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floating point division algorithm how ot calculate
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Floating point division algorithm to compute :

We know that, . So, .

                                                   (4.19)                                                    

Again, . So,                                   (4.20)                                    

 can be computed similarly by the following methodology.

Consider the number  is divided by , where x is the radix. So A can be expressed in terms of B as

              (4.21)

                                                                                                                                                                                                      (4.22)    

Here ‘x’ signifies the radix. 

From equation (4.22), the coefficients of the quotient expression has been shown in Table-1.

 

 

 

 

 

 

Table-4 Coefficients of the quotient expression

This procedure is based on the “Dhvajanka” rule for division described in ancient Indian Vedic mathematics. After the division, the result is shifted to the right by ‘l’ times which have been given as  in equation (4.17).

Illustration: Consider a fourth order function  and a second order function. We have to compute  with the help of “On top of the flag” sutra. Now,

 

 

 

 

 

 

 

, where, and

 .

Computation technique of  and

With the help of Taylor’s series, we know that for very small value of q,  i.e. the angle in radian,

                                                                                                                                              (23)

and                                                                                                                                                               (24)

Here, , if  and , if .

Computation of  and  can be executed in the following steps:-

Computation of

Step-1: Compute n2 by using squaring algorithm.

Step-2: Compute  by using floating point division algorithm.

Step-3: Compute  where,  using squaring algorithm.

Step-4: Compute  by using “Dhvajanka” sutra.

Step-5: Subtract the result from ‘1’.

Step-6: Compute  by using Egyptian multiplication technique.

Computation of

Step-1: Compute n2 by using squaring algorithm.

Step-2: Compute  by using floating point division algorithm.

Step-3: Compute  where,  using squaring algorithm.

Step-4: Compute  by shifting methodology.

Step-5: Subtract the result from ‘1’.