feat(score): update statistics & return user in score

app/calculator.py

@@ -1,12 +1,26 @@
 from __future__ import annotations
 
-from app.database.score import Score
+import math
+from typing import TYPE_CHECKING
+
 from app.models.beatmap import BeatmapAttributes
 from app.models.mods import APIMod
 from app.models.score import GameMode
 
 import rosu_pp_py as rosu
 
+if TYPE_CHECKING:
+    from app.database.score import Score
+
+
+def clamp[T: int | float](n: T, min_value: T, max_value: T) -> T:
+    if n < min_value:
+        return min_value
+    elif n > max_value:
+        return max_value
+    else:
+        return n
+
 
 def calculate_beatmap_attribute(
     beatmap: str,
@@ -32,7 +46,7 @@ def calculate_beatmap_attribute(
 
 
 def calculate_pp(
-    score: Score,
+    score: "Score",
     beatmap: str,
 ) -> float:
     map = rosu.Beatmap(content=beatmap)
@@ -57,3 +71,34 @@ def calculate_pp(
     )
     attrs = perf.calculate(map)
     return attrs.pp
+
+
+# https://osu.ppy.sh/wiki/Gameplay/Score/Total_score
+def calculate_level_to_score(level: int) -> float:
+    if level <= 100:
+        # 55 = 4^3 - 3^2
+        return 5000 / 3 * (55 - level) + 1.25 * math.pow(1.8, level - 60)
+    else:
+        return 26_931_190_827 + 99_999_999_999 * (level - 100)
+
+
+def calculate_score_to_level(score: float) -> int:
+    if score < 5000:
+        return int(55 - (3 * score / 5000))  # 55 = 4^3 - 3^2
+    elif score < 26_931_190_827:
+        return int(60 + math.log(score / 1.25, 1.8))
+    else:
+        return int((score - 26_931_190_827) / 99_999_999_999 + 100)
+
+
+# https://osu.ppy.sh/wiki/Performance_points/Weighting_system
+def calculate_pp_weight(index: int) -> float:
+    return math.pow(0.95, index)
+
+
+def calculate_weighted_pp(pp: float, index: int) -> float:
+    return calculate_pp_weight(index) * pp if pp > 0 else 0.0
+
+
+def calculate_weighted_acc(acc: float, index: int) -> float:
+    return calculate_pp_weight(index) * acc if acc > 0 else 0.0