Floating Point Bit Hacks Every Programmer Should Know (Including Fast Inverse Square Root

Uploaded December 2012 | Updated September 2026, 2 weeks ago

This is the final IEEE tutorial we'll be looking at some incredibly powerful techniques folks have developed for manipulating IEEE floats. These tricks don't give IEEE accuracy but they all rely on a very detailed knowledge of the bit format in order to understand. They can be used to approximate various mathematical functions and some of them can speed the operations up by 4 times!

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$Fixed Point Arithmetic 1: Intro to Fixed Point In this video well look at fixed point arithmetic. This is a technique for performing operations on numbers with fractional parts using integers, instead of the more common floating point. Fixed point has some pretty amazing benefits, depending on how and when it is used. We can use bytes, short ints, ints, or long integers, we can select the precision and range of our variables. Fixed point is very flexible and (sometimes) very fast. Its extremely good at certain types of tasks, for instance, working with image processing matrices. It can also do some things which floating point cannot, such as exactly represent 1/3 or 1/5. Fixed point is not a hack, its a fantastic tool to add to your belt if youve not yet come across it. If you have used fixed point in the past, I hope this tute is a good refresher! Also, I forgot to mention something in the tute: The technique I used to get the fractional part of the fixed point number literally gives us the bits that comprise the fractional part of the number. If your number is negative, then they will not be the correct bits if you print the fixed point to screen. Facebook: https://www.facebook.com/pages/WhatsaCreel/167732956665435$

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