Add Android production release and testing builds workflows

- Introduced `civilization_benchmark.gd` and `legacy_quantity_math.gd` for benchmarking and legacy quantity calculations.
- Created `test_dynamic_math.gd`, `test_frame_evolution.gd`, and `test_sparse_batches.gd` to validate mathematical operations and frame evolution logic.
- Implemented `frame_budget.gd` to manage cooperative work on the main thread, ensuring no partially calculated state is published.
- Added UID files for all new scripts to maintain unique identifiers.

.gitea/workflows/android-release.yml

@@ -0,0 +1,107 @@
+name: Android production release
+
+on:
+  push:
+    tags:
+      - "v*"
+
+jobs:
+  test-build-publish:
+    runs-on: godot
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+          lfs: true
+
+      - name: Verify tag belongs to main
+        run: |
+          git fetch origin main
+          git merge-base --is-ancestor "${GITHUB_SHA}" origin/main
+
+      - name: Show Godot version
+        run: godot --version
+
+      - name: Import project
+        run: |
+          rm -rf .godot
+          godot --headless --path . --editor --import --quit --verbose
+
+      - name: Run all tests
+        shell: bash
+        run: |
+          set -euo pipefail
+          mapfile -t tests < <(find tests -maxdepth 1 -type f -name 'test_*.gd' | sort)
+          test "${#tests[@]}" -gt 0
+
+          for test_file in "${tests[@]}"; do
+            echo "::group::${test_file}"
+            godot --headless --path . --script "res://${test_file}"
+            echo "::endgroup::"
+          done
+
+      - name: Prepare Android signing
+        env:
+          ANDROID_KEYSTORE_BASE64: ${{ secrets.ANDROID_KEYSTORE_BASE64 }}
+        run: |
+          test -n "${ANDROID_KEYSTORE_BASE64}"
+          printf '%s' "${ANDROID_KEYSTORE_BASE64}" | base64 --decode > "${RUNNER_TEMP}/release.keystore"
+          test -s "${RUNNER_TEMP}/release.keystore"
+
+      - name: Configure release AAB
+        env:
+          RELEASE_VERSION: ${{ github.ref_name }}
+          RELEASE_VERSION_CODE: ${{ github.run_number }}
+        run: |
+          python3 - <<'PY'
+          import os
+          import re
+          from pathlib import Path
+
+          path = Path("export_presets.cfg")
+          text = path.read_text()
+          start = text.index('[preset.1.options]')
+          head, android = text[:start], text[start:]
+          replacements = (
+              (r'gradle_build/use_gradle_build=false', 'gradle_build/use_gradle_build=true'),
+              (r'gradle_build/export_format=0', 'gradle_build/export_format=1'),
+              (r'package/signed=false', 'package/signed=true'),
+              (r'version/code=\d+', f'version/code={100000 + int(os.environ["RELEASE_VERSION_CODE"])}'),
+              (r'version/name="[^"]*"', f'version/name="{os.environ["RELEASE_VERSION"].removeprefix("v")}"'),
+          )
+          for pattern, replacement in replacements:
+              android, count = re.subn(pattern, replacement, android, count=1)
+              if count != 1:
+                  raise RuntimeError(f'Expected one Android preset match for {pattern!r}, got {count}')
+          path.write_text(head + android)
+          PY
+
+      - name: Build signed Android App Bundle
+        env:
+          GODOT_ANDROID_KEYSTORE_RELEASE_USER: ${{ secrets.ANDROID_KEYSTORE_ALIAS }}
+          GODOT_ANDROID_KEYSTORE_RELEASE_PASSWORD: ${{ secrets.ANDROID_KEYSTORE_PASSWORD }}
+        run: |
+          export GODOT_ANDROID_KEYSTORE_RELEASE_PATH="${RUNNER_TEMP}/release.keystore"
+          mkdir -p build
+          godot --headless --path . --export-release "Android" build/owniverse-${GITHUB_REF_NAME}.aab
+          test -s "build/owniverse-${GITHUB_REF_NAME}.aab"
+          ls -lh "build/owniverse-${GITHUB_REF_NAME}.aab"
+
+      - name: Publish to Google Play production
+        uses: r0adkll/upload-google-play@v1
+        with:
+          serviceAccountJsonPlainText: ${{ secrets.GOOGLE_PLAY_SERVICE_ACCOUNT_JSON }}
+          packageName: com.KIDGameProduction.Owniverse
+          releaseFiles: build/owniverse-${{ github.ref_name }}.aab
+          tracks: production
+          status: completed
+
+      - name: Upload release bundle
+        uses: actions/upload-artifact@v3
+        with:
+          name: owniverse-${{ github.ref_name }}-aab
+          path: build/owniverse-${{ github.ref_name }}.aab
+          if-no-files-found: error
+          retention-days: 90

.gitea/workflows/android.yml

@@ -1,94 +0,0 @@
-name: Android
-
-on:
-  push:
-    tags:
-      - "v*"
-
-jobs:
-  android:
-    runs-on: godot
-
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v4
-        with:
-          lfs: true
-      - name: Godot version
-        run: godot --version
-
-      - name: Prepare Godot
-        run: |
-          rm -rf .godot
-
-          godot \
-                --headless \
-                --path . \
-                --editor \
-                --import \
-                --quit \
-                --verbose
-
-
-      - name: Build APK
-        run: |
-          mkdir -p build
-
-          godot \
-            --headless \
-            --path . \
-            --editor \
-            --import \
-            --quit
-
-          godot \
-            --headless \
-            --path . \
-            --export-release "Android" \
-            build/app.apk
-
-
-      - name: Check imported resources
-        run: |
-          echo "=== PNG imports ==="
-          find .godot/imported -iname '*habitable*' -o -iname '*civ2*'
-
-          echo "=== PNG files ==="
-          ls -lh ui/4-life/habitable_planet.png
-          ls -lh ui/4-life/civ2.png
-
-
-      - name: Verify APK
-        run: |
-          test -f build/app.apk
-          ls -lh build/app.apk
-
-      - name: Create Release
-        env:
-          GITEA_TOKEN: ${{ secrets.RELEASE_TOKEN }}
-        run: |
-          curl -f \
-            -X POST \
-            -H "Authorization: token ${GITEA_TOKEN}" \
-            -H "Content-Type: application/json" \
-            "https://gt.owad.ru/api/v1/repos/K/owniverse/releases" \
-            -d "{
-              \"tag_name\": \"${GITHUB_REF_NAME}\",
-              \"name\": \"${GITHUB_REF_NAME}\",
-              \"body\": \"Android build ${GITHUB_REF_NAME}\"
-            }"
-
-      - name: Upload APK to Release
-        env:
-          GITEA_TOKEN: ${{ secrets.RELEASE_TOKEN }}
-        run: |
-          RELEASE_ID=$(curl -fsS \
-            -H "Authorization: token ${GITEA_TOKEN}" \
-            "https://gt.owad.ru/api/v1/repos/K/owniverse/releases/tags/${GITHUB_REF_NAME}" \
-            | python3 -c 'import sys,json; print(json.load(sys.stdin)["id"])')
-
-          curl -f \
-            -X POST \
-            -H "Authorization: token ${GITEA_TOKEN}" \
-            -F "attachment=@build/app.apk" \
-            "https://gt.owad.ru/api/v1/repos/K/owniverse/releases/${RELEASE_ID}/assets?name=owniverse-${GITHUB_REF_NAME}.apk"

.gitea/workflows/testing-builds.yml

@@ -0,0 +1,62 @@
+name: Testing builds
+
+on:
+  push:
+    branches:
+      - testing
+
+jobs:
+  test-and-build:
+    runs-on: godot
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          lfs: true
+
+      - name: Show Godot version
+        run: godot --version
+
+      - name: Import project
+        run: |
+          rm -rf .godot
+          godot --headless --path . --editor --import --quit --verbose
+
+      - name: Run all tests
+        shell: bash
+        run: |
+          set -euo pipefail
+          mapfile -t tests < <(find tests -maxdepth 1 -type f -name 'test_*.gd' | sort)
+          test "${#tests[@]}" -gt 0
+
+          for test_file in "${tests[@]}"; do
+            echo "::group::${test_file}"
+            godot --headless --path . --script "res://${test_file}"
+            echo "::endgroup::"
+          done
+
+      - name: Build Android APK
+        run: |
+          mkdir -p build
+          godot --headless --path . --export-release "Android" build/owniverse-testing.apk
+
+      - name: Build Windows EXE
+        run: |
+          godot --headless --path . --export-release "Windows Desktop" build/owniverse-testing.exe
+
+      - name: Verify builds
+        run: |
+          test -s build/owniverse-testing.apk
+          test -s build/owniverse-testing.exe
+          ls -lh build/owniverse-testing.apk build/owniverse-testing.exe
+
+      - name: Upload testing builds
+        uses: actions/upload-artifact@v3
+        with:
+          name: owniverse-testing-${{ github.sha }}
+          path: |
+            build/owniverse-testing.apk
+            build/owniverse-testing.exe
+          if-no-files-found: error
+          retention-days: 14

autoload/global.gd

@@ -1,4 +1,5 @@
 extends Node
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const SPEED_LIMIT: int = 6
 
@@ -57,37 +58,15 @@ func get_description(item_id: String, items: Array = []) -> String:
     return render_template(row, variables)
 
 
-func format_number(value: float, digits: int = 0) -> String:
-    if value == 0: return ""
-    # Keep ordinary quantities readable, grouping thousands with spaces.
-    # Scientific notation is reserved for values whose fixed form would be
-    # unwieldy in the UI.
-    if absf(value) < 1_000_000_000.0:
-        var fixed: String = "%.*f" % [digits, value]
-        var parts: PackedStringArray = fixed.split(".", true)
-        var integer: String = parts[0]
-        var sign_prefix: String = ""
-        if integer.begins_with("-") or integer.begins_with("+"):
-            sign_prefix = integer.left(1)
-            integer = integer.substr(1)
-        var grouped: String = ""
-        while integer.length() > 3:
-            grouped = " " + integer.right(3) + grouped
-            integer = integer.left(integer.length() - 3)
-        grouped = sign_prefix + integer + grouped
-        return grouped + ("." + parts[1] if parts.size() > 1 else "")
-
-    var exp_value = int(floor(log(abs(value)) / log(10.0)))
-    var mantissa = value / pow(10.0, exp_value)
-    
-    return "%.*f" % [digits, mantissa] + "E%+d" % exp_value
+func format_number(value, digits: int = 0) -> String:
+    return E.grouped(value, digits)
 
 
 func _ready() -> void:
     CivilizationRules.clear()
     for row: Dictionary in _read_from_csv("res://data/civilization_rules.txt").values():
         if not CivilizationRules.has(row.stage):
-            CivilizationRules[row.stage] = {"home": row.home, "span": float(row.span), "stars": float(row.stars), "ethics": {},
+            CivilizationRules[row.stage] = {"home": row.home, "span": E.of(row.span), "stars": E.of(row.stars), "ethics": {},
                 "colonizes": row.colonizes == "1", "fights": row.fights == "1", "diplomacy": row.diplomacy == "1", "worships": row.worships == "1"}
         CivilizationRules[row.stage].ethics[row.ethic] = row
     var stages: Array = CivilizationRules.keys()
@@ -104,8 +83,8 @@ func _ready() -> void:
     Locales["en"] = _read_from_csv("res://data/locale.en.txt")
     Locales["ru"] = _read_from_csv("res://data/locale.ru.txt")
     
-    Templates["en"] = _read_from_csv("res://data/templates.en.txt")
-    Templates["ru"] = _read_from_csv("res://data/templates.ru.txt")
+
+    Templates = OwniverseTemplate.get_data()
     
 
 func _read_from_csv(file_path: String) -> Dictionary:

autoload/save_manager.gd

@@ -1,18 +1,19 @@
 # SaveManager.gd (добавить в AutoLoad)
 extends Node
+const E = preload("res://world/owniverse/math/exact.gd")
 
 # ~/Library/Application Support/Godot/app_userdata/Owniverse Adventure/savegame.cfg
-const SETTING_SECTION := "Settings"
+const SETTING_SECTION = "Settings"
 const SAVE_PATH = "user://settings.cfg"
 
-const FORMAT_VERSION: int = 2
+const FORMAT_VERSION : int = 5
 const SimulationTime = preload("res://world/owniverse/simulation_time.gd")
 const WorldParameters = preload("res://world/owniverse/world_parameters.gd")
-const STATE_VERSION: String = SimulationTime.STATE_VERSION
+const STATE_VERSION : String = SimulationTime.STATE_VERSION
 var last_error: String = ""
 var blocked_saves: Dictionary = {}
 var save_directory: String = "user://"
-signal save_completed(filename: String, success: bool, error: String)
+signal save_completed ( filename : String , success : bool , error : String )
 signal saves_drained
 
 # Queue ownership stays on the main thread. The worker only sees its snapshot.
@@ -21,30 +22,28 @@ var _active_filename: String = ""
 var _pending_saves: Dictionary = {}
 
 
-func _process(_delta: float) -> void:
-    if _save_thread != null and not _save_thread.is_alive():
+func _process(_delta: Variant) -> void:
+    if (E.ne(_save_thread, null) and (not _save_thread.is_alive())):
         _finish_save()
 
 
 func is_saving() -> bool:
-    return _save_thread != null or not _pending_saves.is_empty()
+    return (E.ne(_save_thread, null) or (not _pending_saves.is_empty()))
 
 
 func _snapshot(filename: String, password: String, data: Dictionary) -> Dictionary:
-    var payload: Dictionary = data.duplicate(true)
+    var payload: Dictionary = E.encode(data)
     payload.format_version = FORMAT_VERSION
     payload.app_version = str(ProjectSettings.get_setting("application/config/version", ""))
-    return {"filename": filename, "path": save_directory.path_join(filename + ".adventure"), "password": password, "payload": payload,
-        "plaintext": Global.save_plaintext_copy, "speed_limit": Global.SPEED_LIMIT,
-        "stages": Global.CivilizationRules.keys()}
+    return {"filename": filename, "path": save_directory.path_join(E.add(filename, ".adventure")), "password": password, "payload": payload, "plaintext": Global.save_plaintext_copy, "speed_limit": Global.SPEED_LIMIT, "stages": Global.CivilizationRules.keys(), "entities": Global.OwniverseEntities.keys()}
 
 
 ## True means queued, not written. Completion is reported by save_completed.
 func request_save(filename: String, password: String, data: Dictionary) -> bool:
     if blocked_saves.has(filename):
-        return _fail("Save blocked to preserve an unreadable save: " + filename)
+        return _fail(E.add("Save blocked to preserve an unreadable save: ", filename))
     _pending_saves[filename] = _snapshot(filename, password, data)
-    if _save_thread == null:
+    if E.eq(_save_thread, null):
         _start_save()
     return true
 
@@ -57,12 +56,12 @@ func _start_save() -> void:
     _pending_saves.erase(_active_filename)
     _save_thread = Thread.new()
     var error: Error = _save_thread.start(_write_snapshot.bind(job))
-    if error != OK:
+    if E.ne(error, OK):
         _save_thread = null
-        _fail("Cannot start save worker: " + error_string(error))
+        _fail(E.add("Cannot start save worker: ", error_string(error)))
         save_completed.emit(_active_filename, false, last_error)
         _start_save()
-        if not is_saving(): saves_drained.emit()
+        if (not is_saving()): saves_drained.emit()
 
 
 func _finish_save() -> void:
@@ -70,17 +69,17 @@ func _finish_save() -> void:
     var filename: String = _active_filename
     _save_thread = null
     last_error = error
-    if error != "": push_error(error)
-    save_completed.emit(filename, error == "", error)
-    if _save_thread == null: _start_save()
-    if not is_saving(): saves_drained.emit()
+    if E.ne(error, ""): push_error(error)
+    save_completed.emit(filename, E.eq(error, ""), error)
+    if E.eq(_save_thread, null): _start_save()
+    if (not is_saving()): saves_drained.emit()
 
 
 ## Used for application suspension and teardown, when frames may stop arriving.
 func flush_saves() -> void:
     while is_saving():
-        if _save_thread == null: _start_save()
-        if _save_thread != null: _finish_save()
+        if E.eq(_save_thread, null): _start_save()
+        if E.ne(_save_thread, null): _finish_save()
 
 
 func _exit_tree() -> void:
@@ -99,44 +98,44 @@ func save_data(filename: String, password: String, data: Dictionary) -> bool:
     flush_saves()
     last_error = ""
     if blocked_saves.has(filename):
-        return _fail("Save blocked to preserve an unreadable save: " + filename)
+        return _fail(E.add("Save blocked to preserve an unreadable save: ", filename))
     var error: String = _write_snapshot(_snapshot(filename, password, data))
-    return _fail(error) if error != "" else true
+    return (_fail(error) if E.ne(error, "") else true)
 
 
 static func _write_snapshot(job: Dictionary) -> String:
     var payload: Dictionary = job.payload
-    var problem: String = _validate_payload(payload, job.speed_limit, job.stages)
-    if problem != "":
-        return "Invalid save: " + problem
+    var problem: String = _validate_payload(payload, job.speed_limit, job.stages, job.entities)
+    if E.ne(problem, ""):
+        return E.add("Invalid save: ", problem)
     var path: String = job.path
-    var temporary: String = path + ".tmp"
-    var file := FileAccess.open_encrypted_with_pass(temporary, FileAccess.WRITE, job.password)
-    if file == null:
-        return "Cannot write encrypted save: " + temporary
+    var temporary: String = E.add(path, ".tmp")
+    var file = FileAccess.open_encrypted_with_pass(temporary, FileAccess.WRITE, job.password)
+    if E.eq(file, null):
+        return E.add("Cannot write encrypted save: ", temporary)
     file.store_var(payload, false)
     file.close()
     # Check the actual encrypted file, including finalization, before replacing the old save.
-    var verification := FileAccess.open_encrypted_with_pass(temporary, FileAccess.READ, job.password)
-    if verification == null:
-        return "Cannot verify encrypted save: " + temporary
+    var verification = FileAccess.open_encrypted_with_pass(temporary, FileAccess.READ, job.password)
+    if E.eq(verification, null):
+        return E.add("Cannot verify encrypted save: ", temporary)
     var restored: Variant = verification.get_var(false)
     verification.close()
-    if not restored is Dictionary or restored != payload:
-        return "Encrypted save verification failed: " + temporary
-    if DirAccess.rename_absolute(temporary, path) != OK:
-        return "Cannot replace encrypted save: " + path
+    if ((not (restored is Dictionary)) or E.ne(restored, payload)):
+        return E.add("Encrypted save verification failed: ", temporary)
+    if E.ne(DirAccess.rename_absolute(temporary, path), OK):
+        return E.add("Cannot replace encrypted save: ", path)
     if job.plaintext:
-        var plain_path: String = path + ".json"
-        file = FileAccess.open(plain_path + ".tmp", FileAccess.WRITE)
-        if file == null:
-            return "Encrypted save written, but cannot write diagnostic copy: " + plain_path
-        file.store_string(JSON.stringify(payload, "  ", true, true) + "\n")
+        var plain_path: String = E.add(path, ".json")
+        file = FileAccess.open(E.add(plain_path, ".tmp"), FileAccess.WRITE)
+        if E.eq(file, null):
+            return E.add("Encrypted save written, but cannot write diagnostic copy: ", plain_path)
+        file.store_string(E.add(JSON.stringify(payload, "  ", true, true), "\n"))
         file.flush()
         var write_error: Error = file.get_error()
         file.close()
-        if write_error != OK or DirAccess.rename_absolute(plain_path + ".tmp", plain_path) != OK:
-            return "Encrypted save written, but diagnostic copy failed: " + plain_path
+        if (E.ne(write_error, OK) or E.ne(DirAccess.rename_absolute(E.add(plain_path, ".tmp"), plain_path), OK)):
+            return E.add("Encrypted save written, but diagnostic copy failed: ", plain_path)
     return ""
 
 
@@ -144,174 +143,194 @@ func load_data(filename: String, password: String) -> Dictionary:
     flush_saves()
     last_error = ""
     # Plaintext is diagnostic only: never use it as a fallback.
-    var path: String = save_directory.path_join(filename + ".adventure")
-    if not FileAccess.file_exists(path):
+    var path: String = save_directory.path_join(E.add(filename, ".adventure"))
+    if (not FileAccess.file_exists(path)):
         return {}
-    var file := FileAccess.open_encrypted_with_pass(path, FileAccess.READ, password)
-    if file == null:
+    var file = FileAccess.open_encrypted_with_pass(path, FileAccess.READ, password)
+    if E.eq(file, null):
         blocked_saves[filename] = true
-        _fail("Cannot decrypt save: " + path)
+        _fail(E.add("Cannot decrypt save: ", path))
         return {}
     var data: Variant = file.get_var(false)
     file.close()
     # Unsupported formats are archived, never converted or overwritten.
     # Returning no data lets the stage start a new, saveable session.
-    if data is Dictionary and data.get("format_version") != FORMAT_VERSION:
-        var archive: String = path + ".incompatible.bak"
+    if ((data is Dictionary) and E.ne(data.get("format_version"), FORMAT_VERSION)):
+        var archive: String = E.add(path, ".incompatible.bak")
         var index: int = 0
         while FileAccess.file_exists(archive):
-            index += 1
-            archive = path + ".incompatible.bak." + str(index)
+            index = E.add(index, 1)
+            archive = E.add(E.add(path, ".incompatible.bak."), str(index))
         var error: Error = DirAccess.rename_absolute(path, archive)
-        if error != OK:
+        if E.ne(error, OK):
             blocked_saves[filename] = true
-            _fail("Cannot archive incompatible save: " + error_string(error))
+            _fail(E.add("Cannot archive incompatible save: ", error_string(error)))
             return {}
         blocked_saves.erase(filename)
-        push_warning("Incompatible save preserved at " + archive + "; starting a new game.")
+        push_warning(E.add(E.add("Incompatible save preserved at ", archive), "; starting a new game."))
         return {}
     var problem: String = validate_data(data)
-    if problem != "":
+    if E.ne(problem, ""):
         blocked_saves[filename] = true
-        _fail("Invalid save " + path + ": " + problem)
+        _fail(E.add(E.add(E.add("Invalid save ", path), ": "), problem))
         return {}
     blocked_saves.erase(filename)
-    return data
+    return E.decode(data)
 
 
 static func _number(value: Variant, whole: bool = false, nonnegative: bool = true) -> bool:
-    if not (value is int or value is float) or not is_finite(float(value)):
-        return false
-    return (not whole or float(value) == floorf(float(value))) and (not nonnegative or value >= 0)
+    return E.numeric(value) and E.finite(value) and (not value is float or absf(value) < 1e28) and (not whole or E.eq(value, E.floor_value(value))) and (not nonnegative or E.ge(value, 0))
 
 
 static func _number_map(value: Variant, whole: bool = false, nonnegative: bool = true) -> bool:
-    if not value is Dictionary:
+    if (not (value is Dictionary)):
         return false
     for key in value:
-        if not (key is String or key is StringName) or not _number(value[key], whole, nonnegative):
+        if ((not (((key is String) or (key is StringName)))) or (not _number(value[key], whole, nonnegative))):
             return false
     return true
 
 
 static func _plain_tree(value: Variant) -> bool:
-    if value is Dictionary:
+    if (value is Dictionary):
         for key in value:
-            if not (key is String or key is StringName) or not _plain_tree(value[key]):
+            if ((not (((key is String) or (key is StringName)))) or (not _plain_tree(value[key]))):
                 return false
         return true
-    if value is Array:
+    if (value is Array):
         for item in value:
-            if not _plain_tree(item):
+            if (not _plain_tree(item)):
                 return false
         return true
-    return value == null or value is String or value is StringName or value is bool or _number(value, false, false)
+    return ((((E.eq(value, null) or (value is String)) or (value is StringName)) or (value is bool)) or _number(value, false, false))
 
 
 ## Return a diagnostic path on failure; an empty string means the structure is valid.
 func validate_data(data: Variant) -> String:
-    return _validate_payload(data, Global.SPEED_LIMIT, Global.CivilizationRules.keys())
+    return _validate_payload(data, Global.SPEED_LIMIT, Global.CivilizationRules.keys(), Global.OwniverseEntities.keys())
 
