floating

Luna-Flow/floating is arbitrary-precision floating-point arithmetic for MoonBit: binary values with IEEE 754 semantics at any precision, IEEE 754 and General Decimal Arithmetic decimals, and certified interval (ball) arithmetic following IEEE 1788. Precision, rounding, exponent range, special values, status flags, traps and enclosures are explicit values in every API rather than hidden global state. This manual documents the current branch; the current release is 0.8.0.

Install

moon add Luna-Flow/floating@0.8.0

Then import the packages you need in your moon.pkg, for example "Luna-Flow/floating/bin_float". The module needs the MoonBit toolchain 0.10 or later (moonc ≥ 0.10). It depends on Luna-Flow/arithmetic (rounding modes, contexts, checked and contextual traits) and Luna-Flow/luna-generic (algebraic traits); add Luna-Flow/arithmetic yourself when you name its types. Getting started walks through the first program.

Guides

Guide	Read it for
Getting started	choosing a package, installing, first values, contexts and failure models
Numeric semantics	the shared vocabulary: exact value and rounded result, rounding functions, ulp and unit roundoff, flags, quantum, signed zero, NaN, enclosures
Architecture	package layers, the numeric core pipeline, certified elementary functions, invariants
Verification	the gates, the published conformance claims and how to reproduce them
Performance audit	proofs and evidence for the optimized arithmetic paths
Repository conventions	documentation rules and the review checklist

Package map

Each package has a tutorial (how to use it), an API reference (what you can call) and a design page (why it works this way). The four numerical cores also have conformance and performance pages.

Numerical cores

Package	Purpose	Pages
bin_float	arbitrary-precision binary floating point, IEEE 754 binary operations and binary16/32/64/128 interchange	tutorial · API · design · conformance · performance
decimal	IEEE 754 arbitrary-precision decimal with per-operation flags and DPD/BID interchange	tutorial · API · design · conformance · performance
decimal_gda	General Decimal Arithmetic with sticky status and traps	tutorial · API · design · conformance · performance
ball_float	outward-rounded bare and decorated intervals (IEEE 1788)	tutorial · API · design · conformance · performance

Composition and shared vocabulary

Package	Purpose	Pages
def	Sign, PartialOrder, the Floating trait, predicates and re-exported arithmetic types	tutorial · API · design
bin_float_checked	binary pipelines that stop at the first error	tutorial · API · design
decimal_checked	IEEE decimal pipelines that accumulate flags	tutorial · API · design
decimal_gda_checked	GDA pipelines that thread status and stop at traps	tutorial · API · design
ball_float_checked	interval pipelines that stop at the first error	tutorial · API · design
semantic	exact, representation-independent projection for cross-package comparison	tutorial · API · design

Expressions and corpus frontends

Package	Purpose	Pages
numeric_expr	host-independent numeric expression syntax and evaluation	tutorial · API · design
frontend/gda_expr	parse and execute GDA .decTest files	tutorial · API · design
frontend/itl_expr	parse and execute ITF1788 interval test rows	tutorial · API · design
frontend/mpfr_expr	parse and execute pinned MPFR witnesses	tutorial · API · design
frontend/testfloat_expr	parse and execute Berkeley TestFloat vectors	tutorial · API · design

Conformance command line

Package	Purpose	Pages
cli	native dispatcher for the four conformance backends	tutorial · API · design
cli/gda_expr_cli	file and output adapter for .decTest runs	tutorial · API · design
cli/itl_expr_cli	file and JSON adapter for ITF1788 runs	tutorial · API · design
cli/mpfr_expr_cli	command adapter for MPFR witness runs	tutorial · API · design
cli/testfloat_expr_cli	command adapter for TestFloat runs	tutorial · API · design

Infrastructure and evidence

Package	Purpose	Pages
internal	shared exact-rational, big-integer, parsing, normalization and rounding helpers	tutorial · API · design
internal/conformance	source locations, deterministic shards, case dispositions and summaries	tutorial · API · design
internal/runner_cli	shared CLI options, files, diagnostics and JSON	tutorial · API · design
consistency	white-box cross-package laws and API audits	tutorial · API · design
doc_examples	executable documentation examples run by just docs	tutorial · API · design
bench	shared Maremark benchmark infrastructure	tutorial · API · design
bench/bin_float	binary arithmetic and elementary-function benchmarks	tutorial · API · design
bench/decimal	IEEE decimal benchmarks	tutorial · API · design
bench/decimal_gda	GDA decimal benchmarks	tutorial · API · design
bench/ball_float	interval arithmetic benchmarks	tutorial · API · design

The application surface is the numerical cores, def and the checked wrappers; semantic and numeric_expr are provisional integration surfaces. The other packages publish interfaces because repository tools compose them, and their design pages state narrower stability promises.

Reading paths

• New to the library. Read getting started, then the tutorial of the package you chose, for example the bin_float tutorial or the decimal tutorial. Keep numeric semantics open for the vocabulary.
• Using it in an application or library. Read numeric semantics once, then work from the API pages of your packages. Before you rely on a standard behaviour, check the matching conformance page; for pipelines, read the tutorial of the checked wrapper.
• Contributing. Read architecture, verification and the repository conventions, then the design page of the package you change. Changes to an optimized path also need the performance audit and the package’s performance page.

Evidence snapshot

• The pinned GDA official corpus passes 64,986/64,986 legal executable scalar rows, and official0 passes 16,124/16,124. The 141 # placeholder or non-scalar rows are diagnostic exclusions.
• The binary TestFloat level-1 matrix passes 254,227,872 vectors across binary16/32/64/128, including fused multiply-add, remainder, round to integral, integer conversions and the comparison predicates, plus pinned MPFR square-root and elementary-function witnesses.
• The strict ITF1788 aggregate passes 4,656/4,656 selected interval cases.
• The IEEE decimal gate covers decimal32/64/128 DPD and BID encodings, flags and arithmetic on four targets.

These finite results do not imply support for every operation, every future corpus revision or every real input. Read the conformance page of a package before turning a result into a compatibility claim.

Authority

pkg.generated.mbti defines what is public, and source and tests define behaviour; if a page and the generated interface disagree, the interface wins.