Emacs-related articles on Nick Higham's blog.
See also the interesting "What Is" series of articles, mostly on numerical linear algebra.

Software that aims to provide an easy to use (hopefully) universal blackbox for solving polynomials and secular equations.

Among its features you can find:
- Arbitrary precision approximation.
- Guaranteed inclusion radii for the results.
- Exploiting of polynomial structures: it can take advantage of sparsity as well as coefficients in a particular domain (i.e. integers or rationals).

It can be specialized for specific classes of polynomials. As an example, see the roots of the Mandelbrot polynomial of degree 2.097.151 computed in about 10 days on a dual Xeon server.

If you use MPSolve in your research, please cite it as follows:
Bini, Dario A., Fiorentino, Giuseppe, Design, analysis, and implementation of a multiprecision polynomial rootfinder. Numerical Algorithms 23.2-3 (2000): 127-173.
Bini, Dario A., and Robol, Leonardo. Solving secular and polynomial equations: A multiprecision algorithm. Journal of Computational and Applied Mathematics 272 (2014): 276-292.
Found via https://en.m.wikipedia.org/wiki/Aberth_method and https://en.m.wikipedia.org/wiki/MPSolve
See also the GitHub repository http://github.com/robol/MPSolve.git A simpler implementation of the Ehrich-Aberth-method can be found in https://github.com/robol/ea-roots

Polynomial root finder for {dm,hp}42s using Laguerre's method. Found on https://forum.swissmicros.com/viewtopic.php?p=20091#p20091
The Emacs tools for {dm,hp}42 code on https://richmit.github.io/hp42/hp42s-meta.html and the
Lisp library http://www.mitchr.me/SS/mjrcalc/ look interesting too.

mpmath is a free (BSD licensed) Python library for real and complex floating-point arithmetic with arbitrary precision. It has been developed by Fredrik Johansson since 2007, with help from many contributors.

List of the ten Finalists of the lightweight crypto standardization process.

This web page describes a 19-line (769-byte) OCaml program that solves Sudoku puzzles.

PCG is a family of simple fast space-efficient statistically good algorithms for random number generation. Unlike many general-purpose RNGs, they are also hard to predict.

Collection of FFT and related algorithm implementation in various programming languages.

Apart from the blog, there are technical notes https://www.johndcook.com/blog/writing/ and on-line calculators https://www.johndcook.com/blog/online-calculators/
As an example, see Camp-Paulson normal approximation to the binomial distribution https://www.johndcook.com/blog/camp_paulson/

Written by one of the foremost experts in high-performance computing and the inventor of Gustafson's Law, The End of Error: Unum Computing explains a new approach to computer arithmetic: the universal number (unum). The unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic. This new number type obtains more accurate answers than floating-point arithmetic yet uses fewer bits in many cases, saving memory, bandwidth, energy, and power.