Digital Arithmetic

380 eNAPTE~ 7 Iterative Approximation

EXAMPLE 7,2

For the Newton-Raphson method, we compare the number of cycles used in

Scheme A (full multiplier) and Scheme B (rectangular multiplier) to obtain

a reciprocal of d (53 bits) with an error of no more than 2 -54. The initial

approximation R[0] has an error of no more than 2 -8 and has a width of

9 bits.

The multiplier in Scheme A is a standard floating-point multiplier, while

the multiplier in Scheme B is a dedicated multiplier. To achieve the final

error, the operation requires at least three iterations. In order not to increase

the delay, the additional errors ...