Floating point arithmetic is a crucial part of modern computing. A large proportion of the silicon currently being installed consists of ‘floating point units’ and floating point standards continue to emerge to meet the needs of modern machine learning. But where did floating point arithmetic come from and where was it first implemented? Perhaps surprisingly it can trace its beginnings to the origins of the development of the computing universe as we know it today …. Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space. Douglas Adams: The Hitchhikers Guide to the Galaxy Douglas Adams was right. The distance to the nearest star - roughly equivalent in astronomical terms to the chemist down the road - is roughly 40,200,000,000,000 kilometres. We’d normally say 40.2 trillion, which is a lot easier to write than a long list of digits, but has the drawback that you have to remind yourself what a trillion is. Of course we have a better alternative to either of these in the form: This notation has the immediate advantage of giving the reader a sense of scale without having to count lots of digits. It also has the advantage of working for both much bigger and much smaller numbers. The number of atoms in the known universe? Not a problem: it’s roughly: In words that’s roughly ten quadrillion vigintillion, which is really not a useful description at all. The mass of an electron? That’s: The notation has three key elements:
- Mantissa: 9.109 in our last example
- Exponent: -31
- Base: 10 This notation dates back as far as René Descartes and his text La Géométrie of 1637. The term exponent, from the Latin exponere meaning “to put out”, dates back even earlier to German mathematician Michael Stifel in 1544, and mantissa again has a Latin source meaning “makeweight” or something of minor value. We’ve boiled the scale of objects in the universe,...