Exact Computations with Real Numbers
exact-real is a C++/Python library which provides exact lazy computations in the Real Numbers. In particular it implements arithmetic and comparisons of (random) transcendental numbers.
Source tarballs can be downloaded at https://github.com/flatsurf/exact-real/releases.
This repository contains two related projects:
- libexactreal a C++ library
- pyexactreal a Python wrapper for libexactreal
If you have cloned the source directory you will need to setup the configure script and Makefile using autotools. That is
git submodule update --init
./bootstrap
If you obtained a tarball of the sources or if the preceding step worked, you just have to do
./configure
make
make check # to run our test suite
make install # to install into /usr/local
If you happen to have any of the dependencies installed in a non-standard
directory, you will have to specify the CPPFLAGS and LDFLAGS variables for
the configure script
./configure CPPFLAGS=-I/my/path/include LDFLAGS=-L/my/path/lib
For best performance run CXXFLAGS="-O3 -flto -march=native -mtune=native" CXX="g++ -fno-semantic-interposition" ./configure instead of ./configure as
this code greatly benefits from flto inlining. (Unfortunately, libtool filters
out -fno-semantic-interposition as of early 2019 so we can not pass it as
part of CXXFLAGS. If you are using clang, -fno-semantic-interposition does
not seem to be necessary.) Do not use -Ofast or -ffast-math as parts of our
code rely on IEEE compliance. You might want to add -g3 to the CXXFLAGS
which does not hurt performance but gives a better debugging experience. For
the best debugging experience, you might want to replace -O3 with -Og or
even -O0 but the latter results in very poor performance.
If your compiler supports it, you can try to add -fvisibility=hidden -fvisibility-inlines-hidden to your CXXFLAGS. This hides internal bits in
the resulting library which have lead to crashes in the past due to conflicting
header-only libraries.
If your linker supports it, you should use ./configure --with-version-script
to shrink the resulting shared library to an exact curated list of versioned
symbols.
Additionally, you might want to run configure with --disable-static which
improves the build time.
perf works well to profile
when you make sure that CXXFLAGS contains -fno-omit-frame-pointer. You can
then for example run our test suite with perf record --call-graph dwarf make check. Apart from perf itself there are several ways to analyze the output,
hotspot might be the most convenient one at
the time of this writing.
The preferred way to install exact-real is to use your package manager (e.g.
apt-get on Debian or Ubuntu, pacman on Arch Linux, brew on MacOS, etc).
You can use repology for
libexactreal and for
pyexactreal to see if
exact-real is already available for your system. Note that there is an
unrelated package for Haskell
by the same name.
Otherwise, you can build and install this package from source (as outlined above) or install it with conda. Download and install Mambaforge, then run
mamba create -n exactreal libexactreal pyexactreal
conda activate exactreal
You can try out the projects in this repository in a very limited environment online by clicking the following links:
- libexactreal
(might not work currently, due to a bug in xeus-cling)
- pyexactreal
To build all of exact-real, you need a fairly recent C++ compiler and probably some packages that might not be readily available on your system. If you don't want to use your distribution's packages, you can use these dependencies from conda-forge. Download and install Mambaforge, then run
mamba create -n exact-real-build ccache
mamba env update -n exact-real-build -f libexactreal/environment.yml
mamba env update -n exact-real-build -f pyexactreal/environment.yml
conda activate exact-real-build
export CC="ccache cc" # to speed up future compilation
export CXX="ccache c++" # to speed up future compilation
git clone --recurse-submodules https://github.com/flatsurf/exact-real.git
cd exact-real
./bootstrap
./configure --prefix="$CONDA_PREFIX"
make
make check # to run our test suite
make check runs all tests and benchmarks. During development make check TESTS=module
only runs the tests for module. Note that the environment variable
EXACTREAL_CHECK is passed on to the tests and benchmarks, i.e., you could add
EXACTREAL_CHECK="--benchmark_min_time=.02" to not let the benchmarks run as
long as they would usually.
If you have used this project in the preparation of a publication, please cite it as described on our zenodo page.
- Julian Rüth's contributions to this project have been supported by the Simons Foundation Investigator grant of Alex Eskin.