There are many known methods or techniques used to calculate the reciprocal square root of a given value, A. For completeness, the reciprocal square root of A is written
                    x        =                  1                      A                                              (        1        )            
One of these methods applies Newton's method to the equation
                                          1                          x              2                                -          A                =        0                            (        2        )            
After a final iteration, x will be approximately equal to the reciprocal square root of A.
According to the Newton method, in each iteration the following expression is evaluated
                              x                      n            +            1                          =                                            x              n                        2                    ⁢                      (                          3              -                              A                ⁢                                                                  ⁢                                  x                  n                  2                                                      )                                              (        3        )            
After the final iteration has been completed, the square root of A can be calculated, if required, by multiplying the result by A.
FIG. 1 shows how the iterative method in equation (3) is implemented in C code for floating point numbers.
However, the conventional techniques used to implement this method in a digital logic circuit are relatively inefficient.