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arithmetic

Arithmetic capability traits and checked analytic operations for LunaFlow numeric types, with default real-valued instances.

math
arithmetic
elementary-functions
moon add Luna-Flow/arithmetic@0.5.0
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0.5.0
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Apache-2.0
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25 days ago
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README

#Arithmetic

Arithmetic capability traits and checked or contextual numeric boundaries for Luna Flow projects.

#v0.4.0 - Certified Evaluation Failures

This README matches the v0.4.0 repository state. The release adds a structured failure boundary for proof-backed numerical evaluation while retaining the contextual outcomes, diagnostics, and checked capability surface introduced in 0.3.0.

For earlier release notes and repository history, see CHANGELOG.md.

#Release Notes

  • CertificationStage records the proof step that could not establish a result: range reduction, series evaluation, enclosure propagation, or target rounding.
  • CertificationFailureReason distinguishes an uncertified range, missing convergence, invalid enclosure, resource limit, and exhausted refinement budget.
  • CertificationFailureDetail retains the operation, requested and working precision, and the number of refinement attempts.
  • ArithmeticErrorKind::CertificationFailure and ArithmeticError::certification_failure preserve that detail without flattening it into an unstructured message.

#Package Positioning

  • luna-generic expresses algebraic structure such as Ring, Field, and Num.
  • arithmetic expresses analytic functions, checked operations, contextual outcomes, and enclosure-style relations.
  • The package describes small capabilities rather than declaring a bundled “real number” abstraction.
  • Concrete numeric packages should implement only the traits whose semantics they can support faithfully.

#Capability Layers

#Unchecked Elementary Traits

  • Sqrt, Cbrt, Radical
  • Exponential, Logarithmic, Power
  • Trigonometric, InverseTrigonometric
  • Hyperbolic, InverseHyperbolic
  • Constants

These traits preserve direct backend behavior and return Self.

#Checked Traits

  • SqrtChecked, DivChecked, CompareChecked
  • PowNatChecked, PowIntChecked, ParseChecked

Checked traits return Result[..., ArithmeticError] and use ArithmeticContext where the operation needs an explicit context. ArithmeticError can also carry a CertificationFailureDetail when a proof-backed backend cannot certify a result at the requested target.

#Contextual Outcome Traits

  • AddContextual, SubContextual, MulContextual, DivContextual
  • AbsContextual, SqrtContextual, ExpContextual
  • NumericFormatContextual

Contextual operations return ArithmeticOutcome[Self] inside Result, keeping the computed value and diagnostic flags together as immutable data.

#Enclosure Relations

  • Contains, Overlaps
  • DefinitelyLt, DefinitelyLe, MaybeEq

These traits model containment and definite or possible relations without pretending enclosure values form a scalar total order.

#Context Contract

  • ArithmeticContext::new clamps precision to at least 1.
  • If both exponent limits are present, e_min must not exceed e_max.
  • The decimal presets use precisions 7, 16, and 34 with their matching exponent ranges and clamping enabled.
  • ArithmeticDiagnostics::combine merges flags with logical OR, so callers can aggregate a sequence of outcomes explicitly.

The built-in Float and Double contextual implementations do not emulate arbitrary decimal precision, directed rounding, exponent clamping, or IEEE status-flag detection. They currently return exact diagnostics for successful native operations; contextual division and square root delegate validation to their checked counterparts. The richer context and diagnostics are public capability boundaries for numeric backends that can implement those semantics.

#Installation

moon add Luna-Flow/arithmetic@0.4.0
moon add Luna-Flow/luna-generic@0.3.1

Use explicit Luna Flow aliases in moon.pkg:

import {
  "Luna-Flow/luna-generic" @lf_alg,
  "Luna-Flow/arithmetic" @lf_arith,
}

#Quick Start

using @lf_alg { trait Add, trait Mul }
using @lf_arith { trait Sqrt }

fn hypot2[T : Add + Mul + Sqrt](x : T, y : T) -> T {
  Sqrt::sqrt(x * x + y * y)
}

let context = @lf_arith.ArithmeticContext::decimal64()
let outcome = @lf_arith.DivContextual::div_contextual(10.0, 4.0, context).unwrap()
inspect(outcome.value, content="2.5")
inspect(outcome.diagnostics.inexact, content="false")

#Documentation

#Changelog

Historical release notes live in CHANGELOG.md. This README stays focused on the current package baseline and entry points.

