# Algorithms

The orchestration layer that strings together the Haldane / Schreiner equations, Bühlmann M-values, and the Baker gradient-factor ramp into a working dive simulator. The [Decompression-Model](Decompression-Model.md) chapters cover the underlying equations; this section is about how those equations are *called* to produce a dive plan.

## Pipeline

1. The user provides a dive setup: bottom gas + optional deco gases, $GF_{low}$ / $GF_{high}$, and either a full waypoint array or just `{maxDepth, bottomTime}`.
2. `generateDecoProfile(maxDepth, bottomTime, gases, gfLow, gfHigh, …)` (`js/diveSetup.js:326`) is the top-level entry. It calls `calculateNDL()` first; if $t_{bottom} \le NDL$ it returns a simple no-stop profile. Otherwise it simulates descent + bottom time to get tissue state, then hands off to `generateDecoSchedule()`.
3. `generateDecoSchedule()` (`js/decoModel.js`) computes gas-switch MODs, calls `findFirstStopAtGFLow()` to determine `pAnchor` and the first stop in one pass, then runs the deco loop to generate the stop list.
4. Output is a waypoint array (embedded stops + gas switches) plus metadata (total deco time, controlling compartment, `pAnchor`, `anchorDepth`).
5. Chart rendering replays the waypoints at 10-second resolution via `calculateTissueLoading()` (`js/decoModel.js:1178`) and overlays per-timepoint ceilings via `calculateCeilingTimeSeriesDetailed()` (`js/decoModel.js:617`).

```mermaid
flowchart TD
  A[generateDecoProfile<br/>diveSetup.js:326] --> B{bottomTime<br/>vs NDL}
  B -- "t ≤ NDL" --> C[generateSimpleProfile]
  B -- "t > NDL" --> D[simulate descent + bottom]
  D --> E[generateDecoSchedule<br/>decoModel.js:899]
  E --> F[findFirstStopAtGFLow<br/>strict GF_low first-stop search]
  F --> H[deco stop loop]
  H --> I[waypoints + stops]
  I --> J[calculateTissueLoading<br/>decoModel.js:1178]
  I --> K[calculateCeilingTimeSeriesDetailed<br/>decoModel.js:617]
```

The pipeline is single-pass per dive setup: tissue state flows forward from surface, `pAnchor` is computed once at ascent start and passed downstream to every function that needs a GF-ramp reference.

## Chapter TOC

1. [Algo-01-Ascent-Simulation](Algo-01-Ascent-Simulation.md) — replay a waypoint array over all 16 compartments; segment dispatch between Haldane (level) and Schreiner (slope).
2. [Algo-02-NDL-Calculation](Algo-02-NDL-Calculation.md) — binary search for no-decompression limit at a given depth and gas.
3. [Algo-03-First-Stop-Ramped-GF](Algo-03-First-Stop-Ramped-GF.md) — the two-step `pAnchor` → first-stop discovery. The subtlest chapter.
4. [Algo-04-Deco-Stop-Loop](Algo-04-Deco-Stop-Loop.md) — from first stop to surface, generate the stop list; the `DECO_STOP_MAX_MINUTES` safety cap.
5. [Algo-05-Multi-Gas-Switching](Algo-05-Multi-Gas-Switching.md) — MOD calculation, sequential switching, gas-switch waypoint insertion.
6. [Algo-06-Ceiling-Time-Series](Algo-06-Ceiling-Time-Series.md) — per-timepoint ceiling overlay for chart rendering.

Cross-cutting: [Architecture](Architecture.md) for the module/function index; [Decompression-Model](Decompression-Model.md) for the equations themselves; [References](References.md#11-decotengu-documentation--structure-and-rigor-to-match) for the prior-art decotengu docs whose structure these chapters mirror.