rustymath
Rustymath provides fast elementary and special functions, statistics, searching and sorting, random sampling, linear algebra, optimization, polynomials and exact arithmetic in Rust and Python. It is the numerical core of BasedPL.
The Python package needs no NumPy. Its eager operations use the same broadcasting, selection and tolerant-comparison rules as the shared Rust core. For richer array notation, operators and fusion, use BasedPL.
Float functions target four units in the last place (ulps). Rustymath prioritizes speed over last-bit agreement and reproducibility. These functions document wider bounds:
lgammanear its zeros at 1 and 2 is within 4 ulps of 2, not of the result.digammanear its zeros is within 4 ulps of 1, and below -20 within 4 ulps of ln(1 - x).binomandbinom_dnof a non-whole n with a whole k up to 64 are within 2k ulps.binom_dkhas no relative bound near n = 2k, where its two ψ terms cancel.- Normal and log-normal evaluation of
f32inputs usesf32arithmetic, with parameters and precomputed coefficients rounded tof32. Their densities are within 12 ulps and their cdfs within 14 where |z| < 3, z being the standard score of x or of ln x. They lose accuracy as z² grows, to about 80 and 170 ulps at |z| = 12. Their quantiles are within 13 ulps, except near a quantile of 0, where cancellation leaves an absolute error of up to 8 ulps of the standard deviation. These figures exclude additional error from parameter rounding and ill-conditioned location/scale transformations. - Complex functions count ulps of the result’s magnitude, so a much smaller part can carry most of the error. Complex powers, Γ and binomial coefficients allow ulps of their magnitude times one more than the exponent’s magnitude.
expgives an exact direction at the float nearest a whole number of quarter turns, so e^(iπ/2) is exactly i.
Install
pip install rustymath
Rust users can add the crate to Cargo.toml. See Using rustymath from Rust for scalar and slice forms, build settings, accuracy and speed.
import rustymath as rm
Arrays and indexing
Functions take Python numbers, nested lists, rustymath arrays or buffer exporters such as NumPy arrays. Broadcasting aligns leading axes. A two-item vector adds one value to each row of this matrix:
rm.add([[1, 2, 3], [4, 5, 6]], [10, 20])
Array([[11, 12, 13], [24, 25, 26]], dtype=int64)
Arrays and indexing covers construction, dtypes, selection, reshaping, axis names, keys and interoperability.
Maths and statistics
Real and complex functions operate on whole arrays. Float comparisons are exact unless you set a relative tolerance, for one call with ct or for the whole process with set_tolerance:
rm.exp([0., 1, 2]), rm.equal(0.1 + 0.2, 0.3), rm.equal(0.1 + 0.2, 0.3, ct=rm.CT)
(Array([1.0, 2.7182818, 7.3890561], dtype=float64), False, True)
Maths and statistics covers elementary and special functions, reductions, scans, statistics and tolerant comparison.
Searching, sorting and selection
unique retains first-occurrence order and reports each value’s position, class number and count:
rm.unique([3, 1, 3, 2])
Unique(values=Array([3, 1, 2], dtype=int64), firsts=Array([0, 1, 3], dtype=int64), numbers=Array([0, 1, 0, 2], dtype=int64), counts=Array([2, 1, 1], dtype=int64))
Searching, sorting and selection distinguishes tolerant matching from exact ordering.
Random numbers and distributions
Distributions provide density, cumulative probability, quantiles and seeded sampling:
normal = rm.distribution.normal()
normal.cdf([-1.96, 0, 1.96]), normal.sample(3, seed=0)
(Array([0.024997895, 0.5, 0.9750021], dtype=float64),
Array([0.11623959, -0.78285485, -2.3346353], dtype=float64))
Random numbers and distributions covers sampling and probability functions.
Linear algebra
Solve real or complex systems, including least-norm solutions for singular or non-square matrices:
rm.linalg.solve([[4., 1], [1, 3]], [1., 2])
Array([0.090909091, 0.63636364], dtype=float64)
Linear algebra covers matrix products, reusable factorizations, decompositions and least squares.
Optimization and iterative solves
Minimize functions, fit residuals or find roots. Here Brent’s method finds where cos x = x:
rm.optimize.root_scalar(lambda x: rm.cos(x) - x, [0, 1]).root
0.7390851350713886
Optimization and iterative solves also covers matrix-free linear systems.
Polynomials, exact arithmetic and number theory
Polynomial coefficients start from the constant term. Factorization accepts Python integers of any size:
rm.polynomial.polyroots([-6, 11, -6, 1]), rm.number_theory.factor(2**64 + 1)
(Array([(1+0j), (2-0j), (3+0j)], dtype=complex128),
[(274177, 1), (67280421310721, 1)])
Polynomials, exact arithmetic and number theory includes rational matrix solves and calculations with fractions.Fraction.
Accuracy and speed
The Rust page’s Accuracy and speed section compares each function’s speed with Rust’s standard library. It also explains how the 4-ulp bound holds for f16, with and without fused multiply-add, and for pow and root.
Licence
Apache-2.0. Some algorithms and constants come from SLEEF and Arm Optimized Routines. THIRD-PARTY.md has their notices.
1 maintainer
Metadata
1 maintainer
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