Thursday, 19 November 2015

New: BigIntegers

I wrote a new implementation of BigIntegers (almost unlimited size integers) for Delphi. It uses assembler for the low level stuff, although there is a PUREPASCAL version for each of these routines too. Instead of using the GPL-licensed GNU Multi-Precision (GMP) library, I wrote everything from scratch, without using any code from others.

I think it is pretty fast, especially because I optimized many of the routines, either by techniques like loop unrolling or using 64 bits at once, or by using bitwise tricks, or by high-level algorithms like Burnikel-Ziegler, Karatsuba, Toom-Cook 3-way, etc. Results are checked with results generated by .NET. The C# test program is included.

In the course of writing this, I read an enormous numbers of publications on these subjects and I learned a lot, not only about the maths involved, but also about many other mathematical notions. Not so easy for a dentist. I also had some good help on StackOverflow.

Go take a look at my website. I think every Delphi should have BigIntegers.