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Floats

I explain how floats work, also known as floating point numbers. Floats are a type of variable, which are used to approximate real numbers. Other types of variables, such as bytes, shorts, and longs, can only represent integers. So in SM64, those are used to represent Mario's lives, Mario's coin count, Mario's HP, angles, timers, vertices of level geometry, etc. However, some things cannot be represented very well with integers, and so floats are used, since they approximate real numbers. In SM64, floats are used to represent x/y/z positions, speeds, scaling, music volume, etc. For more info on floats, see the resources list down below. The gist of it is that floats use a system similar to scientific notation to represent numbers. Consequently, floats are quite dense near zero, but become increasingly sparse as they increase in value. Thus, they achieve a trade-off between precision and range. There are also some special float values: +Infinity: a value greater than the largest finite float value -Infinity: a value smaller than the smallest finite float value NaN: standing for "Not a Number", a value representing the result of an invalid operation Although floats may seem continuous in practice, they are in fact discrete. So whenever a float operation is computed, such as adding Mario's speed vector to his current position in order to calculate his new position, the result is rounded to the nearest available float. For small numbers (where the gaps are small), this rounding is unnoticeable. But for large numbers (where the gaps are large), this rounding plays a pivotal role. In the video, I demonstrate this by showing that the fish will eventually stop moving once its speed becomes less than half of the gap between floats. Thanks to Peter Fedak for making the ROM hack that allows PUs to be visible. For more info and to download it, you can go to Peter's video about it here:    • Parallel Universes Made Visible   Resources (1) For more general info on floats, you can go here: https://en.wikipedia.org/wiki/Floatin... (2) For more info on the float format, you can go here: http://www.plcdev.com/book/export/html/9. (3) For more info on the float spacing, you can go here: http://www.exploringbinary.com/the-sp.... (4) For a higher resolution version of the float gap table I showed, you can go here: http://i.imgur.com/QfzI4YF.png