https://github.com/chris00/ocaml-interval
An interval library for OCaml
https://github.com/chris00/ocaml-interval
computer-assisted-proof interval-arithmetic ocaml rigorous scientific-computing validated
Last synced: 29 days ago
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An interval library for OCaml
- Host: GitHub
- URL: https://github.com/chris00/ocaml-interval
- Owner: Chris00
- License: lgpl-3.0
- Created: 2017-08-11T11:26:15.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2022-12-09T07:47:27.000Z (over 3 years ago)
- Last Synced: 2025-04-06T05:04:13.367Z (12 months ago)
- Topics: computer-assisted-proof, interval-arithmetic, ocaml, rigorous, scientific-computing, validated
- Language: OCaml
- Homepage:
- Size: 423 KB
- Stars: 16
- Watchers: 3
- Forks: 3
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGES.md
- License: LICENSE.md
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README
Interval
========
This is an [interval arithmetic][] library for OCaml. Here is a small
example in the REPL:
```ocaml
# #require "interval.top";;
...
# open Interval_crlibm;;
# let v = I.singleton 1.;;
val v : Interval_crlibm.I.t = [1, 1]
# I.sin v;;
- : Interval_crlibm.I.t = [0.841471, 0.841471]
# I.Precision.set (Some 16);;
- : unit = ()
# I.sin v;;
- : Interval_crlibm.I.t = [0.8414709848078965, 0.8414709848078966]
```
Several [OPAM][] packages are provided by this repository:
- `interval_base`: basic interval library that defines the datatype
`Interval.t` and uses Intel assembly if possible or C99 instructions
to perform arithmetic operations
(module [Interval](src-base/interval_base.mli)).
- `interval_crlibm`: relies on [crlibm][] to implement the interval
operations. CRlibm provides *proved* correctly-rounded operations,
so this is the library of choice for computer assisted proofs.
- `interval_intel`: use Intel FPU instructions with directed rounding
to implement interval operations. However, the Intel FPU operations
may not always be correctly rounded for, say, trigonometric
functions.
`interval_intel` uses assembly code to compute all operations with
proper rounding, and currently **ONLY** works on Intel processors.
The package has been developed for Linux systems but works on
MacOSX and Windows when compiled with GCC.
- `interval` is a meta-package installing all the packages above. It
also provides `interval.top` used above.
Note that `ocamlopt` does float constant propagation in *round to the
nearest* mode which may invalidate interval computations. Use the
compiler flag `-no-float-const-prop` to deactivate it.
Happy interval programming...
Installation
------------
The easier way to install this library is to use [OPAM][]:
opam install interval
`interval` is a meta-package that will install all packages mentioned above.
If you cloned this repository, first install [dune][] and
type `make` in the main directory. This will compile the libraries,
the examples and run basic tests. You can compile the examples with The
programs of the examples will be in `_build/default/examples/`.
Documentation
-------------
To documentation is build using `dune build @doc` and will be in
`_build/default/_doc/` in HTML format. You can also consult the
interfaces of
- [Interval](src-base/interval.mli),
- [Interval_intel](src-intel/interval_intel.mli) and
[Fpu](src-intel/fpu.mli),
- [Interval_crlibm](src-crlibm/interval_crlibm.mli),
or [online](https://chris00.github.io/ocaml-interval/doc/).
It is extremely wise to read the whole documentation, even if you
intend to only use the `Interval_intel` module.
Some examples are available in the `examples/` directory. There is a
`B_AND_B` sub-directory with an example of a branch-and-bound
algorithm that uses interval arithmetics for function optimization
(the example is for the Griewank function, but you can substitute any
function you like).
Tests
-----
Tests are available in the `tests/` directory. They are mainly for
debugging purpose and quite complicated. You may run them (`make
tests`) to check that everything is working properly for your machine.
The `test` program runs also a speed test for your particular
architecture.
Bug reports should be open at
https://github.com/Chris00/ocaml-interval/issues
Remark: This library was originally published on Jean-Marc Alliot
[website](http://www.alliot.fr/fbbdet.html.fr) but was moved to Github
with the permission of the authors.
[interval arithmetic]: https://en.wikipedia.org/wiki/Interval_arithmetic
[OPAM]: https://opam.ocaml.org/
[crlibm]: https://github.com/Chris00/ocaml-crlibm
[dune]: https://github.com/ocaml/dune