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FPTaylor: A Tool for Rigorous Estimation of Round-off Floating-point Errors

You can run FPTaylor without installation at FPTaylor JS's website.

Publications

Requirements

  • OCaml version 4.03.0 or higher with a native compiler (do not forget make opt if you are building from source code). A recommended way to install OCaml is with OPAM

  • (Required for OCaml >= 4.06) OCaml Num library. This library is included in OCaml < 4.05. For other OCaml versions it can be installed with opam install num.

  • (Included) Interval computation library for OCaml. It is distributed with FPTaylor (see INTERVAL). There is also an alternative interval arithmetic library in simple_interval which has limited functionality but it is portable to different systems.

  • (Optional) Gelpia

  • (Optional) Z3

  • (Optional) Maxima, a Computer Algebra System The easiest way to install Maxima on Ubuntu is sudo apt-get install maxima

macOS and Linux Setup

Steps below have been tested on Ubuntu 12.04, Ubuntu 14.04, Ubuntu 16.04, macOS 10.14, and macOS 10.15.

The following command will build FPTaylor and the interval computation library:

make all

If you encounter a problem during the build process then you may try steps described in the next section (alternative interval arithmetic library). The executable FPTaylor file is called fptaylor. It is recommended to create the environment variable FPTAYLOR_BASE which contains the path to the base FPTaylor directory. If this environment variable is created, then it will be possible to copy fptaylor to different places or to create a symbolic link to it. The environment variable can be created with the following commands (in bash):

export FPTAYLOR_BASE=$(pwd)
echo "export FPTAYLOR_BASE=$(pwd)" >> ~/.bashrc

Alternative Interval Arithmetic Library

The interval computation library INTERVAL may be incompatible with some operating systems and processors. There is an alternative interval arithmetic library distributed with FPTaylor (see simple_interval). This library is under development so it does not support all functions of the INTERVAL library. In particular, trigonometric functions are not supported yet.

The following command will build FPTaylor with the simple interval library:

make fptaylor-simple-interval

Benchmarks and Examples

Benchmarks and examples are in the benchmarks directory.

FPBench Support

FPBench is a benchmark suite and a collection of tools for the floating-point research community. FPBench supports FPTaylor and it has a tool for converting FPCore benchmarks into FPTaylor input files. This works in the other direction as well: FPTaylor can translate its input files into FPCore benchmarks. This translation is done with the export tool which can be built with the following command:

make export-tool

Then it is possible to run

./export -o output_file.fpcore input_file

See Reference for additional information.

Reference

A detailed description of FPTaylor can be found in REFERENCE.md

Formal Verification of FPTaylor Results in HOL Light

See the formal directory for corresponding HOL Light theories and procedures.

JavaScript

FPTaylor can be compiled to JavaScript with Js_of_ocaml.

Install Js_of_ocaml and ocamlfind:

opam install js_of_ocaml js_of_ocaml-ppx js_of_ocaml-lwt ocamlfind

Then run

make clean
make fptaylor-js

The file fptaylor.js will be created in the project directory. This command also creates default_config.js which exports a string representation of the default config file (with some required modifications).

It is also possible to create a debug version of fptaylor.js:

make clean
make fptaylor-js-debug

JavaScript Examples

Copy fptaylor.js and default_config.js to the js directory. Delete the export statement from js/default_config.js. Then start a local server:

cd js
python3 -m http.server

Now open localhost:8000 in your browser.

A full-featured website is also available.