Add exact arithmetic implementation and tests

- Introduced exact arithmetic with support for large integers and fractions in `exact.gd`, `big_integer.gd`, and `exact_value.gd`.
- Implemented a comprehensive test suite in `test_exact_math.gd` to validate arithmetic operations against expected results.
- Added a README in `math` directory to document the exact arithmetic system and its usage.
- Ensured that all arithmetic operations maintain precision without floating-point errors, using a custom representation for large numbers.
- Included methods for encoding and decoding exact values for serialization.

stage/stage.gd

@@ -1,4 +1,5 @@
 extends Control
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const OWNIVERSE_ITEM = preload("uid://d3xjfxwe3w16v")
 
@@ -96,11 +97,11 @@ var owniverse_items: Dictionary[String, OwniverseItem] = {}
 var locked_items: Array = []
 
 
-func set_datetime(value: float):
+func set_datetime(value):
     # Simulation time advances in tenths of a year; displaying five decimal
     # places only adds zeroes and suggests precision the simulation does not
     # have.
-    date_time.text = Global.format_number(value, 1) if value != 0.0 else "0.0"
+    date_time.text = Global.format_number(value, 1) if not E.eq(value, 0) else "0.0"
 
 #region Item manipulations: update and visibility
 
@@ -110,7 +111,7 @@ func set_owniverse_item_value() -> void:
         if owniverse_items.has(item_id):
             owniverse_items[item_id].set_label(owniverse.presentation.pending_amounts[item_id])
     owniverse.presentation.pending_amounts.clear()
-        
+
 
 #endregion
 
@@ -156,8 +157,8 @@ func _update_descriptions(delta: float) -> void:
         return
     for page in description_targets:
         var id: String = description_targets[page].id
-        var total: float = ItemDescription.quantities(owniverse, id).total
-        description_rates[id] = (total - description_samples[id]) / description_elapsed if description_samples.has(id) else 0.0
+        var total = ItemDescription.quantities(owniverse, id).total
+        description_rates[id] = E.divide(E.subtract(total, description_samples[id]), E.of(description_elapsed)) if description_samples.has(id) else 0.0
         description_samples[id] = total
     description_elapsed = 0.0
     _refresh_descriptions()
@@ -167,13 +168,13 @@ func _control_page(item: OwniverseItem) -> void:
     # TODO переписать это ↓
     if !g_active_items.has(item.item_page):
         g_active_items[item.item_page] = null
-        
+
     var current_item: OwniverseItem = g_active_items[item.item_page]
     if current_item == item:
         return
-    
+
     g_active_items[item.item_page] = item
-    
+
     if current_item != null and current_item.item_page == item.item_page:
         current_item.set_selection(false)
 
@@ -202,21 +203,21 @@ func _init_owniverse_items() -> bool:
         item_pages[page].add_child(item)
         item.init_button(item_props)
         item.item_activated.connect(item_activated)
-        
+
         owniverse_items[item_id] = item
-        
+
     return false
 
 
 func item_activated(item: OwniverseItem) -> void:
     _control_page(item)
     _set_item_description(item)
-    
+
     if item.item_id == "S" or item.item_id == "H":
         var _value = owniverse.state.amount[item.item_id]
-        _value = 9 * _value if _value > 0 else 1
+        _value = E.multiply(9, _value) if E.gt(_value, 0) else 1
         owniverse.production.produce_hs(item.item_id, _value)
-    
+
 
 func _check_counters(delta: float) -> Array:
     var actions: Array = []
@@ -224,13 +225,13 @@ func _check_counters(delta: float) -> Array:
         var cnt: Counter = g_counters[k]
         if not cnt.is_active:
             continue
-            
+
         cnt.value += delta
         if cnt.value >= cnt.sec:
             actions.append(k)
             cnt.value = 0
             cnt.is_active = false
-        
+
     return actions
 
 
@@ -245,7 +246,7 @@ func _do_actions(actions: Array) -> void:
 
 func _swipe_to_nearest_page() -> void:
     if stage_page_scroller.scroll_horizontal % PAGE_WIDTH == 0: return
-    
+
     var new_page: int = round(1.0 * stage_page_scroller.scroll_horizontal / PAGE_WIDTH)
 
     if g_tween != null:
@@ -270,34 +271,34 @@ func _input(event: InputEvent) -> void:
     elif event is InputEventScreenTouch:
         pass
 
