Efficient Initial Approximation for Multiplicative Division and Square Root by a Multiplication with Operand Modification

An efficient initial approximation method for multiplicative division and square root is proposed. It is a modification of the piecewise linear approximation. The multiplication and the addition required for the linear approximation are replaced by only one multiplication with a slight modification of the operand. The same accuracy is achieved. The modification of the operand requires only a bit-wise inversion and a one-bit shift, and can be implemented by a very simple circuit. One clock cycle may be saved, because the addition is removed. The required table size is also reduced, because only one coefficient instead of two has to be stored.