abax

A lightweight Rust library providing high-precision mathematical constants and special functions.

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Features

Mathematical Constants:
- Bernoulli numbers (B2n) up to n=16.
- Riemann Zeta function values for integers 2 through 16.
- Euler-Mascheroni constant.
- Stirling series coefficients for asymptotic expansions.
Special Functions:
- Gamma and Polygamma Functions:
  - gamma(x): Gamma function Γ(x) computed with the Lanczos approximation and reflection formula.
  - gammaln(x): Natural logarithm of the Gamma function ln(Γ(x)) using Stirling's approximation.
  - digamma(x), trigamma(x), tetragamma(x): Polygamma functions ψ(n)(x) implemented with reflection and recurrence shifting.
  - psi(k, x): Polygamma interface for arbitrary order $k$ with stable handling of poles and infinities.
  - gammainc(x, a, lower, scaled): Regularized incomplete gamma function with scaling for improved conditioning.
  - gammaincinv(y, a, lower): Robust inverse incomplete gamma function using a combined Halley-Newton-Bisection method.
- Beta Functions:
  - beta(z, w), betaln(z, w): Beta function and its natural logarithm.
  - betainc(x, z, w, lower): Regularized incomplete beta function Ix(z,w).
  - betaincinv(y, z, w, lower): Inverse of the regularized incomplete beta function.
- Error Functions:
  - erf(x), erfc(x), erfcx(x): Error function, complementary error function, and scaled variant.
  - erfinv(x), erfcinv(x): Inverse error functions implemented with piecewise rational approximations.

Probability Distributions:

Family	PDF	CDF	Inverse (Quantile)
Normal	`normpdf(x, μ, σ)`	`normcdf(x, μ, σ, upper)`	`norminv(p, μ, σ)`
Lognormal	`lognpdf(x, μ, σ)`	`logncdf(x, μ, σ, upper)`	`logninv(p, μ, σ)`
Student's T	`tpdf(x, v)`	`tcdf(x, v, upper)`	`tinv(p, v)`
Noncentral T	`nctpdf(x, ν, δ)`	`nctcdf(x, ν, δ, upper)`	`nctinv(p, ν, δ)`
Gamma	`gampdf(x, a, b)`	`gamcdf(x, a, b, upper)`	`gaminv(p, a, b)`
Beta	`betapdf(x, a, b)`	`betacdf(x, a, b, upper)`	`betainv(p, a, b)`
Exponential	`expdf(x, λ)`	`expcdf(x, λ, upper)`	`expinv(p, λ)`
Chi-squared	`chi2pdf(x, v)`	`chi2cdf(x, v, upper)`	`chi2inv(p, v)`
Weibull	`wblpdf(x, a, b)`	`wblcdf(x, a, b, upper)`	`wblinv(p, a, b)`
Extreme Value	`evpdf(x, μ, σ)`	`evcdf(x, μ, σ, upper)`	`evinv(p, μ, σ)`
Generalized Extreme Value	`gevpdf(x, k, σ, μ)`	`gevcdf(x, k, sigma, mu, upper)`	`gevinv(p, k, sigma, mu)`
Poisson	`poisspdf(x, λ)`	`poisscdf(x, λ, upper)`	`poissinv(p, λ)`
Binomial	`binopdf(x, n, p)`	`binocdf(x, n, p, upper)`	`binoinv(y, n, p)`

Add this to your Cargo.toml:

[dependencies]
abax = "*"

This project is licensed under the MIT License - see the LICENSE file for details.

Source code is available on GitHub.