PI Calculators and Precision Files

Journey

C is a stable and high performing programming language introduced in 1972. The GNU Multiple Precision Arithmetic Library was introduced in 1991. The various approaches for calculating PI date from centuries ago to recent decades. Large Language Model training has had a stable and well documented foundation for the requests in building the calculators and content on this website. Surprisingly, the result is that only 1 of the 4 approaches succeeded. Below is a recap of the journey.

Algorithm Evaluation

Leibniz Formula

Leibniz was used to try and create a PI digit generator. This approach failed as divergence after the 11th digit of precision proved to be a persistent problem for Chat-GPT’s approach to writing the code.

FAILURE

Algorithm Evaluation

Chudnovsky Algorithm

Chudnovsky was used to try and create a PI digit generator. This approach failed divergence after the 100th digit as well as segmentation fault issues for Chat-GPT’s approach to writing the code.

FAILURE

Algorithm Evaluation

Gauss-Legendre Algorithm

This algorithm worked perfectly for a PI digit generator and is currently used in the Simple C, PI Time, and PI Digits applications on this site.

SUCCESSFUL

Website Creation

PI Calculators Site

The domain “picalculators.app” was purchased and a simple WordPress site was created.

SUCCESSFUL

Calculator Creation

Simple C

The Simple C calculator was created based on the Gauss-Legendre algorithm and tested using Chat GPT-4.0.

SUCCESSFUL

Precision File Creation

Precision Files

Using the Simple C calculator, a series of example precision files was created for download.

SUCCESSFUL

Calculator Creation

PI Time

PI Time, a modification of the Simple C calculator, was created to measure the time required to calculate PI on various platforms.

SUCCESSFUL

Calculator Creation

PI Digits

PI Digits was created to generate and format PI digits in a tabular, comma separated value, or JSON format.

SUCCESSFUL

Algorithm Evaluation

Ramanujan’s Series

The Ramanujan series was used to create a PI digit generator. This approach could not produce a result that was even close to resembling PI. It was ugly.

FAILURE

Content Creation

Website Content

The majority of content for the site was either generated or revised by AI. The specific use cases were documented.

SUCCESSFUL

Calculator Service Creation

API Only PI Server

PI Server is an event-drive, multithreaded, API only server capable of generating PI at scale. All code and Valgrind interpretations (and solves) were done by Chat GPT-4.0

Port to Golang

Port to Golang

The C version of PI Server was successfully ported to Golang. Additional approaches including
Bailey-Borwein-Plouffe, Ramanujan Algorithm, Go PI, Static lookup, and “the middle school method” were all implemented.

SUCCESSFUL