Sollya.jl

Julia bindings for Sollya: polynomial approximation, symbolic expressions, interval evaluation and correctly rounded BigFloat values.

Uses an installed Sollya 8.0 library and Julia standard libraries only.

Installation

Requires Julia 1.10 or later. Install Sollya with your system package manager:

Platform	Command
macOS	brew install sollya
Debian / Ubuntu	sudo apt-get install sollya libsollya-dev

Install the unregistered Julia package directly from Git:

using Pkg
Pkg.add(url="git@github.com:pc2/Sollya.jl.git")

The Git URL uses SSH access. Set JULIA_PKG_USE_CLI_GIT=true before starting Julia to use the system Git and its SSH configuration.

For a custom native installation, set SOLLYA_LIBRARY to the shared library's path before the first numerical call.

Quick start: polynomial approximation

using Sollya

result = approximate("erf(x)", (0, 1//4);
    basis=5, formats=:single, precision=256)

result.coefficients  # exact Rational{BigInt} values, ascending powers of x
result.norm_bound    # lower and upper bounds on absolute approximation error
result.polynomial    # stored polynomial as a Sollya expression

The bound certifies the mathematical polynomial. Rounding when evaluating that polynomial requires additional error analysis.

Expressions and BigFloat evaluation

with_objects() do keep
    f = keep(sollya"sin(x)+exp(x)")
    println(evaluate(BigFloat, f, 1//2; precision=256))
end

Expressions can contain symbolic constants such as π. BigFloat(obj; precision=256) and evaluate(BigFloat, ...) return correctly rounded finite values. bounds(BigFloat, interval; precision=256) rounds interval endpoints outward. Unresolved rounding raises SollyaError.

Approximation requests and BigFloat conversions default to Julia's current BigFloat precision. Use with_session(Session(; precision=512)) do ... end to scope Sollya settings.

with_objects closes registered objects when the block exits. Return Julia data or an unregistered copy(obj) to retain results. See object lifetime and settings.

Concurrent approximation jobs

requests = [ApproximationRequest("erf(x)", (0, 1//4); precision=bits)
            for bits in (128, 256, 384)]

results = SollyaPool(2) do pool
    approximate_many(pool, requests)
end

Each worker is an independent Julia process. Results preserve input order, and failed jobs raise exceptions.

Calls within one process are serialized. The pool requires localhost sockets and has no timeout or automatic retry. See process pools.

Documentation

• API reference: functions, formats, rounding, errors and proof behavior.
• Verification: tested Julia versions and platforms.
• Contributing: development, testing and formatting.

Exported functions also have Julia help entries: ?approximate, for example.

License

The wrapper is MIT licensed, copyright Gerrit Pape. Sollya and adapted test fixtures retain their upstream license: attribution, license.