arb_sqrt, arb_sqrt_arf, arb_sqrt_fmpz, arb_sqrt_ui
Synopsis
#include <flint/arb.h>Set z to \sqrt{x}. If x contains negative numbers the result is indeterminate; use arb_sqrtpos when the negative part is known to be spurious.
For x = [m \pm r] with 0 \le r \le m the propagated error is bounded by \sqrt{m} - \sqrt{m - r} \le \frac{\sqrt{m}}{2}(r/m + (r/m)^2). The midpoint is computed with arf_sqrt in the relaxed mode ARF_RND_FAST (Newton iteration from 100000 bits); as for arb_div, its inexact flag is reliable, so exact input gives radius 0 exactly when the square root is exact.
Guides#
Cite this page
The FLINT team, “arb_sqrt, arb_sqrt_arf, arb_sqrt_fmpz, arb_sqrt_ui (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_sqrt.html (generated 2026-10-20).
@misc{flint-doc-arb-arb-sqrt,
author = {{The FLINT team}},
title = {{arb\_sqrt, arb\_sqrt\_arf, arb\_sqrt\_fmpz, arb\_sqrt\_ui (arb.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb/arb_sqrt.html},
note = {Generated 2026-10-20}
}