#mbmath

mbmath is an arbitrary-precision numerical computing library for MoonBit. It provides real, complex, and interval arithmetic together with special functions, calculus, root finding, quadrature, matrix algorithms, and ordinary differential equation solvers.

The design follows the layered architecture and numerical semantics of Python's mpmath, while exposing MoonBit-native values, explicit precision and rounding, and typed errors.

#Features

Arbitrary-precision real arithmetic with configurable binary precision and rounding modes
Complex arithmetic, elementary functions, powers, roots, and branch-aware special functions
Real and complex interval arithmetic with outward rounding
Decimal parsing, formatting, base conversion, infinities, signed zero, and NaN support
Elementary functions including logarithms, exponentials, trigonometric, and hyperbolic functions
Gamma, log-gamma, reciprocal gamma, factorial, Bernoulli, psi, harmonic, and zeta functions
Exponential and trigonometric integrals, AGM, and complete elliptic integrals
Numerical differentiation, Taylor expansion, limits, summation, products, convergence acceleration, root finding, and quadrature
Polynomial, Fourier, inverse Laplace, matrix-function, linear algebra, eigensystem, SVD, and ODE utilities

#Packages

Package	Purpose
libmp/mpf	Core arbitrary-precision real representation, arithmetic, conversion, and formatting
libmp/mpc	Arbitrary-precision complex arithmetic and special functions
libmp/libmpi	Real and complex interval arithmetic, interval functions, and interval matrices
libmp/libelefun	Elementary transcendental functions and constants
libmp/gammazeta	Gamma, factorial, Bernoulli, psi, harmonic, and zeta families
libmp/libhyper	Exponential integrals, trigonometric integrals, AGM, and elliptic integrals
libmp/intmath	Integer helpers used by the numerical kernels
ctx/mp	High-level precision context, calculus, numerical methods, matrices, and ODE solvers

#Installation

Add the module to a MoonBit project:

moon add CAIMEOX/moon_floating

Import the high-level context and real-number kernel in moon.pkg:

import {
  "CAIMEOX/moon_floating/ctx/mp",
  "CAIMEOX/moon_floating/libmp/mpf",
}

#Quick Start

let ctx = @mp.new(256, @mpf.round_nearest)
let two = ctx.make_int(2)
let root = ctx.sqrt(two)
println(ctx.to_string(root, dps=50))

The precision passed to @mp.new is measured in bits. Low-level libmp functions also accept precision and rounding explicitly, which makes numerical behavior reproducible and allows directed rounding for interval calculations.

Operations with invalid domains, poles, malformed input, or failed convergence raise package-specific suberrors. Callers can let these errors propagate or handle them with MoonBit's catch syntax.

#mpmath Compatibility

mbmath aims to match mpmath semantics and precision on the operations it implements, including special values and complex branch behavior. It is not a Python binding or a source-compatible translation: APIs use MoonBit types, explicit contexts, and structured errors.

#Development

moon check --target all
moon test --target native
moon fmt

#License

Apache-2.0. See LICENSE.

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