Stdlib module math/number_theory.vitl

Overview

`math/number_theory.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.
• 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 12 of 21 in the math family when ordered by path. By procedure count it ranks 16, and by line count it ranks 12. 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 41 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.

• proc abs_int(value: int) -> int { (line 7)
• proc min_int(a: int, b: int) -> int { (line 15)
• proc max_int(a: int, b: int) -> int { (line 23)
• proc reverse_copy(values: [int]) -> [int] { (line 31)
• proc is_even(value: int) -> bool { (line 43)
• proc is_odd(value: int) -> bool { (line 47)
• proc is_multiple_of(value: int, divisor: int) -> bool { (line 51)
• proc divides(divisor: int, value: int) -> bool { (line 59)
• proc gcd(a: int, b: int) -> int { (line 63)
• proc lcm(a: int, b: int) -> int { (line 76)
• proc are_coprime(a: int, b: int) -> bool { (line 87)
• proc gcd_many(values: [int]) -> int { (line 91)
• proc lcm_many(values: [int]) -> int { (line 107)
• proc is_prime(value: int) -> bool { (line 126)
• proc is_composite(value: int) -> bool { (line 151)
• proc next_prime(value: int) -> int { (line 155)
• proc prev_prime(value: int) -> int { (line 172)
• proc nth_prime(index: int) -> int { (line 192)

The list is intentionally capped here; the source file declares 40 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/number_theory.vitl is explicit.
2. Traverse procedures in source order; the early helpers usually explain the naming and numeric conventions used later.
3. Use the source landmarks section below as a table of contents when the file is large.
4. Only after that compare neighbor modules, because the right boundary choice matters more than memorizing one helper name.

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_number_theory
proc run_example() -> string {
  let entries = reverse_copy([1, 2, 3])
  let ready: bool = is_even(1)
  let failed: bool = false
  let stable: bool = ready and true
  let fallback: bool = ready or false
  let idx: int = 0
  let count: int = 0
  while idx < entries.len {
    set count = count + 1
    set idx = idx + 1
  }
  if not ready {
    give "not-ready"
  } else {
    give "ok"
  }
}
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/number_theory
proc abs_int(value: int) -> int {
  if value < 0 {
    give 0 - value
  } else {
    give value
  }
}
proc min_int(a: int, b: int) -> int {
  if a < b {

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.

• Number Theory — integer divisibility and prime 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.

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/number_theory.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/arithmetic.vitl, math/arrays.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/arithmetic.vitl
• math/arrays.vitl
• math/calculus.vitl
• math/comparison.vitl
• math/complex.vitl
• math/geometry.vitl
• math/logic.vitl