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Fast Algorithms for Computing Floating-Point Reciprocal Cube Root Functions


Leonid Moroz, Volodymyr Samotyy, and Cezary Walczyk


Vol. 23  No. 6  pp. 84-90


In this article the problem of computing floating-point reciprocal cube root functions is considered. Our new algorithms for this task decrease the number of arithmetic operations used for computing. A new approach for selection of magic constants is presented in order to minimize the computation time for reciprocal cube roots of arguments with movable decimal point. The underlying theory enables partitioning of the base argument range x is element of [1,8) into 3 segments, what in turn increases accuracy of initial function approximation and decreases the number of iterations to one. Three best algorithms were implemented and carefully tested on 32-bit microcontroller with ARM core. Their custom C implementations were favourable compared with the algorithm based on cbrtf(x) function taken from C library on three different hardware platforms. As a result, the new fast approximation algorithm for the function 1 was determined that outperforms all other algorithms in terms of computation time and cycle count.


floating-point, cube root, inverse cube root, Newton-Raphson, Householder.