Stdlib module math/arithmetic.vitl

Overview

`math/arithmetic.vitl` is a public stdlib surface inside the `math` family. It should be read as one focused slice of the broader family responsibility: Arithmetic, algebra, comparison, calculus, geometry, modular arithmetic, number theory, probability, statistics, matrix, and vector helpers.

Purpose

This file should be chosen because of responsibility, not because its name “sounds close enough”. Inside the math family, it carries one focused part of the contract and keeps that responsibility separate from neighboring concerns.

• A scoring engine can compute aggregates in `math` while keeping I/O and transport elsewhere.
• A statistics or matrix chapter should explain the workflow around the computation, not just a single formula.

Taxonomy

Think of this page as a generated encyclopedia entry rather than a hand-written tutorial. The goal is to show what kind of module this is, how dense it is, and what reading strategy makes sense before depending on it.

• Large algorithm surface: this file exposes many procedures and likely acts as a domain toolkit rather than a single thin wrapper.
• Owns domain vocabulary: the module declares data shapes in addition to executable helpers, so its types are part of the contract.
• Has tuning constants: part of the module behavior is controlled by named constants that document default precision, limits, or policy.
• Minimal top-level dependencies: the module reads as mostly self-contained from its opening declarations.
• Explicit export surface: the file ends with visible export declarations instead of relying only on implicit namespace discovery.

Implementation profile

This profile is inferred directly from the source text. It does not replace reading the file, but it tells you quickly whether the module is mostly declarative, loop-heavy, branch-heavy, or organized around many small exits.

Top-level API inventory

Imported surfaces

This file does not advertise a top-level `use` surface in its opening declarations. That often means it is either self-contained or an aggregation layer.

Position in family

This file is module 3 of 21 in the math family when ordered by path. By procedure count it ranks 4, and by line count it ranks 4. Those ranks are useful as rough signals of breadth, not as quality judgments.

Declaration map

The declaration map turns raw source into a scan-friendly catalog. It is useful when the file is large enough that a reader wants to orient by kinds of surfaces first.

The table is exhaustive for top-level declarations of the selected kinds. This file declares 84 matching surfaces.

Representative signatures

These signatures are shown in source order so the page keeps the feel of a reference manual, not just a keyword cloud.

• const PI: f64 = 3.141592653589793 (line 7)
• const E: f64 = 2.718281828459045 (line 8)
• const I64_MIN: i64 = 9223372036854775808 (line 10)
• const I64_MAX: i64 = 9223372036854775807 (line 11)
• const F64_INF: f64 = 1000000000000000000.0 (line 13)
• const F64_NAN: f64 = 0.0 (line 14)
• const RAND_A: i64 = 1664525 (line 16)
• const RAND_C: i64 = 1013904223 (line 17)
• const RAND_M: i64 = 2147483647 (line 18)
• pick SafeResult { (line 20)
• form I128 { (line 25)
• proc abs_i64(value: i64) -> i64 { (line 29)
• proc abs_f64(value: f64) -> f64 { (line 37)
• proc add_i64(a: i64, b: i64) -> i64 { (line 45)
• proc sub_i64(a: i64, b: i64) -> i64 { (line 49)
• proc mul_i64(a: i64, b: i64) -> i64 { (line 53)
• proc div_i64(a: i64, b: i64) -> i64 { (line 57)
• proc mod_i64(a: i64, b: i64) -> i64 { (line 65)

The list is intentionally capped here; the source file declares 83 matching signatures in total.

How to use this module

Start by reading the file as an ownership boundary. Ask three questions: what enters this module, what stable types or procedures it exports, and what adjacent module should stay outside of it.

1. Read space and top-level imports first so the ownership boundary of math/arithmetic.vitl is explicit.
2. Scan constants before procedures; they often encode precision, limits, or policy assumptions that explain later behavior.
3. Read declared forms and picks before algorithms so the data vocabulary is stable in your head.
4. Traverse procedures in source order; the early helpers usually explain the naming and numeric conventions used later.
5. Use the source landmarks section below as a table of contents when the file is large.

