Recently, I started to study some division algorithms, and I found your homepage about 珠算 very informative and help me understand it a bit. and that was the first time I started to understand 珠算. At the same time, I found on the internet a document "Review of Basic Classes of Dividers Based on Division Algorithm" by PATANKAR and KOEL. In that review article, there is a FIGURE 4. The distribution of different division algorithms.

Understandably, 珠算 is considered un-important in this modern computer era by most people and it is sad that Figure 4 does not include 單歸法, 歸除法 ... etc. There was a flash in my mind that I would put together these Chinese 珠算 division algorithms into a big picture. However, I am not going to spend the time understand all these 珠算 division algorithms to put them in proper order into the figure and even if I do, I will certainly mis-understand all these different Chinese division algorithm. I would like to ask for your apologize to persuade you to do the same, and put into the your homepage. If I really need that, I will surely quote your webpage.

By the way, I am doing some private research on division algorithms and your homepage on 珠算 is one of bibliography of my on-going work.

As a Chinese living in Hong Kong, I think we have the obligation to let the world know that in fact all these 歸除法 are actually very similar (if not precusor) to those long-division, (non)-restoring, SRT algorithms and others. And I am sure these 歸除法 are not dead.

I will keep you informed of my study and seek your advice if you are willing to help.

By the way, I am retired after being an engineer for more than 30 years.


\begin{thebibliography}{}

\bibitem{1}{Donald E. Knuth, "The Art of Computer Programming", Volume 2 / Seminumerical Algorithms, Addision-Wesley Publishing Company, 1981.}
\bibitem{2}{Udayan S. Patankar , Ants Koel,"Review of Basic Classes of Dividers Based on Division Algorithm", IEEE Access, Volume 9, 2021}
\bibitem{3}{Behrooz Parhami, "Computer Arithmetic, Algorithms and Hardware Designs", Oxford University Press, 2010}
\bibitem{4}{周家發個人網頁,"珠算解難：歸除法",https://chowkafat.net/Abacus3.html}
\bibitem{5}{刘华平,胡伟武, "一种定点除法部件中提前终止循环计算的方法",Patent No. CN 1485725A, 31 March, 2004.}
\bibitem{6}{David M. Russinoff, "A Mechanically Verified Commercial SRT Divider" of "Design and Verification of Microprocessor Systems for High-Assurance Applications",Editors: David S. Hardin, ISBN 978-1-4419-1538-2 e-ISBN 978-1-4419-1539-9, 2020}
\end{thebibliography}{}

In fact, as you can see from the Pentium flaw, the present division algorithm is overly-complicated and I strongly think a NEW division algorithm is urgently needed.

Best Regards,
Ko