Here you find

- the FXT library
- the fxtbook: "Matters Computational" (was: "Algorithms for Programmers")
- the amorphous FFT bucket moved to the fftpage

FXT is a library of low-level algorithms. Its main focus is on bit-manipulations, combinatorial generation, and fast transforms. The library is accompanied by the fxtbook. A strong emphasis is on performance and many of the routines are among the fastest available.

Much of the **bit-magic** is shown on the
bit wizardry page,
demo programs are listed here
and the documentation is here.
The routines about binary polynomials and arithmetic over GF(2^n)
are documented in bpol-doc.txt
and the demos are here.

The routines about **combinatorial generation**
for
combinations,
subsets,
compositions,
integer partitions,
set partitions,
permutations,
mixed radix numbers,
multi sets (subsets and permutations),
Catalan objects and Dyck words,
necklaces and Lyndon words,
and many other types of objects
are documented here,
and the demos are here.
For the combinatorial objects see The Combinatorial Object Server++.

The files documenting the **fast transforms** are as follows:
fast Fourier transforms (FFTs),
real valued FFTs,
fast Hartley transforms,
convolutions,
correlations,
cosine and sine transforms,
Walsh transforms,
Haar transforms,
and
number theoretic transforms (NTTs).

The complete list of demos contains about 500 programs, listed by topic.

Complete list of generated documentation:

bits-doc.txt bit wizardry

bpol-doc.txt binary polynomials and arithmetic over GF(2**n)

comb-doc.txt combinatorics (combinations, partitions etc.)

ds-doc.txt data structures (FIFO, heap etc.)

fft-doc.txt fast Fourier transforms

realfft-doc.txt real valued FFTs

fht-doc.txt fast Hartley transforms

convolution-doc.txt convolution

correlation-doc.txt correlation

dctdst-doc.txt cosine and sine transforms

walsh-doc.txt Walsh transforms

haar-doc.txt Haar transforms

mod-doc.txt modular arithmetics and number theory

ntt-doc.txt number theoretic transforms

perm-doc.txt permutations

sort-doc.txt sorting and searching

aux0-doc.txt auxiliary routines

aux1-doc.txt auxiliary routines for 1-dim arrays

aux2-doc.txt auxiliary routines for 2-dim arrays

An index of all docs

Download the tables of mathematical data as data-fxt.tar.gz (they used to be part of FXT). An overview what is in the archive is the text file 00data-doc.txt.

The table of contents as text file (generated from dvi):
fxtbook-toc.txt.

Short table of contents, giving an quick overview:
fxtbook-toc-short.txt.

The book:
fxtbook.pdf (uncompressed pdf, about 5200kB).

The change log: fxtbook-changes.txt.

fxtbook.dvi.gz (compressed dvi, about 1400kB).

fxtbook.ps.gz (compressed postscript, about 2100kB).

fxtbook.pdf.gz (compressed pdf, about 3200kB).

Last update: 2010-September-07 (17:53)

The list of errata: fxtbook-errata.txt.

The index as text file (generated from dvi):
fxtbook-idx.txt.

List of referenced integer sequences from the On-Line Encyclopedia of Integer Sequences
(OEIS)
as text file (generated from dvi):
fxtbook-oeisref.txt.

If you want to set a link to the fxtbook please use http://www.jjj.de/fxt/#fxtbook instead of directly linking to one of the files (e.g. fxtbook.pdf).

Your feedback is appreciated.

jj (Jörg Arndt)

Last modified 2024-January-14 (16:24)

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