pyintval
Rigorous interval arithmetic for Python — every operation returns an interval that is mathematically guaranteed to contain the true result.
Released on PyPI, with prebuilt wheels for Linux, macOS, and Windows on CPython 3.10–3.14. Validated against the ITF1788 reference conformance suite for IEEE 1788-2015.
What it provides
- IEEE 1788-2015 set-based interval arithmetic over double-precision endpoints: empty and unbounded intervals propagate instead of raising, so bulk computations never abort mid-sweep.
- Correctly rounded endpoints for
+,-,*,/,sqrt,fmavia error-free transformations (no rounding-mode switching, thread-safe), and elementary functions (exp,log,sin,cos,tan, their inverses, hyperbolics,pow,atan2,hypot,cbrt,expm1,log1p,erf,erfc, ...) built on the correctly rounded CORE-MATH kernels, widened one ulp per side — enclosures at most a couple of ulps wider than optimal. - Correct handling of the hard cases: periodic extrema of
sin/cos/tanacross wrapping intervals,atan2's branch cut, and domain restriction (e.g.sqrtof a partly-negative interval,logtoward zero). - Verified against a high-precision mpmath oracle across millions of inputs, and the rounding primitives cross-checked bit-for-bit against hardware directed rounding.
Also provides decorated intervals — a machine-checked certificate that a composed function is defined and continuous on its input box. NumPy-style interval arrays are planned.
At a glance
import pyintval as iv
x = iv.Interval("0.1") # rigorously encloses the decimal 0.1
y = iv.sqrt(x) + iv.sin(x) * 2 # guaranteed enclosure of the true image
print(y.lo, y.hi)
iv.Interval(1) / iv.Interval(-1, 1) # -> Interval('[entire]'), never raises
iv.exp(iv.log(iv.Interval(5))) # encloses 5
math_pi_in = 3.141592653589793 in iv.pi()
Installation
Once released:
pip install pyintval
From source (requires a C++20 compiler):
pip install .
On Windows, building from source requires clang-cl (the vendored CORE-MATH kernels use features MSVC lacks); prebuilt wheels have no such requirement.
Documentation
📖 pyintval.readthedocs.io — the user guide and full API reference.
Built with Sphinx from docs/; build it locally with:
pip install ".[docs]"
sphinx-build -b html docs docs/_build/html
Development
# Python tests
pip install -e ".[test]"
pytest
# C++ unit tests
cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release
ctest --test-dir build -C Release --output-on-failure
# Lint / format
pip install pre-commit
pre-commit run --all-files
See RELEASING.md for the wheel-building and PyPI publishing process.
Examples
The examples/ directory has runnable scripts: basic usage,
rigorous range enclosure, an intermediate-value-theorem root proof, certified
transcendental bounds, and a continuity certificate via decorated intervals.
License
MIT. Vendored components: doctest (MIT)
and the CORE-MATH correctly-rounded
kernels (MIT); see third_party/.
1 maintainer
Metadata
1 maintainer
Release files for pyintval 0.3.0
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| pyintval-0.3.0.tar.gz | 603.1 kB | Details |
Built distributions (wheels)
Total release size: 19.6 MB
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