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## High Speed Arbitrary Precision Algorithms.

 From: Kanwal Subject: High Speed Arbitrary Precision Algorithms. Date: Fri, 29 Sep 2000 00:15:29 +0530

```Dear Sir,
I am a final year undergraduate student of Computer Science.
Over the past month, I have developed a set of high-speed and high-precision
algorithms for doing a number of mathematical computations. The techniques have
been developed entirely by me, and enable the calculations to be done without
constraints of hardware register sizes or software floating point sizes for
both integer values, as well as floating point numbers.
With these algorithms, it is possible to do the basic mathematical computations
to any degree of precision and at pretty good speeds.
For instance, to divide two 200 digit numbers upto an accuracy of 100,000
digits it takes 300 milliseconds.
The maximum accuracy for the mathematical operations that I have developed are
as follows:
Operation                Accurate upto:
---------                  ---------------
Multiplication:      4.5 million digits
Division:              20 million digits
Square Roots:       20 million digits
Subtraction:          20 million digits

Language used: Java 1.2.1
Operating System: Windows 95
System Configuration: Pentium II 220 Mhz, 64Mb Ram.

The times taken for each operation and the size of the answer are as follows:

Operation                                       Average Time(ms)
---------                                          ---------------------
Multiplication(of10,000 digits)              5340
Division (of 200,000 digits)                    300
Square Roots (of 10,000 digits)           3900
Subtraction (any size)                           110

I am currently working on algorithms for cube roots, logarithms and
trigonometric calculations.

The area, in which I would like your opinion is, whether there is any future or
practical use of these algorithms, or whether they will remain only a pleasant
diversion for me.
Or, if you could direct me to the person who would be in a better position to
guide me on this.
Thanking you,
Kanwal Kumar Mookhey

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