 
-static func _validate_payload(data: Variant, speed_limit: int, stages: Array) -> String:
-    if not data is Dictionary or not _plain_tree(data):
+static func _validate_payload(data: Variant, speed_limit: int, stages: Array, entities: Array) -> String:
+    if not E.valid_encoded(data): return "invalid exact number encoding"
+    data = E.decode(data)
+    if ((not (data is Dictionary)) or (not _plain_tree(data))):
         return "save must contain plain finite values"
-    if data.get("format_version") != FORMAT_VERSION or not data.get("app_version") is String:
+    if (E.ne(data.get("format_version"), FORMAT_VERSION) or (not (data.get("app_version") is String))):
         return "unsupported save format"
-    if not data.get("ui") is Dictionary or not data.ui.get("current_page") is int or data.ui.current_page < 0:
+    if (((not (data.get("ui") is Dictionary)) or (not E.numeric(data.ui.get("current_page")))) or E.lt(data.ui.current_page, 0)):
         return "invalid ui.current_page"
-    if not data.get("state") is Dictionary:
+    if (not (data.get("state") is Dictionary)):
         return "state must be a Dictionary"
     var saved: Dictionary = data.state
-    var required := [
-        "version", "time", "speed", "speed_in_year", "energy", "batches", "batch_origins",
-        "binds", "amount", "distribution", "auto_resources", "auto_star_deficits",
-        "production_remainders", "resource_remainders", "evolution_remainders", "life_remainders",
-        "planet_remainders", "blast_remainders", "destruction_remainders", "civilization_remainders",
-        "civilization_stats", "civilization_homes", "ethics", "stats",
-    ]
+    var required = ["version", "time", "speed", "speed_in_year", "energy", "batches", "batch_origins", "binds", "amount", "distribution", "auto_resources", "auto_star_deficits", "production_remainders", "resource_remainders", "evolution_remainders", "life_remainders", "planet_remainders", "blast_remainders", "destruction_remainders", "civilization_remainders", "civilization_stats", "civilization_homes", "ethics", "stats"]
     # Optional additions to the current format. Saves predating indicators keep
     # their quantities and receive neutral defaults from Owniverse on load.
     for field in saved:
-        if field not in required and field not in ["world_parameters", "trends"]:
+        if (not E.contains(required, field) and not E.contains(["world_parameters", "trends"], field)):
             return "unsupported state structure"
     if saved.has("world_parameters"):
-        if not _number_map(saved.world_parameters) or saved.world_parameters.size() != WorldParameters.defaults().size():
+        if ((not _number_map(saved.world_parameters)) or E.ne(saved.world_parameters.size(), WorldParameters.defaults().size())):
             return "invalid state.world_parameters"
         for key in WorldParameters.defaults():
-            if not saved.world_parameters.has(key) or saved.world_parameters[key] < 1.0:
-                return "invalid world parameter " + key
-            if key in ["Bur", "Exp", "Agg"] and saved.world_parameters[key] > 19.0:
-                return "invalid world scale " + key
+            if ((not saved.world_parameters.has(key)) or E.lt(saved.world_parameters[key], 1)):
+                return E.add("invalid world parameter ", key)
+            if (E.contains(["Bur", "Exp", "Agg"], key) and E.gt(saved.world_parameters[key], 19)):
+                return E.add("invalid world scale ", key)
     if saved.has("trends"):
-        if not _number_map(saved.trends) or saved.trends.size() != WorldParameters.TRENDS.size():
+        if ((not _number_map(saved.trends)) or E.ne(saved.trends.size(), WorldParameters.TRENDS.size())):
             return "invalid state.trends"
         for key in WorldParameters.TRENDS:
-            if not saved.trends.has(key) or saved.trends[key] >= 1.0:
-                return "invalid trend " + key
+            if ((not saved.trends.has(key)) or E.ge(saved.trends[key], 1)):
+                return E.add("invalid trend ", key)
     for field in required:
-        if not saved.has(field):
-            return "missing state." + field
-    if saved.version != STATE_VERSION:
+        if (not saved.has(field)):
+            return E.add("missing state.", field)
+    if E.ne(saved.version, STATE_VERSION):
         return "unsupported state.version"
-    if not saved.time is Dictionary or not _number(saved.time.get("datetime")) or not _number(saved.time.get("year")):
+    if (((not (saved.time is Dictionary)) or (not _number(saved.time.get("datetime")))) or (not _number(saved.time.get("year")))):
         return "invalid state.time"
-    if not is_finite(float(saved.time.datetime) * 10.0) or saved.time.year != SimulationTime.processed_year(saved.time.datetime):
+    if E.ne(saved.time.year, SimulationTime.processed_year(saved.time.datetime)):
         return "invalid processed time"
-    if not _number(saved.speed, true) or saved.speed < 1 or saved.speed > speed_limit:
+    if saved.time.has("tick_remainder"):
+        if not E.finite(saved.time.tick_remainder) or E.ge(E.absolute(saved.time.tick_remainder), 1):
+            return "invalid fractional tick"
+    if (((not _number(saved.speed, true)) or E.lt(saved.speed, 1)) or E.gt(saved.speed, speed_limit)):
         return "invalid state.speed"
-    if not _number(saved.speed_in_year) or saved.speed_in_year != pow(10.0, saved.speed - 1):
+    if ((not _number(saved.speed_in_year)) or E.ne(saved.speed_in_year, E.power(10, E.subtract(saved.speed, 1)))):
         return "invalid state.speed_in_year"
-    if not _number(saved.energy, true) or not _number_map(saved.amount, true):
+    if data.has("simulation"):
+        var checkpoint: Variant = data.simulation
+        if not checkpoint is Dictionary or not checkpoint.get("productions") is Array:
+            return "invalid simulation checkpoint"
+        if not _number(checkpoint.get("speed"), true) or E.lt(checkpoint.speed, 1) or E.gt(checkpoint.speed, speed_limit):
+            return "invalid simulation speed"
+        for name in ["requested_clock", "active_clock"]:
+            var clock: Variant = checkpoint.get(name)
+            if not clock is Dictionary: return "invalid simulation clock"
+            if clock.is_empty(): continue
+            if not _number(clock.get("datetime")) or not _number(clock.get("year")):
+                return "invalid simulation clock"
+            if E.lt(clock.datetime, saved.time.datetime) or E.ne(clock.year, SimulationTime.processed_year(clock.datetime)):
+                return "invalid simulation clock"
+            if not E.finite(clock.get("tick_remainder", 0)) or E.ge(E.absolute(clock.get("tick_remainder", 0)), 1):
+                return "invalid simulation tick"
+        if not checkpoint.active_clock.is_empty():
+            if checkpoint.requested_clock.is_empty() or E.gt(checkpoint.active_clock.datetime, checkpoint.requested_clock.datetime):
+                return "invalid simulation clock order"
+        for command in checkpoint.productions:
+            if not command is Dictionary or not entities.has(command.get("id")) or not command.get("resource") is bool or not _number(command.get("amount")):
+                return "invalid queued production"
+            if command.resource and command.id not in ["S", "H"]: return "invalid queued resource production"
+    if ((not _number(saved.energy, true)) or (not _number_map(saved.amount, true))):
         return "invalid state resources"
-    if not saved.stats is Dictionary or not _number_map(saved.stats.get("total_amount"), true):
+    if ((not (saved.stats is Dictionary)) or (not _number_map(saved.stats.get("total_amount"), true))):
         return "invalid state.stats.total_amount"
-    if saved.amount.keys() != saved.stats.total_amount.keys():
+    if E.ne(saved.amount.keys(), saved.stats.total_amount.keys()):
         return "amount and total_amount keys differ"
-    if not saved.binds is Dictionary or not saved.batches is Dictionary:
+    if ((not (saved.binds is Dictionary)) or (not (saved.batches is Dictionary))):
         return "state.binds and state.batches must be Dictionaries"
     for owner_id in saved.binds:
-        if not saved.amount.has(owner_id) or not _number_map(saved.binds[owner_id], true):
-            return "invalid state.binds." + owner_id
+        if ((not saved.amount.has(owner_id)) or (not _number_map(saved.binds[owner_id], true))):
+            return E.add("invalid state.binds.", owner_id)
         for id in saved.binds[owner_id]:
-            if not saved.amount.has(id):
-                return "unknown bound resource " + id
+            if (not saved.amount.has(id)):
+                return E.add("unknown bound resource ", id)
     for id in saved.batches:
-        if not saved.amount.has(id) or not saved.batches[id] is Array:
-            return "invalid state.batches." + id
+        if ((not saved.amount.has(id)) or (not (saved.batches[id] is Array))):
+            return E.add("invalid state.batches.", id)
         for batch in saved.batches[id]:
-            if not batch is Dictionary or not _number(batch.get("amount"), true) or not _number(batch.get("start_year")) or not _number(batch.get("end_year")):
-                return "invalid batch in " + id
-            if batch.end_year < batch.start_year:
-                return "reversed batch interval in " + id
-            if batch.has("created_from") != batch.has("created_to"):
-                return "incomplete batch creation interval in " + id
-            if batch.has("created_from") and (not _number(batch.created_from) or not _number(batch.created_to) or batch.created_to <= batch.created_from or batch.start_year < batch.created_from):
-                return "invalid batch creation interval in " + id
-            if batch.has("processed_until") and (not _number(batch.processed_until) or batch.processed_until < batch.start_year or batch.processed_until > batch.end_year):
-                return "invalid batch.processed_until in " + id
-            if batch.has("withdraw_remainder") and (not _number(batch.withdraw_remainder) or batch.withdraw_remainder > batch.amount):
-                return "invalid batch.withdraw_remainder in " + id
+            if ((((not (batch is Dictionary)) or (not _number(batch.get("amount"), true))) or (not _number(batch.get("start_year")))) or (not _number(batch.get("end_year")))):
+                return E.add("invalid batch in ", id)
+            if E.lt(batch.end_year, batch.start_year):
+                return E.add("reversed batch interval in ", id)
+            if E.ne(batch.has("created_from"), batch.has("created_to")):
+                return E.add("incomplete batch creation interval in ", id)
+            if (batch.has("created_from") and (((((not _number(batch.created_from)) or (not _number(batch.created_to))) or E.le(batch.created_to, batch.created_from)) or E.lt(batch.start_year, batch.created_from)))):
+                return E.add("invalid batch creation interval in ", id)
+            if (batch.has("processed_until") and ((((not _number(batch.processed_until)) or E.lt(batch.processed_until, batch.start_year)) or E.gt(batch.processed_until, batch.end_year)))):
+                return E.add("invalid batch.processed_until in ", id)
+            if (batch.has("withdraw_remainder") and (((not _number(batch.withdraw_remainder)) or E.gt(batch.withdraw_remainder, batch.amount)))):
+                return E.add("invalid batch.withdraw_remainder in ", id)
     for field in ["batch_origins", "distribution", "production_remainders", "evolution_remainders", "planet_remainders", "blast_remainders", "destruction_remainders", "life_remainders", "civilization_remainders", "civilization_stats"]:
-        if not _number_map(saved[field], false, false):
-            return "invalid state." + field
-    if not _number_map(saved.auto_resources, true) or not _number_map(saved.auto_star_deficits, false, false):
+        if (not _number_map(saved[field], false, false)):
+            return E.add("invalid state.", field)
+    if ((not _number_map(saved.auto_resources, true)) or (not _number_map(saved.auto_star_deficits, false, false))):
         return "invalid automatic production state"
-    if not saved.resource_remainders is Dictionary or saved.resource_remainders.keys().size() != 2 or not saved.resource_remainders.has("basic") or not saved.resource_remainders.has("automatic"):
+    if ((((not (saved.resource_remainders is Dictionary)) or E.ne(saved.resource_remainders.keys().size(), 2)) or (not saved.resource_remainders.has("basic"))) or (not saved.resource_remainders.has("automatic"))):
         return "invalid state.resource_remainders"
     for channel in ["basic", "automatic"]:
-        if not _number_map(saved.resource_remainders[channel], false, false):
-            return "invalid state.resource_remainders." + channel
-    if not saved.ethics is Dictionary or not saved.civilization_homes is Dictionary:
+        if (not _number_map(saved.resource_remainders[channel], false, false)):
+            return E.add("invalid state.resource_remainders.", channel)
+    if ((not (saved.ethics is Dictionary)) or (not (saved.civilization_homes is Dictionary))):
         return "invalid civilization state"
     for id in saved.ethics:
-        if id not in stages or not _number_map(saved.ethics[id], true):
-            return "invalid state.ethics." + str(id)
+        if (not E.contains(stages, id) or (not _number_map(saved.ethics[id], true))):
+            return E.add("invalid state.ethics.", str(id))
         for ethic in saved.ethics[id]:
-            if ethic not in ["m", "l", "w", "d", "c", "b"]:
-                return "invalid ethic " + str(ethic)
+            if not E.contains(["m", "l", "w", "d", "c", "b"], ethic):
+                return E.add("invalid ethic ", str(ethic))
     for id in saved.civilization_homes:
-        if not _number_map(saved.civilization_homes[id], true):
+        if (not _number_map(saved.civilization_homes[id], true)):
             return "invalid civilization homes"
     return ""
 
@@ -322,7 +341,7 @@ static func _validate_payload(data: Variant, speed_limit: int, stages: Array) ->
 #region Settings
 func save_settings():
     var config = ConfigFile.new()
-    
+
     for item in Global.Settings:
         config.set_value(SETTING_SECTION, item, Global.Settings[item])
     config.save(SAVE_PATH)
@@ -330,7 +349,7 @@ func save_settings():
 func load_settings():
     var config = ConfigFile.new()
     var err = config.load(SAVE_PATH)
-    if err != OK:
+    if E.ne(err, OK):
         return false
     for item in Global.Settings:
         Global.Settings[item] = config.get_value(SETTING_SECTION, item, Global.Settings[item])

data/csv_loader.gd

@@ -0,0 +1,36 @@
+class_name CSVLoader
+
+const SPLITTER = '|'
+
+static func load(csv_text: String) -> Dictionary:
+    var result: Dictionary = {}
+
+    var lines := csv_text.strip_edges().split("\n")
+
+    if lines.size() < 2:
+        return result
+
+    var headers := lines[0].split(SPLITTER)
+
+    for i in range(1, lines.size()):
+        var line := lines[i].strip_edges()
+
+        if line.is_empty():
+            continue
+
+        var values := line.split(SPLITTER)
+
+        if values.size() != headers.size():
+            push_warning(
+                "CSV row %d has %d columns, expected %d"
+                % [i + 1, values.size(), headers.size()]
+            )
+            continue
+
+        var elem: Dictionary = {}
+
+        for j in range(headers.size()):
+            elem[headers[j].strip_edges()] = values[j].strip_edges()
+
+        result[elem[headers[0]]] = elem
+    return result

data/csv_loader.gd.uid

@@ -0,0 +1 @@
+uid://bfe1fyutcw0cx

data/owniverse_template.gd.uid

@@ -0,0 +1 @@
+uid://cunl2sqmcj1ff

data/templates.en.txt.import

@@ -1,3 +0,0 @@
-[remap]
-
-importer="keep"

data/templates.ru.txt.import

@@ -1,3 +0,0 @@
-[remap]
-
-importer="skip"

default_bus_layout.tres

@@ -0,0 +1,15 @@
+[gd_resource type="AudioBusLayout" format=3 uid="uid://b5g7p85k5do0m"]
+
+[resource]
+bus/1/name = &"Music"
+bus/1/solo = false
+bus/1/mute = false
+bus/1/bypass_fx = false
+bus/1/volume_db = 0.0
+bus/1/send = &"Master"
+bus/2/name = &"FX"
+bus/2/solo = false
+bus/2/mute = false
+bus/2/bypass_fx = false
+bus/2/volume_db = 0.0
+bus/2/send = &"Master"

simulation_rules.md

@@ -1,5 +1,12 @@
 # Эволюция звёзд Owniverse.GI
 
+Числа симуляции хранят целую часть в двух блоках int64, дробный остаток — в
+float. Весь порядок E27 сохраняет целые единицы. Возраст разделён на целые
+годы и дробную часть с шагом 10^-9 года; большие промежуточные произведения
+распределений вычисляются через `mul_div`. Границы точности, допуск переноса
+дробей и несовместимый со старым формат сохранения 4 описаны в
+[документации математики](world/owniverse/math/README.md).
+
 Механики перенесены из Owniverse.U с согласованными изменениями GI: постепенные партии, детерминированные дробные остатки, уязвимость цивилизаций до C1.2 и передача выживших планет преемнику. Баланс таблицы GI сохраняется.
 
 ## Порядок расчёта

stage/stage.gd

@@ -1,4 +1,5 @@
 extends Control
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const OWNIVERSE_ITEM = preload("uid://d3xjfxwe3w16v")
 
@@ -90,17 +91,19 @@ var g_counters: Dictionary[String, Counter] = {
 var g_active_items: Dictionary = {}
 
 var pending_page: int = -1
+var active_actions_dirty: bool = true
+var active_actions_elapsed: float = 0.0
 
 var owniverse:Owniverse = Owniverse.new()
 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 +113,7 @@ 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 +159,8 @@ 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 +170,14 @@ 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
-    
+    active_actions_dirty = true
+
     if current_item != null and current_item.item_page == item.item_page:
         current_item.set_selection(false)
 
@@ -202,21 +206,21 @@ 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
-        owniverse.production.produce_hs(item.item_id, _value)
-    
+        _value = E.multiply(9, _value) if E.gt(_value, 0) else 1
+        owniverse.request_production(item.item_id, _value, true)
+
 
 func _check_counters(delta: float) -> Array:
     var actions: Array = []
@@ -224,13 +228,13 @@ 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 +249,7 @@ 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:
@@ -270,35 +274,35 @@ 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:
-        owniverse.production.produce(item_id, action_amount)
+
+    if E.gt(action_amount, 0):
+        owniverse.request_production(item_id, action_amount)
 
 
 #endregion
@@ -310,7 +314,7 @@ func _ready() -> void:
     create_new_universe()
     load_data()
     _refresh_universe_ui()
-    
+
     g_counters.swipe.sec = 0.2
 
     for pa in page_actions:
@@ -337,6 +341,8 @@ func create_new_universe() -> void:
     description_samples.clear()
     description_rates.clear()
     description_elapsed = 0.0
+    active_actions_dirty = true
+    active_actions_elapsed = 0.0
     for label in g_item_descriptions:
         label.text = ""
     for item in owniverse_items.values():
@@ -360,10 +366,10 @@ 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)
+
+    owniverse.evolute_frame(delta, get_tree())
     indicator_elapsed += delta
     if indicator_elapsed >= 0.1:
         indicator_elapsed = 0.0
@@ -371,21 +377,27 @@ 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()
+    # Production limits are expensive (they walk the resource ledger). Refresh
+    # them when selection changes and at a modest cadence instead of every
+    # rendered frame. The simulation itself continues to run every frame.
+    active_actions_elapsed += delta
+    if active_actions_dirty or active_actions_elapsed >= 0.1:
+        active_actions_elapsed = 0.0
+        active_actions_dirty = false
+        _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 +415,14 @@ 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()
@@ -437,6 +449,7 @@ func load_data() -> bool:
     var complete: Dictionary = owniverse.state.duplicate(true)
     complete.merge(restored, true)
     owniverse.state = complete
+    owniverse.restore_frame_checkpoint(game_data.get("simulation", {}))
 
     owniverse.evolution.initialize_life_batches()
     owniverse.presentation.refresh(owniverse.state, owniverse.catalog)
@@ -459,6 +472,7 @@ func save_data() -> void:
         page = clampi(roundi(float(stage_page_scroller.scroll_horizontal) / PAGE_WIDTH), 0, PAGE_COUNT - 1)
     SaveManager.request_save("owniverse", "qwerty", {
         "state": owniverse.state,
+        "simulation": owniverse.frame_checkpoint(),
         "ui": {"current_page": page},
     })
 
@@ -493,17 +507,17 @@ 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)
 

tests/README.md

@@ -1,5 +1,36 @@
 # Проверки поэтапного переноса из Owniverse.U
 
+## Производительность на сохранении
+
+```sh
+godot --headless --path Owniverse.GI --script res://tests/benchmark_saved_state.gd -- /tmp/save.adventure.json
+```
+
+Читает диагностический JSON формата 4 в отдельные экземпляры мира и замеряет
+шесть последовательных шагов на скоростях 1, 4, 6. Запись сохранений не вызывается.
+Последним аргументом можно задать длительность шага в реальных секундах
+(по умолчанию 1/60). Это время расчёта симуляции, без отрисовки интерфейса.
+
+На диагностической копии с 120 партиями прежняя рациональная арифметика после
+оптимизации пустых окон давала 90–99 мс на шаг 1/60 секунды на скорости 6.
+После перехода на целые блоки и устранения повторного построения физических
+количеств повторный замер дал 53–58 мс. При шаге 0,1 секунды: 65–67 мс вместо
+117–138 мс. Это замеры расчёта на данной
+копии, а не обещание FPS. Для сравнения старый JSON был преобразован только
+во временный тестовый файл; в загрузчик игры миграция не добавлена.
+Разреженные сценарии сравниваются с полным расчётом в `test_short_lived_events.gd`.
+
+## Целые блоки и дробные остатки
+
+`godot --headless --path Owniverse.GI --script res://tests/test_exact_math.gd`
+
+Независимый эталон Python Fraction: 160 пар с произведением внутри E27; целые
+проверяются точно, дроби — с допуском 10^-12. Также границы int64/E27, сериализация,
+рецепты с дробными стоимостями, сохранение сумм, время и 100 циклов с меняющимися
+долями. Все остальные тесты используют числовое сравнение и сериализацию через
+`E`, а не сравнение ссылок на большие числа. Границы точности и новый формат
+сохранения описаны в [документации арифметики](../world/owniverse/math/README.md).
+
 ## Модули симуляции
 
 `godot --headless --path Owniverse.GI --script res://tests/test_module_lifecycle.gd`
@@ -61,14 +92,14 @@ godot --headless --path Owniverse.GI --script res://tests/test_time.gd
 
 Проверяются границы десятых долей года, производство ресурсов на этих границах, накопление дробного остатка, скорости 1–10 000 лет/сек, продолжение после загрузки и недопустимые интервалы.
 
-Схема состояния `0.1.1` хранит:
+Схема состояния `0.3.0` хранит:
 
 - `time.datetime` — накопленный возраст, включая необработанную дробную часть;
 - `time.year` — последний рассчитанный возраст с точностью до десятой доли года.
 
-Сохранения используют формат 2 и актуальную структуру состояния. Проверяются целостность данных, фоновая запись и повторная загрузка; поддержка и миграция прежних форматов отсутствуют.
+Сохранения используют формат 4 и актуальную структуру состояния. Проверяются целостность данных, фоновая запись и повторная загрузка; поддержка и миграция прежних форматов отсутствуют.
 
-Файл с несовместимым номером формата при загрузке переносится в `*.adventure.incompatible.bak` (при совпадении имени добавляется числовой суффикс). Игра начинает новую сессию и может сохранять её в формате 2. Прогресс несовместимого файла не переносится, исходные байты сохраняются в архиве. Ошибка архивирования, расшифровки или повреждение данных текущего формата по-прежнему блокируют перезапись.
+Файл с несовместимым номером формата при загрузке переносится в `*.adventure.incompatible.bak` (при совпадении имени добавляется числовой суффикс). Игра начинает новую сессию и может сохранять её в формате 4. Прогресс несовместимого файла не переносится, исходные байты сохраняются в архиве. Ошибка архивирования, расшифровки или повреждение данных текущего формата по-прежнему блокируют перезапись.
 
