Division of Large Numbers - Epilogue and Tests
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Now the first thing you may observe about the performance of this method is that it's dependent upon how far we will take the calculation of the inverse number. If we have some easier numbers, let's say two, for which the inverse can be calculated instantly, the process will require only a very little time. Needless to say, once we move to three this process gets more complicated and it will require consistently more time.
Here are the run times first for one divided by two, then by two.
+1
+2
Division:
+0.5
And then for three:
+1
+3
Division:
+0.3333333333333333333333333333333333333333333333............
The iteration depends mainly how fast we can multiply; as we have to multiply a 5*2^i number at each step (where i stays for the current iteration number). Finally, we must say that the result won't be perfect. An error rate of 5*2^i precision exists, as after that the inverse is not calculated, so we should round the result for a perfect operation. Due to this 2/6 is not 0.5, instead you'll get 0,4999.... You get the picture. Here you have the archived source files of the entire project:
There we have it, folks, a class that can handle the basic operations with some really large or precise numbers. It may seem at first like a difficult job to do it right, but it turned out to be not too hard to accomplish. Now I invite you to implement other functions and/or operations into it. For example, why not try one that will calculate the factorial of a number if it is of the integer type? Or try calculating the square of a number; it can be resolved in the same fashion as the division using Newton's Iteration.
I want to thank you for investing time in reading this article and also encourage you to ask any question you might have here on the blog or on our friendly forum over the DevHardware. Have a great day!
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