"Both engineers and computational scientists alike will benefit greatly from having a standard test set for Initial Value Problems (IVPs) which includes documentation of the test problems, experimental results from a number of proven solvers, and Fortran subroutines providing a common interface to the defining problem functions. Engineers will be able to see at a glance which methods will be most effective for their class of problems. Researchers will be able to compare their new methods with the results of existing ones without incurring additional programming workload; they will have a reference with which their colleagues are familiar. This test set tries to fulfill these demands and tries to set a standard for IVP solver testing."
Found on John Butcher's page https://www.jcbutcher.com/rkclub

The RAN # function of HP-11C and -15C computes
 x_{i+1}=(33(29⋅2010667⋅x_i+131⋅449⋅641)) mod 10^{10}

Mentioned on the PiDP-10 group https://groups.google.com/g/pidp-10/c/S3cp5G7ylWQ/m/dDYKkCLKDAAJ which links to https://www.linkedin.com/pulse/maintain-basis-inverse-noah-smith-qzcwe?utm_source=share&utm_medium=member_android&utm_campaign=share_via
It appears to be part of a blog/story about the "lost in space" problem, numerical linear algebra, 36-bit computers from DEC and IBM.

The description below sounds intriguing.
In numerical analysis, the ITP method, short for Interpolate Truncate and Project, is the first root-finding algorithm that achieves the superlinear convergence of the secant method[1] while retaining the optimal[2] worst-case performance of the bisection method.[3] It is also the first method with guaranteed average performance strictly better than the bisection method under any continuous distribution.[3] In practice it performs better than traditional interpolation and hybrid based strategies (Brent's Method, Ridders, Illinois), since it not only converges super-linearly over well behaved functions but also guarantees fast performance under ill-behaved functions where interpolations fail.[3]

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.