 ## Согласованные правила эволюции
 
@@ -124,3 +155,53 @@ godot --headless --path Owniverse.GI --script res://tests/test_civilization_evol
 ```
 
 Проверяются реальные коэффициенты C0.2, войны и побочный ущерб C2.0, замена планет колониями с сохранением хозяина, дипломатическое влияние, бонус периода от структур и деградация при их отсутствии. Ускоренная модель проходит все стадии C0.2 → C4.4 → Ct. Проверки контролируют сохранение населения, целочисленность этик, валидацию сохранения и детерминированное продолжение после сериализации.
+
+## Профиль цивилизаций на шестой скорости
+
+```sh
+godot --headless --path Owniverse.GI --script res://tests/benchmark_civilizations.gd -- frames=20 profile
+godot --path Owniverse.GI --script res://tests/benchmark_civilizations.gd -- ui scenario=mixed frames=10 profile
+```
+
+Сценарии `mixed`, `large`, `fragmented` заполняют все стадии и этики, синхронизируя
+переходы; `large` использует по 6e20 цивилизаций, `fragmented` — десять партий.
+Это искусственные стрессовые сценарии. `scenario=stable` использует штатные
+сроки стадий. Параметр `snapshot=/tmp/civil` сохраняет состояние каждого сценария
+для сравнения до и после изменения. UI запускает настоящую сцену со страницей
+жизни и реальным delta, без загрузки и записи сохранения игрока.
+
+`profile` выводит суммарные микросекунды и число вызовов по этапам. Вложенные
+этапы входят во время родительских; складывать их нельзя. В игре сбор выключен.
+Кэши физических количеств принадлежат отдельному миру и проверяют изменения
+количеств, вложенных привязок и индексов каталога. Кэш структуры правил не входит
+в сохранение: при изменении Claim/бонусов нужно перестроить индексы каталога,
+при изменении home в существующей таблице — invalidate_civilization_layout().
+
+После оптимизации на M4 Pro, по 20 шагов 1/60 секунды, среднее время:
+`mixed` 295 → 235 мс, `large` 666 → 539 мс, `fragmented` 359 → 282 мс.
+Полные состояния всех трёх сценариев после 20 шагов совпали до и после изменения.
+Дополнительно тест распределений сравнивает новый путь с прежним на 300
+случайных наборах, включая 1e40 и накопленные долги округления.
+
+## Расчёт между кадрами
+
+`godot --headless --path Owniverse.GI --script res://tests/test_frame_evolution.gd`
+
+Stage вызывает `evolute_frame`: транзакция получает бюджет 40 мс и уступает
+следующему кадру внутри создания партий и обработки стадий. Расчёт остаётся
+на главном потоке, состояние публикуется только после полного завершения.
+Длительность одной транзакции ограничена обычным шагом 1/60 секунды выбранной
+скорости. Запрошенное время хранится отдельно, поэтому отставание не превращается
+в один всё более тяжёлый шаг. При предельной нагрузке время симуляции может
+отставать от запрошенного; это не ограничение FPS интерфейса и не удаление событий.
+
+Производство во время транзакции выполняется после её завершения. Запрошенное
+время, активный интервал, скорость и очередь производства входят в сохранение;
+при загрузке незавершённый интервал пересчитывается с опубликованного состояния.
+Сброс мира отменяет отложенный расчёт. Тест проверяет точное совпадение непрерывного
+и распределённого расчёта, очереди, переключение скорости, восстановление и отмену.
+
+На M4 Pro, 180 кадров реального UI на шестой скорости: смешанный сценарий
+15.9 FPS (максимальный кадр 98 мс), большие количества 17.5 FPS (106 мс),
+много партий 16.3 FPS (97 мс).
+Это FPS отрисовки, а не число завершённых транзакций симуляции в секунду.

tests/benchmark_civilizations.gd

@@ -0,0 +1,74 @@
+extends SceneTree
+const Fixture = preload("res://tests/fixtures/civilization_benchmark.gd")
+
+func _initialize(): call_deferred("run")
+
+func run():
+    var ui: bool = "ui" in OS.get_cmdline_user_args()
+    var scenarios: Array = ["mixed", "large", "fragmented"]
+    var frames: int = 120
+    var step_delta: float = 1.0 / 60.0
+    for argument in OS.get_cmdline_user_args():
+        if argument.begins_with("scenario="): scenarios = [argument.trim_prefix("scenario=")]
+        if argument.begins_with("delta="): step_delta = float(argument.trim_prefix("delta="))
+        if argument.begins_with("frames="): frames = maxi(2, int(argument.trim_prefix("frames=")))
+    Engine.max_fps = 60
+    if ui: DisplayServer.window_set_size(Vector2i(540, 960))
+    for scenario in scenarios:
+        var scene
+        var stage
+        var world
+        if ui:
+            scene = load("res://world/world.tscn").instantiate()
+            stage = scene.get_node("Stage")
+            stage.owniverse.free()
+            stage.set_script(load("res://tests/fixtures/benchmark_ui_stage.gd"))
+            root.add_child(scene)
+            await process_frame
+            await process_frame
+            world = stage.owniverse
+        else:
+            world = load("res://world/owniverse/owniverse.gd").new()
+            world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+        Fixture.seed(world, root.get_node("Global"), scenario == "fragmented", scenario == "large", scenario == "stable")
+        world.profile_enabled = "profile" in OS.get_cmdline_user_args()
+        var samples: Array = []
+        if ui:
+            stage.stage_page_scroller.scroll_horizontal = 4 * stage.PAGE_WIDTH
+            for item in stage.owniverse_items.values(): item.visible = true
+            for page in stage.item_pages: page.visible = true
+            stage._set_item_description(stage.owniverse_items["C2.0"])
+            stage._refresh_universe_ui()
+            for warmup in 10: await process_frame
+            stage.measuring = true
+            for frame in frames:
+                await process_frame
+                if (frame + 1) % 10 == 0:
+                    print("%s: measured %d UI frames" % [scenario, frame + 1])
+            stage.measuring = false
+            samples = stage.process_samples
+            report(scenario + " UI frame", stage.frame_samples)
+        else:
+            for frame in frames:
+                var started: int = Time.get_ticks_usec()
+                world.evolute(step_delta)
+                samples.append((Time.get_ticks_usec() - started) / 1000.0)
+        report(scenario + (" UI handler" if ui else " CPU"), samples)
+        if ui:
+            print("Completed simulation transactions: ", world.frame_commits, "; published year: ", world.state.time.year, "; requested year: ", world.frame_clock.get("year", 0))
+        print("Statistics ", world.state.civilization_stats)
+        if world.profile_enabled: print("Profile microseconds/calls: ", world.profile)
+        for argument in OS.get_cmdline_user_args():
+            if argument.begins_with("snapshot="):
+                var file = FileAccess.open(argument.trim_prefix("snapshot=") + "-" + scenario + ".json", FileAccess.WRITE)
+                file.store_string(JSON.stringify(world.E.encode(world.state)))
+        for entity in world.catalog.entities.values(): entity.free()
+        world.free()
+        if ui: scene.free()
+    quit()
+
+func report(label: String, samples: Array):
+    var total: float = 0.0
+    for sample in samples: total += sample
+    samples.sort()
+    print("%s: mean %.2f ms, p95 %.2f ms, max %.2f ms, %.1f per second" % [label, total / samples.size(), samples[ceili(samples.size() * 0.95) - 1], samples.back(), samples.size() * 1000 / total])

tests/benchmark_civilizations.gd.uid

@@ -0,0 +1 @@
+uid://b5w4sp6eepypa

tests/benchmark_saved_state.gd

@@ -0,0 +1,47 @@
+extends SceneTree
+## Read-only benchmark. Loads a diagnostic JSON, never invokes SaveManager.
+const E = preload("res://world/owniverse/math/exact.gd")
+
+func _initialize():
+    call_deferred("run")
+
+func restore_json_integers(value):
+    # JSON parses ordinary integer tokens as float. Large integers are $exact.
+    if value is float and value == floorf(value) and absf(value) <= 9007199254740991:
+        return int(value)
+    if value is Dictionary:
+        for key in value: value[key] = restore_json_integers(value[key])
+    elif value is Array:
+        for i in value.size(): value[i] = restore_json_integers(value[i])
+    return value
+
+func run():
+    var args = OS.get_cmdline_user_args()
+    if args.is_empty():
+        print("Usage: --script tests/benchmark_saved_state.gd -- /path/to/save.adventure.json [delta_seconds]")
+        quit(1)
+        return
+    var data = JSON.parse_string(FileAccess.get_file_as_string(args[0]))
+    if not data is Dictionary or data.get("format_version") != 5:
+        push_error("Expected diagnostic JSON format 5")
+        quit(1)
+        return
+    var initial: Dictionary = E.decode(restore_json_integers(data)).state
+    var delta: float = args[1].to_float() if args.size() > 1 else 1.0 / 60.0
+    if not is_finite(delta) or delta <= 0:
+        quit(1)
+        return
+    for speed in [1, 4, 6]:
+        var world = load("res://world/owniverse/owniverse.gd").new()
+        world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+        world.state = initial.duplicate(true)
+        world.speed = speed
+        var elapsed: Array = []
+        for cycle in 6:
+            var start: int = Time.get_ticks_usec()
+            world.evolute(delta)
+            elapsed.append((Time.get_ticks_usec() - start) / 1000.0)
+        print("Speed %d, six consecutive %s-second steps, ms: %s" % [speed, delta, elapsed])
+        for entity in world.catalog.entities.values(): entity.free()
+        world.free()
+    quit()

tests/benchmark_saved_state.gd.uid

@@ -0,0 +1 @@
+uid://dji1apht4pn5y

tests/benchmark_speed6.gd

@@ -0,0 +1,40 @@
+extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
+
+func _initialize(): call_deferred("run")
+
+func run():
+    for scenario in ["ordinary", "hypergiants"]:
+        var world = load("res://world/owniverse/owniverse.gd").new()
+        world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+        for id in world.catalog.entities:
+            world.state.amount[id] = 0
+            world.state.stats.total_amount[id] = 0
+            var group: String = world.catalog.entities[id].group_as
+            if group != "":
+                world.state.amount[group] = 0
+                world.state.stats.total_amount[group] = 0
+        world.speed = 6
+        world.state.amount.S = E.of("1e24")
+        world.state.amount.H = E.of("1e24")
+        for entry in [["RD", 1234567], ["YD", 765432], ["STN", 654321]]:
+            world.state.amount[entry[0]] = entry[1]
+            world.batches.append_batch(world.state, entry[0], entry[1], 0, 0)
+        if scenario == "hypergiants":
+            world.state.amount.HG = E.of("1e20")
+            world.batches.append_batch(world.state, "HG", E.of("1e20"), 0, 0)
+            var start_year = E.subtract(world.catalog.entities.HG.lifespan, 1000)
+            world.state.time = {"datetime": start_year, "year": start_year}
+        var samples: Array = []
+        var total: int = 0
+        for frame in 600:
+            var started: int = Time.get_ticks_usec()
+            world.evolute(1.0 / 60.0)
+            var duration: int = Time.get_ticks_usec() - started
+            samples.append(duration)
+            total += duration
+        samples.sort()
+        print("Speed 6 %s: 600 frames, mean %.3f ms, p95 %.3f ms, max %.3f ms, %.1f cycles/sec" % [scenario, total / 600000.0, samples[569] / 1000.0, samples.back() / 1000.0, 600000000.0 / total])
+        for entity in world.catalog.entities.values(): entity.free()
+        world.free()
+    quit()

tests/benchmark_speed6.gd.uid

@@ -0,0 +1 @@
+uid://bboo6op14es24

tests/benchmark_ui_speed6.gd

@@ -0,0 +1,56 @@
+extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
+
+func _initialize(): call_deferred("run")
+
+func report(label: String, samples: Array):
+    var total: float = 0.0
+    var slow: int = 0
+    for sample in samples:
+        total += sample
+        if sample > 33.333: slow += 1
+    samples.sort()
+    print("%s: %d samples, mean %.3f ms, p95 %.3f ms, max %.3f ms, >33ms %d" % [label, samples.size(), total / samples.size(), samples[int(samples.size() * 0.95) - 1], samples.back(), slow])
+
+func run():
+    Engine.max_fps = 60
+    DisplayServer.window_set_size(Vector2i(540, 960))
+    print("Renderer: ", RenderingServer.get_current_rendering_method(), " adapter: ", RenderingServer.get_video_adapter_name())
+    for scenario in ["ordinary", "hypergiants"]:
+        for page in ([2] if "stars" in OS.get_cmdline_user_args() else [1, 2]):
+            var scene = load("res://world/world.tscn").instantiate()
+            var stage = scene.get_node("Stage")
+            stage.owniverse.free()
+            stage.set_script(load("res://tests/fixtures/benchmark_ui_stage.gd"))
+            root.add_child(scene)
+            await process_frame
+            await process_frame
+            var world = stage.owniverse
+            world.speed = 6
+            world.state.amount.S = E.of("1e24")
+            world.state.amount.H = E.of("1e24")
+            for entry in [["RD", 1234567], ["YD", 765432], ["STN", 654321]]:
+                world.state.amount[entry[0]] = entry[1]
+                world.batches.append_batch(world.state, entry[0], entry[1], 0, 0)
+            if scenario == "hypergiants":
+                world.state.amount.HG = E.of("1e20")
+                world.batches.append_batch(world.state, "HG", E.of("1e20"), 0, 0)
+                var start_year = E.subtract(world.catalog.entities.HG.lifespan, 1000)
+                world.state.time = {"datetime": start_year, "year": start_year}
+            stage.stage_page_scroller.scroll_horizontal = page * stage.PAGE_WIDTH
+            for item in stage.owniverse_items.values(): item.visible = true
+            if page == 2: stage._control_page(stage.owniverse_items.HG)
+            stage._set_item_description(stage.owniverse_items.HG if page == 2 else stage.owniverse_items.H)
+            stage._refresh_universe_ui()
+            for warmup in 30: await process_frame
+            stage.measuring = true
+            for frame in 600: await process_frame
+            stage.measuring = false
+            var label: String = "%s page %d" % [scenario, page]
+            report(label + " Stage CPU", stage.process_samples)
+            report(label + " frame wall", stage.frame_samples)
+            print("UI counters: H=", stage.owniverse_items.H.description.text, " HG=", stage.owniverse_items.HG.description.text, " date=", stage.date_time.text)
+            for entity in world.catalog.entities.values(): entity.free()
+            world.free()
+            scene.free()
+    quit()

tests/benchmark_ui_speed6.gd.uid

@@ -0,0 +1 @@
+uid://b3gmlo2vq6kk4

tests/fixtures/benchmark_ui_stage.gd

@@ -0,0 +1,19 @@
+extends "res://stage/stage.gd"
+
+var measuring: bool = false
+var process_samples: Array = []
+var frame_samples: Array = []
+var previous_frame: int = 0
+
+# Exercise the production Stage, with isolated state and no player-save I/O.
+func load_data() -> bool: return false
+func save_data() -> void: pass
+func _notification(_what: int) -> void: pass
+
+func _process(delta: float) -> void:
+    if not measuring: return
+    var started: int = Time.get_ticks_usec()
+    if previous_frame: frame_samples.append((started - previous_frame) / 1000.0)
+    previous_frame = started
+    super._process(delta)
+    process_samples.append((Time.get_ticks_usec() - started) / 1000.0)

tests/fixtures/benchmark_ui_stage.gd.uid

@@ -0,0 +1 @@
+uid://d1wm7nav71y3o

tests/fixtures/civilization_benchmark.gd

@@ -0,0 +1,30 @@
+extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
+
+static func seed(world, global, fragmented: bool = false, large: bool = false, stable: bool = false):
+    for id in world.catalog.entities:
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        var entity = world.catalog.entities[id]
+        if entity.group_as != "":
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
+    for id in ["RD", "BG", "TWD", "SNS", "MGT", "BH25", "SMBH", "SCD", "GEM", "LGG", "LSC", "LGF", "LGW", "LUB"]:
+        world.state.amount[id] = E.of("1e48")
+    world.state.amount.S = E.of("1e50")
+    world.state.amount.H = E.of("1e48")
+    world.state.binds.RD = {"HP": E.of("1e30"), "RP": E.of("1e30"), "GG": E.of("1e30"), "AB": E.of("1e30")}
+    var count = E.of("6e20") if large else 6000
+    for id in global.CivilizationRules:
+        if E.le(global.CivilizationRules[id].span, 0): continue
+        world.state.amount[id] = count
+        world.state.ethics[id] = {}
+        for ethic in ["m", "l", "w", "d", "c", "b"]:
+            world.state.ethics[id][ethic] = E.divide(count, 6)
+        world.state.batches[id] = []
+        var parties: int = 10 if fragmented else 1
+        for i in parties:
+            var lifespan = E.of(global.CivilizationRules[id].span) if stable else 1
+            world.state.batches[id].append({"amount": E.divide(count, parties), "created_from": i * 100, "created_to": 1000 + i * 100, "start_year": E.add(lifespan, i * 100), "end_year": E.add(lifespan, 1000 + i * 100)})
+    world.ledger.refresh_groups(world.state)
+    world.speed = 6

tests/fixtures/civilization_benchmark.gd.uid

@@ -0,0 +1 @@
+uid://bjloakx4qdpsj

tests/fixtures/legacy_quantity_math.gd

@@ -0,0 +1,59 @@
+extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
+# Frozen apportionment before the civilization performance refactor.
+
+static func allocate_whole(requests: Dictionary, limit: Variant) -> Dictionary:
+    var total: Variant = 0
+    for amount in requests.values():
+        total = E.add(total, E.floor_value(E.maximum(0, amount)))
+    var available: Variant = E.floor_value(E.minimum(E.maximum(0, limit), total))
+    var result: Dictionary = {}
+    var order: Array = []
+    var assigned: Variant = 0
+    for id in requests:
+        var expected: Variant = (E.mul_div(E.floor_value(E.maximum(0, requests[id])), available, total) if E.gt(total, 0) else 0)
+        result[id] = E.floor_value(expected)
+        assigned = E.add(assigned, result[id])
+        order.append({"id": id, "rest": E.subtract(expected, result[id])})
+    order.sort_custom(func ( a : Dictionary , b : Dictionary ) -> bool : return (E.gt(a.rest, b.rest) if E.ne(a.rest, b.rest) else E.lt(str(a.id), str(b.id))))
+    for item : Dictionary in order:
+        if E.ge(assigned, available):
+            break
+        if E.lt(result[item.id], E.floor_value(requests[item.id])):
+            result[item.id] = E.add(result[item.id], 1)
+            assigned = E.add(assigned, 1)
+    return result
+
+
+static func sum(pop: Dictionary) -> Variant:
+    var result: Variant = 0
+    for n in pop.values(): result = E.add(result, n)
+    return result
+
+
+static func split(remainders: Dictionary, key: String, count: Variant, weights: Dictionary) -> Dictionary:
+    var result: Dictionary = {}
+    var sum_weights: Variant = sum(weights)
+    if (E.le(count, 0) or E.le(sum_weights, 0)): return result
+    var expected: Dictionary = {}
+    var positive_sum: Variant = 0
+    for id in weights:
+        expected[id] = E.add(E.mul_div(count, weights[id], sum_weights), remainders.get(E.add(E.add(key, ":"), id), 0))
+        positive_sum = E.add(positive_sum, E.maximum(0, expected[id]))
+    var order: Array = []
+    var assigned: Variant = 0
+    for id in weights:
+        var normalized: Variant = (E.mul_div(E.maximum(0, expected[id]), count, positive_sum) if E.gt(positive_sum, 0) else 0)
+        result[id] = E.floor_value(normalized)
+        assigned = E.add(assigned, result[id])
+        order.append({"id": id, "rest": E.subtract(normalized, result[id])})
+    order.sort_custom(func ( a , b ) : return (E.gt(a.rest, b.rest) if E.ne(a.rest, b.rest) else E.lt(str(a.id), str(b.id))))
+    for entry in order:
+        if E.ge(assigned, count): break
+        result[entry.id] = E.add(result[entry.id], 1)
+        assigned = E.add(assigned, 1)
+    for id in weights:
+        remainders[E.add(E.add(key, ":"), id)] = E.clamp_value(E.subtract(expected[id], result[id]), E.neg(1), 1)
+    return result
+
+

tests/fixtures/legacy_quantity_math.gd.uid

@@ -0,0 +1 @@
+uid://dxsly3qpyqrjy

tests/test_action_values.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 
 var failures: int = 0
 var checks: int = 0
@@ -7,41 +8,41 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(value: bool, message: String) -> void:
-    checks += 1
-    if not value:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not value):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func run() -> void:
     var actions = load("res://ui/actions/actions.tscn").instantiate()
     root.add_child(actions)
-    for maximum in [0.0, 0.1, 0.99, 1.0, 1.9, 10.0, 100.0, 123.0, 1000.0, 10000.0, 1e9, 1.1e9, 1e150]:
+    for maximum in [0, E.of("0.1"), E.of("0.99"), 1, E.of("1.9"), 10, 100, 123, 1000, 10000, E.of("1e9"), E.of("1.1e9"), E.of("9e27")]:
         actions.set_actions("test", maximum)
         var labels: Array = []
         var values: Array = []
         for i in 5:
-            var value: float = actions.action_values[i]
+            var value: Variant = actions.action_values[i]
             var text: String = actions.action_labels[i].text
-            check(value == floorf(value) and value <= floorf(maximum), "Whole affordable request")
-            if value > 0.0:
-                check(not values.has(value) and not labels.has(text), "Unique requests and displayed labels")
+            check((E.eq(value, E.floor_value(value)) and E.le(value, E.floor_value(maximum))), "Whole affordable request")
+            if E.gt(value, 0):
+                check(((not values.has(value)) and (not labels.has(text))), "Unique requests and displayed labels")
                 values.append(value)
                 labels.append(text)
             else:
-                check(text == "" and actions.action_labels[i].get_parent().get_node("TextureButton").disabled, "Unused button blank and disabled")
-        if maximum >= 1.0: check(values.back() == floorf(maximum), "Maximum retained")
-    actions.set_actions("test", 100.0)
-    check(actions.action_values.values() == [1.0, 10.0, 100.0, 0.0, 0.0], "Exact power of ten not duplicated")
-    actions.set_actions("SMBH", 25.0, func(_request): return 25.0)
-    check(actions.action_values.values() == [25.0, 0.0, 0.0, 0.0, 0.0], "Identical SMBH previews collapse to one button")
-    actions.set_actions("step", 123.0, func(request): return floorf(request / 5.0) * 5.0)
-    check(actions.action_values.values() == [10.0, 100.0, 123.0, 0.0, 0.0], "Unproducible small requests omitted")
-    check(actions.action_labels[2].text == "120", "Recipe preview displayed while original request retained")
+                check((E.eq(text, "") and actions.action_labels[i].get_parent().get_node("TextureButton").disabled), "Unused button blank and disabled")
+        if E.ge(maximum, 1): check(E.eq(values.back(), E.floor_value(maximum)), "Maximum retained")
+    actions.set_actions("test", 100)
+    check(E.eq(actions.action_values.values(), [1, 10, 100, 0, 0]), "Exact power of ten not duplicated")
+    actions.set_actions("SMBH", 25, func ( _request ) : return 25)
+    check(E.eq(actions.action_values.values(), [25, 0, 0, 0, 0]), "Identical SMBH previews collapse to one button")
+    actions.set_actions("step", 123, func ( request ) : return E.multiply(E.floor_value(E.divide(request, 5)), 5))
+    check(E.eq(actions.action_values.values(), [10, 100, 123, 0, 0]), "Unproducible small requests omitted")
+    check(E.eq(actions.action_labels[2].text, "120"), "Recipe preview displayed while original request retained")
     var emitted: Array = []
-    actions.action_pressed.connect(func(_page, amount): emitted.append(amount))
+    actions.action_pressed.connect(func ( _page , amount ) : emitted.append(amount))
     actions._on_action_button_pressed(2)
     actions._on_action_button_pressed(4)
-    check(emitted == [123.0], "Only active button emits its matching request")
+    check(E.eq(emitted, [123]), "Only active button emits its matching request")
     actions.queue_free()
-    print("Action values: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Action values: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_async_save.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 
 var failures: int = 0
 var checks: int = 0
@@ -8,89 +9,106 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(value: bool, message: String) -> void:
-    checks += 1
-    if not value:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not value):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func run() -> void:
     var manager = load("res://autoload/save_manager.gd").new()
-    var directory: String = "/tmp/owniverse-async-%s-%s" % [OS.get_process_id(), Time.get_ticks_usec()]
+    var directory: String = ("/tmp/owniverse-async-%s-%s" % [OS.get_process_id(), Time.get_ticks_usec()])
     DirAccess.make_dir_recursive_absolute(directory)
     manager.save_directory = directory
     root.add_child(manager)
-    manager.save_completed.connect(func(filename, success, error): completions.append([filename, success, error]))
+    manager.save_completed.connect(func ( filename , success , error ) : completions.append([filename, success, error]))
     var world = load("res://world/owniverse/owniverse.gd").new()
+    world.state.energy = E.subtract(world.state.energy, 1)
+    world.state.time = preload("res://world/owniverse/simulation_time.gd").advance({"datetime": E.of("1e27")}, 0.000000001, 1)
     var data: Dictionary = {"state": world.state, "ui": {"current_page": 1}}
-    var initial_energy: float = world.state.energy
+    var initial_energy: Variant = world.state.energy
     var global: Node = root.get_node("Global")
     var old_plaintext: bool = global.save_plaintext_copy
     global.save_plaintext_copy = true
     check(manager.request_save("snapshot", "test-password", data), "Snapshot queued")
-    data.state.energy = 99.0
+    data.state.energy = 99
     data.ui.current_page = 2
     var frames: int = 0
-    var deadline: int = Time.get_ticks_msec() + 10000
-    while manager.is_saving() and Time.get_ticks_msec() < deadline:
-        frames += 1
+    var deadline: int = E.add(Time.get_ticks_msec(), 10000)
+    while (manager.is_saving() and E.lt(Time.get_ticks_msec(), deadline)):
+        frames = E.add(frames, 1)
         await process_frame
-    check(not manager.is_saving() and frames > 0, "Frames continue while save is pending")
+    check(((not manager.is_saving()) and E.gt(frames, 0)), "Frames continue while save is pending")
     var saved: Dictionary = manager.load_data("snapshot", "test-password")
-    check(saved.state.energy == initial_energy and saved.ui.current_page == 1, "Worker owns a deep snapshot")
+    check((E.eq(saved.state.energy, initial_energy) and E.eq(saved.ui.current_page, 1)), "Worker owns a deep snapshot")
+    check(E.eq(saved.state.time, world.state.time), "Encrypted save preserves exact ticks at huge age")
     var plain: Dictionary = JSON.parse_string(FileAccess.get_file_as_string(directory.path_join("snapshot.adventure.json")))
-    check(plain.state.energy == initial_energy, "Diagnostic JSON uses same snapshot")
-    check(completions.size() == 1 and completions[0][1], "Completion reports successful write")
+    check(E.eq(E.decode(plain.state.energy), initial_energy), "Diagnostic JSON uses same snapshot")
+    check(E.eq(E.decode(plain.state.time), saved.state.time), "Diagnostic JSON preserves fractional time")
+    check((E.eq(completions.size(), 1) and completions[0][1]), "Completion reports successful write")
 
     completions.clear()
-    data.state.energy = 1.0
+    data.state.energy = 1
     manager.request_save("latest", "test-password", data)
-    data.state.energy = 2.0
+    data.state.energy = 2
     manager.request_save("latest", "test-password", data)
-    data.state.energy = 3.0
+    data.state.energy = 3
     manager.request_save("latest", "test-password", data)
-    data.state.energy = 4.0
+    data.state.energy = 4
     manager.flush_saves()
-    check(completions.size() == 2, "Repeated requests coalesce behind active write")
-    check(manager.load_data("latest", "test-password").state.energy == 3.0, "Last queued snapshot wins")
+    check(E.eq(completions.size(), 2), "Repeated requests coalesce behind active write")
+    check(E.eq(manager.load_data("latest", "test-password").state.energy, 3), "Last queued snapshot wins")
+
+    var pending_clock: Dictionary = preload("res://world/owniverse/simulation_time.gd").advance(world.state.time, 0.01, 1)
+    data.simulation = {"requested_clock": pending_clock, "active_clock": pending_clock, "speed": 1, "productions": [{"id": "H", "amount": 7, "resource": true}]}
+    manager.request_save("checkpoint", "test-password", data)
+    manager.flush_saves()
+    check(E.eq(manager.load_data("checkpoint", "test-password").simulation, data.simulation), "Encrypted save preserves requested time and queued production")
+    var malformed: Dictionary = manager._snapshot("probe", "test-password", data).payload
+    malformed.simulation.productions[0].id = "missing-entity"
+    check(manager.validate_data(malformed).contains("queued production"), "Unknown queued production is rejected before resume")
+    malformed = manager._snapshot("probe", "test-password", data).payload
+    malformed.simulation.requested_clock.year = -1
+    check(manager.validate_data(malformed).contains("simulation clock"), "Invalid requested clock is rejected before resume")
+    data.erase("simulation")
 
     var incompatible_path: String = directory.path_join("incompatible.adventure")
     var incompatible = FileAccess.open_encrypted_with_pass(incompatible_path, FileAccess.WRITE, "test-password")
-    incompatible.store_var({"format_version": -1, "state": {"unknown": true}}, false)
+    incompatible.store_var({"format_version": E.neg(1), "state": {"unknown": true}}, false)
     incompatible.close()
     var original: PackedByteArray = FileAccess.get_file_as_bytes(incompatible_path)
-    var previous_archive = FileAccess.open(incompatible_path + ".incompatible.bak", FileAccess.WRITE)
+    var previous_archive = FileAccess.open(E.add(incompatible_path, ".incompatible.bak"), FileAccess.WRITE)
     previous_archive.store_string("keep previous backup")
     previous_archive.close()
     manager.blocked_saves.incompatible = true
-    check(manager.load_data("incompatible", "test-password").is_empty() and manager.last_error == "", "Unsupported format permits a fresh session")
-    check(not manager.blocked_saves.has("incompatible") and not FileAccess.file_exists(incompatible_path), "Incompatible file no longer blocks saving")
-    check(FileAccess.get_file_as_bytes(incompatible_path + ".incompatible.bak.1") == original, "Unsupported save archived without losing bytes")
-    check(FileAccess.get_file_as_string(incompatible_path + ".incompatible.bak") == "keep previous backup", "Earlier archive preserved")
+    check((manager.load_data("incompatible", "test-password").is_empty() and E.eq(manager.last_error, "")), "Unsupported format permits a fresh session")
+    check(((not manager.blocked_saves.has("incompatible")) and (not FileAccess.file_exists(incompatible_path))), "Incompatible file no longer blocks saving")
+    check(E.eq(FileAccess.get_file_as_bytes(E.add(incompatible_path, ".incompatible.bak.1")), original), "Unsupported save archived without losing bytes")
+    check(E.eq(FileAccess.get_file_as_string(E.add(incompatible_path, ".incompatible.bak")), "keep previous backup"), "Earlier archive preserved")
     check(manager.request_save("incompatible", "test-password", data), "New session can queue a save")
     manager.flush_saves()
-    check(manager.load_data("incompatible", "test-password").state == data.state, "New format saves and reloads after incompatible file")
