On Division by Functional Iteration

In order to avoid the time delays associated with linearly convergent division based on subtraction, other iterative schemes can be used. These are based on 1) series expansion of the reciprocal, 2) multiplicative sequence, or 3) additive sequence convergent to the quotient. These latter techniques are based on finding the root of an arbitrary function at either the quotient or reciprocal value. A Newton-Raphson iteration or root finding iteration can be used. The most useful techniques are quadratically convergent (i.e., errori+,=O (errori)2). These techniques generally require two arithmetic operations (add or multiply) to double the precision of the quotient.