FLINT3.7.0-dev
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radix_sqrt_approx_rsqrtmul, radix_sqrt_approx

Synopsis#include <flint/radix.h>
void radix_sqrt_approx_rsqrtmul(nn_ptr q, nn_srcptr a, slong an, slong n, const radix_t radix)source
void radix_sqrt_approx(nn_ptr q, nn_srcptr a, slong an, slong n, const radix_t radix)source

With aa as for radix_rsqrt_approx, set (q,n+2)(q, n + 2) to an approximation of a∈[1/B,1)\sqrt a \in [1/B, 1) with nn fraction limbs and two integral limbs (normally zero, though the value can round up to 1), with absolute error less than 4B−n/a4 B^{-n}/\sqrt a. The error is proportional to 1/a1/\sqrt a rather than to a\sqrt a, because the corrections of the last iteration are multiplied by an approximation of 1/a≤B1/\sqrt a \le B.

Cite this page

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