Stdlib module math/calculus.vitl

Overview

`math/calculus.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 5 of 21 in the math family when ordered by path. By procedure count it ranks 8, and by line count it ranks 10. 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 62 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 EPS: f64 = 0.000001 (line 3)
• const MAX_ITER: i64 = 32 (line 4)
• form Complex { re: f64, im: f64 } (line 6)
• form CSR { rows: [int], cols: [int], values: [f64], width: int } (line 7)
• form Dual { real: f64, dual: f64 } (line 8)
• proc poly_eval(coeffs: [f64], x: f64) -> f64 { (line 10)
• proc deriv_forward(coeffs: [f64], x: f64, h: f64) -> f64 { (line 20)
• proc deriv_backward(coeffs: [f64], x: f64, h: f64) -> f64 { (line 28)
• proc deriv_central(coeffs: [f64], x: f64, h: f64) -> f64 { (line 36)
• proc deriv2(coeffs: [f64], x: f64, h: f64) -> f64 { (line 46)
• proc gradient(coeff_x: [f64], coeff_y: [f64], x: f64, y: f64, h: f64) -> [f64] { (line 57)
• proc integrate_trap(samples: [f64], h: f64) -> f64 { (line 63)
• proc integrate_simpson(samples: [f64], h: f64) -> f64 { (line 80)
• proc limit(left: f64, right: f64) -> f64 { (line 98)
• proc deriv_coeffs(coeffs: [f64]) -> [f64] { (line 103)
• proc newton(coeffs: [f64], guess: f64) -> f64 { (line 116)
• proc bisection(coeffs: [f64], low0: f64, high0: f64) -> f64 { (line 132)
• proc taylor_exp(x: f64, terms: int) -> f64 { (line 155)

The list is intentionally capped here; the source file declares 61 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/calculus.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. 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_calculus
const SAMPLE_LABEL: string = "demo"
form UserReport {
  label: string,
  ready: bool
}
proc run_example() -> UserReport {
  let entries = gradient([1.0, 2.0, 3.0], [1.0, 2.0, 3.0], 1.0, 1.0, 1.0)
  let ready: bool = calculus_ready()
  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 ready {
    give UserReport { label: "not-ready", ready: false }
  } else {
    give UserReport { label: "ok", ready: true }
  }
  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/calculus
const EPS: f64 = 0.000001
const MAX_ITER: i64 = 32
form Complex { re: f64, im: f64 }
form CSR { rows: [int], cols: [int], values: [f64], width: int }
form Dual { real: f64, dual: f64 }
proc poly_eval(coeffs: [f64], x: f64) -> f64 {
  let out: f64 = 0.0
  let i: int = 0
  while i < coeffs.len {

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.

• Line 1: space vitte/stdlib/math/calculus
• Line 3: const EPS: f64 = 0.000001
• Line 4: const MAX_ITER: i64 = 32
• Line 6: form Complex { re: f64, im: f64 }
• Line 7: form CSR { rows: [int], cols: [int], values: [f64], width: int }
• Line 8: form Dual { real: f64, dual: f64 }
• Line 10: proc poly_eval(coeffs: [f64], x: f64) -> f64 {
• Line 20: proc deriv_forward(coeffs: [f64], x: f64, h: f64) -> f64 {

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