IEEE, 2019, doi:10.1109/IEEESTD.2019.8766229
W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed., Cambridge Univ. Press, 2007, doi:10.1017/CBO9780511813890
N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, 2002, doi:10.1137/1.9780898718027
A. Meurer et al., "SymPy: symbolic computing in Python," PeerJ Comput. Sci., vol. 3, e103, 2017, doi:10.7717/peerj-cs.103
Oppenheim, A. V., & Schafer, R. W. 2010. Discrete-Time Signal Processing. 3rd ed. Pearson. ISBN: 9780131988422
Haykin, S., & Moher, M. 2022. Communication Systems. 6th ed. Wiley. ISBN: 978-1-119-82826-6
J. L. Bentley, "Programming Pearls: Eliminating Branches from a Binary Search," Communications of the ACM, vol. 32, no. 12, pp. 1492-1498, 1989, doi:10.1145/76380.76381
D. E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Addison-Wesley, 1998, doi:10.5555/280635
Burden, R. L., Faires, J. D., & Burden, A. M. 2024. Numerical Analysis. 11th ed. Pearson. ISBN: 978-0137343888
J. Stoer и R. Bulirsch, Introduction to Numerical Analysis, 3rd ed., Springer, 2002, doi:10.1007/978-0-387-21738-3
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Authors

This work is licensed under a Creative Commons Attribution 4.0 International License.



