`n_cbrt, n_cbrtrem`

Synopsis#include <flint/ulong_extras.h>

ulong n_cbrt(ulong n)source

ulong n_cbrtrem(ulong * remainder, ulong n)source

Returns $\lfloor n^{1/3} \rfloor$ ; n_cbrtrem also sets the remainder.

n_cbrt takes a first approximation from n_cbrt_estimate. For $n > 2^{46}$ the result is computed with n_cbrt_chebyshev_approx; otherwise the iteration $x \leftarrow x - (x^3 - a) x / (2 x^3 + a)$ of Kahan [Kahan1991] is used.

References#

[Kahan1991] Kahan, William: Computing a Real Cube Root. https://csclub.uwaterloo.ca/~pbarfuss/qbrt.pdf

Cite this page

The FLINT team, “n_cbrt, n_cbrtrem (ulong_extras.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/ulong_extras/n_cbrt.html (generated 2026-11-02).

@misc{flint-doc-ulong-extras-n-cbrt,
  author       = {{The FLINT team}},
  title        = {{n\_cbrt, n\_cbrtrem (ulong\_extras.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/ulong_extras/n_cbrt.html},
  note         = {Generated 2026-11-02}
}

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