d1b_rsqrt, d2b_rsqrt, d3b_rsqrt, d4b_rsqrt
Synopsis
#include <flint/dfloat.h>int d1b_rsqrt(d1b_t res, d1b_srcptr x)int d2b_rsqrt(d2b_t res, d2b_srcptr x)int d3b_rsqrt(d3b_t res, d3b_srcptr x)int d4b_rsqrt(d4b_t res, d4b_srcptr x)Reciprocal square root. Returns GR_DOMAIN if x is entirely nonpositive, GR_UNABLE if it contains zero, and GR_SUCCESS otherwise.
For the computed r and e' = 1 - x' r^2, x'^{-1/2} = r (1 - e')^{-1/2}, so that |x'^{-1/2} - r| \le |r| (|e'|/2)(1 + |e'|) for |e'| \le 1/4, where |e'| \le |1 - x r^2| + r_x r^2 and 1 - x r^2 is enclosed by the tracked kernels (two products and a subtraction, which makes the ball version relatively more expensive than the ball square root, whose residual needs one product).
Cite this page
The FLINT team, “d1b_rsqrt, d2b_rsqrt, d3b_rsqrt, d4b_rsqrt (dfloat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/dfloat/d1b_rsqrt.html (generated 2026-10-20).
@misc{flint-doc-dfloat-d1b-rsqrt,
author = {{The FLINT team}},
title = {{d1b\_rsqrt, d2b\_rsqrt, d3b\_rsqrt, d4b\_rsqrt (dfloat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/dfloat/d1b_rsqrt.html},
note = {Generated 2026-10-20}
}