<sod>In order to determine the inverse square root, an approximation for <math>x^{-1/2}</math> would be determined by the software, then some numerical method would revise that approximation until it came within an acceptable error range of the actual result.  [[Methods of computing square roots|Common software methods]] in the early 1990s drew a first approximation from a [[lookup table]].{{sfntag|Eberly|2001|p=504}}  This bit of code proved faster than table lookups and approximately four times faster than regular floating point division.{{sfntag|Lomont|2003|p=1}}  Some loss of precision occurred, but was offset by the significant gains in performance.{{sfntag|McEniry|2007|p=1}}  The algorithm was designed with the [[IEEE 754-1985]] 32-bit floating point specification in mind, but investigation from Chris Lomont and later Charles McEniry showed that it could be implemented in other floating point specifications.<eod>
<sod>At the time, the general method to compute the inverse square root was to calculate an approximation for {{math|1/{{radical|''x''}}}}, then revise that approximation via another method until it came within an acceptable error range of the actual result. [[Methods of computing square roots|Common software methods]] in the early 1990s drew approximations from a [[lookup table]].{{Sfn|Eberly|2001|p=504}} The key of the fast inverse square root was to directly compute an approximation by exploiting 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.{{Sfn|Lomont|2003|p=1}} Some loss of precision occurred, but was offset by the significant gains in performance.{{Sfn|McEniry|2007|p=1}} The algorithm was designed with the [[IEEE 754-1985]] 32-bit floating point specification in mind, but investigation from Chris Lomont and later Charles McEniry showed that it could be implemented in other floating point specifications.<eod>