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>
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docs/language/math/math-atan2.md
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docs/language/math/math-atan2.md
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---
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id: math-atan2
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name: Math.atan2
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category: math
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kind: namespace-method
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tokens: Math.atan2
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sig: Math.atan2(y, x) -> fixed
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tip: The angle of the vector (x, y), in radians.
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order: 26
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ns: Math
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member: atan2
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---
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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.
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```ludic
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program Demo {
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handler Step phase Update {
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let heading = Math.atan2(target_y - y, target_x - x)
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}
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}
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```
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