User example

This example is generated from the actual stdlib module surface. Its job is not to be the smallest snippet possible; its job is to show a realistic consumer-shaped file that exercises the module and mirrors the language keywords the module itself relies on.

space demo/math_arithmetic
const SAMPLE_LABEL: string = "demo"
form UserReport {
  label: string,
  ready: bool
}
pick UserOutcome {
  case Ready(message: string)
  case Empty(reason: string)
}
proc run_example() -> UserOutcome {
  let result = abs_i64(1)
  let ready: bool = is_prime(1)
  let failed: bool = false
  let stable: bool = ready and true
  let fallback: bool = ready or false
  let idx: int = 0
  while idx < 1 {
    set idx = idx + 1
  }
  if ready {
    give UserOutcome.Empty("module not ready")
  } else {
    let state: UserOutcome = UserOutcome.Ready("ok")
    match state {
      case UserOutcome.Ready(message) {
        give UserOutcome.Ready(message)
      }
      case UserOutcome.Empty(reason) {
        give UserOutcome.Empty(reason)
      }
    }
  }
  let copies: f64 = 1 as f64
}
export run_example

Keyword coverage

This table makes the “all keywords of the module” requirement auditable. It compares the detected Vitte keywords in the source file with the generated consumer example above.

The generated snippet exercises every detected Vitte keyword used by this module.

Source shape

space vitte/stdlib/math/arithmetic
const PI: f64 = 3.141592653589793
const E: f64 = 2.718281828459045
const I64_MIN: i64 = 9223372036854775808
const I64_MAX: i64 = 9223372036854775807
const F64_INF: f64 = 1000000000000000000.0
const F64_NAN: f64 = 0.0
const RAND_A: i64 = 1664525
const RAND_C: i64 = 1013904223
const RAND_M: i64 = 2147483647

The excerpt is not meant to replace the file. It exists to make the module recognizable at first glance, the same way a Wikipedia infobox helps the reader orient before reading the whole article.

Source landmarks

Large files are easier to retain when they have visible landmarks. When the source contains explicit section banners, they are surfaced here; otherwise the first major declarations are used as anchors.

• Arithmetic — scalar arithmetic and numeric helpers

Source organization

When a file carries its own internal chaptering, those chapters usually reveal the intended reading order better than a flat symbol list. This section reconstructs that organization from the source itself.

Complete API catalog

This catalog is the exhaustive file-level index for the module. It is intentionally closer to a generated encyclopedia appendix than to a tutorial summary.

Constants

Data surfaces

Procedures

Exports

Integration boundaries

Within math, this file should remain focused. If a future helper changes the host boundary, scheduling boundary, or data-shape boundary, it probably belongs in a neighbor module instead of being added here by convenience.

• Family responsibility: Arithmetic, algebra, comparison, calculus, geometry, modular arithmetic, number theory, probability, statistics, matrix, and vector helpers.
• Family architecture role: Use `math` when the transformation itself is the feature. This family exists so algorithmic intent stays visible and testable.

Composition guidance

Choose this module when

• Choose math/arithmetic.vitl when the main question is owned by this module rather than by transport, storage, orchestration, or user-interface code.
• A scoring engine can compute aggregates in `math` while keeping I/O and transport elsewhere.
• A statistics or matrix chapter should explain the workflow around the computation, not just a single formula.

Pause before extending it when

• Avoid extending this file when the new helper mostly changes the boundary to host I/O, runtime coordination, or foreign integration instead of staying inside math.
• Check nearby modules such as math/algebra.vitl, math/arrays.vitl, math/calculus.vitl before adding convenience wrappers here.

Relationship table

This table keeps the page closer to a real encyclopedia entry: a module is easier to understand when compared with its nearest alternatives in the same family.

Neighbor modules

• math/algebra.vitl
• math/arrays.vitl
• math/calculus.vitl
• math/comparison.vitl
• math/complex.vitl
• math/geometry.vitl
• math/logic.vitl
• math/matrix.vitl