You can run FPTaylor without installation at FPTaylor JS's website.
A. Solovyev, M. Baranowski, I. Briggs, C. Jacobsen, Z. Rakamaric, G. Gopalakrishnan Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions. (ACM Transactions on Programming Languages and Systems)
A. Solovyev, C. Jacobsen, Z. Rakamaric, G. Gopalakrishnan, Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions. (FM 2015)
C. Jacobsen, A. Solovyev, G. Gopalakrishnan, A parametrized Floating-Point Formalization in HOL Light. (NSV 2015)
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
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 allIf 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)" >> ~/.bashrcThe 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-intervalBenchmarks and examples are in the benchmarks directory.
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-toolThen it is possible to run
./export -o output_file.fpcore input_fileSee Reference for additional information.
A detailed description of FPTaylor can be found in REFERENCE.md
See the formal directory for corresponding HOL Light theories and procedures.
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 ocamlfindThen run
make clean
make fptaylor-jsThe 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-debugCopy 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.serverNow open localhost:8000 in your browser.
A full-featured website is also available.