pyintval

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Rigorous interval arithmetic for Python — every operation returns an interval that is mathematically guaranteed to contain the true result.

Status: under active development. The rigorous kernel, the Python bindings, and the full set of elementary functions are implemented and tested; packaging polish (wheels, docs) and decorated intervals are in progress.

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, fma via 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/tan across wrapping intervals, atan2's branch cut, and domain restriction (e.g. sqrt of a partly-negative interval, log toward 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.

Planned: decorated intervals (a machine-checked certificate that a composed function is defined and continuous on its input box), NumPy-style interval arrays, and prebuilt wheels on PyPI.

Planned API (illustrative)

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

Full documentation — guide and API reference — is built with Sphinx from docs/ and hosted on Read the 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/.

Project links

Data verified by PyPI on Aug 10, 2026
Data provided by the project maintainers, verified at the time the release was uploaded to PyPI.

Key dates

PyPI data
Data sourced directly from PyPI's database.
  • Released:
Newer release available (0.3.0)

1 maintainer

PyPI data
Data sourced directly from PyPI's database.
Avatar for gameiro from gravatar.com gameiro

Credits

Author: Marcio Gameiro

GitHub Statistics

Data verified by PyPI on Aug 10, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

MIT
View SPDX License List

Requires

Python >=3.10

Provides Extra

test docs dev

Tags

interval arithmetic rigorous numerics verified computation IEEE 1788 correct rounding

Classifiers

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