#Development

Useful local commands:

moon fmt
moon info
moon check --target all
moon test

#Release Checklist

  1. Bump moon.mod to the intended release version.
  2. Update README.md, all three localized documentation trees, and CHANGELOG.md.
  3. Run moon fmt --check, moon info, moon build --target all, moon check --target all --frozen, and the default, JavaScript, and native test suites.
  4. Trigger publish-package with the exact moon.mod version. The workflow repeats the checks, publishes to mooncakes, and creates the matching GitHub release.

The workflow publishes the version declared in moon.mod to mooncakes; it does not accept a mismatched release version.

#
AbsContextual

source
pub(open) trait AbsContextual {
  fn abs_contextual(Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
AddContextual

source
pub(open) trait AddContextual {
  fn add_contextual(Self, Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
Cbrt

source
pub(open) trait Cbrt {
  fn cbrt(Self) -> Self
}

impl Cbrt for Float
impl Cbrt for Double

#
CompareChecked

source
pub(open) trait CompareChecked {
  fn compare_checked(Self, Self) -> Result[Int, ArithmeticError]
}

#
Constants

source
pub(open) trait Constants {
  fn pi() -> Self
  fn tau() -> Self
  fn e() -> Self
}

impl Constants for Float
impl Constants for Double

#
Contains

source
pub(open) trait Contains {
  fn contains(Self, Self) -> Bool
}

#
DefinitelyLe

source
pub(open) trait DefinitelyLe {
  fn definitely_le(Self, Self) -> Bool
}

#
DefinitelyLt

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pub(open) trait DefinitelyLt {
  fn definitely_lt(Self, Self) -> Bool
}

#
DivChecked

source
pub(open) trait DivChecked {
  fn div_checked(Self, Self, ArithmeticContext) -> Result[Self, ArithmeticError]
}

impl DivChecked for Float

#
DivContextual

source
pub(open) trait DivContextual {
  fn div_contextual(Self, Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
ExpContextual

source
pub(open) trait ExpContextual {
  fn exp_contextual(Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
Exponential

source
pub(open) trait Exponential {
  fn exp(Self) -> Self
  fn exp2(Self) -> Self
}

#
Hyperbolic

source
pub(open) trait Hyperbolic {
  fn sinh(Self) -> Self
  fn cosh(Self) -> Self
  fn tanh(Self) -> Self
}

impl Hyperbolic for Float

#
InverseHyperbolic

source
pub(open) trait InverseHyperbolic {
  fn asinh(Self) -> Self
  fn acosh(Self) -> Self
  fn atanh(Self) -> Self
}

#
InverseTrigonometric

source
pub(open) trait InverseTrigonometric {
  fn asin(Self) -> Self
  fn acos(Self) -> Self
  fn atan(Self) -> Self
  fn atan2(Self, Self) -> Self
}

#
Logarithmic

source
pub(open) trait Logarithmic {
  fn ln(Self) -> Self
  fn log2(Self) -> Self
  fn log10(Self) -> Self
}

#
MaybeEq

source
pub(open) trait MaybeEq {
  fn maybe_eq(Self, Self) -> Bool
}

#
MulContextual

source
pub(open) trait MulContextual {
  fn mul_contextual(Self, Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
NumericFormatContextual

source
pub(open) trait NumericFormatContextual {
  fn zero_contextual(ArithmeticContext) -> Self
  fn one_contextual(ArithmeticContext) -> Self
  fn epsilon_contextual(ArithmeticContext) -> Self
  fn min_normal_contextual(ArithmeticContext) -> Self
  fn max_finite_contextual(ArithmeticContext) -> Self
  fn classify_contextual(Self) -> FpClass
}

