This book sits somewhere between "Hackers Delight" and "Numerical Recipes". The coverage is truly broad and detailed. It walks you through an implementation by the author called FXT (a library of algorithms) - https://www.jjj.de/fxt/ and https://www.jjj.de/
For some reason, the book is not well known and the author hates to advertise. But this is truly one of a kind book and deserves all the adulation from us (i own a print version).
The author also co-authored a book about historical and state-of-the-art pi computations called Pi Unleashed (https://link.springer.com/book/10.1007/978-3-642-56735-3). The code and additional resources are available at https://extras.springer.com/?query=978-3-642-56735-3. Though somewhat dated (circa 2000), there’s a lot of fascinating information in the 229 Mb zip download, including a 133 char C program (pitiny.c) that computes 15000 digits of pi.
Glad you mentioned Pi Unleashed. That tiny pitiny.c program is legendary in its own right. It really highlights the minimalism—squeezing out every bit of performance and precision.
I borrowed Hackers Delight from my local library, even though I didn’t fullt grasp every chapter I still found the book interesting and beautiful. Planning on buying it.
I’ll check out Numerical Recipes and Matters Computational ideas etc.
I am quite sure that very few people can "fully grasp" everything in the three books mentioned. The subject matter is inherently difficult. The way i approach them is as a catalog of reference implementations which i can consult, copy from and modify as needed. The idea is to become aware of knowledge that one didn't know before.
Some caveats; consider criticisms of Numerical Recipes book as advisory and not gospel. When reading these sorts of books you are looking to understand the algorithms (w.r.t. a reference implementation) and not bother with programming style/software engineering discipline etc. which are all irrelevant in this case. The specialized domain knowledge is what is important and not software techniques.
Numerical Recipes is an old book, and received its share of criticism. It's also expensive, so beware before you buy. E.g. "`This chapter describes numerical methods for ODE's from the viewpoint of 1970."
This is the PDF of the following 2011 book focused on FFTs and fast arithmetic for both real numbers and finite fields. https://www.amazon.com/Matters-Computational-Ideas-Algorithm...
The author is Jörg Arndt: born 1964 in Berlin, Germany. Study of theoretical physics at the University of Bayreuth, and the Technical University of Berlin, Diploma in 1995. PhD in Mathematics, supervised by Richard Brent, at the Australian National University, Canberra, in 2010.
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For some reason, the book is not well known and the author hates to advertise. But this is truly one of a kind book and deserves all the adulation from us (i own a print version).
The author also co-authored a book about historical and state-of-the-art pi computations called Pi Unleashed (https://link.springer.com/book/10.1007/978-3-642-56735-3). The code and additional resources are available at https://extras.springer.com/?query=978-3-642-56735-3. Though somewhat dated (circa 2000), there’s a lot of fascinating information in the 229 Mb zip download, including a 133 char C program (pitiny.c) that computes 15000 digits of pi.
I’ll check out Numerical Recipes and Matters Computational ideas etc.
Some caveats; consider criticisms of Numerical Recipes book as advisory and not gospel. When reading these sorts of books you are looking to understand the algorithms (w.r.t. a reference implementation) and not bother with programming style/software engineering discipline etc. which are all irrelevant in this case. The specialized domain knowledge is what is important and not software techniques.
Here are some links to the above;
1) Numerical Recipes book website - https://www.numerical.recipes/
2) Wikipedia - https://en.wikipedia.org/wiki/Numerical_Recipes
3) Alternatives - https://www.stat.uchicago.edu/~lekheng/courses/302/wnnr/nr-a...
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