AbscissaMantissaSchmisha


Page Created: 6/25/2014   Last Modified: 3/18/2016   Last Generated: 12/11/2017

In 1989, one of my friends who was studying for a dual major in Electrical & Computer Engineering at Boston University said he was assigned a difficult project, to write a program to compute the factorial of 255. He said his class was given two weeks to complete this project.

He knew that I was obsessed with the Commodore64, but he thought he was in the big leagues at Boston using a more powerful IBM PC-compatible computer that I could not afford.

I said "I can do this on a Commodore 64 in 1 day."

"No way!" he said. "If you can do that, I will buy you dinner!" He said he would stop by the next day.

So I spent the rest of the day, and worked all night into the early hours in the morning to prove him wrong. I was also envious that he was bragging that he visited Isaac Asimov in his Boston University office and obtained his autograph. We were both Asimov fans.

Around 3 am, I ran the program, but it took hours to run, so I went to sleep and had it save the result to floppy disk since the number was so large.

If you're not familiar with performing math on a computer, mathematical operations are limited in size to a certain number of bytes. When numbers exceed that size, the computer only approximates to a limited amount of significant digits, like a calculator does when the number exceeds the screen size. But the task was to compute it exactly, not approximate it, and the factorial of such a number is huge.

My friend did not think I realized this, since he was just learning it himself, and even so, it is fairly difficult to overcome. What he didn't realize what that on my own, I was trying to compute Pi to thousands of digits and perform Public Key cryptography on the Commodore 64 based on an article I read in Scientific American called "The Mathematics of Public-Key Cryptography" by Martin E. Hellman, and cryptography uses very large numbers. Even so, I had never done it until then.

I didn't learn about recursion until years later, and the factorial can be computed using a recursive algorithm, but Commodore 64 BASIC variables are all global in scope, so recursion would require some tricks. And even if I knew how to do this, I would still have needed somewhere to store those gigantic numbers, which was the primary problem.

The next morning, I checked and it was done processing. When my friend showed up, I showed him my program and the output via the sequential file.

I said, "I don't know if it is correct, since it ended with all of these zeros."

He then frowned and said "No, I think it is correct. It is supposed to end with a lot of zeros."

He then bought me dinner.

He couldn't understand how I did it and I explained to him that I created large arrays to hold the digits and simply performed a long multiplication algorithm on them. He was taught some other method of accomplishing this, but thought my method was clever.

I never knew if I was really right, but I just checked while writing this page, and Wolfram Alpha↗ concurs.

The Commodore 64, back in 1989, took several hours, but computed this:

Wolfram Alpha in 2014, in just a few seconds, computed this:

Wolfram Alpha LLC. 2014. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=255!

They are an exact match.

My friend was no slouch. He was a gifted student, the captian of my cross-country team, and I greatly admire him. He went on to become a captain in the US Army Special Forces. But this was one of my greatest personal victories, since I was still stuck in the prison of Calculus Monte Cristo and was being mocked for still using a Commodore 64 in the PC era.

Here is my source code.

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