Security News
New React Server Components Vulnerabilities: DoS and Source Code Exposure
New DoS and source code exposure bugs in React Server Components and Next.js: what’s affected and how to update safely.
By Sarah Gooding - Dec 12, 2025
🚨 Shai-Hulud Strikes Again:834 Packages Compromised.Technical Analysis →
Overview
The focus is to find real roots of real coefficient polynomials from degree 1 up to about degree 20 as accurately and as fast as possible, e.g.
// some polynomial with double precision coefficients, i.e. x^6 - 21x^5 + 175x^4 - 735x^3 + 1624x^2 - 1764 + 720
const p = [1, -21, 175, -735, 1624, -1764, 720];
allRoots(p); //=> [0.9999999999999997, 2.0000000000000013, 2.9999999999999316, 4.00000000000096, 5.000000000000012, 6.00000000000028]
However, the above function, allRoots, does not take error bounds into account and
can thus be inaccurate if the roots have high condition numbers.
For extremely accurate (no matter how high the condition number) certified results use e.g.:
const p = [1, -21, 175, -735, 1624, -1764, 720]; // some polynomial with double precision coefficients
allRootsCertifiedSimplified(p);
or for a more flexible function that takes the input polynomial coefficients
as double-double precision and the ability to specify error bounds on the coefficients
in addition to a fallback function to specify exact coefficients
(in the form of Shewchuk expansions)
use allRootsCertified.
Though the focus is on root finding, the library include numerous useful operators
on polynomials with double, double-double, Shewchuk expansion and bigint coefficients, e.g
add([1,2,3], [3,4]); //=> [1,5,7]
Why only up to about degree 20?
This isn't a hard limit. Roughly speaking, since the roots are found
using Rolle's Theorem
it becomes asymptotically slower (compared to Descartes Methods), i.e.
roughly O(n²) vs O(n) the higher the polynomial degree, n.
Another reason is that evaluation of the polynomial at x when |x| >> 1 can result in
overflow when the result is larger than about 1.8 x 10^308 (the max value a double precision floating point value can be).
Documentation
For more in-depth documentation please read the docs!.
Installation
npm install flo-poly
This package is ESM only
and can be used in Node.js (or in a browser when bundled using e.g. Webpack).
Additionally, self-contained ECMAScript Module (ESM) files index.js and
index.min.js in the ./browser folder is provided.
Usage
Node.js
import { allRoots } from 'flo-poly';
// some polynomial with double precision coefficients, i.e. x^6 - 21x^5 + 175x^4 - 735x^3 + 1624x^2 - 1764 + 720
const p = [1, -21, 175, -735, 1624, -1764, 720];
const roots = allRoots(p);
if (roots.length === 6) {
console.log('success! 😁'); // we should get to here!
} else {
console.log('failure! 😥'); // ...and not here
}
Browsers - directly, without a bundler, using the pre-bundled minified .js file
Please note that no tree shaking will take place in this case.
<!doctype html>
<html lang="en">
<head>
<script type="module">
import { allRoots } from "./node_modules/flo-poly/browser/index.min.js";
// some polynomial with double precision coefficients, i.e. x^6 - 21x^5 + 175x^4 - 735x^3 + 1624x^2 - 1764 + 720
const p = [1, -21, 175, -735, 1624, -1764, 720];
const roots = allRoots(p);
if (roots.length === 6) {
console.log('success! 😁'); // we should get to here!
} else {
console.log('failure! 😥'); // ...and not here
}
</script>
</head>
<body>Check the console.</body>
</html>
Bundlers (Webpack, Rollup, ...)
Webpack will be taken as an example here.
Since your webpack config file might still use CommonJS you must rename
webpack.config.js to webpack.config.cjs.
If you are using TypeScript:
Since this is an ESM only
library you must use resolve-typescript-plugin
(at least until webpack catches up with ESM?) in your webpack.config.cjs file.
npm install --save-dev resolve-typescript-plugin
and follow the instructions given at resolve-typescript-plugin.
Additionally, follow this guide.
Keywords
FAQs
A practical, root-focused JavaScript polynomial utility library.
The npm package flo-poly receives a total of 25,683 weekly downloads. As such, flo-poly popularity was classified as popular.
We found that flo-poly demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 1 open source maintainer collaborating on the project.
Package last updated on 12 Sep 2025
Did you know?
Socket for GitHub automatically highlights issues in each pull request and monitors the health of all your open source dependencies. Discover the contents of your packages and block harmful activity before you install or update your dependencies.
Related posts
Security News
Software Engineering Daily Podcast: Feross on AI, Open Source, and Supply Chain Risk
Socket CEO Feross Aboukhadijeh joins Software Engineering Daily to discuss modern software supply chain attacks and rising AI-driven security risks.
By Sarah Gooding - Dec 11, 2025
Security News
npm Revokes Classic Tokens, as OpenJS Warns Maintainers About OIDC Gaps
GitHub has revoked npm classic tokens for publishing; maintainers must migrate, but OpenJS warns OIDC trusted publishing still has risky gaps for critical projects.
By Sarah Gooding - Dec 10, 2025