+    check(E.eq(manager.load_data("incompatible", "test-password").state, data.state), "New format saves and reloads after incompatible file")
 
     # Expected failures below must leave the last good encrypted file intact.
-    data.state.energy = -1.0
+    data.state.energy = E.neg(1)
     manager.request_save("latest", "test-password", data)
     manager.flush_saves()
-    check(not completions.back()[1] and manager.last_error.contains("Invalid save"), "Worker validation error reaches main thread")
-    check(manager.load_data("latest", "test-password").state.energy == 3.0, "Invalid snapshot preserves previous save")
+    check(((not completions.back()[1]) and manager.last_error.contains("Invalid save")), "Worker validation error reaches main thread")
+    check(E.eq(manager.load_data("latest", "test-password").state.energy, 3), "Invalid snapshot preserves previous save")
     manager.blocked_saves.latest = true
-    check(not manager.request_save("latest", "test-password", data), "Unreadable save protection also applies to queue")
+    check((not manager.request_save("latest", "test-password", data)), "Unreadable save protection also applies to queue")
     # A valid snapshot exercises an actual I/O failure, not validation.
-    data.state.energy = 5.0
+    data.state.energy = 5
     manager.request_save("missing/failure", "test-password", data)
     manager.flush_saves()
     check(manager.last_error.contains("Cannot write"), "I/O error reported without hanging queue")
 
     manager.request_save("shutdown", "test-password", data)
-    data.state.energy = 6.0
+    data.state.energy = 6
     manager.request_save("shutdown", "test-password", data)
     manager.free()
     var reader = load("res://autoload/save_manager.gd").new()
     reader.save_directory = directory
-    check(reader.load_data("shutdown", "test-password").state.energy == 6.0, "Teardown drains final pending snapshot")
+    check(E.eq(reader.load_data("shutdown", "test-password").state.energy, 6), "Teardown drains final pending snapshot")
     reader.free()
     world.free()
     # Exercise the stage entry point too: manager tests alone do not catch a
@@ -100,12 +118,12 @@ func run() -> void:
     shared_manager.save_directory = directory
     var stage = load("res://stage/stage.gd").new()
     stage.pending_page = 2
-    stage.owniverse.state.energy = 42.0
+    stage.owniverse.state.energy = 42
     stage.save_data()
     check(shared_manager.is_saving(), "Stage queues a background save instead of waiting for disk")
-    stage.owniverse.state.energy = 43.0
+    stage.owniverse.state.energy = 43
     shared_manager.flush_saves()
-    check(shared_manager.load_data("owniverse", "qwerty").state.energy == 42.0, "Stage save writes an independent snapshot")
+    check(E.eq(shared_manager.load_data("owniverse", "qwerty").state.energy, 42), "Stage save writes an independent snapshot")
     stage.owniverse.free()
     stage.free()
     shared_manager.save_directory = original_directory
@@ -113,5 +131,5 @@ func run() -> void:
     for filename in DirAccess.get_files_at(directory):
         DirAccess.remove_absolute(directory.path_join(filename))
     DirAccess.remove_absolute(directory)
-    print("Async save: %d checks, %d failures (validation/block/I/O errors above are intentional)" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Async save: %d checks, %d failures (validation/block/I/O errors above are intentional)" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_batch_boundaries.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -37,21 +38,21 @@ func dispose(world) -> void:
 
 func run() -> void:
     var world = fixture()
-    world.state.batch_origins.LGRB = 10357034.80000000074505806
-    var boundary: float = 41215289.79999999701976776
-    for interval in [[boundary - 2.5, boundary + 2.25], [boundary, boundary + 2.0]]:
+    world.state.batch_origins.LGRB = E.of("10357034.80000000074505806")
+    var boundary: Variant = E.of("41215289.79999999701976776")
+    for interval in [[E.subtract(boundary, E.of("2.5")), E.add(boundary, E.of("2.25"))], [boundary, E.add(boundary, 2)]]:
         world.state.batches.LGRB = []
-        world.batches.append_batch(world.state, "LGRB", 100.0, interval[0], interval[1])
-        var total: float = 0.0
-        var last: float = -INF
-        for batch: Dictionary in world.state.batches.LGRB:
-            total += batch.amount
-            check(batch.created_from > last, "Batch windows advance monotonically")
-            check(batch.created_to > batch.created_from, "Positive window duration")
-            check(batch.amount >= 0.0, "No negative batch amounts")
+        world.batches.append_batch(world.state, "LGRB", 100, interval[0], interval[1])
+        var total: Variant = 0
+        var last: Variant = E.neg(INF)
+        for batch : Dictionary in world.state.batches.LGRB:
+            total = E.add(total, batch.amount)
+            check(E.gt(batch.created_from, last), "Batch windows advance monotonically")
+            check(E.gt(batch.created_to, batch.created_from), "Positive window duration")
+            check(E.ge(batch.amount, 0), "No negative batch amounts")
             last = batch.created_from
-        check(total == 100.0, "Boundary correction preserves all objects")
-        check(world.state.batches.LGRB.size() <= 7, "Finite number of windows")
+        check(E.eq(total, 100), "Boundary correction preserves all objects")
+        check(E.le(world.state.batches.LGRB.size(), 7), "Finite number of windows")
     dispose(world)
-    print("Batch boundaries: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Batch boundaries: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_civilization_evolution.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -35,130 +36,130 @@ func dispose(world) -> void:
         entity.free()
     world.free()
 
-func seed_population(world, id: String, count: float, time: float = 1.0) -> void:
-    world.state.amount.N = 0.0
+func seed_population(world, id: String, count: Variant, time: Variant = 1.0) -> void:
+    world.state.amount.N = 0
     world.state.amount[id] = count
     world.state.batches[id] = [{"amount": count, "start_year": time, "end_year": time}]
     world.evolution.initialize_life_batches()
 
-func sum_ethics(world, id: String) -> float:
-    var result: float = 0.0
-    for n in world.state.ethics.get(id, {}).values(): result += n
+func sum_ethics(world, id: String) -> Variant:
+    var result: Variant = 0
+    for n in world.state.ethics.get(id, {}).values(): result = E.add(result, n)
     return result
 
 func invariants(world) -> void:
     var physical: Dictionary = world.ledger.physical_amounts(world.state)
     for id in world.state.ethics:
-        check(sum_ethics(world, id) == physical.get(id, 0.0), "Ethics equal physical population for " + id)
+        check(E.eq(sum_ethics(world, id), physical.get(id, 0)), E.add("Ethics equal physical population for ", id))
         for n in world.state.ethics[id].values():
-            if n < 0.0 or n != floorf(n): check(false, "Invalid ethic amount")
-    check(root.get_node("SaveManager").validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Civilization state validates")
+            if (E.lt(n, 0) or E.ne(n, E.floor_value(n))): check(false, "Invalid ethic amount")
+    check(E.eq(root.get_node("SaveManager").validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Civilization state validates")
 
 func run() -> void:
     var global: Node = root.get_node("Global")
     var baseline: Dictionary = global.CivilizationRules.duplicate(true)
     var world = fixture()
-    seed_population(world, "C0.2", 60000.0)
-    world.evolution.evolve_batches(world.state, 1.0)
-    check(world.state.amount["C0.3"] > 0.0, "C0.2 actually progresses")
-    check(world.state.amount["C0.1"] > 0.0, "C0.2 actually degrades")
-    check(world.state.civilization_stats.get("wars", 0.0) == 0.0, "Table disables early wars")
-    check(world.state.amount["C0.2"] + world.state.amount["C0.3"] + world.state.amount["C0.1"] == 60000.0, "Ordinary evolution conserves population")
-    check(world.state.stats.total_amount["C0.2"] == 0.0, "Survivors do not count as new civilizations")
-    check(world.state.civilization_stats.worship > 0.0, "Worship derived from surviving ethics")
+    seed_population(world, "C0.2", 60000)
+    world.evolution.evolve_batches(world.state, 1)
+    check(E.gt(world.state.amount["C0.3"], 0), "C0.2 actually progresses")
+    check(E.gt(world.state.amount["C0.1"], 0), "C0.2 actually degrades")
+    check(E.eq(world.state.civilization_stats.get("wars", 0), 0), "Table disables early wars")
+    check(E.eq(E.add(E.add(world.state.amount["C0.2"], world.state.amount["C0.3"]), world.state.amount["C0.1"]), 60000), "Ordinary evolution conserves population")
+    check(E.eq(world.state.stats.total_amount["C0.2"], 0), "Survivors do not count as new civilizations")
+    check(E.gt(world.state.civilization_stats.worship, 0), "Worship derived from surviving ethics")
     invariants(world)
     var restored = fixture()
-    restored.state = bytes_to_var(var_to_bytes(world.state))
-    world.evolution.evolve_batches(world.state, 2100.0)
-    restored.evolution.evolve_batches(restored.state, 2100.0)
-    check(world.state == restored.state, "Save resumes deterministic ethical evolution")
+    restored.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
+    world.evolution.evolve_batches(world.state, 2100)
+    restored.evolution.evolve_batches(restored.state, 2100)
+    check(E.eq(world.state, restored.state), "Save resumes deterministic ethical evolution")
     invariants(world)
     dispose(restored)
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 1e8
-    seed_population(world, "C2.0", 60000.0)
-    world.state.amount["C1.9"] = 10000.0
+    world.state.amount.RD = 100000000
+    seed_population(world, "C2.0", 60000)
+    world.state.amount["C1.9"] = 10000
     world.evolution.initialize_life_batches()
-    world.evolution.evolve_batches(world.state, 1.0)
-    check(world.state.civilization_stats.wars > 0.0, "Wars execute when enabled")
-    check(world.state.civilization_stats.collateral > 0.0, "Wars affect previous-stage populations")
-    check(world.state.amount["C2.1"] > 0.0, "Winners and peaceful progress reach next stage")
+    world.evolution.evolve_batches(world.state, 1)
+    check(E.gt(world.state.civilization_stats.wars, 0), "Wars execute when enabled")
+    check(E.gt(world.state.civilization_stats.collateral, 0), "Wars affect previous-stage populations")
+    check(E.gt(world.state.amount["C2.1"], 0), "Winners and peaceful progress reach next stage")
     invariants(world)
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 1.0
-    world.state.binds.RD = {"HP": 5.0, "GG": 5.0, "AB": 5.0, "RP": 5.0}
-    seed_population(world, "C1.6", 60000.0)
-    for row: Dictionary in global.CivilizationRules["C1.6"].ethics.values(): row.degradation = "0"
-    world.evolution.evolve_batches(world.state, 1.0)
+    world.state.amount.RD = 1
+    world.state.binds.RD = {"HP": 5, "GG": 5, "AB": 5, "RP": 5}
+    seed_population(world, "C1.6", 60000)
+    for row : Dictionary in global.CivilizationRules["C1.6"].ethics.values(): row.degradation = "0"
+    world.evolution.evolve_batches(world.state, 1)
     var after: Dictionary = world.ledger.physical_amounts(world.state)
-    check(world.state.civilization_stats.colonies == 20.0, "Colonization limited to real targets")
-    check(after.HP + after.GG + after.AB + after.RP == 0.0, "Colonized objects consumed once")
-    check(world.state.binds.RD.get("C1.4", 0.0) == 20.0, "Colonies retain target host and use two-stages-earlier level")
-    var totals: float = 0.0
+    check(E.eq(world.state.civilization_stats.colonies, 20), "Colonization limited to real targets")
+    check(E.eq(E.add(E.add(E.add(after.HP, after.GG), after.AB), after.RP), 0), "Colonized objects consumed once")
+    check(E.eq(world.state.binds.RD.get("C1.4", 0), 20), "Colonies retain target host and use two-stages-earlier level")
+    var totals: Variant = 0
     for id in after:
-        if world.catalog.entities[id].group_as == "Planet": totals += after[id]
-    check(totals == 60020.0, "Colonization replaces planets, does not create extra worlds")
+        if E.eq(world.catalog.entities[id].group_as, "Planet"): totals = E.add(totals, after[id])
+    check(E.eq(totals, 60020), "Colonization replaces planets, does not create extra worlds")
     invariants(world)
     dispose(world)
 
     global.CivilizationRules = baseline.duplicate(true)
     world = fixture()
-    world.state.amount.RD = 1e25
-    world.state.amount.BG = 1e25
-    world.state.amount.TWD = 1e25
-    world.state.amount.SNS = 1e25
-    world.state.amount.MGT = 1e25
-    world.state.amount.BH25 = 1e25
-    world.state.amount.SMBH = 1e26
+    world.state.amount.RD = E.of("1e25")
+    world.state.amount.BG = E.of("1e25")
+    world.state.amount.TWD = E.of("1e25")
+    world.state.amount.SNS = E.of("1e25")
+    world.state.amount.MGT = E.of("1e25")
+    world.state.amount.BH25 = E.of("1e25")
+    world.state.amount.SMBH = E.of("1e26")
     for id in world.catalog.entities:
-        if world.catalog.entities[id].claim != "": world.state.amount[id] = 1e12
+        if E.ne(world.catalog.entities[id].claim, ""): world.state.amount[id] = E.of("1e12")
     # Accelerated deterministic fixture traverses every enabled stage, including Ct.
     for id in global.CivilizationRules:
-        if id == "Ct": continue
+        if E.eq(id, "Ct"): continue
         global.CivilizationRules[id].fights = false
         global.CivilizationRules[id].colonizes = false
         global.CivilizationRules[id].diplomacy = false
-        for row: Dictionary in global.CivilizationRules[id].ethics.values():
+        for row : Dictionary in global.CivilizationRules[id].ethics.values():
             row.progress = "1"
             row.degradation = "0"
-        world.catalog.entities[id].lifespan = 1.0
-        world.catalog.entities[id].lifespan_delta = 1.0
-        global.CivilizationRules[id].span = 1.0
-    seed_population(world, "C0.2", 6.0)
-    world.evolution.evolve_batches(world.state, 1000.0)
-    check(world.state.amount.Ct == 6.0, "Complete C0.2 -> C4.4 -> Ct chain runs")
-    check(not world.state.batches.has("Ct"), "Transcendence is terminal")
+        world.catalog.entities[id].lifespan = 1
+        world.catalog.entities[id].lifespan_delta = 1
+        global.CivilizationRules[id].span = 1
+    seed_population(world, "C0.2", 6)
+    world.evolution.evolve_batches(world.state, 1000)
+    check(E.eq(world.state.amount.Ct, 6), "Complete C0.2 -> C4.4 -> Ct chain runs")
+    check((not world.state.batches.has("Ct")), "Transcendence is terminal")
     invariants(world)
     dispose(world)
     global.CivilizationRules = baseline
 
     world = fixture()
-    world.state.amount.RD = 10000.0
-    world.state.amount.SCS = 1.0
-    world.state.amount["C2.4"] = 1.0
+    world.state.amount.RD = 10000
+    world.state.amount.SCS = 1
+    world.state.amount["C2.4"] = 1
     world.evolution.initialize_life_batches()
-    var span: float = world.state.batches["C2.4"][0].start_year
-    check(is_equal_approx(span, 20000.0 / 3.6), "Structure bonus shortens newly registered lifespan")
+    var span: Variant = world.state.batches["C2.4"][0].start_year
+    check(E.near(span, E.divide(20000, E.of("3.6"))), "Structure bonus shortens newly registered lifespan")
     dispose(world)
     var evolution = load("res://world/owniverse/civilization_evolution.gd")
-    var balanced: Dictionary = {"m": 10000.0, "l": 10000.0, "w": 10000.0, "d": 10000.0, "c": 10000.0, "b": 10000.0}
+    var balanced: Dictionary = {"m": 10000, "l": 10000, "w": 10000, "d": 10000, "c": 10000, "b": 10000}
     var neutral: Dictionary = evolution.drift({}, "test", balanced, global.CivilizationRules["C2.0"].ethics)
     var diplomatic: Dictionary = evolution.drift({}, "test", balanced, global.CivilizationRules["C2.0"].ethics, true)
-    check(neutral == balanced, "Ordinary drift preserves balanced ethics")
-    check(diplomatic.d > diplomatic.w, "Diplomacy uses per-ethic influence")
-    check(evolution.total(diplomatic) == 60000.0, "Diplomacy conserves population")
+    check(E.eq(neutral, balanced), "Ordinary drift preserves balanced ethics")
+    check(E.gt(diplomatic.d, diplomatic.w), "Diplomacy uses per-ethic influence")
+    check(E.eq(evolution.total(diplomatic), 60000), "Diplomacy conserves population")
 
     world = fixture()
-    world.state.amount.RD = 1e15
-    world.state.amount.BG = 1e15
-    world.state.amount["C3.0"] = 6.0
+    world.state.amount.RD = E.of("1e15")
+    world.state.amount.BG = E.of("1e15")
+    world.state.amount["C3.0"] = 6
     world.evolution.initialize_life_batches()
-    check(world.state.amount["C3.0"] == 0.0 and world.state.amount["C2.9"] == 6.0, "Missing mandatory structures degrade existing civilizations")
+    check((E.eq(world.state.amount["C3.0"], 0) and E.eq(world.state.amount["C2.9"], 6)), "Missing mandatory structures degrade existing civilizations")
     invariants(world)
     dispose(world)
-    print("Civilization evolution: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Civilization evolution: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_civilization_state.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -38,97 +39,97 @@ func dispose(world) -> void:
 func run() -> void:
     var world = fixture()
     var global: Node = root.get_node("Global")
-    check(global.CivilizationRules.size() == 44, "Load all ethical civilization stages")
-    for row: Dictionary in global.CivilizationRules.values():
-        check(row.ethics.size() == 6 or row.span == 0.0, "Every ethical stage has six rules")
-    world.state.amount.RD = 12.0
-    world.state.amount["C0.2"] = 8.0
-    world.state.binds.RD = {"C2.0": 12.0, "C1.9": 3.0}
+    check(E.eq(global.CivilizationRules.size(), 44), "Load all ethical civilization stages")
+    for row : Dictionary in global.CivilizationRules.values():
+        check((E.eq(row.ethics.size(), 6) or E.eq(row.span, 0)), "Every ethical stage has six rules")
+    world.state.amount.RD = 12
+    world.state.amount["C0.2"] = 8
+    world.state.binds.RD = {"C2.0": 12, "C1.9": 3}
     world.evolution.initialize_life_batches()
-    check(world.state.amount["C2.0"] == 12.0 and world.state.binds.RD["C2.0"] == 0.0, "Old space civilizations detach without loss")
-    check(world.state.binds.RD["C1.9"] == 3.0, "Planetary civilizations retain their host")
-    check(world.state.ethics["C0.2"] == {"m": 2.0, "l": 2.0, "w": 1.0, "d": 1.0, "c": 1.0, "b": 1.0}, "Migration uses equal ethics and deterministic remainder")
-    check(world.state.ethics["C2.0"].values().all(func(n): return n == 2.0), "Bound civilization ethics count physical population")
+    check((E.eq(world.state.amount["C2.0"], 12) and E.eq(world.state.binds.RD["C2.0"], 0)), "Old space civilizations detach without loss")
+    check(E.eq(world.state.binds.RD["C1.9"], 3), "Planetary civilizations retain their host")
+    check(E.eq(world.state.ethics["C0.2"], {"m": 2, "l": 2, "w": 1, "d": 1, "c": 1, "b": 1}), "Migration uses equal ethics and deterministic remainder")
+    check(world.state.ethics["C2.0"].values().all(func ( n ) : return E.eq(n, 2)), "Bound civilization ethics count physical population")
     var before: Dictionary = world.state.duplicate(true)
     world.evolution.initialize_life_batches()
-    check(world.state == before, "Repeated initialization preserves ethics")
-    world.state.ethics["C0.2"] = {"m": 8.0, "l": 0.0, "w": 0.0, "d": 0.0, "c": 0.0, "b": 0.0}
+    check(E.eq(world.state, before), "Repeated initialization preserves ethics")
+    world.state.ethics["C0.2"] = {"m": 8, "l": 0, "w": 0, "d": 0, "c": 0, "b": 0}
     world.evolution.initialize_life_batches()
-    check(world.state.ethics["C0.2"].m == 8.0, "Existing unequal distribution is retained")
-    world.state.amount["C0.2"] = 3.0
+    check(E.eq(world.state.ethics["C0.2"].m, 8), "Existing unequal distribution is retained")
+    world.state.amount["C0.2"] = 3
     world.evolution.initialize_life_batches()
-    check(world.state.ethics["C0.2"].m == 3.0, "Losses reduce ethics without inventing population")
-    check(root.get_node("SaveManager").validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Ethics state validates")
+    check(E.eq(world.state.ethics["C0.2"].m, 3), "Losses reduce ethics without inventing population")
+    check(E.eq(root.get_node("SaveManager").validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Ethics state validates")
     var restored = fixture()
-    restored.state = bytes_to_var(var_to_bytes(world.state))
+    restored.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
     restored.evolution.initialize_life_batches()
-    check(restored.state == world.state, "Save roundtrip preserves ethics and ownership")
+    check(E.eq(restored.state, world.state), "Save roundtrip preserves ethics and ownership")
     dispose(restored)
     dispose(world)
     world = fixture()
-    world.state.amount.RD = 10.0
-    for row: Dictionary in global.CivilizationRules["C1.9"].ethics.values():
+    world.state.amount.RD = 10
+    for row : Dictionary in global.CivilizationRules["C1.9"].ethics.values():
         row.progress = "1"
         row.degradation = "0"
         row.colonization = "0"
-    world.state.binds.RD = {"C1.9": 10.0}
-    world.state.batches["C1.9"] = [{"amount": 10.0, "start_year": 1.0, "end_year": 1.0}]
-    world.evolution.evolve_batches(world.state, 1.0)
-    check(world.state.amount["C2.0"] == 10.0 and world.state.binds.RD.get("C2.0", 0.0) == 0.0, "Space successor does not inherit planetary binding")
+    world.state.binds.RD = {"C1.9": 10}
+    world.state.batches["C1.9"] = [{"amount": 10, "start_year": 1, "end_year": 1}]
+    world.evolution.evolve_batches(world.state, 1)
+    check((E.eq(world.state.amount["C2.0"], 10) and E.eq(world.state.binds.RD.get("C2.0", 0), 0)), "Space successor does not inherit planetary binding")
     dispose(world)
     var capacity = load("res://world/owniverse/civilization_state.gd")
     world = fixture()
-    world.state.amount.RD = 10.0
-    world.state.amount["C2.0"] = 8.0
+    world.state.amount.RD = 10
+    world.state.amount["C2.0"] = 8
     var budget: Dictionary = capacity.stellar_budget(world, world.state, global.CivilizationRules)
-    check(capacity.admit_transition(budget, global.CivilizationRules, "C1.9", "C2.0", 5.0) == 2.0, "Growth consumes only remaining stellar capacity")
-    check(capacity.admit_transition(budget, global.CivilizationRules, "C1.9", "C2.0", 5.0) == 0.0, "A reservation cannot be spent twice")
-    world.state.amount["C2.0"] = 1.0
+    check(E.eq(capacity.admit_transition(budget, global.CivilizationRules, "C1.9", "C2.0", 5), 2), "Growth consumes only remaining stellar capacity")
+    check(E.eq(capacity.admit_transition(budget, global.CivilizationRules, "C1.9", "C2.0", 5), 0), "A reservation cannot be spent twice")
+    world.state.amount["C2.0"] = 1
     budget = capacity.stellar_budget(world, world.state, global.CivilizationRules)
-    check(capacity.admit_transition(budget, global.CivilizationRules, "C2.0", "C2.1", 1.0) == 1.0, "A transition reuses the source reservation")
-    check(budget.free.DwStar == 0.0, "C2.1 reserves ten dwarf stars")
-    world.state.amount["C2.0"] = 0.0
-    world.state.binds.SC = {"RD": 10.0}
+    check(E.eq(capacity.admit_transition(budget, global.CivilizationRules, "C2.0", "C2.1", 1), 1), "A transition reuses the source reservation")
+    check(E.eq(budget.free.DwStar, 0), "C2.1 reserves ten dwarf stars")
+    world.state.amount["C2.0"] = 0
+    world.state.binds.SC = {"RD": 10}
     budget = capacity.stellar_budget(world, world.state, global.CivilizationRules)
-    check(budget.capacity.DwStar == 20.0, "Stars inside structures are counted once")
+    check(E.eq(budget.capacity.DwStar, 20), "Stars inside structures are counted once")
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 12.0
-    world.state.amount["C2.1"] = 2.0
-    world.state.amount["C2.0"] = 5.0
+    world.state.amount.RD = 12
+    world.state.amount["C2.1"] = 2
+    world.state.amount["C2.0"] = 5
     world.evolution.initialize_life_batches()
-    check(world.state.amount["C2.1"] == 1.0 and world.state.amount["C2.0"] == 2.0, "Shared budget supports advanced civilizations first")
-    check(world.state.binds.RD["C1.9"] == 4.0, "Excess cascades to supported planetary stage")
+    check((E.eq(world.state.amount["C2.1"], 1) and E.eq(world.state.amount["C2.0"], 2)), "Shared budget supports advanced civilizations first")
+    check(E.eq(world.state.binds.RD["C1.9"], 4), "Excess cascades to supported planetary stage")
     var snapshot: Dictionary = world.state.duplicate(true)
     world.evolution.initialize_life_batches()
-    check(world.state == snapshot, "Capacity enforcement is idempotent")
-    world.state.amount.RD = 0.0
+    check(E.eq(world.state, snapshot), "Capacity enforcement is idempotent")
+    world.state.amount.RD = 0
     world.evolution.initialize_life_batches()
-    check(world.state.amount["C2.1"] == 0.0 and world.state.amount["C2.0"] == 0.0, "Vanished stars force all unsupported space civilizations down")
-    check(world.ledger.physical_amounts(world.state)["C1.9"] == 7.0, "Forced degradation conserves civilizations")
+    check((E.eq(world.state.amount["C2.1"], 0) and E.eq(world.state.amount["C2.0"], 0)), "Vanished stars force all unsupported space civilizations down")
+    check(E.eq(world.ledger.physical_amounts(world.state)["C1.9"], 7), "Forced degradation conserves civilizations")
     dispose(world)
 
     world = fixture()
-    world.state.amount.LGW = 20.0
-    world.state.amount.SMBH = 2.0e22
-    world.state.amount["C4.2"] = 3.0
+    world.state.amount.LGW = 20
+    world.state.amount.SMBH = E.of("2.0e22")
+    world.state.amount["C4.2"] = 3
     world.evolution.initialize_life_batches()
-    check(world.state.amount["C4.2"] == 2.0, "SMBH capacity uses stellar mass equivalent")
-    check(world.ledger.physical_amounts(world.state)["C1.9"] == 1.0, "Unsupported civilization degrades through missing habitat families")
-    check(root.get_node("SaveManager").validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Capacity-limited state validates")
+    check(E.eq(world.state.amount["C4.2"], 2), "SMBH capacity uses stellar mass equivalent")
+    check(E.eq(world.ledger.physical_amounts(world.state)["C1.9"], 1), "Unsupported civilization degrades through missing habitat families")
+    check(E.eq(root.get_node("SaveManager").validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Capacity-limited state validates")
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 2.0
-    for row: Dictionary in global.CivilizationRules["C1.9"].ethics.values():
+    world.state.amount.RD = 2
+    for row : Dictionary in global.CivilizationRules["C1.9"].ethics.values():
         row.progress = "1"
         row.degradation = "0"
         row.colonization = "0"
-    world.state.binds.RD = {"C1.9": 5.0}
-    world.state.batches["C1.9"] = [{"amount": 5.0, "start_year": 1.0, "end_year": 1.0}]
-    world.evolution.evolve_batches(world.state, 1.0)
-    check(world.state.amount["C2.0"] == 2.0 and world.state.binds.RD["C1.9"] == 3.0, "Unfunded transition retains the original planetary civilization")
+    world.state.binds.RD = {"C1.9": 5}
+    world.state.batches["C1.9"] = [{"amount": 5, "start_year": 1, "end_year": 1}]
+    world.evolution.evolve_batches(world.state, 1)
+    check((E.eq(world.state.amount["C2.0"], 2) and E.eq(world.state.binds.RD["C1.9"], 3)), "Unfunded transition retains the original planetary civilization")
     dispose(world)
-    print("Civilization state: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Civilization state: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_descriptions.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -39,39 +40,39 @@ func run() -> void:
     var global: Node = root.get_node("Global")
     var description = load("res://world/owniverse/item_description.gd")
     var world = fixture()
-    world.state.amount.H = 8.0
-    world.state.amount.He = 2.0
+    world.state.amount.H = 8
+    world.state.amount.He = 2
     for locale in ["en", "ru"]:
         global.Locale = locale
         var text: String = description.render(world, global, "RD")
-        check(text.contains("[b]") and not text.contains("%value"), "Localized template resolved: " + locale)
-        check(text.contains("#40cc40"), "Affordable cost green: " + locale)
-        check(text.contains("4.0000E+10"), "Lifespan substituted: " + locale)
+        check((text.contains("[b]") and (not text.contains("%value"))), E.add("Localized template resolved: ", locale))
+        check(text.contains("#40cc40"), E.add("Affordable cost green: ", locale))
+        check(text.contains("40 000 000 000"), E.add("Lifespan substituted: ", locale))
         text = description.render(world, global, "He")
-        check(text.contains("He: 20.00% / H: 80.00%") and not text.contains("%value"), "Helium metadata and mixture: " + locale)
+        check((text.contains("He: 20.00% / H: 80.00%") and (not text.contains("%value"))), E.add("Helium metadata and mixture: ", locale))
         text = description.render(world, global, "Shovelin", "Force")
-        check(text.count("]—[/color]") == 4, "Missing force levels use dash: " + locale)
+        check(E.eq(text.count("]—[/color]"), 4), E.add("Missing force levels use dash: ", locale))
         text = description.render(world, global, "YD")
-        check(text.contains("#ff6060"), "Insufficient cost red: " + locale)
+        check(text.contains("#ff6060"), E.add("Insufficient cost red: ", locale))
     var reordered: Dictionary = {"text": "%value0% / %value1%", "value0": "lifespan", "value1": "amount"}
-    check(global.render_template(reordered, {"amount": "12", "lifespan": "99"}) == "99 / 12", "Metadata chooses variables, not fixed argument positions")
-    world.state.amount.RD = 2.0
-    world.state.binds.G = {"RD": 3.0, "HP": 7.0}
-    var values: Dictionary = description.variables(world, global, "RD", -2.0)
-    check(values.amount.contains("2") and values.amount.contains("(5)") and values.amount.contains("#888888"), "Free and total counts with gray binding total")
-    check(values.amount.contains("#ff6060") and values.amount.contains("−2.0"), "Real-time decrease red")
+    check(E.eq(global.render_template(reordered, {"amount": "12", "lifespan": "99"}), "99 / 12"), "Metadata chooses variables, not fixed argument positions")
+    world.state.amount.RD = 2
+    world.state.binds.G = {"RD": 3, "HP": 7}
+    var values: Dictionary = description.variables(world, global, "RD", E.neg(2))
+    check(((values.amount.contains("2") and values.amount.contains("(5)")) and values.amount.contains("#888888")), "Free and total counts with gray binding total")
+    check((values.amount.contains("#ff6060") and values.amount.contains("−2.0")), "Real-time decrease red")
     values = description.variables(world, global, "HP")
-    check(values.amount == "7", "Planet description includes bound planets")
-    world.state.amount.EON1 = 2.0
-    world.state.binds.G.EON2 = 3.0
+    check(E.eq(values.amount, "7"), "Planet description includes bound planets")
+    world.state.amount.EON1 = 2
+    world.state.binds.G.EON2 = 3
     var saved_state: Dictionary = world.state.duplicate(true)
     var counters: Dictionary = world.presentation.amounts(world.state, world.catalog)
-    check(counters.HP == 7.0 and counters.LP == 5.0 and counters.Planet == 12.0, "Planet counters include bound objects and aggregate eons")
-    check(counters.RD == 2.0, "Star counters retain available quantity")
-    check(world.state == saved_state, "Reading counters does not mutate simulation")
-    check(world.presentation.amounts(world.state, world.catalog, true).HP == 0.0, "Produced counters remain independent of current population")
