["< 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 still showed that it could be implemented in other floating point specifications. < eod > < sod > at the time, the general method to compute computed 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 results faster than table lookups. the resulting 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 [ [ 10 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 floating point specifications. < eod >"]