Wednesday, 3 January 2018

A Listing As High As The Moon!

Did you know that the source code for the Apollo Guidance Computer would reach all the way to the moon if it was printed out?

No? Good - because it's not true and we'll do the math here. There's a whole world of computing mythology that's sprung up over the decades. A classic claim is that the computers on the Apollo spacecraft were less powerful than the computer inside a typical digital watch.

That means there's more software on that watch than you need to reach the Moon!

It's all rubbish. The Apollo Guidance Computer was relatively complex; it was a 16-bit machine that had 36KW of firmware on it and ran. It would take a typical software engineer years to write the code that filled it, and in fact it did take a team of talented software engineers (headed by Margaret Hamilton who coined the term software engineer) years to write its code - in assembler.

Fortunately we can see the source code for the AGC these days as it's on github. Based on the Wikipedia article and assuming each Timing Pulse is 1.024MHz, then instructions would typically take between 12 timing pulses, which gives 85.3 KIPs and most instructions might require twice as much as that (assuming a memory access took another 12 pulses), giving speeds between 42.7KIPs and 85.3KIPs (which can be verified here).

36KW of firmware is equivalent to about 72Kb of firmware. That means the computer could handle software about as complex as microcomputers from the year 1984, where the limits of 16-bit addressing and the shift from writing in assembler to writing in high level languages were being tested. Some microcomputers from that era did have more RAM (e.g. the ACT Sirius), but here I'm taking common home computers as the baseline.

When you look at the software in GitHub you find that there are a reasonable number of files, usually of a reasonable length. The source code there has a GitHub header of about 26 lines on every file, but the rest of it is the original software.

Let's first think about how much code might be on there. Each assembler line is probably 1 instruction, which is one word (though it might be more if they used a macro assembler). Typical listing paper had 66 lines per page, So, 36,864 words would be 36,864/66 = 558.5 pages. So, how thick is a page? You can still buy listing paper, and it works out at 24.1cm for 700 pages, so the whole listing is, at a minimum: 558.5/700*24.1cm = 19.22cm high, just under half-way up to my knee.

So, at a first guess, it's not very high. But I could be badly wrong, because the real software was different for the Command module and the Lunar module; and also they would have had many comments in the code, which would have lengthened it. So, I took a look at the actual source files.

Helpfully, they have page numbers in them. Luminary099, which was the Lunar module's software has 1510 pages, and the command module's software in Commanche055 had 1516 pages. The total is thus: 3026 pages which is: 114.5cm tall. That's a bit more like the diagram, but it still only goes up to my chest.

Again this might not quite be accurate, because some of the code could have been shared, I hope to post a future update when I've figured out how much is!

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