#
Overlaps

source
pub(open) trait Overlaps {
  fn overlaps(Self, Self) -> Bool
}

#
ParseChecked

source
pub(open) trait ParseChecked {
  fn parse_checked(String, ArithmeticContext) -> Result[Self, ArithmeticError]
}

#
PowIntChecked

source
pub(open) trait PowIntChecked {
  fn pow_int_checked(Self, Int, ArithmeticContext) -> Result[Self, ArithmeticError]
}

#
PowNatChecked

source
pub(open) trait PowNatChecked {
  fn pow_nat_checked(Self, UInt, ArithmeticContext) -> Result[Self, ArithmeticError]
}

#
Power

source
pub(open) trait Power {
  fn pow(Self, Self) -> Self
}

impl Power for Int
impl Power for Int16
impl Power for Int64
impl Power for UInt
impl Power for UInt16
impl Power for UInt64
impl Power for Float
impl Power for Double
impl Power for BigInt

#
Radical

source
pub(open) trait Radical : Sqrt + Cbrt {
}

impl Radical for Float
impl Radical for Double

#
Sqrt

source
pub(open) trait Sqrt {
  fn sqrt(Self) -> Self
}

impl Sqrt for Float
impl Sqrt for Double

#
SqrtChecked

source
pub(open) trait SqrtChecked {
  fn sqrt_checked(Self, ArithmeticContext) -> Result[Self, ArithmeticError]
}

#
SqrtContextual

source
pub(open) trait SqrtContextual {
  fn sqrt_contextual(Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
SubContextual

source
pub(open) trait SubContextual {
  fn sub_contextual(Self, Self, ArithmeticContext) -> Result[ArithmeticOutcome[Self], ArithmeticError]
}

#
Trigonometric

source
pub(open) trait Trigonometric {
  fn sin(Self) -> Self
  fn cos(Self) -> Self
  fn tan(Self) -> Self
}

#
ArithmeticContext

source
pub struct ArithmeticContext {
  precision : Int
  rounding : RoundingMode
  e_min : Int?
  e_max : Int?
  clamp : Bool
} derive(Eq)

#
ArithmeticContext::decimal128

source

#
ArithmeticContext::decimal32

source

#
ArithmeticContext::decimal64

source

#
ArithmeticContext::new

source
fn ArithmeticContext::new(precision : Int, rounding? : RoundingMode, e_min? : Int, e_max? : Int, clamp? : Bool) -> ArithmeticContext

#
ArithmeticDiagnostics

source
pub struct ArithmeticDiagnostics {
  inexact : Bool
  rounded : Bool
  overflow : Bool
  underflow : Bool
  subnormal : Bool
  clamped : Bool
} derive(Eq, 
Debug)

#
ArithmeticDiagnostics::combine

source

#
ArithmeticDiagnostics::empty

source

#
ArithmeticDiagnostics::new

source
fn ArithmeticDiagnostics::new(inexact? : Bool, rounded? : Bool, overflow? : Bool, underflow? : Bool, subnormal? : Bool, clamped? : Bool) -> ArithmeticDiagnostics

#
ArithmeticError

source
pub struct ArithmeticError {
  kind : ArithmeticErrorKind
  message : String
} derive(Eq)

#
ArithmeticError::certification_failure

source
fn ArithmeticError::certification_failure(detail : CertificationFailureDetail) -> ArithmeticError

#
ArithmeticError::certification_failure_detail

source
fn ArithmeticError::certification_failure_detail(self : ArithmeticError) -> CertificationFailureDetail?