-    values = description.variables(world, global, "RD", 2.0)
-    check(values.amount.contains("#40cc40") and values.amount.contains("+2.0"), "Increase green")
+    check(((E.eq(counters.HP, 7) and E.eq(counters.LP, 5)) and E.eq(counters.Planet, 12)), "Planet counters include bound objects and aggregate eons")
+    check(E.eq(counters.RD, 2), "Star counters retain available quantity")
+    check(E.eq(world.state, saved_state), "Reading counters does not mutate simulation")
+    check(E.eq(world.presentation.amounts(world.state, world.catalog, true).HP, 0), "Produced counters remain independent of current population")
+    values = description.variables(world, global, "RD", 2)
+    check((values.amount.contains("#40cc40") and values.amount.contains("+2.0")), "Increase green")
     var stage_script = load("res://stage/stage.gd")
     check(stage_script.can_instantiate(), "Stage integration compiles")
     var stage = stage_script.new()
@@ -81,9 +82,9 @@ func run() -> void:
     stage.g_item_descriptions = [label]
     stage.description_targets[0] = {"id": "RD", "category": "Entity"}
     stage._refresh_descriptions()
-    check(label.bbcode_enabled and label.text.contains("Красный карлик"), "Stage displays localized rich text")
+    check((label.bbcode_enabled and label.text.contains("Красный карлик")), "Stage displays localized rich text")
     stage._update_descriptions(0.25)
-    world.state.amount.RD += 1.0
+    world.state.amount.RD = E.add(world.state.amount.RD, 1)
     stage._update_descriptions(0.25)
     check(label.text.contains("+4.0"), "Selected description refreshes with rate per real second")
     global.Locale = "en"
@@ -92,5 +93,5 @@ func run() -> void:
     label.free()
     stage.free()
     dispose(world)
-    print("Descriptions: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Descriptions: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_dynamic_math.gd

@@ -0,0 +1,72 @@
+extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
+const B = preload("res://world/owniverse/math/big_integer.gd")
+var checks: int = 0
+var failures: int = 0
+
+func verify(condition: bool, label: String):
+    checks += 1
+    if not condition:
+        failures += 1
+        push_error(label)
+
+func _initialize():
+    call_deferred("run")
+
+func run():
+    var rng = RandomNumberGenerator.new()
+    rng.seed = 619
+    for trial in 300:
+        var n: int = rng.randi_range(0, 100)
+        var m: int = rng.randi_range(1, 100)
+        var a: int = rng.randi_range(0, 1000)
+        var b: int = rng.randi_range(0, 1000)
+        var expected: int = 0
+        for i in n: expected += (a * i + b) / m
+        verify(E.eq(E.floor_sum(n, a, b, m), expected), "floor sum matches explicit windows")
+    var huge = E.of("1e40")
+    verify(E.lt(E.of("1e1000"), INF), "finite huge number is below positive infinity")
+    verify(E.gt(E.of("-1e1000"), -INF), "finite huge negative number is above negative infinity")
+    verify(E.gt(INF, E.of("1e1000")), "positive infinity is above finite huge number")
+    verify(not E.eq(E.of("1e1000"), INF), "huge number is not infinity")
+    verify(E.eq(E.floor_sum(huge, 2, 1, 2), E.divide(E.multiply(huge, E.subtract(huge, 1)), 2)), "floor sum supports huge window counts")
+    var rows = JSON.parse_string(FileAccess.get_file_as_string("res://tests/fixtures/big_integer_oracle.json"))
+    for row in rows:
+        var a: Array = B.parse(row[0])
+        var b: Array = B.parse(row[1])
+        var qr: Array = B.divmod(a, b)
+        verify(B.decimal(B.add(a, b)) == row[2], "independent big sum")
+        verify(B.decimal(B.multiply(a, b)) == row[3], "independent big product")
+        verify(B.decimal(qr[0]) == row[4], "independent big quotient")
+        verify(B.decimal(qr[1]) == row[5], "independent big remainder")
+        verify(E.fixed(E.multiply(E.of(row[0]), E.of(row[1]))) == row[3], "dynamic product")
+        verify(E.eq(E.mul_div(E.of(row[0]), E.of(row[1]), E.of(row[1])), E.of(row[0])), "fused conservation")
+    for text in ["9223372036854775807", "-9223372036854775808", "9223372036854775808", "-9223372036854775809", "1e300", "1e1000"]:
+        var n = E.of(text)
+        verify(E.eq(E.subtract(E.add(n, 1), n), 1), "unit preserved at " + text)
+        verify(E.eq(E.decode(JSON.parse_string(JSON.stringify(E.encode(n)))), n), "round trip " + text)
+    for text in ["1.25", "-1.25", "123.5"]:
+        verify(E.approx(E.of(text)) == float(text), "approx fraction " + text)
+    verify(not E.valid_encoded({"$exact": [[], "0000000000000000", 1]}), "reject empty blocks")
+    verify(not E.valid_encoded({"$exact": [[1, 0], "0000000000000000", 1]}), "reject noncanonical blocks")
+    verify(E.gt(E.power(E.of("1e400"), -1), 0) == false, "float fraction underflows beyond its range")
+    verify(absf(E.approx(E.logarithm(E.of("1e1000"))) - 1000 * log(10.0)) < 1e-8, "logarithm beyond float range")
+    verify(E.eq(E.square_root(E.of("1e1000")), E.of("1e500")), "square root beyond float range")
+    var world = load("res://world/owniverse/owniverse.gd").new()
+    world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+    for id in world.catalog.entities:
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        var group: String = world.catalog.entities[id].group_as
+        if group != "":
+            world.state.amount[group] = 0
+            world.state.stats.total_amount[group] = 0
+    world.state.amount.H = E.of("1e1000")
+    world.state.amount.S = E.of("1e1000")
+    var environment: Dictionary = world.environment.stellar_environment(world.state)
+    verify(E.finite(environment.density) and E.gt(environment.density, 0), "huge density remains finite")
+    verify(E.near(environment.blast, 1), "huge geometric ratio stays valid")
+    for entity in world.catalog.entities.values(): entity.free()
+    world.free()
+    print("Dynamic math: %d checks, %d failures" % [checks, failures])
+    quit(1 if failures else 0)

tests/test_dynamic_math.gd.uid

@@ -0,0 +1 @@
+uid://8vkudj0tlnng

tests/test_exact_math.gd

@@ -0,0 +1,101 @@
+extends SceneTree
+
+const E = preload("res://world/owniverse/math/exact.gd")
+const Q = preload("res://world/owniverse/quantity_math.gd")
+const Clock = preload("res://world/owniverse/simulation_time.gd")
+var checks: int = 0
+var failures: int = 0
+
+func _initialize():
+    call_deferred("run")
+
+func check(actual, expected: String, label: String):
+    checks += 1
+    if str(actual) != expected:
+        failures += 1
+        push_error(label + ": " + str(actual) + " != " + expected)
+
+func check_number(actual, expected: String, label: String):
+    var reference = E.of(expected)
+    checks += 1
+    if E.gt(E.absolute(E.subtract(actual, reference)), E.of("1e-12")):
+        failures += 1
+        push_error(label + ": " + str(actual) + " != " + expected)
+
+func run():
+    # Expected strings were generated independently with Python fractions.Fraction.
+    var cases = JSON.parse_string(FileAccess.get_file_as_string("res://tests/fixtures/exact_oracle.json"))
+    for row in cases:
+        var a = E.of(row[0])
+        var b = E.of(row[1])
+        check_number(E.add(a, b), row[2], "sum")
+        check_number(E.subtract(a, b), row[3], "difference")
+        check_number(E.multiply(a, b), row[4], "product")
+        check_number(E.divide(a, b), row[5], "quotient")
+        check(E.floor_value(E.divide(a, b)), row[6], "floor")
+    for text in ["9223372036854775807", "-9223372036854775808", "9007199254740993", "1000000000000000000000000001", "-1/10000000000000"]:
+        var value = E.of(text)
+        check(E.eq(E.decode(JSON.parse_string(JSON.stringify(E.encode(value)))), value), "true", "JSON round trip")
+    check(E.add(E.of("9223372036854775807"), 1), "9223372036854775808", "int64 overflow promoted")
+    check(E.subtract(E.of("-9223372036854775808"), 1), "-9223372036854775809", "int64 underflow promoted")
+    check(Q.production_step([E.of("1e27")]), "1", "large integral recipe")
+    check(Q.production_step([E.of("1e-13")]), "10000000000000", "tiny fractional recipe")
+    var count = E.of("1000000000000000000000000001")
+    var allocation = Q.allocate_whole({"a": count, "b": count, "c": count}, count)
+    check(Q.sum(allocation), str(count), "allocation conserves every unit")
+    check(allocation.a, "333333333333333333333333334", "deterministic remainder")
+    var clock = Clock.advance({"datetime": E.of("1e27")}, 0.000000001, 1)
+    check_number(E.subtract(clock.datetime, E.of("1e27")), "1/1000000000", "single tick at huge age")
+    var world = load("res://world/owniverse/owniverse.gd").new()
+    world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+    for id in world.catalog.entities:
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        var group: String = world.catalog.entities[id].group_as
+        if group != "":
+            world.state.amount[group] = 0
+            world.state.stats.total_amount[group] = 0
+    world.production.produce_hs("H", 1)
+    check(world.state.energy, "999999999999999999999999999", "spend one energy")
+    var life = world.life.life_products(world.state, world.catalog.entities.EON5, count)
+    check(Q.sum(life), str(count), "life conservation at 1e27")
+    check(E.bounded(count), str(count), "integer counts never quantized")
+    check(E.mul_div(E.of("1e27"), 15, 100), "150000000000000000000000000", "exact percentage")
+    check(E.mul_div(count, count, count), str(count), "fused product beyond storage range")
+    var limit = E.of("1e27")
+    check(E.floor_value(E.mul_div(E.subtract(limit, 1), E.subtract(limit, 3), E.subtract(limit, 2))), "999999999999999999999999997", "fused ratio immediately below whole boundary")
+    check(E.floor_value(E.divide(E.MIN_INT, -3)), "3074457345618258602", "MIN_INT division preserves quotient")
+    check(E.floor_value(E.divide(-10, 3)), "-4", "native negative fractional division")
+    check(E.mul_div(E.MAX_INT, 0, 7), "0", "native zero fused product")
+    check(E.subtract(E.add(count, 1), count), "1", "single unit at E27")
+    check(E.floor_value(E.divide(E.subtract(count, 1), count)), "0", "division must not round up a whole object")
+    check(E.fixed(E.add(count, E.of("0.125")), 3), "1000000000000000000000000001.125", "formatting without oversized intermediate")
+    check(E.scientific(E.of("9.999999e27"), 2), "1.00E+28", "display rounding at upper boundary")
+    check(absf(E.approx(E.power(10, -100)) / E.approx(E.of("1e-100")) - 1.0) < 1e-15, "true", "negative power retains float precision without huge intermediate")
+    var largest = E.of("9999999999999999999999999999")
+    check(E.eq(E.decode(E.encode(largest)), largest), "true", "upper range round trip")
+    check(E.valid_encoded(E.encode(largest)), "true", "upper range encoding valid")
+    for tiny in ["1e-13", "1e-20", "1e-100", "1e-310"]:
+        var value = E.of(tiny)
+        check(E.gt(value, 0), "true", "tiny fraction remains nonzero")
+        check(E.eq(value, E.decode(JSON.parse_string(JSON.stringify(E.encode(value))))), "true", "tiny float round trip")
+    for invalid in [{"$fixed": ["0", "0", "ffffffffffffffff", 1]}, {"$fixed": ["0", "-1", "0000000000000000", 1]}, {"$exact": "1/3"}, {"$exact": "10000000000000000000000000000"}, 1e100]:
+        check(E.valid_encoded(invalid), "false", "reject invalid saved number")
+    world.state.amount.S = E.of("1e24")
+    world.state.amount.H = E.of("1e24")
+    world.state.amount.RD = 1234567
+    world.state.amount.YD = 765432
+    world.state.amount.STN = 654321
+    world.speed = 6
+    var started: int = Time.get_ticks_msec()
+    for i in 100:
+        world.state.amount.RD = E.add(world.state.amount.RD, i + 1)
+        world.evolute(0.1)
+        check(str(world.state.auto_star_deficits).length() < 500, "true", "fraction storage stays bounded")
+    print("100 changing-composition cycles: %d ms" % (Time.get_ticks_msec() - started))
+    var saves = root.get_node("SaveManager")
+    check(saves.validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), "", "long-running state saves")
+    for entity in world.catalog.entities.values(): entity.free()
+    world.free()
+    print("Exact math: %d checks, %d failures" % [checks, failures])
+    quit(0 if failures == 0 else 1)

tests/test_exact_math.gd.uid

@@ -0,0 +1 @@
+uid://wxhre4pgx1lb

tests/test_frame_evolution.gd

@@ -0,0 +1,100 @@
+extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
+const Clock = preload("res://world/owniverse/simulation_time.gd")
+const Fixture = preload("res://tests/fixtures/civilization_benchmark.gd")
+var checks: int = 0
+var failures: int = 0
+
+func _initialize(): call_deferred("run")
+func check(condition: bool, message: String):
+    checks += 1
+    if not condition:
+        failures += 1
+        push_error(message)
+func fixture():
+    var world = load("res://world/owniverse/owniverse.gd").new()
+    world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+    Fixture.seed(world, root.get_node("Global"))
+    return world
+func dispose(world):
+    for entity in world.catalog.entities.values(): entity.free()
+    world.free()
+
+func run():
+    Engine.max_fps = 0
+    var direct = fixture()
+    var sliced = fixture()
+    for delta in [1.0 / 60.0, 0.133333333333]:
+        direct.evolute(delta)
+        var clock: Dictionary = Clock.advance(sliced.state.time, delta, sliced.speed)
+        var budget = load("res://world/owniverse/frame_budget.gd").new(self, 1)
+        await sliced.evolution.evolute_to_datetime(clock.datetime, clock, budget)
+        check(E.eq(direct.state, sliced.state), "Sliced transaction exactly matches uninterrupted evolution")
+    dispose(direct)
+    dispose(sliced)
+    direct = fixture()
+    sliced = fixture()
+    var initial_h: Variant = sliced.state.amount.H
+    sliced.evolute_frame(1.0 / 60.0, self)
+    check(sliced.frame_busy, "Heavy transaction yields before publishing")
+    check(E.eq(sliced.state.time.year, 0), "Published clock stays at completed transaction")
+    sliced.request_production("H", 1, true)
+    check(E.eq(sliced.state.amount.H, initial_h), "Player action waits for transaction commit")
+    sliced.evolute_frame(0.01, self)
+    var requested: Dictionary = sliced.frame_clock.duplicate()
+    sliced.speed = 3
+    check(sliced.speed == 3 and sliced.state.speed == 6, "Speed change is visible and cannot mutate an unfinished transaction")
+    while sliced.frame_busy: await process_frame
+    direct.evolute(1.0 / 60.0)
+    direct.production.produce_hs("H", 1)
+    direct.speed = 3
+    check(E.eq(direct.state, sliced.state), "Queued action and speed change survive publication")
+    sliced.evolute_frame(0.001, self)
+    var second_clock: Dictionary = Clock.advance(requested, 0.001, 3)
+    var active: Dictionary = sliced.frame_active_clock.duplicate()
+    while sliced.frame_busy: await process_frame
+    direct.evolution.evolute_to_datetime(active.datetime, active)
+    check(E.eq(direct.state, sliced.state), "Bounded frame transaction matches its exact target clock")
+    check(E.eq(sliced.frame_clock, second_clock), "All elapsed time during a busy frame remains in the requested clock")
+    check(sliced.frame_commits == 2, "Only complete simulation states are committed")
+    dispose(direct)
+    dispose(sliced)
+    var original = fixture()
+    original.evolute_frame(1.0 / 60.0, self)
+    original.request_production("H", 123, true)
+    original.evolute_frame(0.01, self)
+    original.speed = 3
+    var checkpoint: Dictionary = E.decode(E.encode(original.frame_checkpoint()))
+    var published: Dictionary = E.decode(E.encode(original.state))
+    var expected_clock: Dictionary = original.frame_active_clock.duplicate()
+    dispose(original)
+    for frame in 3: await process_frame
+    var resumed = fixture()
+    var expected = fixture()
+    resumed.state = published.duplicate(true)
+    expected.state = published.duplicate(true)
+    resumed.restore_frame_checkpoint(checkpoint)
+    resumed.evolute_frame(0.0, self)
+    while resumed.frame_busy: await process_frame
+    expected.evolution.evolute_to_datetime(expected_clock.datetime, expected_clock)
+    expected.production.produce_hs("H", 123)
+    expected.speed = 3
+    check(E.eq(expected.state, resumed.state), "Checkpoint recomputes interrupted transaction and preserves queued production")
+    check(E.eq(resumed.frame_clock, checkpoint.requested_clock), "Checkpoint preserves all requested elapsed time")
+    dispose(resumed)
+    dispose(expected)
+    var cancelled = fixture()
+    cancelled.evolute_frame(0.133333333333, self)
+    check(cancelled.frame_busy, "Cancellation fixture has suspended work")
+    var budget_ref: RefCounted = cancelled.frame_budget
+    dispose(cancelled)
+    for frame in 3: await process_frame
+    check(budget_ref.cancelled, "Resetting the world cancels suspended work without publishing")
+    var invalid = fixture()
+    var before: Dictionary = invalid.state.duplicate(true)
+    invalid.evolute_frame(1e308, self)
+    invalid.evolute(1e308)
+    check(not invalid.frame_busy and invalid.frame_clock.is_empty() and E.eq(before, invalid.state), "Overflowing elapsed float cannot enter either clock API")
+    dispose(invalid)
+    print("Frame evolution: %d checks, %d failures" % [checks, failures])
+    quit(1 if failures else 0)

tests/test_frame_evolution.gd.uid

@@ -0,0 +1 @@
+uid://te15r63sqhxs

tests/test_group_index.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -40,19 +41,19 @@ func run() -> void:
     for id in world.catalog.entities:
         var expected: Array = []
         for key in world.catalog.entities:
-            if world.catalog.entities[key].group_as == id:
+            if E.eq(world.catalog.entities[key].group_as, id):
                 expected.append(key)
-        check(world.catalog.is_group(id) == (not expected.is_empty()), "Group classification: " + id)
-        check(world.catalog.members(id) == (expected if not expected.is_empty() else [id]), "Group members: " + id)
+        check(E.eq(world.catalog.is_group(id), ((not expected.is_empty()))), E.add("Group classification: ", id))
+        check(E.eq(world.catalog.members(id), ((expected if (not expected.is_empty()) else [id]))), E.add("Group members: ", id))
     var members: Array = world.catalog.members("Star")
     members.clear()
-    check(not world.catalog.members("Star").is_empty(), "Returned members are independent")
+    check((not world.catalog.members("Star").is_empty()), "Returned members are independent")
     world.catalog.entities.N.group_as = "TestGroup"
     world.catalog.rebuild_group_index()
-    check(world.catalog.members("TestGroup") == ["N"], "Explicit definition reload")
+    check(E.eq(world.catalog.members("TestGroup"), ["N"]), "Explicit definition reload")
     world.catalog.entities.N.free()
     world.catalog.entities.erase("N")
-    check(not world.catalog.is_group("TestGroup"), "Removed definition invalidates index")
-    print("Group index: %d checks, %d failures" % [checks, failures])
+    check((not world.catalog.is_group("TestGroup")), "Removed definition invalidates index")
+    print(("Group index: %d checks, %d failures" % [checks, failures]))
     dispose(world)
-    quit(1 if failures else 0)
+    quit((1 if failures else 0))

tests/test_life.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -37,87 +38,87 @@ func dispose(world) -> void:
 
 func run() -> void:
     var world = fixture()
-    world.state.amount.N = 0.0
-    world.state.amount.HP = 40000.0
+    world.state.amount.N = 0
+    world.state.amount.HP = 40000
     world.evolution.initialize_life_batches()
-    check(world.state.batches.HP.size() == 1, "Old HP receives life cohort")
-    check(world.state.batches.HP[0].start_year == 5e6, "HP uses source span")
+    check(E.eq(world.state.batches.HP.size(), 1), "Old HP receives life cohort")
+    check(E.eq(world.state.batches.HP[0].start_year, 5000000), "HP uses source span")
     var before: Dictionary = world.state.duplicate(true)
     world.evolution.initialize_life_batches()
-    check(world.state == before, "Initialization is idempotent")
-    world.evolution.evolve_batches(world.state, 5e6 + 5e6 / 40.0)
-    check(world.state.amount.EON1 == 10.0, "HP abiogenesis follows source probability")
-    check(world.state.amount.RP == 100.0, "HP degradation produces RP")
-    check(world.state.amount.HP == 39890.0, "Unchanged planets retry, not disappear")
-    check(world.state.stats.total_amount.HP == 0.0, "Retry does not inflate creation statistics")
-    check(world.state.batches.HP.size() > 0, "Survivors get next attempt")
+    check(E.eq(world.state, before), "Initialization is idempotent")
+    world.evolution.evolve_batches(world.state, E.add(5000000, E.divide(5000000, 40)))
+    check(E.eq(world.state.amount.EON1, 10), "HP abiogenesis follows source probability")
+    check(E.eq(world.state.amount.RP, 100), "HP degradation produces RP")
+    check(E.eq(world.state.amount.HP, 39890), "Unchanged planets retry, not disappear")
+    check(E.eq(world.state.stats.total_amount.HP, 0), "Retry does not inflate creation statistics")
+    check(E.gt(world.state.batches.HP.size(), 0), "Survivors get next attempt")
     var physical: Dictionary = world.ledger.physical_amounts(world.state)
-    check(physical.HP + physical.EON1 + physical.RP == 40000.0, "Life conserves planets")
-    check(root.get_node("SaveManager").validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Life save validates")
+    check(E.eq(E.add(E.add(physical.HP, physical.EON1), physical.RP), 40000), "Life conserves planets")
+    check(E.eq(root.get_node("SaveManager").validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Life save validates")
     var restored = fixture()
-    restored.state = bytes_to_var(var_to_bytes(world.state))
-    world.evolution.evolve_batches(world.state, 11e6)
-    restored.evolution.evolve_batches(restored.state, 11e6)
-    check(world.state == restored.state, "Life continuation preserves cohorts and carries")
+    restored.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
+    world.evolution.evolve_batches(world.state, 11000000)
+    restored.evolution.evolve_batches(restored.state, 11000000)
+    check(E.eq(world.state, restored.state), "Life continuation preserves cohorts and carries")
     dispose(restored)
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 1.0
-    world.state.binds.RD = {"EON5": 40000.0}
+    world.state.amount.RD = 1
+    world.state.binds.RD = {"EON5": 40000}
     world.evolution.initialize_life_batches()
-    world.evolution.evolve_batches(world.state, 5e5 + 5e5 / 40.0)
-    check(world.state.binds.RD["C0.0"] == 10.0, "Intelligence emerges at the same host star")
-    check(world.state.amount["C0.0"] == 0.0, "Life transition keeps planet bound")
+    world.evolution.evolve_batches(world.state, E.add(500000, E.divide(500000, 40)))
+    check(E.eq(world.state.binds.RD["C0.0"], 10), "Intelligence emerges at the same host star")
+    check(E.eq(world.state.amount["C0.0"], 0), "Life transition keeps planet bound")
     check(world.state.batches.has("C0.0"), "New C0.0 starts civilization evolution")
     dispose(world)
 
     world = fixture()
-    var progress: float = 0.0
-    var degraded: float = 0.0
+    var progress: Variant = 0
+    var degraded: Variant = 0
     var valid_outcomes: bool = true
     for i in 4001:
-        var products: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1.0)
-        var total: float = 0.0
+        var products: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1)
+        var total: Variant = 0
         for value in products.values():
-            total += value
-            valid_outcomes = valid_outcomes and value >= 0.0 and value == floorf(value)
-        valid_outcomes = valid_outcomes and total == 1.0
-        progress += products.get("EON1", 0.0)
-        degraded += products.get("RP", 0.0)
+            total = E.add(total, value)
+            valid_outcomes = ((valid_outcomes and E.ge(value, 0)) and E.eq(value, E.floor_value(value)))
+        valid_outcomes = (valid_outcomes and E.eq(total, 1))
+        progress = E.add(progress, products.get("EON1", 0))
+        degraded = E.add(degraded, products.get("RP", 0))
     check(valid_outcomes, "Every single-planet attempt has whole outcomes and conserves population")
-    check(progress == 1.0 and degraded == 10.0, "Rare outcomes accumulate deterministically")
+    check((E.eq(progress, 1) and E.eq(degraded, 10)), "Rare outcomes accumulate deterministically")
     dispose(world)
 
     world = fixture()
-    world.state.time = {"datetime": 123.4, "year": 123.4}
-    world.state.binds.RD = {"HP": 2.0}
+    world.state.time = {"datetime": E.of("123.4"), "year": E.of("123.4")}
+    world.state.binds.RD = {"HP": 2}
     world.evolution.initialize_life_batches()
-    check(world.state.batches.HP[0].created_from == 123.4, "Old bound worlds begin life at load time")
-    world.stellar.destroy_planets(world.state, "RD", 1.0, 1)
-    world.evolution.evolve_batches(world.state, 1e7)
-    check(world.ledger.physical_amounts(world.state).HP == 0.0 and world.state.binds.RD.RP == 2.0, "Destroyed life does not resurrect from cohort")
+    check(E.eq(world.state.batches.HP[0].created_from, E.of("123.4")), "Old bound worlds begin life at load time")
+    world.stellar.destroy_planets(world.state, "RD", 1, 1)
+    world.evolution.evolve_batches(world.state, 10000000)
+    check((E.eq(world.ledger.physical_amounts(world.state).HP, 0) and E.eq(world.state.binds.RD.RP, 2)), "Destroyed life does not resurrect from cohort")
     dispose(world)
     world = fixture()
-    world.state.time = {"datetime": 123.4, "year": 123.4}
-    world.state.amount["C0.0"] = 40000.0
+    world.state.time = {"datetime": E.of("123.4"), "year": E.of("123.4")}
+    world.state.amount["C0.0"] = 40000
     world.evolution.initialize_life_batches()
-    check(world.state.batches["C0.0"][0].created_from == 123.4, "Civilization cohorts begin at the current time")
+    check(E.eq(world.state.batches["C0.0"][0].created_from, E.of("123.4")), "Civilization cohorts begin at the current time")
     before = world.state.duplicate(true)
     world.evolution.initialize_life_batches()
-    check(world.state == before, "Life batch initialization is idempotent")
-    world.evolution.evolve_batches(world.state, 2173.4)
-    check(world.state.amount["C0.1"] == 700.0 and world.state.amount.EON5 == 1000.0, "C0.0 progresses and degrades by Unity rates")
-    check(world.state.amount["C0.0"] == 38300.0, "C0.0 remainder stays alive")
+    check(E.eq(world.state, before), "Life batch initialization is idempotent")
+    world.evolution.evolve_batches(world.state, E.of("2173.4"))
+    check((E.eq(world.state.amount["C0.1"], 700) and E.eq(world.state.amount.EON5, 1000)), "C0.0 progresses and degrades by Unity rates")
+    check(E.eq(world.state.amount["C0.0"], 38300), "C0.0 remainder stays alive")
     dispose(world)
     world = fixture()
-    world.state.amount.RD = 1.0
-    world.state.binds.RD = {"C0.1": 40000.0}
+    world.state.amount.RD = 1
+    world.state.binds.RD = {"C0.1": 40000}
     world.evolution.initialize_life_batches()
-    world.evolution.evolve_batches(world.state, 2050.0)
-    check(world.state.binds.RD["C0.2"] == 700.0, "C0.1 reaches ethical civilization without losing host")
-    check(world.state.binds.RD["C0.0"] == 1000.0, "C0.1 degradation follows Unity")
-    check(root.get_node("SaveManager").validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Extended life save validates")
+    world.evolution.evolve_batches(world.state, 2050)
+    check(E.eq(world.state.binds.RD["C0.2"], 700), "C0.1 reaches ethical civilization without losing host")
+    check(E.eq(world.state.binds.RD["C0.0"], 1000), "C0.1 degradation follows Unity")
+    check(E.eq(root.get_node("SaveManager").validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Extended life save validates")
     dispose(world)
-    print("Life: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Life: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_life_icons.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(value: bool, message: String) -> void:
-    checks += 1
-    if not value:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not value):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func run() -> void:
@@ -21,48 +22,48 @@ func run() -> void:
     await process_frame
     await process_frame
     var world = stage.owniverse
-    world.state.binds.RD = {"EON1": 10.0, "EON2": 4.0, "C0.0": 3.0}
-    world.state.amount.EON1 = 2.0
-    world.state.stats.total_amount.EON1 = 12.0
-    world.state.stats.total_amount.EON2 = 4.0
-    world.state.stats.total_amount["C0.0"] = 3.0
+    world.state.binds.RD = {"EON1": 10, "EON2": 4, "C0.0": 3}
+    world.state.amount.EON1 = 2
+    world.state.stats.total_amount.EON1 = 12
+    world.state.stats.total_amount.EON2 = 4
+    world.state.stats.total_amount["C0.0"] = 3
     var before: Dictionary = world.state.duplicate(true)
     stage._refresh_universe_ui()
     var counts: Dictionary = world.presentation.amounts(world.state, world.catalog)
-    check(counts.EON1 == 12.0 and counts.EON2 == 4.0 and counts.LP == 16.0, "Individual eons and their total include bound planets")
-    check(counts["C0.0"] == 3.0 and counts.C0 == 3.0 and counts.Planet == 19.0, "Civilization detail does not double the planetary total")
-    check(world.presentation.amounts(world.state, world.catalog, true).EON1 == 12.0 and world.presentation.amounts(world.state, world.catalog, true).LP == 16.0, "Historical counts retain individual and aggregate values")
-    check(world.state == before, "Presentation does not modify simulation state")
+    check(((E.eq(counts.EON1, 12) and E.eq(counts.EON2, 4)) and E.eq(counts.LP, 16)), "Individual eons and their total include bound planets")
+    check(((E.eq(counts["C0.0"], 3) and E.eq(counts.C0, 3)) and E.eq(counts.Planet, 19)), "Civilization detail does not double the planetary total")
+    check((E.eq(world.presentation.amounts(world.state, world.catalog, true).EON1, 12) and E.eq(world.presentation.amounts(world.state, world.catalog, true).LP, 16)), "Historical counts retain individual and aggregate values")
+    check(E.eq(world.state, before), "Presentation does not modify simulation state")
     var pending: Array = ["EON1", "EON2", "EON3", "C0.0"]
     var pending_before: Array = pending.duplicate()
     var decision: Dictionary = world.presentation.unlocks(world.state, world.catalog, pending)
-    check(decision.remaining == ["EON3"], "Only unmet requirements remain pending")
+    check(E.eq(decision.remaining, ["EON3"]), "Only unmet requirements remain pending")
     for id in ["EON1", "EON2", "LP", "C0.0", "C0"]:
-        check(decision.visible.has(id), "Unlock projection includes detail and alias: " + id)
-    check(pending == pending_before and world.state == before, "Unlock evaluation leaves inputs untouched")
+        check(decision.visible.has(id), E.add("Unlock projection includes detail and alias: ", id))
+    check((E.eq(pending, pending_before) and E.eq(world.state, before)), "Unlock evaluation leaves inputs untouched")
     var snapshot: Dictionary = world.presentation.pending_amounts.duplicate()
     world.presentation.deferred_updates = true
-    world.state.amount.EON1 += 1.0
+    world.state.amount.EON1 = E.add(world.state.amount.EON1, 1)
     world.presentation.refresh(world.state, world.catalog)
-    check(world.presentation.dirty and world.presentation.pending_amounts == snapshot, "Deferred refresh retains pending snapshot")
+    check((world.presentation.dirty and E.eq(world.presentation.pending_amounts, snapshot)), "Deferred refresh retains pending snapshot")
     world.presentation.refresh(world.state, world.catalog, true)
