perf(feed): a shuffle walks a stored random key instead of sorting the whole scope

Every video carries a random number drawn once (videos.shuffle_key, migration 0118, indexed with
id). A seed picks a point on that ring: the feed's Shuffle sort pages along it and wraps, and the
Home surprise reads a 500-video window of it and shuffles that window by the seed, so no video is
favoured for sitting after a wide gap. The md5(id || seed) order read and sorted the whole feed
scope on every call: ~350 ms on prod per surprise, 381-767 ms per Shuffle page on localdev, now
14 ms and 4 ms.

backend/app/feedquery.py

@@ -13,7 +13,19 @@ import binascii
 import json
 from datetime import date, datetime, timedelta, timezone
 
-from sqlalchemy import BigInteger, Select, and_, case, cast, false, func, or_, select
+from sqlalchemy import (
+    BigInteger,
+    Select,
+    and_,
+    case,
+    cast,
+    false,
+    func,
+    literal,
+    or_,
+    select,
+    tuple_,
+)
 from sqlalchemy.orm import Session, aliased
 
 from app.collation import collated
@@ -536,15 +548,17 @@ def sort_keys(sort: str, seed: int, rank_expr=None, lang: str | None = None) ->
             },
             pub,
         ],
-        # Deterministic per-seed shuffle: the same seed yields the same total order, so
-        # the cursor stays valid across pages of one shuffled run.
+        # The ring of stored random keys from the seed's point (`shuffle_walk`): the keys at or after
+        # it, then the ones before. The same seed yields the same total order, so the cursor stays
+        # valid across pages; `feed_page` reads it as two index ranges, never as this sort.
         "shuffle": [
             {
-                "expr": func.md5(func.concat(Video.id, str(seed))),
+                "expr": case((Video.shuffle_key < shuffle_start(seed), 1), else_=0),
                 "asc": True,
                 "nullable": False,
-                "kind": "str",
-            }
+                "kind": "num",
+            },
+            {"expr": Video.shuffle_key, "asc": True, "nullable": False, "kind": "num"},
         ],
     }
     # Relevance (search-result ranking) only exists when there's a query to rank against;
@@ -700,6 +714,40 @@ class BadCursor(ValueError):
     """A `cursor` this module did not write (or one from another sort): the caller's bad input."""
 
 
+# The golden ratio's fraction: consecutive seeds land far apart on the ring, never next to each other.
+_GOLDEN = 0.6180339887498949
+
+
+def shuffle_start(seed: int) -> float:
+    """The point in [0, 1) where a seed's shuffle starts on the ring of `Video.shuffle_key`."""
+    return (seed * _GOLDEN) % 1.0
+
+
+def shuffle_walk(
+    db: Session, query: Select, seed: int, n: int, after: tuple[int, float, str] | None = None
+) -> list:
+    """Up to `n` rows of `query` in the seed's ring order: shuffle_key from the seed's point upwards,
+    then from 0 up to that point. `after` is a cursor's (phase, key, id): the walk resumes past it.
+
+    Each arc is an ascending range read along ix_videos_shuffle_key with the scope's filters checked
+    row by row, so a draw costs the rows it reads, not a sort of the scope — the md5(id || seed) order
+    it replaced read and sorted every row the filters let through (~350 ms on prod for ~213k)."""
+    start = shuffle_start(seed)
+    phase_from, key, last_id = after if after is not None else (0, None, None)
+    rows: list = []
+    for phase in (0, 1):
+        if phase < phase_from or len(rows) >= n:
+            continue
+        arc = Video.shuffle_key >= start if phase == 0 else Video.shuffle_key < start
+        q = query.where(arc)
+        if key is not None and phase == phase_from:
+            q = q.where(
+                tuple_(Video.shuffle_key, Video.id) > tuple_(literal(key), literal(last_id))
+            )
+        rows += db.execute(q.order_by(Video.shuffle_key, Video.id).limit(n - len(rows))).all()
+    return rows
+
+
 def feed_page(
     db: Session,
     user: User,
@@ -734,6 +782,14 @@ def feed_page(
             k["value"] = v
     if ranked and window is not None:
         rows = windowed_relevance_rows(db, query, keys, window, cursor_id, limit + 1)
+    elif sort == "shuffle":
+        after = None
+        if vals is not None and cursor_id is not None:
+            try:
+                after = (int(vals[0]), float(vals[1]), str(cursor_id))
+            except (TypeError, ValueError) as e:
+                raise BadCursor("Invalid feed cursor") from e
+        rows = shuffle_walk(db, query, seed, limit + 1, after)
     else:
         query = query.order_by(*order_by(keys))
         if cursor_id is not None: