id Software (the method is older; its origins have been traced to Greg Walsh and Cleve Moler), 1999
Lighting a 3D scene means normalising millions of vectors a second, and each one needs one over the square root of a number. In 1999 that was expensive. This function, found in the Quake III Arena source when id Software released it under the GPL in 2005, does it in a handful of integer operations, to within a fifth of a percent.
The trick is to treat the bits of a floating-point number as an integer. Because of how IEEE 754 lays out exponent and mantissa, shifting that integer right by one and subtracting it from a magic constant gives a surprisingly good first guess at the inverse square root; one step of Newton's method then polishes it. The constant 0x5f3759df was found by search, and its origin was traced back through Ardent Computer and SGI in the late 1980s. The comments are part of the work. "What the fuck?" records the reaction of whoever read it next, and it has been quoted ever since as the moment the method became folklore. Today the hardware does this directly. The function remains the clearest example of code that is fast because its author understood what numbers are made of.