-    check(not world.presentation.dirty and world.presentation.pending_amounts.EON1 == 13.0, "Forced refresh publishes latest amounts")
-    world.state.amount.EON1 -= 1.0
+    check(((not world.presentation.dirty) and E.eq(world.presentation.pending_amounts.EON1, 13)), "Forced refresh publishes latest amounts")
+    world.state.amount.EON1 = E.subtract(world.state.amount.EON1, 1)
     world.presentation.deferred_updates = false
     world.presentation.refresh(world.state, world.catalog)
     for id in ["EON1", "EON2", "LP", "C0.0", "C0"]:
-        check(stage.owniverse_items[id].visible, "Unlock both levels: " + id)
-        check(stage.owniverse_items[id].description.text != "", "Populate the icon counter: " + id)
-    check(not stage.owniverse_items.EON3.visible, "Unreached eon remains locked")
+        check(stage.owniverse_items[id].visible, E.add("Unlock both levels: ", id))
+        check(E.ne(stage.owniverse_items[id].description.text, ""), E.add("Populate the icon counter: ", id))
+    check((not stage.owniverse_items.EON3.visible), "Unreached eon remains locked")
     stage.item_activated(stage.owniverse_items.LP)
     check(stage.owniverse_items.EON1.is_visible_in_tree(), "Selecting LP shows its unlocked eons")
     stage.item_activated(stage.owniverse_items.C0)
-    check(stage.owniverse_items["C0.0"].is_visible_in_tree() and not stage.owniverse_items.EON1.is_visible_in_tree(), "Selecting C0 switches the detail panel")
-    world.state.binds.RD.EON2 = 0.0
+    check((stage.owniverse_items["C0.0"].is_visible_in_tree() and (not stage.owniverse_items.EON1.is_visible_in_tree())), "Selecting C0 switches the detail panel")
+    world.state.binds.RD.EON2 = 0
     stage._refresh_universe_ui()
-    check(stage.owniverse_items.EON2.visible and stage.owniverse_items.EON2.description.text == "", "Previously reached stage stays unlocked after extinction with no stale count")
+    check((stage.owniverse_items.EON2.visible and E.eq(stage.owniverse_items.EON2.description.text, "")), "Previously reached stage stays unlocked after extinction with no stale count")
     for entity in world.catalog.entities.values(): entity.free()
     world.free()
     scene.free()
-    print("Life icons: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Life icons: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_module_lifecycle.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func run() -> void:
@@ -19,20 +20,20 @@ func run() -> void:
     var names: Array = ["batches", "ledger", "production", "automatic", "stellar", "life", "environment", "evolution"]
     var references: Array = []
     for name in names:
-        check(first.get(name) != second.get(name), "World has its own " + name)
-        check(first.get(name).world == first, "Module refers to its owner: " + name)
+        check(E.ne(first.get(name), second.get(name)), E.add("World has its own ", name))
+        check(E.eq(first.get(name).world, first), E.add("Module refers to its owner: ", name))
         references.append(weakref(first.get(name)))
-    first.state.amount.H = 123.0
-    first.presentation.pending_amounts.H = 123.0
-    check(not second.state.amount.has("H") and second.presentation.pending_amounts.is_empty(), "State and pending presentation are isolated")
+    first.state.amount.H = 123
+    first.presentation.pending_amounts.H = 123
+    check(((not second.state.amount.has("H")) and second.presentation.pending_amounts.is_empty()), "State and pending presentation are isolated")
     first.free()
     for reference in references:
-        check(reference.get_ref() == null, "Module is released with its world")
-    check(second.evolution.world == second, "Other world remains usable")
+        check(E.eq(reference.get_ref(), null), "Module is released with its world")
+    check(E.eq(second.evolution.world, second), "Other world remains usable")
     var snapshot: Dictionary = second.state.duplicate(true)
     second.evolute(NAN)
-    second.evolute(-1.0)
-    check(second.state == snapshot, "Entry point rejects invalid time deltas")
+    second.evolute(E.neg(1))
+    check(E.eq(second.state, snapshot), "Entry point rejects invalid time deltas")
     second.free()
-    print("Module lifecycle: %d checks, %d failures" % [checks, failures])
-    quit(1 if failures else 0)
+    print(("Module lifecycle: %d checks, %d failures" % [checks, failures]))
+    quit((1 if failures else 0))

tests/test_production_transaction.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -38,21 +39,34 @@ func dispose(world) -> void:
 func run() -> void:
     var world = fixture()
     world.evolution.initialize_life_batches()
-    world.catalog.entities.N.cost = {"H": 2.0}
-    world.catalog.entities.N.bind = {"S": 3.0}
-    world.state.amount.H = 10.0
-    world.state.amount.S = 0.0
-    world.state.auto_resources = {"H": 10.0}
-    world.state.batches.H = [{"amount": 10.0, "start_year": 1.0, "end_year": 2.0}]
+    world.catalog.entities.N.cost = {"H": 2}
+    world.catalog.entities.N.bind = {"S": 3}
+    world.state.amount.H = 10
+    world.state.amount.S = 0
+    check(E.eq(world.production.calculate_max_producible(world.catalog.entities.N), 0), "Default maximum respects missing bindings")
+    world.state.amount.S = 30
+    check(E.eq(world.production.calculate_max_producible(world.catalog.entities.N), 5), "Default maximum uses recipe resources without an oversized sentinel")
+    check(E.eq(world.production.calculate_max_producible(world.catalog.entities.N, 2), 2), "Explicit production limit is preserved")
+    world.state.amount.H = E.of("1e27")
+    world.state.amount.S = E.of("1e27")
+    check(E.eq(world.production.calculate_max_producible(world.catalog.entities.N), E.floor_value(E.divide(E.of("1e27"), 3))), "Default maximum at E27 retains integer precision")
+    world.state.amount.BH25 = 4
+    check(E.eq(world.production.calculate_max_producible(world.catalog.entities.SMBH), world.production.smbh_available()), "Default SMBH maximum uses available black-hole mass")
+    world.state.amount.BH25 = 0
+    check(E.eq(world.production.calculate_max_producible(world.catalog.entities.SMBH), 0), "Empty SMBH maximum is zero")
+    world.state.amount.H = 10
+    world.state.amount.S = 0
+    world.state.auto_resources = {"H": 10}
+    world.state.batches.H = [{"amount": 10, "start_year": 1, "end_year": 2}]
     var before: Dictionary = world.state.duplicate(true)
-    check(not world.production.try_production(world.state, world.catalog.entities.N, 1.0, true), "Binding failure rejects production")
-    check(world.state == before, "Failure preserves costs, batches and budget")
-    world.state.amount.S = 10.0
+    check((not world.production.try_production(world.state, world.catalog.entities.N, 1, true)), "Binding failure rejects production")
+    check(E.eq(world.state, before), "Failure preserves costs, batches and budget")
+    world.state.amount.S = 10
     var old_batches: Array = world.state.batches.H
-    check(world.production.try_production(world.state, world.catalog.entities.N, 2.0, true), "Funded production succeeds")
-    check(world.state.amount.H == 6.0 and world.state.amount.S == 4.0, "Exact cost and binding")
-    check(world.state.auto_resources.H == 6.0, "Exact automatic budget")
-    check(old_batches[0].amount == 10.0 and world.state.batches.H[0].amount == 6.0, "Consumed batches isolated")
-    print("Transaction: %d checks, %d failures" % [checks, failures])
+    check(world.production.try_production(world.state, world.catalog.entities.N, 2, true), "Funded production succeeds")
+    check((E.eq(world.state.amount.H, 6) and E.eq(world.state.amount.S, 4)), "Exact cost and binding")
+    check(E.eq(world.state.auto_resources.H, 6), "Exact automatic budget")
+    check((E.eq(old_batches[0].amount, 10) and E.eq(world.state.batches.H[0].amount, 6)), "Consumed batches isolated")
+    print(("Transaction: %d checks, %d failures" % [checks, failures]))
     dispose(world)
-    quit(1 if failures else 0)
+    quit((1 if failures else 0))

tests/test_quantity_catalog.gd

@@ -1,6 +1,8 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const Math = preload("res://world/owniverse/quantity_math.gd")
+const Legacy = preload("res://tests/fixtures/legacy_quantity_math.gd")
 var checks: int = 0
 var failures: int = 0
 
@@ -8,56 +10,103 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func run() -> void:
+    var rng = RandomNumberGenerator.new()
+    rng.seed = 65432
+    var old_remainders: Dictionary = {}
+    var new_remainders: Dictionary = {}
+    for sample in 300:
+        var requests: Dictionary = {}
+        var weights: Dictionary = {}
+        for id in ["w", "m", "b", "c", "d", "l"]:
+            requests[id] = E.of(str(rng.randi_range(-10, 100)) + "." + str(rng.randi_range(0, 9)))
+            weights[id] = rng.randi_range(0, 100)
+        if sample % 3 == 0:
+            for id in requests: requests[id] = E.multiply(requests[id], E.of("1e40"))
+        var limit: Variant = E.multiply(rng.randi_range(0, 600), E.of("1e40")) if sample % 3 == 0 else rng.randi_range(0, 600)
+        check(E.eq(Math.allocate_whole(requests, limit), Legacy.allocate_whole(requests, limit)), "Allocation matches legacy with limits, ties and big integers")
+        var count: Variant = limit
+        check(E.eq(Math.split(new_remainders, "population", count, weights), Legacy.split(old_remainders, "population", count, weights)), "Split matches legacy rounding")
+        check(E.eq(new_remainders, old_remainders), "Signed remainder debt matches legacy")
+    check_ledger_cache()
     var Catalog = load("res://world/owniverse/entity_catalog.gd")
-    check(Math.allocate_whole({}, 10.0) == {}, "Empty allocation")
-    check(Math.allocate_whole({"b": 1.0, "a": 1.0}, 1.0) == {"a": 1.0, "b": 0.0}, "Stable lexical tie")
+    check(E.eq(Math.allocate_whole({}, 10), {}), "Empty allocation")
+    check(E.eq(Math.allocate_whole({"b": 1, "a": 1}, 1), {"a": 1, "b": 0}), "Stable lexical tie")
     for limit in range(30):
-        var requests: Dictionary = {"a": 3.9, "b": 9.1, "c": -2.0, "d": 7.0}
+        var requests: Dictionary = {"a": E.of("3.9"), "b": E.of("9.1"), "c": E.neg(2), "d": 7}
         var result: Dictionary = Math.allocate_whole(requests, limit)
-        check(Math.sum(result) == minf(limit, 19.0), "Conserve bounded allocation")
+        check(E.eq(Math.sum(result), E.minimum(limit, 19)), "Conserve bounded allocation")
         for id in result:
-            check(result[id] == floorf(result[id]) and result[id] >= 0.0 and result[id] <= floorf(maxf(0.0, requests[id])), "Whole bounded branch")
-    check(Math.normalize_distribution({"a": -1.0, "b": 0.0}) == {}, "Nonpositive weights")
-    check(Math.normalize_distribution({"a": 2.0, "b": 6.0}) == {"a": 0.25, "b": 0.75}, "Normalize weights")
-    check(Math.production_step([0.25, 0.1, 2.0]) == 20.0, "Common whole production step")
-    check(Math.production_step([]) == 1.0, "Free production step")
+            check(((E.eq(result[id], E.floor_value(result[id])) and E.ge(result[id], 0)) and E.le(result[id], E.floor_value(E.maximum(0, requests[id])))), "Whole bounded branch")
+    check(E.eq(Math.normalize_distribution({"a": E.neg(1), "b": 0}), {}), "Nonpositive weights")
+    check(E.eq(Math.normalize_distribution({"a": 2, "b": 6}), {"a": E.of("0.25"), "b": E.of("0.75")}), "Normalize weights")
+    check(E.eq(Math.production_step([E.of("0.25"), E.of("0.1"), 2]), 20), "Common whole production step")
+    check(E.eq(Math.production_step([]), 1), "Free production step")
     var target: Dictionary = {}
-    var produced: float = 0.0
+    var produced: Variant = 0
     for i in 10:
-        produced += Math.accumulate_whole(target, "remainders", "a", 0.1)
-    check(produced == 1.0, "Fractional production carries")
+        produced = E.add(produced, Math.accumulate_whole(target, "remainders", "a", E.of("0.1")))
+    check(E.eq(produced, 1), "Fractional production carries")
     var remainders: Dictionary = {}
-    var totals: Dictionary = {"a": 0.0, "b": 0.0, "c": 0.0}
+    var totals: Dictionary = {"a": 0, "b": 0, "c": 0}
     for i in 30:
-        var result: Dictionary = Math.split(remainders, "split", 1.0, {"a": 1.0, "b": 1.0, "c": 1.0})
-        check(Math.sum(result) == 1.0, "Split conserves count")
-        for id in result: totals[id] += result[id]
-    check(totals == {"a": 10.0, "b": 10.0, "c": 10.0}, "Rounding debt distributes over time")
-    produced = 0.0
-    for i in 10: produced += Math.accumulate_rate(remainders, "rate", 1.0, 0.1)
-    check(produced == 1.0, "Rate carries")
+        var result: Dictionary = Math.split(remainders, "split", 1, {"a": 1, "b": 1, "c": 1})
+        check(E.eq(Math.sum(result), 1), "Split conserves count")
+        for id in result: totals[id] = E.add(totals[id], result[id])
+    check(E.eq(totals, {"a": 10, "b": 10, "c": 10}), "Rounding debt distributes over time")
+    produced = 0
+    for i in 10: produced = E.add(produced, Math.accumulate_rate(remainders, "rate", 1, E.of("0.1")))
+    check(E.eq(produced, 1), "Rate carries")
     var catalog = Catalog.new()
     var rows: Dictionary = root.get_node("Global").OwniverseEntities
     catalog.load_definitions(rows)
-    check(catalog.entities.size() == rows.size(), "Catalog loads all definitions")
+    check(E.eq(catalog.entities.size(), rows.size()), "Catalog loads all definitions")
     for id in catalog.entities:
         var entity = catalog.entities[id]
-        check(catalog.automatic_producers.has(entity) == (entity.product_per_year_type != ""), "Producer index")
-        check(catalog.unlockable_entities.has(entity) == (not entity.unlock.is_empty()), "Unlock index")
-        if entity.group_as != "":
-            check(catalog.groups[entity.group_as].has(id) and catalog.members(entity.group_as).has(id), "Group index")
-        if entity.event_group != "":
+        check(E.eq(catalog.automatic_producers.has(entity), (E.ne(entity.product_per_year_type, ""))), "Producer index")
+        check(E.eq(catalog.unlockable_entities.has(entity), ((not entity.unlock.is_empty()))), "Unlock index")
+        if E.ne(entity.group_as, ""):
+            check((catalog.groups[entity.group_as].has(id) and catalog.members(entity.group_as).has(id)), "Group index")
+        if E.ne(entity.event_group, ""):
             check(catalog.event_groups[entity.event_group].has(id), "Event index")
     var members: Array = catalog.members("Star")
     members.clear()
-    check(not catalog.members("Star").is_empty(), "Group results are independent")
+    check((not catalog.members("Star").is_empty()), "Group results are independent")
     check(Catalog.new().entities.is_empty(), "Catalog instances are independent")
     for entity in catalog.entities.values(): entity.free()
-    print("Quantity and catalog: %d checks, %d failures" % [checks, failures])
-    quit(1 if failures else 0)
+    print(("Quantity and catalog: %d checks, %d failures" % [checks, failures]))
+    quit((1 if failures else 0))
+
+func check_ledger_cache() -> void:
+    var world = load("res://world/owniverse/owniverse.gd").new()
+    world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+    world.state.amount.RD = E.of("1e40")
+    world.state.binds.GEM = {"RD": 7}
+    check(E.eq(world.ledger.physical_amounts(world.state).RD, E.add(E.of("1e40"), 7)), "Initial cached physical amount")
+    var returned: Dictionary = world.ledger.physical_amounts(world.state)
+    returned.RD = 0
+    check(E.gt(world.ledger.physical_amounts(world.state).RD, 0), "Caller cannot mutate cached physical totals")
+    world.state.binds.GEM.RD = 11
+    check(E.eq(world.ledger.physical_amounts(world.state).RD, E.add(E.of("1e40"), 11)), "Nested binding change invalidates physical cache")
+    world.state.amount.RD = 2
+    check(E.eq(world.ledger.physical_amounts(world.state).RD, 13), "Direct count change invalidates physical cache")
+    var other: Dictionary = world.state.duplicate(true)
+    other.binds.clear()
+    check(E.eq(world.ledger.physical_amounts(other).RD, 2), "Alternate state has independent physical totals")
+    check(E.eq(world.ledger.physical_amounts(world.state).RD, 13), "Returning to original state refreshes cache")
+    var revision: int = world.catalog.index_revision
+    world.catalog.rebuild_group_index()
+    check(world.catalog.index_revision > revision, "Catalog rebuild invalidates cached membership")
+    check(E.eq(world.ledger.physical_amounts(world.state).RD, 13), "Rebuild retains correct physical totals")
+    var rules: Dictionary = root.get_node("Global").CivilizationRules.duplicate(true)
+    var original_stages: int = world.catalog.civilization_layout(rules).stages.size()
+    rules["C2.0"].home = ""
+    world.catalog.invalidate_civilization_layout()
+    check(world.catalog.civilization_layout(rules).stages.size() == original_stages - 1, "Explicit rules change rebuilds civilization layout")
+    for entity in world.catalog.entities.values(): entity.free()
+    world.free()

tests/test_short_lived_events.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 var checks: int = 0
 var failures: int = 0
 
@@ -6,20 +7,20 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture(legacy: bool):
-    var world = load("res://tests/fixtures/legacy_stellar_events.gd" if legacy else "res://world/owniverse/owniverse.gd").new()
+    var world = load(("res://tests/fixtures/legacy_stellar_events.gd" if legacy else "res://world/owniverse/owniverse.gd")).new()
     for id in root.get_node("Global").OwniverseEntities:
         world.catalog.entities[id] = load("res://world/owniverse/owniverse_entity.gd").new(root.get_node("Global").OwniverseEntities[id])
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if world.catalog.entities[id].group_as != "":
-            world.state.amount[world.catalog.entities[id].group_as] = 0.0
-            world.state.stats.total_amount[world.catalog.entities[id].group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(world.catalog.entities[id].group_as, ""):
+            world.state.amount[world.catalog.entities[id].group_as] = 0
+            world.state.stats.total_amount[world.catalog.entities[id].group_as] = 0
     return world
 
 func dispose(world) -> void:
@@ -27,52 +28,83 @@ func dispose(world) -> void:
     world.free()
 
 func equivalent(a: Variant, b: Variant) -> bool:
-    if a is Dictionary and b is Dictionary:
-        if a.size() != b.size(): return false
+    if ((a is Dictionary) and (b is Dictionary)):
+        if E.ne(a.size(), b.size()): return false
         for key in a:
-            if not b.has(key) or not equivalent(a[key], b[key]): return false
+            if ((not b.has(key)) or (not equivalent(a[key], b[key]))): return false
         return true
-    if a is Array and b is Array:
-        if a.size() != b.size(): return false
+    if ((a is Array) and (b is Array)):
+        if E.ne(a.size(), b.size()): return false
         for i in a.size():
-            if not equivalent(a[i], b[i]): return false
+            if (not equivalent(a[i], b[i])): return false
         return true
-    if (a is float or a is int) and (b is float or b is int):
-        return absf(float(a) - float(b)) < 1e-6
-    return a == b
+    if E.numeric(a) and E.numeric(b):
+        # Counts must match exactly. Fractional float remainders can differ
+        # when the analytic integral replaces thousands of subtractions.
+        if not E.eq(E.floor_value(a), E.floor_value(b)): return false
+        return E.le(E.absolute(E.subtract(a, b)), E.of("1e-8"))
+    return E.eq(a, b)
 
 func run() -> void:
     for parent in ["LRG", "HRG", "RSG", "RHG"]:
-        for year in [101.0, 101.5, 104.75, 1767.3, 3005.0]:
+        for year in [101, E.of("101.5"), E.of("104.75"), E.of("1767.3"), 3005]:
             var fast = fixture(false)
             var legacy = fixture(true)
-            fast.state.amount[parent] = 20000.0
-            fast.state.amount.RD = 100000.0
-            fast.state.amount.HP = 50.0
-            fast.state.amount.Met = 100.0
-            fast.state.binds.RD = {"HP": 2000.0, "C0.1": 100.0}
-            fast.state.binds[parent] = {"HP": 10.0}
-            fast.state.batches[parent] = [{"amount": 20000.0, "start_year": 100.3, "end_year": 3000.7}]
+            fast.state.amount[parent] = 20000
+            fast.state.amount.RD = 100000
+            fast.state.amount.HP = 50
+            fast.state.amount.Met = 100
+            fast.state.binds.RD = {"HP": 2000, "C0.1": 100}
+            fast.state.binds[parent] = {"HP": 10}
+            fast.state.batches[parent] = [{"amount": 20000, "start_year": E.of("100.3"), "end_year": E.of("3000.7")}]
             # Existing short-lived populations test integration with new arrivals.
-            fast.state.amount.SN = 3.0
-            fast.batches.append_batch(fast.state, "SN", 3.0, 100.5, 100.5)
-            if year == 104.75: fast.state.energy = 7.0
+            fast.state.amount.SN = 3
+            fast.batches.append_batch(fast.state, "SN", 3, E.of("100.5"), E.of("100.5"))
+            if E.eq(year, E.of("104.75")): fast.state.energy = 7
             legacy.state = fast.state.duplicate(true)
             fast.evolution.evolve_batches(fast.state, year)
             legacy.evolution.evolve_batches(legacy.state, year)
             for field in fast.state:
-                check(equivalent(fast.state[field], legacy.state[field]), "%s at %s: %s matches materialized events" % [parent, year, field])
+                check(equivalent(fast.state[field], legacy.state[field]), ("%s at %s: %s matches materialized events" % [parent, year, field]))
             for id in ["SN", "DSN", "BSN", "HN", "GRB", "SGRB", "LGRB", "HGRB"]:
-                check(fast.state.batches.get(id, []).size() <= 3, "Only surviving event windows remain")
+                check(E.le(fast.state.batches.get(id, []).size(), 3), "Only surviving event windows remain")
             dispose(fast)
             dispose(legacy)
     var fast = fixture(false)
     var pending: Dictionary = {}
-    fast.batches.append_batch(fast.state, "SN", 10000.0, 0.25, 1667.25, pending, 1667.25)
-    check(fast.state.batches.SN.size() <= 2 and pending.SN.size() == 1, "Completed windows aggregate without transient batch allocation")
-    var total: float = pending.SN[0].amount
-    for batch in fast.state.batches.SN: total += batch.amount
-    check(total == 10000.0, "Direct completions plus survivors conserve event count")
+    fast.batches.append_batch(fast.state, "SN", 10000, E.of("0.25"), E.of("1667.25"), pending, E.of("1667.25"))
+    check((E.le(fast.state.batches.SN.size(), 2) and E.eq(pending.SN.size(), 1)), "Completed windows aggregate without transient batch allocation")
+    var total: Variant = pending.SN[0].amount
+    for batch in fast.state.batches.SN: total = E.add(total, batch.amount)
+    check(E.eq(total, 10000), "Direct completions plus survivors conserve event count")
     dispose(fast)
-    print("Short-lived events: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    # Dense completed events must not iterate a million elapsed windows.
+    # An aligned, fully completed cohort produces exactly count * lifespan.
+    fast = fixture(false)
+    pending = {}
+    var lifespan: Variant = fast.catalog.entities.SN.lifespan
+    var window: Variant = E.divide(lifespan, root.get_node("Global").batch_count) if E.gt(lifespan, 10) else lifespan
+    var creation_end: Variant = E.multiply(window, 1000000)
+    var dense_count: Variant = E.of("1e20")
+    var integral: Variant = fast.batches.append_batch(fast.state, "SN", dense_count, 0, creation_end, pending, E.add(creation_end, lifespan))
+    check(E.eq(pending.SN[0].amount, dense_count), "Million-window aggregation conserves every event")
+    check(E.eq(integral, E.multiply(dense_count, lifespan)), "Million-window aggregation preserves lifetime integral")
+    check(fast.state.batches.SN.is_empty(), "Completed million-window cohort leaves no transient batches")
+    dispose(fast)
+    # Sparse explosions: thousands of time windows but very few actual events.
+    # Exact interval edges and partial final windows exercise the jump boundary.
+    for count in [1, 3, 17]:
+        for year in [500, 1001]:
+            fast = fixture(false)
+            var legacy = fixture(true)
+            fast.state.amount.RHG = count
+            fast.state.batches.RHG = [{"amount": count, "start_year": E.of("0.25"), "end_year": E.of("1000.25")}]
+            legacy.state = fast.state.duplicate(true)
+            fast.evolution.evolve_batches(fast.state, year)
+            legacy.evolution.evolve_batches(legacy.state, year)
+            for field in fast.state:
+                check(equivalent(fast.state[field], legacy.state[field]), "Sparse %s at %s: %s" % [count, year, field])
+            dispose(fast)
+            dispose(legacy)
+    print(("Short-lived events: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_sparse_batches.gd

@@ -0,0 +1,52 @@
+extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
+var checks: int = 0
+var failures: int = 0
+func _initialize(): call_deferred("run")
+func check(value: bool, message: String):
+    checks += 1
+    if not value:
+        failures += 1
+        push_error(message)
+func run():
+    var world = load("res://world/owniverse/owniverse.gd").new()
+    world.catalog.load_definitions(root.get_node("Global").OwniverseEntities)
+    world.catalog.entities.N.lifespan = 24
+    var width: Variant = E.divide(24, root.get_node("Global").batch_count)
+    for count in [1, 2, 7, 11, 100, E.of("1e40")]:
+        for interval in [[E.of("0.25"), E.of("101.75")], [0, 120], [3, 3]]:
+            world.state.batches = {}
+            world.state.batch_origins = {"N": E.of("0.125")}
+            var expected: Array = []
+            var origin: Variant = world.state.batch_origins.N
+            var index: Variant = E.floor_value(E.divide(E.subtract(interval[0], origin), width))
+            var assigned: Variant = 0
+            var cursor: Variant = interval[0]
+            while true:
+                var start: Variant = E.add(origin, E.multiply(index, width))
+                var end: Variant = E.add(origin, E.multiply(E.add(index, 1), width))
+                if E.le(end, cursor):
+                    index = E.add(index, 1)
+                    continue
+                var until: Variant = E.minimum(interval[1], end)
+                var amount: Variant = E.subtract(count, assigned)
+                if E.gt(interval[1], interval[0]) and E.lt(until, interval[1]):
+                    amount = E.subtract(E.floor_value(E.mul_div(count, E.subtract(until, interval[0]), E.subtract(interval[1], interval[0]))), assigned)
+                if E.gt(amount, 0):
+                    expected.append({"created_from": start, "created_to": end, "start_year": E.add(start, 24), "end_year": E.add(end, 24), "amount": amount})
+                assigned = E.add(assigned, amount)
+                if E.ge(until, interval[1]): break
+                cursor = end
+                index = E.add(index, 1)
+            world.batches.append_batch(world.state, "N", count, interval[0], interval[1])
+            var actual: Array = []
+            for batch in world.state.batches.N:
+                if E.gt(batch.amount, 0): actual.append(batch)
+            check(E.eq(actual, expected), "Sparse jump preserves every nonempty quota and boundary")
+            var total: Variant = 0
+            for batch in actual: total = E.add(total, batch.amount)
+            check(E.eq(total, count), "Sparse jump preserves complete whole population")
+    for entity in world.catalog.entities.values(): entity.free()
+    world.free()
+    print("Sparse batches: %d checks, %d failures" % [checks, failures])
+    quit(1 if failures else 0)

tests/test_sparse_batches.gd.uid

@@ -0,0 +1 @@
+uid://gtvie7p6j62x

tests/test_stellar_rules.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 var checks: int = 0
 var failures: int = 0
 
@@ -6,9 +7,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -17,16 +18,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -37,226 +38,226 @@ func dispose(world) -> void:
 func run() -> void:
     var world = fixture()
     for id in ["DSN", "SN", "BSN", "HN", "SGRB", "GRB", "LGRB", "HGRB"]:
-        check(world.stellar.evolution_products(world.state, world.catalog.entities[id], 3.0).blast == 3.0 * world.catalog.entities[id].blast, "Entity blast determines power: " + id)
-    world.catalog.entities.SN.output_and.blast = 999.0
+        check(E.eq(world.stellar.evolution_products(world.state, world.catalog.entities[id], 3).blast, E.multiply(3, world.catalog.entities[id].blast)), E.add("Entity blast determines power: ", id))
+    world.catalog.entities.SN.output_and.blast = 999
     world.catalog.entities.SN.blast = 4
-    check(world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2.0).blast == 8.0, "Imported output cannot override or double blast power")
+    check(E.eq(world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2).blast, 8), "Imported output cannot override or double blast power")
     world.catalog.entities.SN.blast = 0
-    check(not world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2.0).has("blast"), "Zero entity blast disables external event")
-    world.catalog.entities.SN.output_or = {"positive": "blast:999", "negative": "blast:999", "chance": 50.0}
-    check(not world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2.0).has("blast"), "Alternative output cannot restore disabled blast")
+    check((not world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2).has("blast")), "Zero entity blast disables external event")
+    world.catalog.entities.SN.output_or = {"positive": "blast:999", "negative": "blast:999", "chance": 50}
+    check((not world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2).has("blast")), "Alternative output cannot restore disabled blast")
     dispose(world)
     world = fixture()
     var rd = world.catalog.entities.RD
-    check(rd.planets.HP.chance == 0.01, "Preserve fractional planet probability")
-    check(rd.planets.GG.amount == 2.0 and rd.planets.GG.chance == 0.08, "Read count and chance separately")
-    check(rd._parse_planet_string("HP:1:0.01") == {"HP": {"amount": 1.0, "chance": 0.01}}, "Accept a single planet term")
+    check(E.eq(rd.planets.HP.chance, E.of("0.01")), "Preserve fractional planet probability")
+    check((E.eq(rd.planets.GG.amount, 2) and E.eq(rd.planets.GG.chance, E.of("0.08"))), "Read count and chance separately")
+    check(E.eq(rd._parse_planet_string("HP:1:0.01"), {"HP": {"amount": 1, "chance": E.of("0.01")}}), "Accept a single planet term")
     check(rd._parse_planet_string("").is_empty(), "Empty planet definitions stay empty")
     for id in ["HP", "EON1", "C0.9", "C1.2"]:
-        check(world.catalog.entities[id].blastability, "Blast vulnerable: " + id)
+        check(world.catalog.entities[id].blastability, E.add("Blast vulnerable: ", id))
     for id in ["RP", "GG", "AB", "C1.3", "C1.4", "C1.5"]:
-        check(not world.catalog.entities[id].blastability, "Blast protected: " + id)
+        check((not world.catalog.entities[id].blastability), E.add("Blast protected: ", id))
 
     # Actual GI table: HRG -> SN, with 1% GRB; no random rounding.
     var totals: Dictionary = {}
     for i in 100:
-        var products: Dictionary = world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 1.0)
+        var products: Dictionary = world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 1)
         for id in products:
-            totals[id] = totals.get(id, 0.0) + products[id]
-    check(totals.get("SN") == 99.0 and totals.get("GRB") == 1.0, "GI rare outcomes accumulate deterministically")
+            totals[id] = E.add(totals.get(id, 0), products[id])
+    check((E.eq(totals.get("SN"), 99) and E.eq(totals.get("GRB"), 1)), "GI rare outcomes accumulate deterministically")
