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,
arrangements,
mixed radix numbers,
multi sets (subsets and permutations),
Catalan objects and Dyck words,
necklaces and Lyndon words,
ascent sequences,
Cayley permutations,
Young tableaux,
Motzkin paths,
various restricted growths strings (RGS),
and many other types of objects
are documented here
and the demos are here,
Fred Lunnon's routine for n-dimensional Hilbert curves
is documented here

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.

For the combinatorial objects see The Combinatorial Object Server++.

Here is a short description, the Linux Software Map (LSM) file fxt.lsm

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

data-doc.txt tables of mathematical data.
The tables can be accessed via the mathdata page.

An index of all docs

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 change log: fxtbook-changes.txt.

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

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

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

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

fxtbook.pdf (UNCOMPRESSED pdf, about 5200kB).

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 2021-April-06 (16:00)

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