At the time, the general method to compute the inverse square root was to calculate an approximation for \frac{1}{\sqrt{x}}, then revise that approximation via another method until it came within an acceptable error range of the actual result. Common software methods in the early 1990s drew approximations from a lookup table. The key of the fast inverse square root was to directly compute an approximation by utilizing the structure of floating-point numbers, proving faster than table lookups. The algorithm was approximately four times faster than computing the square root with another method and calculating the reciprocal via floating-point division. The algorithm was designed with the IEEE 754-1985 32-bit floating-point specification in mind, but investigation from Chris Lomont showed that it could be implemented in other floating-point specifications.