     var restored = fixture()
-    restored.state = bytes_to_var(var_to_bytes(world.state))
-    check(world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 37.0) == restored.stellar.evolution_products(restored.state, restored.catalog.entities.HRG, 37.0), "Evolution carry survives serialization")
+    restored.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
+    check(E.eq(world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 37), restored.stellar.evolution_products(restored.state, restored.catalog.entities.HRG, 37)), "Evolution carry survives serialization")
     dispose(restored)
 
     # Real RD lifespan, four stars spread over the existing lifespan/40 window.
-    world.state.amount.N = 0.0
-    world.state.amount.RD = 4.0
-    world.batches.append_batch(world.state, "RD", 4.0, 0.0, 0.0)
-    var lifespan: float = rd.lifespan
-    var width: float = rd.lifespan_delta
+    world.state.amount.N = 0
+    world.state.amount.RD = 4
+    world.batches.append_batch(world.state, "RD", 4, 0, 0)
+    var lifespan: Variant = rd.lifespan
+    var width: Variant = rd.lifespan_delta
     world.evolution.evolve_batches(world.state, lifespan)
-    check(world.state.amount.RD == 4.0, "Window start does not kill the whole batch")
-    world.evolution.evolve_batches(world.state, lifespan + width / 4.0)
-    check(world.state.amount.RD == 3.0 and world.state.amount.TWD == 1.0, "One quarter of a batch evolves")
-    world.evolution.evolve_batches(world.state, lifespan + width / 2.0)
-    check(world.state.amount.RD == 2.0 and world.state.amount.TWD == 2.0, "Half the batch evolves")
-    world.evolution.evolve_batches(world.state, lifespan + width)
-    check(world.state.amount.RD == 0.0 and world.state.amount.TWD == 4.0, "Window end completes evolution")
+    check(E.eq(world.state.amount.RD, 4), "Window start does not kill the whole batch")
+    world.evolution.evolve_batches(world.state, E.add(lifespan, E.divide(width, 4)))
+    check((E.eq(world.state.amount.RD, 3) and E.eq(world.state.amount.TWD, 1)), "One quarter of a batch evolves")
+    world.evolution.evolve_batches(world.state, E.add(lifespan, E.divide(width, 2)))
+    check((E.eq(world.state.amount.RD, 2) and E.eq(world.state.amount.TWD, 2)), "Half the batch evolves")
+    world.evolution.evolve_batches(world.state, E.add(lifespan, width))
+    check((E.eq(world.state.amount.RD, 0) and E.eq(world.state.amount.TWD, 4)), "Window end completes evolution")
     check(world.state.batches.RD.is_empty(), "Completed batch removed")
     dispose(world)
     # Creation accumulates independently for each star/planet pair.
     world = fixture()
-    world.state.amount.RD = 100.0
+    world.state.amount.RD = 100
     for i in 100:
-        world.stellar.create_planets(world.state, "RD", 1.0, 0.0, 0.0, 1.0)
-    check(world.state.binds.RD.HP == 1.0, "100 RD at metallicity 1 produce one HP")
-    check(world.state.binds.RD.RP == 21.0, "Rocky planet probability retains fractions")
-    check(world.state.binds.RD.GG == 16.0 and world.state.binds.RD.AB == 120.0, "Planet multiplicity applied")
-    check(world.state.amount.HP == 0.0 and world.state.stats.total_amount.HP == 1.0, "Created planets are bound, counted once")
+        world.stellar.create_planets(world.state, "RD", 1, 0, 0, 1)
+    check(E.eq(world.state.binds.RD.HP, 1), "100 RD at metallicity 1 produce one HP")
+    check(E.eq(world.state.binds.RD.RP, 21), "Rocky planet probability retains fractions")
+    check((E.eq(world.state.binds.RD.GG, 16) and E.eq(world.state.binds.RD.AB, 120)), "Planet multiplicity applied")
+    check((E.eq(world.state.amount.HP, 0) and E.eq(world.state.stats.total_amount.HP, 1)), "Created planets are bound, counted once")
     var saves: Node = root.get_node("SaveManager")
-    check(saves.validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Planet carry save validates")
+    check(E.eq(saves.validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Planet carry save validates")
     restored = fixture()
-    restored.state = bytes_to_var(var_to_bytes(world.state))
-    world.stellar.create_planets(world.state, "RD", 37.0, 0.0, 0.0, 0.7)
-    restored.stellar.create_planets(restored.state, "RD", 37.0, 0.0, 0.0, 0.7)
-    check(world.state == restored.state, "Planet carry continues after save")
+    restored.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
+    world.stellar.create_planets(world.state, "RD", 37, 0, 0, E.of("0.7"))
+    restored.stellar.create_planets(restored.state, "RD", 37, 0, 0, E.of("0.7"))
+    check(E.eq(world.state, restored.state), "Planet carry continues after save")
     dispose(restored)
     dispose(world)
 
     # A partially dying dwarf sterilizes HP; survivors and RP move to its heir.
     world = fixture()
-    world.state.amount.RD = 4.0
-    world.state.binds.RD = {"HP": 8.0, "RP": 4.0, "C1.2": 4.0, "C1.3": 4.0, "GG": 4.0}
-    world.batches.append_batch(world.state, "RD", 4.0, 0.0, 0.0)
-    world.evolution.evolve_batches(world.state, lifespan + width / 2.0)
-    check(world.state.amount.RD == 2.0 and world.state.amount.TWD == 2.0, "Partial star transition with planets")
-    check(world.state.binds.RD.HP + world.state.binds.TWD.HP == 4.0, "Half of HP sterilized")
-    check(world.state.binds.RD["C1.3"] == 2.0 and world.state.binds.TWD["C1.3"] == 2.0, "Protected civilization splits between parent and heir")
-    check(world.state.binds.RD.RP + world.state.binds.TWD.RP == 10.0, "Sterilized planets become RP without loss")
-    check(world.state.amount.RP == 0.0 and world.state.amount["C1.3"] == 0.0, "Inherited planets never become free")
-    world.evolution.evolve_batches(world.state, lifespan + width)
-    check(world.state.binds.RD["C1.3"] == 0.0 and world.state.binds.TWD["C1.3"] == 4.0, "No planets left at extinct parent type")
-    check(saves.validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Inherited state validates")
+    world.state.amount.RD = 4
+    world.state.binds.RD = {"HP": 8, "RP": 4, "C1.2": 4, "C1.3": 4, "GG": 4}
+    world.batches.append_batch(world.state, "RD", 4, 0, 0)
+    world.evolution.evolve_batches(world.state, E.add(lifespan, E.divide(width, 2)))
+    check((E.eq(world.state.amount.RD, 2) and E.eq(world.state.amount.TWD, 2)), "Partial star transition with planets")
+    check(E.eq(E.add(world.state.binds.RD.HP, world.state.binds.TWD.HP), 4), "Half of HP sterilized")
+    check((E.eq(world.state.binds.RD["C1.3"], 2) and E.eq(world.state.binds.TWD["C1.3"], 2)), "Protected civilization splits between parent and heir")
+    check(E.eq(E.add(world.state.binds.RD.RP, world.state.binds.TWD.RP), 10), "Sterilized planets become RP without loss")
+    check((E.eq(world.state.amount.RP, 0) and E.eq(world.state.amount["C1.3"], 0)), "Inherited planets never become free")
+    world.evolution.evolve_batches(world.state, E.add(lifespan, width))
+    check((E.eq(world.state.binds.RD["C1.3"], 0) and E.eq(world.state.binds.TWD["C1.3"], 4)), "No planets left at extinct parent type")
+    check(E.eq(saves.validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Inherited state validates")
     dispose(world)
 
     world = fixture()
-    world.state.amount.WS = 2.0
-    world.state.binds.WS = {"HP": 4.0, "C1.3": 4.0, "RP": 4.0, "GG": 4.0}
-    world.batches.append_batch(world.state, "WS", 2.0, 0.0, 0.0)
-    world.evolution.evolve_batches(world.state, world.catalog.entities.WS.lifespan + world.catalog.entities.WS.lifespan_delta)
+    world.state.amount.WS = 2
+    world.state.binds.WS = {"HP": 4, "C1.3": 4, "RP": 4, "GG": 4}
+    world.batches.append_batch(world.state, "WS", 2, 0, 0)
+    world.evolution.evolve_batches(world.state, E.add(world.catalog.entities.WS.lifespan, world.catalog.entities.WS.lifespan_delta))
     var physical: Dictionary = world.ledger.physical_amounts(world.state)
-    check(physical.HP == 0.0 and physical["C1.3"] == 0.0 and physical.RP == 0.0 and physical.GG == 0.0, "Level 2 removes all planets, including protected civilization")
-    check(world.state.amount.LRG == 2.0, "Giant evolves after local destruction")
+    check((((E.eq(physical.HP, 0) and E.eq(physical["C1.3"], 0)) and E.eq(physical.RP, 0)) and E.eq(physical.GG, 0)), "Level 2 removes all planets, including protected civilization")
+    check(E.eq(world.state.amount.LRG, 2), "Giant evolves after local destruction")
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 10.0
-    world.state.binds.RD = {"HP": 10.0, "C1.2": 10.0, "C1.3": 10.0, "RP": 0.0}
-    world.stellar.apply_blast(world.state, 5.0, {"blast": 1.0, "density": 1.0})
-    check(world.state.binds.RD.HP == 5.0 and world.state.binds.RD["C1.2"] == 5.0, "Blast damages vulnerable worlds proportionally")
-    check(world.state.binds.RD["C1.3"] == 10.0 and world.state.binds.RD.RP == 10.0, "Blast protects C1.3 and creates RP")
-    world.stellar.apply_blast(world.state, 1e6, {"blast": 1.0, "density": 1.0})
-    check(world.state.binds.RD.HP == 0.0 and world.state.binds.RD.RP == 20.0, "Overwhelming blast is capped at available planets")
-    check(not world.state.amount.has("blast"), "Blast is not a resource")
+    world.state.amount.RD = 10
+    world.state.binds.RD = {"HP": 10, "C1.2": 10, "C1.3": 10, "RP": 0}
+    world.stellar.apply_blast(world.state, 5, {"blast": 1, "density": 1})
+    check((E.eq(world.state.binds.RD.HP, 5) and E.eq(world.state.binds.RD["C1.2"], 5)), "Blast damages vulnerable worlds proportionally")
+    check((E.eq(world.state.binds.RD["C1.3"], 10) and E.eq(world.state.binds.RD.RP, 10)), "Blast protects C1.3 and creates RP")
+    world.stellar.apply_blast(world.state, 1000000, {"blast": 1, "density": 1})
+    check((E.eq(world.state.binds.RD.HP, 0) and E.eq(world.state.binds.RD.RP, 20)), "Overwhelming blast is capped at available planets")
+    check((not world.state.amount.has("blast")), "Blast is not a resource")
     dispose(world)
 
     world = fixture()
-    world.state.amount.RD = 1.0
-    world.state.binds.RD = {"HP": 1.0}
+    world.state.amount.RD = 1
+    world.state.binds.RD = {"HP": 1}
     for i in 10:
-        world.stellar.apply_blast(world.state, 1.0, {"blast": 1.0, "density": 0.1})
-    check(world.state.binds.RD.HP == 0.0 and world.state.binds.RD.RP == 1.0, "Small blast effects accumulate across cycles")
+        world.stellar.apply_blast(world.state, 1, {"blast": 1, "density": E.of("0.1")})
+    check((E.eq(world.state.binds.RD.HP, 0) and E.eq(world.state.binds.RD.RP, 1)), "Small blast effects accumulate across cycles")
     dispose(world)
 
     # Actual supernova output: one SN gives a neutron star, resources, and an event.
     world = fixture()
-    world.state.amount.SN = 1.0
-    world.batches.append_batch(world.state, "SN", 1.0, 0.0, 0.0)
-    world.evolution.evolve_batches(world.state, 2.0)
-    check(world.state.amount.SN == 0.0 and world.state.amount.LNS == 1.0, "Supernova produces a remnant")
-    check(world.state.amount.H == 8.0 and world.state.amount.He == 50.0 and world.state.amount.Met == 11.0, "Supernova returns table resources")
-    check(not world.state.amount.has("blast"), "Supernova dispatches blast output")
-    check(saves.validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Blast state validates")
+    world.state.amount.SN = 1
+    world.batches.append_batch(world.state, "SN", 1, 0, 0)
+    world.evolution.evolve_batches(world.state, 2)
+    check((E.eq(world.state.amount.SN, 0) and E.eq(world.state.amount.LNS, 1)), "Supernova produces a remnant")
+    check(((E.eq(world.state.amount.H, 8) and E.eq(world.state.amount.He, 50)) and E.eq(world.state.amount.Met, 11)), "Supernova returns table resources")
+    check((not world.state.amount.has("blast")), "Supernova dispatches blast output")
+    check(E.eq(saves.validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Blast state validates")
     dispose(world)
 
     world = fixture()
-    world.state.amount.H = 1000.0
-    world.state.amount.Met = 100.0
-    check(world.production.produce("RD", 100.0) == 100.0, "Manual star creation succeeds")
-    check(world.state.binds.RD.HP >= 1.0, "Manual creation dispatches planet formation")
-    check(world.state.amount.H == 900.0, "Planet creation does not duplicate or spend stellar fuel")
+    world.state.amount.H = 1000
+    world.state.amount.Met = 100
+    check(E.eq(world.production.produce("RD", 100), 100), "Manual star creation succeeds")
+    check(E.ge(world.state.binds.RD.HP, 1), "Manual creation dispatches planet formation")
+    check(E.eq(world.state.amount.H, 900), "Planet creation does not duplicate or spend stellar fuel")
     dispose(world)
 
     world = fixture()
-    world.state.amount.N = 0.0
-    world.state.amount.RD = 1.0
-    world.state.amount.H = 100.0
-    world.state.amount.Met = 100.0
-    world.state.auto_resources.H = 100.0
-    world.evolute(0.1)
-    check(world.state.amount.RD == 101.0 and world.state.amount.H == 0.0, "Automatic formation uses its resource budget")
-    check(world.state.binds.RD.HP >= 1.0, "Automatic formation also creates planets")
+    world.state.amount.N = 0
+    world.state.amount.RD = 1
+    world.state.amount.H = 100
+    world.state.amount.Met = 100
+    world.state.auto_resources.H = 100
+    world.evolute(E.of("0.1"))
+    check((E.eq(world.state.amount.RD, 101) and E.eq(world.state.amount.H, 0)), "Automatic formation uses its resource budget")
+    check(E.ge(world.state.binds.RD.HP, 1), "Automatic formation also creates planets")
     dispose(world)
 
     world = fixture()
-    world.catalog.entities.N.auto = 1.0
+    world.catalog.entities.N.auto = 1
     # 1000 newly produced automatic H reserve 1 H, enough for 10 HBD.
-    world.evolute(100.0)
-    check(world.state.amount.HBD == 10.0, "Brown dwarfs form without existing ordinary stars")
-    check(world.state.amount.H == 999.0 and world.state.auto_resources.H == 999.0, "Brown dwarfs consume exactly their reserved hydrogen")
-    check(world.presentation.amounts(world.state, world.catalog).BD == 10.0 and world.state.batches.HBD.size() > 0, "Brown dwarfs appear in counter and evolution batches")
-    world.catalog.entities.N.product_per_year_amount = 0.0
-    world.evolute(100.0)
-    check(world.state.amount.HBD == 10.0, "Stored automatic budget is not taxed repeatedly")
+    world.evolute(100)
+    check(E.eq(world.state.amount.HBD, 10), "Brown dwarfs form without existing ordinary stars")
+    check((E.eq(world.state.amount.H, 999) and E.eq(world.state.auto_resources.H, 999)), "Brown dwarfs consume exactly their reserved hydrogen")
+    check((E.eq(world.presentation.amounts(world.state, world.catalog).BD, 10) and E.gt(world.state.batches.HBD.size(), 0)), "Brown dwarfs appear in counter and evolution batches")
+    world.catalog.entities.N.product_per_year_amount = 0
+    world.evolute(100)
+    check(E.eq(world.state.amount.HBD, 10), "Stored automatic budget is not taxed repeatedly")
     dispose(world)
 
     world = fixture()
-    world.catalog.entities.N.auto = 1.0
-    world.state.amount.RD = 1.0
-    world.evolute(50.0)
-    check(world.state.amount.HBD == 5.0 and is_equal_approx(world.state.auto_star_deficits.HBD_fuel, 0.5), "Individual dwarfs retain prepaid fractional fuel")
-    check(world.state.amount.H == 0.0, "Prepaid fuel is not available to ordinary stars")
+    world.catalog.entities.N.auto = 1
+    world.state.amount.RD = 1
+    world.evolute(50)
+    check((E.eq(world.state.amount.HBD, 5) and E.near(world.state.auto_star_deficits.HBD_fuel, E.of("0.5"))), "Individual dwarfs retain prepaid fractional fuel")
+    check(E.eq(world.state.amount.H, 0), "Prepaid fuel is not available to ordinary stars")
     var resumed = fixture()
-    resumed.catalog.entities.N.auto = 1.0
-    resumed.state = bytes_to_var(var_to_bytes(world.state))
-    world.evolute(50.0)
-    resumed.evolute(50.0)
-    check(world.state.amount.HBD == 10.0, "Accumulated quota eventually creates a whole batch")
-    check(world.state == resumed.state, "Brown dwarf quota survives serialization deterministically")
-    check(world.state.amount.RD == 1000.0 and world.state.amount.H == 0.0, "Shared automatic hydrogen is spent once")
-    world.state.batches.HBD = [{"amount": 10.0, "start_year": 101.0, "end_year": 101.0}]
-    world.evolution.evolve_batches(world.state, 101.0)
-    check(world.state.amount.HBD == 0.0 and world.state.amount.CBD == 10.0 and world.presentation.amounts(world.state, world.catalog).BD == 10.0, "Cooling preserves aggregate brown dwarf count")
+    resumed.catalog.entities.N.auto = 1
+    resumed.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
+    world.evolute(50)
+    resumed.evolute(50)
+    check(E.eq(world.state.amount.HBD, 10), "Accumulated quota eventually creates a whole batch")
+    check(E.eq(world.state, resumed.state), "Brown dwarf quota survives serialization deterministically")
+    check((E.eq(world.state.amount.RD, 1000) and E.eq(world.state.amount.H, 0)), "Shared automatic hydrogen is spent once")
+    world.state.batches.HBD = [{"amount": 10, "start_year": 101, "end_year": 101}]
+    world.evolution.evolve_batches(world.state, 101)
+    check(((E.eq(world.state.amount.HBD, 0) and E.eq(world.state.amount.CBD, 10)) and E.eq(world.presentation.amounts(world.state, world.catalog).BD, 10)), "Cooling preserves aggregate brown dwarf count")
     dispose(resumed)
     dispose(world)
 
     world = fixture()
     var saw_individual: bool = false
     for i in range(250):
-        world.state.amount.H += 1.0
-        world.state.auto_resources.H = world.state.auto_resources.get("H", 0.0) + 1.0
-        var before: float = world.state.amount.HBD
-        world.automatic.produce_brown_dwarfs(world.state, 1.0, float(i), float(i + 1))
-        var born: float = world.state.amount.HBD - before
-        check(born == 0.0 or born == 1.0, "Small fuel increments produce individual dwarfs")
-        saw_individual = saw_individual or born == 1.0
+        world.state.amount.H = E.add(world.state.amount.H, 1)
+        world.state.auto_resources.H = E.add(world.state.auto_resources.get("H", 0), 1)
+        var before: Variant = world.state.amount.HBD
+        world.automatic.produce_brown_dwarfs(world.state, 1, E.of(i), E.of(E.add(i, 1)))
+        var born: Variant = E.subtract(world.state.amount.HBD, before)
+        check((E.eq(born, 0) or E.eq(born, 1)), "Small fuel increments produce individual dwarfs")
+        saw_individual = (saw_individual or E.eq(born, 1))
     check(saw_individual, "Random rounding does not wait for ten dwarfs")
     resumed = fixture()
-    resumed.state = bytes_to_var(var_to_bytes(world.state))
+    resumed.state = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
     for i in range(250, 500):
         for simulation in [world, resumed]:
-            simulation.state.amount.H += 1.0
-            simulation.state.auto_resources.H += 1.0
-            simulation.automatic.produce_brown_dwarfs(simulation.state, 1.0, float(i), float(i + 1))
-    check(world.state == resumed.state, "Random sequence and prepaid fuel survive saving")
-    check(is_equal_approx(world.state.amount.H + world.state.amount.HBD * 0.1 + world.state.auto_star_deficits.HBD_fuel, 500.0), "Individual production conserves fuel including prepaid reserve")
-    check(is_equal_approx(world.state.amount.HBD + world.state.auto_star_deficits.HBD, 5.0), "Signed remainder preserves the 0.1 percent allocation")
-    var paused_count: float = world.state.amount.HBD
-    for i in 10: world.automatic.produce_brown_dwarfs(world.state, 0.0, 500.0, 501.0)
-    check(world.state.amount.HBD == paused_count, "No repeated random attempts without new fuel")
+            simulation.state.amount.H = E.add(simulation.state.amount.H, 1)
+            simulation.state.auto_resources.H = E.add(simulation.state.auto_resources.H, 1)
+            simulation.automatic.produce_brown_dwarfs(simulation.state, 1, E.of(i), E.of(E.add(i, 1)))
+    check(E.eq(world.state, resumed.state), "Random sequence and prepaid fuel survive saving")
+    check(E.near(E.add(E.add(world.state.amount.H, E.multiply(world.state.amount.HBD, E.of("0.1"))), world.state.auto_star_deficits.HBD_fuel), 500), "Individual production conserves fuel including prepaid reserve")
+    check(E.near(E.add(world.state.amount.HBD, world.state.auto_star_deficits.HBD), 5), "Signed remainder preserves the 0.1 percent allocation")
+    var paused_count: Variant = world.state.amount.HBD
+    for i in 10: world.automatic.produce_brown_dwarfs(world.state, 0, 500, 501)
+    check(E.eq(world.state.amount.HBD, paused_count), "No repeated random attempts without new fuel")
     dispose(resumed)
     dispose(world)
 
     # Two simultaneous successors share surviving planets in the same 99:1 ratio.
     world = fixture()
     world.catalog.entities.HRG.destroy_level = 0
-    world.state.amount.HRG = 100.0
-    world.state.binds.HRG = {"C1.3": 100.0}
-    world.state.batches.HRG = [{"start_year": 0.1, "end_year": 0.1, "amount": 100.0}]
-    world.evolution.evolve_batches(world.state, 0.1)
-    check(world.state.binds.SN["C1.3"] == 99.0 and world.state.binds.GRB["C1.3"] == 1.0, "Planets split among actual alternative successors")
-    check(world.state.binds.HRG["C1.3"] == 0.0, "Alternative evolution leaves no orphan bindings")
+    world.state.amount.HRG = 100
+    world.state.binds.HRG = {"C1.3": 100}
+    world.state.batches.HRG = [{"start_year": E.of("0.1"), "end_year": E.of("0.1"), "amount": 100}]
+    world.evolution.evolve_batches(world.state, E.of("0.1"))
+    check((E.eq(world.state.binds.SN["C1.3"], 99) and E.eq(world.state.binds.GRB["C1.3"], 1)), "Planets split among actual alternative successors")
+    check(E.eq(world.state.binds.HRG["C1.3"], 0), "Alternative evolution leaves no orphan bindings")
     dispose(world)
 
     world = fixture()
-    world.state.amount.N = 0.0
-    world.state.amount.HRG = 1.0
-    world.state.batches.HRG = [{"start_year": 0.1, "end_year": 0.1, "amount": 1.0}]
-    world.evolute(3.0)
-    check(world.state.amount.LNS == 1.0 and world.state.amount.SN == 0.0, "Long step follows multiple stellar generations")
-    check(world.state.amount.S >= 99.0, "Short-lived newborn supernova emits S before disappearing")
+    world.state.amount.N = 0
+    world.state.amount.HRG = 1
+    world.state.batches.HRG = [{"start_year": E.of("0.1"), "end_year": E.of("0.1"), "amount": 1}]
+    world.evolute(3)
+    check((E.eq(world.state.amount.LNS, 1) and E.eq(world.state.amount.SN, 0)), "Long step follows multiple stellar generations")
+    check(E.ge(world.state.amount.S, 99), "Short-lived newborn supernova emits S before disappearing")
     dispose(world)
 
-    print("Stellar rules: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("Stellar rules: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_time.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const Clock = preload("res://world/owniverse/simulation_time.gd")
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -18,16 +19,16 @@ func fixture():
     for id in global.OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(global.OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     world.catalog.entities["N"].life_product = {}
     world.catalog.entities["N"].product_per_year_type = "H"
-    world.catalog.entities["N"].product_per_year_amount = 10.0
-    world.catalog.entities["N"].auto = 0.0
-    world.state.amount.N = 1.0
+    world.catalog.entities["N"].product_per_year_amount = 10
+    world.catalog.entities["N"].auto = 0
+    world.state.amount.N = 1
     return world
 
 func dispose(world) -> void:
@@ -38,55 +39,55 @@ func dispose(world) -> void:
 func run() -> void:
     var saves: Node = root.get_node("SaveManager")
     var world = fixture()
-    world.evolute(0.09)
-    check(world.state.time.year == 0.0, "Do not process before a tenth boundary")
-    check(world.state.amount.H == 0.0, "No premature production")
-    world.evolute(0.01)
-    check(world.state.time.year == 0.1, "Process the first tenth")
-    check(world.state.amount.H == 1.0, "Production runs at 0.1 year")
-    world.evolute(0.2)
-    check(world.state.time.year == 0.3 and world.state.amount.H == 3.0, "Do not reprocess previous tenths")
+    world.evolute(E.of("0.09"))
+    check(E.eq(world.state.time.year, 0), "Do not process before a tenth boundary")
+    check(E.eq(world.state.amount.H, 0), "No premature production")
+    world.evolute(E.of("0.01"))
+    check(E.eq(world.state.time.year, E.of("0.1")), "Process the first tenth")
+    check(E.eq(world.state.amount.H, 1), "Production runs at 0.1 year")
+    world.evolute(E.of("0.2"))
+    check((E.eq(world.state.time.year, E.of("0.3")) and E.eq(world.state.amount.H, 3)), "Do not reprocess previous tenths")
     var before: Dictionary = world.state.duplicate(true)
-    for invalid in [0.0, -1.0, NAN, INF, 1e308]:
+    for invalid in [0, E.neg(1), NAN, INF, 1e308]:
         world.evolute(invalid)
-        check(world.state == before, "Invalid/overflow interval rejected")
-    check(saves.validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": world.state}) == "", "Fractional save is valid")
+        check(E.eq(world.state, before), "Invalid/overflow interval rejected")
+    check(E.eq(saves.validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": world.state}), ""), "Fractional save is valid")
     var invalid_save: Dictionary = world.state.duplicate(true)
-    invalid_save.time.year = 0.25
-    check(saves.validate_data({"format_version": 2, "app_version": "", "ui": {"current_page": 0}, "state": invalid_save}) != "", "Reject inconsistent fractional clock")
+    invalid_save.time.year = E.of("0.25")
+    check(E.ne(saves.validate_data({"format_version": 5, "app_version": "", "ui": {"current_page": 0}, "state": invalid_save}), ""), "Reject inconsistent fractional clock")
     dispose(world)
 
     for fps in [30, 60, 144]:
         world = fixture()
         for frame in fps:
-            world.evolute(1.0 / fps)
-        check(world.state.time.year == 1.0, "One second at %d fps" % fps)
-        check(world.state.amount.H == 10.0, "Production across frames at %d fps" % fps)
+            world.evolute(E.divide(1, fps))
+        check(E.eq(world.state.time.year, 1), ("One second at %d fps" % fps))
+        check(E.eq(world.state.amount.H, 10), ("Production across frames at %d fps" % fps))
         dispose(world)
 
     world = fixture()
-    world.evolute(0.05)
+    world.evolute(E.of("0.05"))
     world.speed = 2
-    world.evolute(0.005)
-    check(world.state.time.year == 0.1, "Speed change preserves accumulated fraction")
+    world.evolute(E.of("0.005"))
+    check(E.eq(world.state.time.year, E.of("0.1")), "Speed change preserves accumulated fraction")
     world.speed = 100
     var speed_limit: int = root.get_node("Global").SPEED_LIMIT
-    check(world.speed == speed_limit and world.state.speed_in_year == pow(10.0, speed_limit - 1), "Configured upper speed limit")
-    world.speed = -10
-    check(world.speed == 1 and world.state.speed_in_year == 1.0, "Lower speed limit unchanged")
+    check((E.eq(world.speed, speed_limit) and E.eq(world.state.speed_in_year, E.power(10, E.subtract(speed_limit, 1)))), "Configured upper speed limit")
+    world.speed = E.neg(10)
+    check((E.eq(world.speed, 1) and E.eq(world.state.speed_in_year, 1)), "Lower speed limit unchanged")
     dispose(world)
 
     world = fixture()
     dispose(world)
 
     world = fixture()
-    world.catalog.entities.N.output_and = {"He": 1.0}
+    world.catalog.entities.N.output_and = {"He": 1}
     world.catalog.entities.N.output_or = {}
-    world.state.batches.N = [{"start_year": 0.1, "end_year": 0.1, "amount": 1.0}]
-    world.evolute(0.1)
-    check(world.state.amount.N == 0.0 and world.state.amount.He == 1.0, "Existing evolution executes at fractional boundary")
+    world.state.batches.N = [{"start_year": E.of("0.1"), "end_year": E.of("0.1"), "amount": 1}]
+    world.evolute(E.of("0.1"))
+    check((E.eq(world.state.amount.N, 0) and E.eq(world.state.amount.He, 1)), "Existing evolution executes at fractional boundary")
     dispose(world)
-    check(Clock.processed_year(0.099) == 0.0, "Do not round a genuine incomplete tenth forward")
-    check(Clock.processed_year(1e9 + 0.45) == 1e9 + 0.4, "Large ages preserve fractional precision")
-    print("Time state: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    check(E.eq(Clock.processed_year(E.of("0.099")), 0), "Do not round a genuine incomplete tenth forward")
+    check(E.eq(Clock.processed_year(E.add(E.of("1e9"), E.of("0.45"))), E.add(E.of("1e9"), E.of("0.4"))), "Large ages preserve fractional precision")
+    print(("Time state: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_ui_updates.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 
 var checks: int = 0
 var failures: int = 0
@@ -7,9 +8,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(value: bool, message: String) -> void:
-    checks += 1
-    if not value:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not value):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func run() -> void:
@@ -22,39 +23,39 @@ func run() -> void:
     await process_frame
     stage.stage_page_scroller.scroll_horizontal = stage.PAGE_WIDTH
     await process_frame
-    stage.owniverse.state.amount.H = 1000.0
-    stage.owniverse.state.amount.RD = 2.0
+    stage.owniverse.state.amount.H = 1000
+    stage.owniverse.state.amount.RD = 2
     stage.owniverse.presentation.refresh(stage.owniverse.state, stage.owniverse.catalog)
     stage.set_owniverse_item_value()
     var hydrogen = stage.owniverse_items.H
     var dwarf = stage.owniverse_items.RD
-    check(hydrogen.description.text == "1 000", "Pending quantities reach controls")
-    check(dwarf.description.text == "2", "Other page receives its current quantity")
+    check(E.eq(hydrogen.description.text, "1 000"), "Pending quantities reach controls")
+    check(E.eq(dwarf.description.text, "2"), "Other page receives its current quantity")
     check(stage.owniverse.presentation.pending_amounts.is_empty(), "Published queue is consumed by Stage")
     stage.owniverse.presentation.deferred_updates = true
-    stage.owniverse.state.amount.H = 2000.0
+    stage.owniverse.state.amount.H = 2000
     stage.owniverse.presentation.refresh(stage.owniverse.state, stage.owniverse.catalog)
-    check(stage.owniverse.presentation.dirty and stage.owniverse.presentation.pending_amounts.is_empty(), "Deferred refresh marks dirty without republishing")
+    check((stage.owniverse.presentation.dirty and stage.owniverse.presentation.pending_amounts.is_empty()), "Deferred refresh marks dirty without republishing")
     stage.set_owniverse_item_value()
-    check(hydrogen.description.text == "1 000", "Labels retain last published quantity")
+    check(E.eq(hydrogen.description.text, "1 000"), "Labels retain last published quantity")
     stage.owniverse.presentation.refresh(stage.owniverse.state, stage.owniverse.catalog, true)
     stage.set_owniverse_item_value()
-    check(hydrogen.description.text == "2 000" and not stage.owniverse.presentation.dirty, "Forced refresh publishes latest state")
+    check((E.eq(hydrogen.description.text, "2 000") and (not stage.owniverse.presentation.dirty)), "Forced refresh publishes latest state")
     stage.owniverse.presentation.deferred_updates = false
     stage.item_activated(hydrogen)
     stage.set_owniverse_item_value()
-    check(hydrogen.description.text == root.get_node("Global").format_number(stage.owniverse.state.amount.H), "Player production publishes the new quantity")
-    check(stage.owniverse.state.amount.H > 2000.0, "Production action actually executed")
+    check(E.eq(hydrogen.description.text, root.get_node("Global").format_number(stage.owniverse.state.amount.H)), "Player production publishes the new quantity")
+    check(E.gt(stage.owniverse.state.amount.H, 2000), "Production action actually executed")
