ludic/docs/language/math/math-atan2.md
Orkuncakilkaya a38195128f feat(stdlib): namespaced standard library (issue #2)
Implement the bulk of the namespaced-stdlib proposal (workshopsoft/ludic#2):
156 namespace methods across Math, Text, List, Ease, Collide, World, Net,
Sys, Save, Mem, extended Screen, Color functions, extended Random, and Time.
All deterministic fixed-point; self-hosting (C-free bootstrap fixpoint holds).

Compiler (selfhost/):
- Math.*: sqrt/sin/cos/tan/atan2/asin/acos (fixed-point runtime prelude —
  bit-by-bit isqrt, 256-entry interpolated sine table, Ross atan2), plus
  hypot/dist/dist2/deg_to_rad/rad_to_deg/posmod/wrap/ping_pong/snapped/
  move_toward/smoothstep/lerp/remap/sign/floor/ceil/round.
- Text.* (complete): upper/lower/trim/repeat/pad, split/join/replace,
  and the libc-backed queries.
- List.* (complete): insert/remove_at/remove/sort plus the earlier ops.
- Ease.* (in/out/in_out/back/bounce) and Collide.* (rects/point_rect/
  circles/rect_circle).
- Phase 3: World/Net/Sys/Save namespaced over the bare builtins (byte-
  identical IR) and Mem.* (bytes/words/copy/fill/peek/poke).
- Screen.* extended (line/circle/fill_circle/triangle/fill_triangle via new
  runtime primitives; sprite/sprite_scaled aliases), Color.* functions,
  Random.* (value/int/sign), Time.* (frame/delta/elapsed/now — new
  game-loop frame counter).
- Fix a lexer bug: fixed-point literals with >4 fractional digits overflowed.

Docs & tooling:
- 129 new per-symbol doc pages; gen.py made data-driven (namespaces
  discovered from the docs, no hardcoded list); new check-impl.py enforces
  that every implemented namespace method / keyword / type / phase has a
  doc page, wired into `x test-tools`. Document the previously-undocumented
  keywords (break/continue/where/entry/new/public + and/or/not tokens).
- LSP: namespaced signature help (ns_method_sig) covering every namespace.

Tests: 12 new self-host/regression tests + a golden render for the drawing
primitives. All suites green (selfhost 21, regression 45, tools 29).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-08-30 00:26:19 +03:00

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Markdown

---
id: math-atan2
name: Math.atan2
category: math
kind: namespace-method
tokens: Math.atan2
sig: Math.atan2(y, x) -> fixed
tip: The angle of the vector (x, y), in radians.
order: 26
ns: Math
member: atan2
---
Returns the angle in radians from the positive x-axis to the point <code>(x, y)</code>, in the full range <code>-pi</code>..<code>pi</code> — the standard way to get a heading from a direction vector. Note the argument order is <code>y</code> then <code>x</code>. Deterministic fixed-point, accurate to within about a degree.
```ludic
program Demo {
handler Step phase Update {
let heading = Math.atan2(target_y - y, target_x - x)
}
}
```