Collaborate Disseminate
Once the domain of esoteric scientific and business computing, floating point calculations are now practically everywhere. From video games to large language models and kin, it would seem that a …read more Continue reading Using Integer Addition to Approximate Float Multiplication
How hard can it be to write a simple four-function calculator program? After all, computers are good at math, and making a calculator isn’t exactly blazing a new trail, right? …read more Continue reading How Hard is it to Write a Calculator App?
The early 1990s were an interesting time in the PC world, mainly because PCs were entering the zeitgeist for the first time. This was fueled in part by companies like …read more Continue reading A Die-Level Look at the Pentium FDIV Bug
If you are used to writing software for modern machines, you probably don’t think much about computing something like one divided by three. Modern computers handle floating point quite well. …read more Continue reading Fixed Point Math Exposed
An unfortunate reality of trying to represent continuous real numbers in a fixed space (e.g. with a limited number of bits) is that this comes with an inevitable loss of …read more Continue reading Making Floating Point Calculations Less Cursed When Accuracy Matters
Even with ten fingers to work with, math can be hard. Microprocessors, with the silicon equivalent of just two fingers, can have an even harder time with calculations, often taking multiple machine cycles to figure out something as simple as pi. And so 40 years ago, Intel decided to give …read more
Continue reading Looking for Pi in the 8087 Math Coprocessor Chip
Microsoft’s new Xbox Series X, formerly known as Project Scarlet, is slated for release in the holiday period of 2020. Like any new console release, it promises better graphics, more immersive gameplay, and all manner of other superlatives in the press releases. In a sharp change from previous generations, however, …read more
Continue reading The New Xbox: Just How Fast Is 12 teraFLOPS?
Dividing by zero — the fundamental no-can-do of arithmetic. It is somewhat surrounded by mystery, and is a constant source for internet humor, whether it involves exploding microcontrollers, the collapse of the universe, or crashing your own world by having Siri tell you that you have no friends.
It’s also one of the few things gcc will warn you about by default, which caused a rather vivid discussion with interesting insights when I recently wrote about compiler warnings. And if you’re running a modern operating system, it might even send you a signal that something’s gone wrong and let you …read more
Continue reading Creating Black Holes: Division By Zero In Practice
People learn in different ways, but sometimes the establishment fixates on explaining a concept in one way. If that’s not your way you might be out of luck. If you have trouble internalizing floating point number representations, the Internet is your friend. [Fabian Sanglard] (author of Game Engine Black Book: Wolfenstein 3D) didn’t like the traditional presentation of floating point numbers, so he decided to explain them a different way.
Instead of thinking of an exponent and a mantissa — the traditional terms — [Fabian] calls the exponent as a “window” that determines the range of the number between two …read more