#
ArithmeticError::division_by_zero

source
fn ArithmeticError::division_by_zero(message : String) -> ArithmeticError

#
ArithmeticError::domain_error

source
fn ArithmeticError::domain_error(message : String) -> ArithmeticError

#
ArithmeticError::format_error

source
fn ArithmeticError::format_error(message : String) -> ArithmeticError

#
ArithmeticError::is_certification_failure

source
fn ArithmeticError::is_certification_failure(self : ArithmeticError) -> Bool

#
ArithmeticError::is_division_by_zero

source
fn ArithmeticError::is_division_by_zero(self : ArithmeticError) -> Bool

#
ArithmeticError::is_domain_error

source
fn ArithmeticError::is_domain_error(self : ArithmeticError) -> Bool

#
ArithmeticError::is_format_error

source
fn ArithmeticError::is_format_error(self : ArithmeticError) -> Bool

#
ArithmeticError::is_parse_error

source
fn ArithmeticError::is_parse_error(self : ArithmeticError) -> Bool

#
ArithmeticError::is_unordered_comparison

source
fn ArithmeticError::is_unordered_comparison(self : ArithmeticError) -> Bool

#
ArithmeticError::is_unsupported

source
fn ArithmeticError::is_unsupported(self : ArithmeticError) -> Bool

#
ArithmeticError::parse_error

source
fn ArithmeticError::parse_error(message : String) -> ArithmeticError

#
ArithmeticError::unordered_comparison

source
fn ArithmeticError::unordered_comparison(message : String) -> ArithmeticError

#
ArithmeticError::unsupported

source
fn ArithmeticError::unsupported(message : String) -> ArithmeticError

#
ArithmeticErrorKind

source
pub enum ArithmeticErrorKind {
  DivisionByZero
  ParseError
  DomainError
  FormatError
  UnsupportedOperation
  UnorderedComparison
  CertificationFailure(CertificationFailureDetail)
} derive(Eq)

#
ArithmeticOutcome

source
pub struct ArithmeticOutcome[T] {
  value : T
  diagnostics : ArithmeticDiagnostics
} derive(Eq, 
Debug)

#
ArithmeticOutcome::exact

source
fn[T] ArithmeticOutcome::exact(value : T) -> ArithmeticOutcome[T]

#
ArithmeticOutcome::with_diagnostics

source
fn[T] ArithmeticOutcome::with_diagnostics(value : T, diagnostics : ArithmeticDiagnostics) -> ArithmeticOutcome[T]

#
CertificationFailureDetail

source
pub struct CertificationFailureDetail {
  operation : String
  stage : CertificationStage
  reason : CertificationFailureReason
  target_precision : Int
  work_precision : Int
  refinements : Int
} derive(Eq)

#
CertificationFailureDetail::new

source
fn CertificationFailureDetail::new(operation : String, stage : CertificationStage, reason : CertificationFailureReason, target_precision : Int, work_precision : Int, refinements : Int) -> CertificationFailureDetail

#
CertificationFailureDetail::operation

source

#
CertificationFailureDetail::reason

source

#
CertificationFailureDetail::refinements

source

#
CertificationFailureDetail::stage

source

#
CertificationFailureDetail::target_precision

source
fn CertificationFailureDetail::target_precision(self : CertificationFailureDetail) -> Int

#
CertificationFailureDetail::work_precision

source
fn CertificationFailureDetail::work_precision(self : CertificationFailureDetail) -> Int

#
CertificationFailureReason

source
pub(all) enum CertificationFailureReason {
  RangeNotCertified
  SeriesDidNotConverge
  InvalidEnclosure
  ResourceLimit
  RefinementBudgetExhausted
} derive(Eq)

#
CertificationStage

source
pub(all) enum CertificationStage {
  RangeReduction
  SeriesEvaluation
  EnclosurePropagation
  TargetRounding
} derive(Eq)

#
FpClass

source
pub(all) enum FpClass {
  Finite
  Infinity
  NaN
} derive(Eq, 
Debug)

#
RoundingMode

source
pub(all) enum RoundingMode {
  ToNearestEven
  TowardZero
  TowardPositive
  TowardNegative
  AwayFromZero
} derive(Eq)

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