pyintval

Rigorous interval arithmetic for Python. Every operation returns an interval that is mathematically guaranteed to contain the true result, using correctly rounded double-precision endpoints and IEEE 1788-2015 set-based semantics.

Installation

pip install pyintval

Wheels are provided for Linux (x86-64, aarch64), macOS (arm64, x86-64), and Windows (AMD64) on CPython 3.10–3.14. Building from source requires a C++20 compiler; on Windows that must be clang-cl (the vendored CORE-MATH kernels use features MSVC lacks).

Quickstart

import pyintval as iv

# A string literal is parsed with correct OUTWARD rounding, so it provably
# encloses the exact decimal value (0.1 is not representable in binary64):
x = iv.Interval("0.1")
print(x.lo < x.hi)              # True: a nondegenerate 1-ulp enclosure of 1/10

# Arithmetic returns guaranteed enclosures.
y = iv.sqrt(x) + iv.Interval(2) * x
print(y.lo, y.hi)

# Set-based division never raises; it widens toward the unbounded result.
print(iv.Interval(1) / iv.Interval(-1, 1))     # Interval('[entire]')

# Elementary functions are correctly rounded, widened one ulp per side.
print(iv.exp(iv.log(iv.Interval(5))))          # encloses 5
print(3.141592653589793 in iv.pi())            # True

# A DecoratedInterval certifies "defined and continuous on this box".
d = iv.DecoratedInterval(1.0, 4.0)
print(iv.sqrt(d).decoration)                   # 'com'
print(iv.sqrt(iv.DecoratedInterval(-1.0, 4.0)).decoration)  # 'trv'

What makes it rigorous

  • Correctly rounded arithmetic. +, -, *, /, sqrt, and fma are computed with error-free transformations and directed one ulp outward — no rounding-mode switching, thread-safe, and cross-validated bit-for-bit against hardware directed rounding.

  • Correctly rounded elementary functions. exp, log, trigonometric and hyperbolic functions and their inverses, pow, atan2, hypot, erf, and more are built on the CORE-MATH kernels and widened one ulp per endpoint, giving enclosures at most a couple of ulps wider than optimal. They are verified against a high-precision mpmath oracle over millions of inputs.

  • Set-based semantics. Empty and unbounded intervals propagate instead of raising, so a single out-of-domain box never aborts a bulk computation.

  • Decorations. An opt-in DecoratedInterval tracks an IEEE 1788 decoration that certifies, through any composition, whether the evaluated function is defined and continuous on its input — the hypothesis many computer-assisted proofs require.

  • Conformance-tested. Validated against the ITF1788 reference suite for IEEE 1788-2015 (~7,200 cases); every result is checked to enclose the standard’s tightest interval, gated in CI on every release.

See the User guide for the guarantees in detail, or the API reference for the full reference.