-    
+
 func _set_active_page_actions() -> void:
     for pa in page_actions:
         if !g_active_items.has(pa): continue
-        
+
         var item_id: String = g_active_items[pa].item_id
         var entity: OwniverseEntity = owniverse.catalog.entities[item_id]
 
         #var amount = owniverse.get_available_to_produce(item_id)
-        
+
         #var amount = owniverse.get_available_to_produce(entity)
         var amount = owniverse.production.calculate_max_producible(entity)
         #print(item_id, " : ", amount)
         if item_id == "SMBH":
-            var preview: Callable = func(requested: float) -> float:
+            var preview: Callable = func(requested):
                 return owniverse.production.calculate_max_producible(entity, requested)
             page_actions[pa].set_actions(item_id, amount, preview)
         else:
             page_actions[pa].set_actions(item_id, amount)
 
 
-func _page_action_pressed(page_id: int, action_amount: float) -> void:
+func _page_action_pressed(page_id: int, action_amount) -> void:
     if !g_active_items.has(page_id):
         return
-        
+
     var item_id: String = g_active_items[page_id].item_id
-    
-    if action_amount > 0:
+
+    if E.gt(action_amount, 0):
         owniverse.production.produce(item_id, action_amount)
 
 
@@ -310,7 +311,7 @@ func _ready() -> void:
     create_new_universe()
     load_data()
     _refresh_universe_ui()
-    
+
     g_counters.swipe.sec = 0.2
 
     for pa in page_actions:
@@ -360,9 +361,9 @@ func _refresh_universe_ui() -> void:
     set_owniverse_item_value()
     _unlock_items()
     if world_indicators != null: world_indicators.update(owniverse)
-    
+
 func _process(delta: float) -> void:
-    
+
     owniverse.evolute(delta)
     indicator_elapsed += delta
     if indicator_elapsed >= 0.1:
@@ -371,21 +372,21 @@ func _process(delta: float) -> void:
     _update_descriptions(delta)
     set_owniverse_item_value()
     set_datetime(owniverse.state.time.year)
-    
+
     #owniverse.cycle(delta)
-    
+
     #owniverse.cycle_legacy(year_delta)
-    
+
     var actions = _check_counters(delta)
     _do_actions(actions)
-    
+
     _set_active_page_actions()
 
 
 func _change_speed(delta: int) -> void:
-    
+
     owniverse.speed = owniverse.speed + delta
-    
+
     var speed: int = owniverse.speed
     var ind: int = 1
     for icon in g_speed_icons:
@@ -403,14 +404,14 @@ func _change_speed(delta: int) -> void:
     else:
         g_time_minus.texture_normal = load(SPEED_TEXTURE_NAME_TEMPLATE % str(speed - 1))
         g_time_plus.texture_normal = load(SPEED_TEXTURE_NAME_TEMPLATE % str(speed + 1))
- 
-   
+
+
 func _on_topmenu_button_pressed(screen_name: String) -> void:
-    
+
     for screen_id in screens:
         #print(screen_name, " ←→ ", screen_id)
         screens[screen_id].visible = screen_id == screen_name
-    
+
 
 func _on_unlock_and_save_timeout() -> void:
     save_data()
@@ -493,17 +494,17 @@ func init_enitities() -> Dictionary:
     owniverse.catalog.load_definitions(Global.OwniverseEntities)
     for entity_id in owniverse.catalog.entities:
         var entity: OwniverseEntity = owniverse.catalog.entities[entity_id]
-        
+
         owniverse.state.stats.total_amount[entity_id] = 0
         owniverse.state.amount[entity_id] = 0
-        if entity.lifespan > 0:
+        if E.gt(entity.lifespan, 0):
             owniverse.state.batches[entity.id] = []
             owniverse.batches.add_entity_to_batch(entity_id, 0, 0)
         if entity.group_as != "":
             owniverse.state.amount[entity.group_as] = 0
 
             owniverse.state.stats.total_amount[entity.group_as] = 0
-        
+
         if entity.unlock != {}:
             _result.locked_items.append(entity.id)