     dwarf.visible = true
-    stage.stage_page_scroller.scroll_horizontal = 2 * stage.PAGE_WIDTH
+    stage.stage_page_scroller.scroll_horizontal = E.multiply(2, stage.PAGE_WIDTH)
     await process_frame
     stage._refresh_universe_ui()
-    check(dwarf.description.text == "2", "Newly visible page receives cached latest values")
-    stage.owniverse.state.time.year = 1234.5
+    check(E.eq(dwarf.description.text, "2"), "Newly visible page receives cached latest values")
+    stage.owniverse.state.time.year = E.of("1234.5")
     stage._refresh_universe_ui()
-    check(stage.date_time.text == "1 234.5", "Time displays tenths with thousands separator")
+    check(E.eq(stage.date_time.text, "1 234.5"), "Time displays tenths with thousands separator")
     for entity in stage.owniverse.catalog.entities.values(): entity.free()
     stage.owniverse.free()
     scene.free()
-    print("UI updates: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("UI updates: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

tests/test_world_indicators.gd

@@ -1,4 +1,5 @@
 extends SceneTree
+const E = preload("res://world/owniverse/math/exact.gd")
 const CivilizationState = preload("res://world/owniverse/civilization_state.gd")
 const CivilizationEvolution = preload("res://world/owniverse/civilization_evolution.gd")
 
@@ -11,9 +12,9 @@ func _initialize() -> void:
     call_deferred("run")
 
 func check(condition: bool, message: String) -> void:
-    checks += 1
-    if not condition:
-        failures += 1
+    checks = E.add(checks, 1)
+    if (not condition):
+        failures = E.add(failures, 1)
         push_error(message)
 
 func fixture():
@@ -21,11 +22,11 @@ func fixture():
     for id in root.get_node("Global").OwniverseEntities:
         var entity = load("res://world/owniverse/owniverse_entity.gd").new(root.get_node("Global").OwniverseEntities[id])
         world.catalog.entities[id] = entity
-        world.state.amount[id] = 0.0
-        world.state.stats.total_amount[id] = 0.0
-        if entity.group_as != "":
-            world.state.amount[entity.group_as] = 0.0
-            world.state.stats.total_amount[entity.group_as] = 0.0
+        world.state.amount[id] = 0
+        world.state.stats.total_amount[id] = 0
+        if E.ne(entity.group_as, ""):
+            world.state.amount[entity.group_as] = 0
+            world.state.stats.total_amount[entity.group_as] = 0
     return world
 
 func dispose(world) -> void:
@@ -35,116 +36,116 @@ func dispose(world) -> void:
 func run() -> void:
     var global: Node = root.get_node("Global")
     var world = fixture()
-    world.state.amount.RD = 400.0
-    world.batches.append_batch(world.state, "RD", 400.0, 0.0, 0.0)
-    var end: float = world.state.batches.RD[0].end_year
-    world.environment.modify_world_parameter("Bur", 9.0)
-    check(is_equal_approx(world.state.batches.RD[0].end_year, end / 10.0), "Burnability accelerates existing cohorts")
-    var count: float = world.state.batches.RD[0].amount
-    world.environment.modify_world_parameter("Bur", -9.0)
-    check(is_equal_approx(world.state.batches.RD[0].end_year, end) and world.state.batches.RD[0].amount == count, "Changing burnability back preserves population and lifetime")
-    world.environment.modify_world_parameter("Bur", 9.0)
-    world.batches.append_batch(world.state, "YD", 10.0, 0.0, 0.0)
-    check(is_equal_approx(world.state.batches.YD[0].start_year, world.catalog.entities.YD.lifespan / 10.0), "New stars use the same burnability")
-    world.state.time = {"datetime": end / 10.0 - 0.1, "year": end / 10.0 - 0.1}
+    world.state.amount.RD = 400
+    world.batches.append_batch(world.state, "RD", 400, 0, 0)
+    var end: Variant = world.state.batches.RD[0].end_year
+    world.environment.modify_world_parameter("Bur", 9)
+    check(E.near(world.state.batches.RD[0].end_year, E.divide(end, 10)), "Burnability accelerates existing cohorts")
+    var count: Variant = world.state.batches.RD[0].amount
+    world.environment.modify_world_parameter("Bur", E.neg(9))
+    check((E.near(world.state.batches.RD[0].end_year, end) and E.eq(world.state.batches.RD[0].amount, count)), "Changing burnability back preserves population and lifetime")
+    world.environment.modify_world_parameter("Bur", 9)
+    world.batches.append_batch(world.state, "YD", 10, 0, 0)
+    check(E.near(world.state.batches.YD[0].start_year, E.divide(world.catalog.entities.YD.lifespan, 10)), "New stars use the same burnability")
+    world.state.time = {"datetime": E.subtract(E.divide(end, 10), E.of("0.1")), "year": E.subtract(E.divide(end, 10), E.of("0.1"))}
     world.batches.withdraw_batches(world.state, "RD", world.state.time.year)
-    world.environment.modify_world_parameter("Bur", -18.0)
-    check(world.state.batches.RD[0].end_year >= world.state.time.year, "Slowing a partially evolved cohort keeps its remaining window in the future")
-    world.environment.modify_world_parameter("Exp", 9.0)
-    check(world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2.0).blast == 180.0, "Explosion power includes world explosiveness")
-    var products: Dictionary = world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 1000.0)
-    check(products.get("GRB", 0.0) == 100.0 and products.get("SN", 0.0) == 900.0, "Explosiveness raises rare-event probability without duplicating stars")
-    world.catalog.entities.HRG.output_or.chance = 50.0
-    products = world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 100.0)
-    check(products.get("GRB", 0.0) == 100.0 and products.get("SN", 0.0) == 0.0, "Rare-event probability is bounded at one")
+    world.environment.modify_world_parameter("Bur", E.neg(18))
+    check(E.ge(world.state.batches.RD[0].end_year, world.state.time.year), "Slowing a partially evolved cohort keeps its remaining window in the future")
+    world.environment.modify_world_parameter("Exp", 9)
+    check(E.eq(world.stellar.evolution_products(world.state, world.catalog.entities.SN, 2).blast, 180), "Explosion power includes world explosiveness")
+    var products: Dictionary = world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 1000)
+    check((E.eq(products.get("GRB", 0), 100) and E.eq(products.get("SN", 0), 900)), "Explosiveness raises rare-event probability without duplicating stars")
+    world.catalog.entities.HRG.output_or.chance = 50
+    products = world.stellar.evolution_products(world.state, world.catalog.entities.HRG, 100)
+    check((E.eq(products.get("GRB", 0), 100) and E.eq(products.get("SN", 0), 0)), "Rare-event probability is bounded at one")
     dispose(world)
 
     world = fixture()
-    var ordinary: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000.0)
+    var ordinary: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000)
     world.state.life_remainders.clear()
-    world.environment.modify_world_parameter("Agg", 9.0)
-    var aggressive: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000.0)
-    check(aggressive.EON1 > ordinary.EON1, "Aggression accelerates primitive evolution")
+    world.environment.modify_world_parameter("Agg", 9)
+    var aggressive: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000)
+    check(E.gt(aggressive.EON1, ordinary.EON1), "Aggression accelerates primitive evolution")
     world.state.life_remainders.clear()
-    world.state.world_parameters.Order = 10.0
-    var orderly: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000.0)
-    check(orderly.RP < aggressive.RP, "Order reduces degradation")
+    world.state.world_parameters.Order = 10
+    var orderly: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000)
+    check(E.lt(orderly.RP, aggressive.RP), "Order reduces degradation")
     world.state.life_remainders.clear()
-    world.state.world_parameters.Enlightenment = 10.0
-    var enlightened: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000.0)
-    check(enlightened.EON1 > orderly.EON1, "Enlightenment increases primitive progress")
+    world.state.world_parameters.Enlightenment = 10
+    var enlightened: Dictionary = world.life.life_products(world.state, world.catalog.entities.HP, 1000000)
+    check(E.gt(enlightened.EON1, orderly.EON1), "Enlightenment increases primitive progress")
     dispose(world)
 
     world = fixture()
     var hotter = fixture()
     for simulation in [world, hotter]:
-        simulation.state.amount.RD = 1000000.0
-        simulation.batches.append_batch(simulation.state, "RD", 1000000.0, 0.0, 0.0)
-    hotter.environment.modify_world_parameter("Bur", 9.0)
-    world.evolute(1000.0)
-    hotter.evolute(1000.0)
-    check(hotter.state.amount.S > world.state.amount.S, "Burnability changes actual space production")
-    check(hotter.state.energy + hotter.state.amount.S == Parameters.INITIAL_ENERGY, "Enhanced production still spends the GI energy budget")
+        simulation.state.amount.RD = 1000000
+        simulation.batches.append_batch(simulation.state, "RD", 1000000, 0, 0)
+    hotter.environment.modify_world_parameter("Bur", 9)
+    world.evolute(1000)
+    hotter.evolute(1000)
+    check(E.gt(hotter.state.amount.S, world.state.amount.S), "Burnability changes actual space production")
+    check(E.eq(E.add(hotter.state.energy, hotter.state.amount.S), Parameters.INITIAL_ENERGY), "Enhanced production still spends the GI energy budget")
     dispose(world)
     dispose(hotter)
 
     world = fixture()
-    world.state.amount["C0.2"] = 1000000.0
-    world.state.ethics["C0.2"] = {"m": 1000000.0}
+    world.state.amount["C0.2"] = 1000000
+    world.state.ethics["C0.2"] = {"m": 1000000}
     var baseline: Dictionary = world.state.duplicate(true)
     var advanced: Dictionary = baseline.duplicate(true)
-    advanced.world_parameters.Agg = 19.0
+    advanced.world_parameters.Agg = 19
     var next_stage: String = global.CivilizationRules["C0.2"].next
     var outcomes: Array = []
     for target in [baseline, advanced]:
-        var expired: Dictionary = {"C0.2": [{"amount": 1000000.0, "from": 0.0, "to": 1.0}]}
+        var expired: Dictionary = {"C0.2": [{"amount": 1000000, "from": 0, "to": 1}]}
         var budget: Dictionary = CivilizationState.stellar_budget(world, target, global.CivilizationRules)
-        CivilizationEvolution.prepare(world, target, expired, 1.0, budget, global.CivilizationRules)
-        outcomes.append(expired["C0.2"][0].products.get(next_stage, 0.0))
-    check(outcomes[1] > outcomes[0], "Aggression changes actual ethical civilization transitions")
+        CivilizationEvolution.prepare(world, target, expired, 1, budget, global.CivilizationRules)
+        outcomes.append(expired["C0.2"][0].products.get(next_stage, 0))
+    check(E.gt(outcomes[1], outcomes[0]), "Aggression changes actual ethical civilization transitions")
     dispose(world)
 
     # Trends use ethical proportions and stage weights, not population magnitude.
     world = fixture()
     var rules: Dictionary = {"C2.0": {"home": "DwStar"}, "C2.1": {"home": "DwStar"}}
-    world.state.ethics = {"C2.0": {"d": 100.0}, "C2.1": {"d": 100.0}}
+    world.state.ethics = {"C2.0": {"d": 100}, "C2.1": {"d": 100}}
     var source: Dictionary = world.state.duplicate(true)
     var single: Dictionary = source.duplicate(true)
     var split: Dictionary = source.duplicate(true)
-    Parameters.advance(source, single, rules, 1.0e6)
-    for i in 10: Parameters.advance(source, split, rules, 1.0e5)
-    check(is_equal_approx(single.trends.Integration, 0.018), "Trend integrates elapsed years and doubled stage weights")
+    Parameters.advance(source, single, rules, 1000000)
+    for i in 10: Parameters.advance(source, split, rules, 100000)
+    check(E.near(single.trends.Integration, E.of("0.018")), "Trend integrates elapsed years and doubled stage weights")
     for key in Parameters.TRENDS:
-        check(is_equal_approx(single.trends[key], split.trends[key]), "Trend is independent of frame partition: " + key)
-    source.ethics["C2.0"].d = 1000000.0
+        check(E.near(single.trends[key], split.trends[key]), E.add("Trend is independent of frame partition: ", key))
+    source.ethics["C2.0"].d = 1000000
     var larger: Dictionary = world.state.duplicate(true)
-    Parameters.advance(source, larger, rules, 1.0e6)
-    check(is_equal_approx(larger.trends.Integration, single.trends.Integration), "Population proportions determine trend influence")
-    world.state.trends.Integration = 0.99
-    Parameters.advance(source, world.state, rules, 1.0e8)
-    check(world.state.civilization_stats["trend:Integration"] == 2.0, "Long steps process every crossed threshold")
-    check(is_equal_approx(world.state.trends.Integration, 0.79), "Threshold crossing preserves the fractional remainder")
-    check(world.state.world_parameters.Federation > 1.0 or world.state.world_parameters.Enlightenment > 1.0 or world.state.world_parameters.Order > 1.0, "Integration events change the world")
-    var restored: Dictionary = bytes_to_var(var_to_bytes(world.state))
-    Parameters.advance(source, world.state, rules, 1.0e8)
-    Parameters.advance(source, restored, rules, 1.0e8)
-    check(world.state == restored, "Trend events resume identically after serialization")
-    Parameters.advance(source, world.state, rules, 1.0e12)
-    check(world.state.trends.Integration >= 0.0 and world.state.trends.Integration < 1.0, "Very large intervals finish with a valid trend fraction")
-    check(world.state.world_parameters.Agg >= 1.0, "Repeated integration events cannot reduce aggression below the scale")
-    var payload: Dictionary = {"format_version": 2, "app_version": "test", "ui": {"current_page": 1}, "state": world.state}
+    Parameters.advance(source, larger, rules, 1000000)
+    check(E.near(larger.trends.Integration, single.trends.Integration), "Population proportions determine trend influence")
+    world.state.trends.Integration = E.of("0.99")
+    Parameters.advance(source, world.state, rules, 100000000)
+    check(E.eq(world.state.civilization_stats["trend:Integration"], 2), "Long steps process every crossed threshold")
+    check(E.near(world.state.trends.Integration, E.of("0.79")), "Threshold crossing preserves the fractional remainder")
+    check(((E.gt(world.state.world_parameters.Federation, 1) or E.gt(world.state.world_parameters.Enlightenment, 1)) or E.gt(world.state.world_parameters.Order, 1)), "Integration events change the world")
+    var restored: Dictionary = E.decode(bytes_to_var(var_to_bytes(E.encode(world.state))))
+    Parameters.advance(source, world.state, rules, 100000000)
+    Parameters.advance(source, restored, rules, 100000000)
+    check(E.eq(world.state, restored), "Trend events resume identically after serialization")
+    Parameters.advance(source, world.state, rules, E.of("1.0e12"))
+    check((E.ge(world.state.trends.Integration, 0) and E.lt(world.state.trends.Integration, 1)), "Very large intervals finish with a valid trend fraction")
+    check(E.ge(world.state.world_parameters.Agg, 1), "Repeated integration events cannot reduce aggression below the scale")
+    var payload: Dictionary = {"format_version": 5, "app_version": "test", "ui": {"current_page": 1}, "state": world.state}
     var manager: Node = root.get_node("SaveManager")
-    check(manager.validate_data(payload) == "", "New parameters and trends pass save validation")
+    check(E.eq(manager.validate_data(payload), ""), "New parameters and trends pass save validation")
     var old: Dictionary = payload.duplicate(true)
     old.state.erase("world_parameters")
     old.state.erase("trends")
-    check(manager.validate_data(old) == "", "Existing current-format saves remain readable")
-    payload.state.world_parameters.Agg = 20.0
-    check(manager.validate_data(payload) != "", "Out-of-range scales are rejected")
+    check(E.eq(manager.validate_data(old), ""), "Existing current-format saves remain readable")
+    payload.state.world_parameters.Agg = 20
+    check(E.ne(manager.validate_data(payload), ""), "Out-of-range scales are rejected")
     dispose(world)
 
-    for sample in [[1e-7, 0.0], [1e-6, 0.5], [1e-5, 1.0], [0.9, 0.0], [0.95, 0.5], [1.0, 1.0]]:
-        check(is_equal_approx(Parameters.density_display(sample[0]).position, sample[1]), "Density boundary " + str(sample[0]))
+    for sample in [[E.of("1e-7"), 0], [E.of("1e-6"), E.of("0.5")], [E.of("1e-5"), 1], [E.of("0.9"), 0], [E.of("0.95"), E.of("0.5")], [1, 1]]:
+        check(E.near(Parameters.density_display(sample[0]).position, sample[1]), E.add("Density boundary ", str(sample[0])))
     # The fixture overrides saving/loading; the player's save is never accessed.
     var scene = load("res://world/world.tscn").instantiate()
     var stage = scene.get_node("Stage")
@@ -153,40 +154,36 @@ func run() -> void:
     root.add_child(scene)
     await process_frame
     await process_frame
-    stage.owniverse.state.energy = Parameters.INITIAL_ENERGY / 4.0
-    stage.owniverse.state.world_parameters.Bur = 19.0
-    stage.owniverse.state.trends.Integration = 0.75
+    stage.owniverse.state.energy = E.divide(Parameters.INITIAL_ENERGY, 4)
+    stage.owniverse.state.world_parameters.Bur = 19
+    stage.owniverse.state.trends.Integration = E.of("0.75")
     stage.world_indicators.update(stage.owniverse)
     var warning: TextureRect = scene.get_node("Background/WarningBorder")
-    check(warning.mouse_filter == Control.MOUSE_FILTER_IGNORE, "Warning overlay does not block input")
-    var environments: Array = [
-        [1.0e-7, "ff0000ff"], [1.0e-6, "df2020bf"], [1.0e-5, "c040407f"],
-        [0.1, "00000000"], [0.9, "40a0c07f"], [0.97, "20b0dfbf"], [1.0, "00c0ffff"],
-        [0.1, "00000000"],
-    ]
+    check(E.eq(warning.mouse_filter, Control.MOUSE_FILTER_IGNORE), "Warning overlay does not block input")
+    var environments: Array = [[E.of("1.0e-7"), "ff0000ff"], [E.of("1.0e-6"), "df2020bf"], [E.of("1.0e-5"), "c040407f"], [E.of("0.1"), "00000000"], [E.of("0.9"), "40a0c07f"], [E.of("0.97"), "20b0dfbf"], [1, "00c0ffff"], [E.of("0.1"), "00000000"]]
     for sample in environments:
-        check(Parameters.density_warning_color(sample[0]).is_equal_approx(Color.html(sample[1])), "Unity warning threshold: " + str(sample[0]))
-    stage.owniverse.state.amount.H = 1e14
+        check(Parameters.density_warning_color(sample[0]).is_equal_approx(Color.html(sample[1])), E.add("Unity warning threshold: ", str(sample[0])))
+    stage.owniverse.state.amount.H = E.of("1e14")
     stage.world_indicators.update(stage.owniverse)
     check(warning.self_modulate.is_equal_approx(Color.html("00c0ffff")), "Compression warning uses current universe density")
-    stage.owniverse.state.amount.H = 0.0
-    stage.owniverse.state.amount.S = 1e24
+    stage.owniverse.state.amount.H = 0
+    stage.owniverse.state.amount.S = E.of("1e24")
     stage.world_indicators.update(stage.owniverse)
     check(warning.self_modulate.is_equal_approx(Color.html("ff0000ff")), "Rip warning replaces compression warning")
-    stage.owniverse.state.amount.S = 0.0
+    stage.owniverse.state.amount.S = 0
     stage.world_indicators.update(stage.owniverse)
-    check(warning.self_modulate.a == 0.0, "Warning clears when density returns to normal")
+    check(E.eq(warning.self_modulate.a, 0), "Warning clears when density returns to normal")
     for bar in stage.world_indicators.energy_bars:
-        check(bar.scale.x == 0.25, "Energy fill is synchronized on both pages")
+        check(E.eq(bar.scale.x, E.of("0.25")), "Energy fill is synchronized on both pages")
     var pointer: Control = stage.world_indicators.pointers.Bur
-    check(is_equal_approx(pointer.position.x + pointer.size.x / 2.0, 304.0), "Burnability pointer reaches the correct scale endpoint")
-    check(stage.world_indicators.trend_bars[1].scale.y == 0.75, "Trend bar displays its stored level")
+    check(E.near(E.add(pointer.position.x, E.divide(pointer.size.x, 2)), 304), "Burnability pointer reaches the correct scale endpoint")
+    check(E.eq(stage.world_indicators.trend_bars[1].scale.y, E.of("0.75")), "Trend bar displays its stored level")
     for locale in ["en", "ru"]:
         global.Locale = locale
         for id in ["Energy", "Density", "Burnability", "Explosiveness", "Aggression", "Trends"]:
             var description: String = Descriptions.render(stage.owniverse, global, id, "Indicator")
-            check(not description.contains("—") and not description.contains("%value"), "Resolved indicator description: " + locale + "/" + id)
+            check(((not description.contains("—")) and (not description.contains("%value"))), E.add(E.add(E.add("Resolved indicator description: ", locale), "/"), id))
     dispose(stage.owniverse)
     scene.free()
-    print("World indicators: %d checks, %d failures" % [checks, failures])
-    quit(0 if failures == 0 else 1)
+    print(("World indicators: %d checks, %d failures" % [checks, failures]))
+    quit((0 if E.eq(failures, 0) else 1))

ui/actions/actions.gd

@@ -1,29 +1,18 @@
 extends HBoxContainer
 class_name OwniverseAction
+const E = preload("res://world/owniverse/math/exact.gd")
 
-signal action_pressed(page_id, amount: float)
+signal action_pressed ( page_id , amount : Variant )
 
-@onready var action_labels: Array = [
-    $ActionControl0/Label,
-    $ActionControl1/Label,
-    $ActionControl2/Label,
-    $ActionControl3/Label,
-    $ActionControl4/Label,
-]
+@onready var action_labels : Array = [$ActionControl0/Label, $ActionControl1/Label, $ActionControl2/Label, $ActionControl3/Label, $ActionControl4/Label]
 
-var page_id: int = -1
+var page_id: int = E.neg(1)
 var current_item_id = ""
 
-var action_values: Dictionary = {
-    0: 0,
-    1: 0,
-    2: 0,
-    3: 0,
-    4: 0,
-}
+var action_values: Dictionary = {0: 0, 1: 0, 2: 0, 3: 0, 4: 0}
 
 
-func set_actions(item_id: String, value: float, preview: Callable = Callable()) -> void:
+func set_actions(item_id: String, value: Variant, preview: Callable = Callable()) -> void:
     current_item_id = item_id
     var requests: Array = _get_distribution(value)
     var unique_requests: Array = []
@@ -31,32 +20,33 @@ func set_actions(item_id: String, value: float, preview: Callable = Callable())
     var labels: Dictionary = {}
     # Prefer the largest request (including MAX) when previews or rounded
     # scientific labels coincide. Keep the request paired with its preview.
-    for i in range(requests.size() - 1, -1, -1):
-        if requests[i] <= 0.0: continue
-        var amount: float = preview.call(requests[i]) if preview.is_valid() else requests[i]
-        if not is_finite(amount) or amount < 1.0 or amount != floorf(amount): continue
+    for i in range(E.subtract(requests.size(), 1), E.neg(1), E.neg(1)):
+        if E.le(requests[i], 0): continue
+        var amount: Variant = (preview.call(requests[i]) if preview.is_valid() else requests[i])
+        if (((not E.finite(amount)) or E.lt(amount, 1)) or E.ne(amount, E.floor_value(amount))): continue
         var text: String = _format_action_value(amount)
-        if displayed.has(amount) or labels.has(text): continue
+        if (E.contains(displayed, amount) or labels.has(text)): continue
         labels[text] = true
         unique_requests.push_front(requests[i])
         displayed.push_front(amount)
-    while unique_requests.size() < 5:
-        unique_requests.append(0.0)
-        displayed.append(0.0)
+    while E.lt(unique_requests.size(), 5):
+        unique_requests.append(0)
+        displayed.append(0)
     _set_action_values(unique_requests, displayed)
 
-func _get_distribution(value: float) -> Array:
-    if value < 1.0 or not is_finite(value):
-        return [0.0, 0.0, 0.0, 0.0, 0.0]
-    value = floorf(value)
+func _get_distribution(value: Variant) -> Array:
+    if (E.lt(value, 1) or (not E.finite(value))):
+        return [0, 0, 0, 0, 0]
+    value = E.floor_value(value)
     var distribution: Array = []
-    var power: float = 1.0
-    while power < value:
+    var power: Variant = 1
+    while E.lt(power, value):
         distribution.append(power)
-        if distribution.size() > 4: distribution.pop_front()
-        power *= 10.0
+        if E.gt(distribution.size(), 4): distribution.pop_front()
+        if E.ge(power, E.of("1e27")): break
+        power = E.multiply(power, 10)
     distribution.append(value)
-    while distribution.size() < 5: distribution.append(0.0)
+    while E.lt(distribution.size(), 5): distribution.append(0)
     return distribution
 
 func _set_action_values(values: Array, displayed: Array) -> void:
@@ -64,17 +54,17 @@ func _set_action_values(values: Array, displayed: Array) -> void:
         action_values[ind] = values[ind]
         # Keep the original request for execution; show the exact planned output.
         var text: String = _format_action_value(displayed[ind])
-        if action_labels[ind].text != text:
+        if E.ne(action_labels[ind].text, text):
             action_labels[ind].text = text
-        action_labels[ind].get_parent().get_node("TextureButton").disabled = values[ind] <= 0.0
+        action_labels[ind].get_parent().get_node("TextureButton").disabled = E.le(values[ind], 0)
 
 
-func _format_action_value(value: float) -> String:
-    if value < 1.0 or not is_finite(value) or value != floorf(value):
+func _format_action_value(value: Variant) -> String:
+    if ((E.lt(value, 1) or (not E.finite(value))) or E.ne(value, E.floor_value(value))):
         return ""
     return Global.format_number(value)
-        
+
 
 func _on_action_button_pressed(button_id: int) -> void:
-    if action_values.get(button_id, 0.0) > 0.0:
+    if E.gt(action_values.get(button_id, 0), 0):
         action_pressed.emit(page_id, action_values[button_id])

ui/indicators/world_indicators.gd

@@ -1,4 +1,5 @@
 extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const Parameters = preload("res://world/owniverse/world_parameters.gd")
 var energy_bars: Array = []
@@ -32,21 +33,21 @@ func _ignore_mouse_on_children(node: Node) -> void:
 
 func update(world) -> void:
     var source: Dictionary = world.state
-    var energy: float = clampf(source.energy / Parameters.INITIAL_ENERGY, 0.0, 1.0)
+    var energy: float = E.approx(E.clamp_value(E.divide(source.energy, Parameters.INITIAL_ENERGY), 0, 1))
     for bar in energy_bars: bar.scale.x = energy
-    var density_value: float = world.environment.stellar_environment(source).density
+    var density_value = world.environment.stellar_environment(source).density
     var density: Dictionary = Parameters.density_display(density_value)
     warning_border.self_modulate = Parameters.density_warning_color(density_value)
     for indicator in density_indicators:
         for mode in ["Density", "DensityRip", "DensityCrunch"]:
             indicator.get_node(mode).visible = mode == density.mode
         var pointer: Control = indicator.get_node("Pointer")
-        pointer.position.x = 16.0 + 288.0 * density.position - pointer.size.x / 2.0
+        pointer.position.x = 16.0 + 288.0 * E.approx(density.position) - pointer.size.x / 2.0
         pointer.self_modulate = Color.BLACK if density.mode == "DensityCrunch" else Color.WHITE
     for key in pointers:
         var pointer: Control = pointers[key]
-        pointer.position.x = 16.0 * clampf(Parameters.value(source, key), 1.0, 19.0) - pointer.size.x / 2.0
+        pointer.position.x = 16.0 * E.approx(E.clamp_value(Parameters.value(source, key), 1, 19)) - pointer.size.x / 2.0
     for i in trend_bars.size():
         var bar: Control = trend_bars[i]
         bar.pivot_offset = Vector2(0.0, bar.size.y)
-        bar.scale.y = clampf(source.get("trends", {}).get(Parameters.TRENDS[i], 0.0), 0.0, 1.0)
+        bar.scale.y = E.approx(E.clamp_value(source.get("trends", {}).get(Parameters.TRENDS[i], 0), 0, 1))

ui/owniverse_item/owniverse_item.gd

@@ -1,5 +1,6 @@
 extends Control
 class_name OwniverseItem
+const E = preload("res://world/owniverse/math/exact.gd")
 
 signal item_activated(item)
 
@@ -19,8 +20,8 @@ var item_sub_page: int = -1
 var item_type = ""
 
 
-func set_label(value: float) -> void:
-    var text: String = Global.format_number(value)
+func set_label(value) -> void:
+    var text: String = E.scientific(value, 5) if E.gt(E.absolute(value), 1000000000) else (E.grouped(value, 0, false) if E.ne(value, 0) else "")
     if description.text != text:
         description.text = text
     #description.text = str(value)

world/owniverse/README.md

@@ -5,7 +5,7 @@
 - `quantity_math.gd`: нормализация положительных весов, ограниченное целочисленное распределение методом наибольших остатков, распределение с накоплением ошибки округления, накопление дробного выпуска и минимальный целый размер производственной партии.
 - `entity_catalog.gd`: загрузка определений, индексы групп и событий, списки автоматических производителей и разблокируемых сущностей.
 
-Математика не обращается к дереву сцены, Global или Owniverse. Методы накопления изменяют переданный словарь остатков; остальные методы возвращают результат. Для распределения `split` количество должно быть целым, веса — неотрицательными. Равные остатки разрешаются по строковому ID. Сохранены прежние точности округления: 1e-12 для выпуска и 1e-10 для событий цивилизаций.
+Математика не обращается к дереву сцены, Global или Owniverse. Методы накопления изменяют переданный словарь остатков; остальные методы возвращают результат. Для распределения `split` количество должно быть целым, веса — неотрицательными. Равные остатки разрешаются по строковому ID. Количества считаются целочисленно в диапазоне E27, дробные остатки хранятся в `float`. [Модуль арифметики](math/README.md) описывает допуск дробных переносов, точные отношения и формат сохранения 4.
 
 Каталог получает словарь исходных строк через `load_definitions(rows)`, вызываемый один раз для нового экземпляра. Конструктор OwniverseEntity по-прежнему использует настройки Global. Каталог не хранит количества, партии или состояние интерфейса. Определения пока остаются Node: освобождает их владелец мира, как до рефакторинга.
 
@@ -41,6 +41,11 @@ Stage обращается непосредственно к `world.presentation
 
 В `owniverse.gd` остались создание состояния и модулей, скорость и проверка входного delta перед запуском эволюции. Дублирующее поле new_state и закомментированная старая реализация удалены. Единственный источник текущего состояния — `world.state`.
 
+Внутри одной фазы снимок физических количеств переиспользуется для сверки
+этик, звёздного бюджета и бюджета структур. После списания партий или переходов
+создаётся новый снимок. Операции над одним типом объекта используют
+`physical_amount`, не пересчитывая полную карту вселенной.
+
 ### Порядок шага
 
 1. Определить обработанную десятую года. При продвижении времени восстановить недостающие партии жизни и проверить вместимость.

world/owniverse/automatic_production.gd

@@ -1,58 +1,59 @@
 extends "res://world/owniverse/simulation_module.gd"
+const E = preload("res://world/owniverse/math/exact.gd")
 const WorldParameters = preload("res://world/owniverse/world_parameters.gd")
 const QuantityMath = preload("res://world/owniverse/quantity_math.gd")
 
 func yearly_products(entity: OwniverseEntity) -> Dictionary:
     var products: Dictionary = {}
-    if not entity.life_product.is_empty() and entity.lifespan > 0.0:
+    if ((not entity.life_product.is_empty()) and E.gt(entity.lifespan, 0)):
         for resource in entity.life_product:
-            products[resource] = maxf(0.0, entity.life_product[resource]) / entity.lifespan
-    elif entity.product_per_year_type != "":
-        products[entity.product_per_year_type] = maxf(0.0, entity.product_per_year_amount)
+            products[resource] = E.divide(E.maximum(0, entity.life_product[resource]), entity.lifespan)
+    elif E.ne(entity.product_per_year_type, ""):
+        products[entity.product_per_year_type] = E.maximum(0, entity.product_per_year_amount)
     return products
 
 
-func produce_for_period(previous: Dictionary, target: Dictionary, quantities: Dictionary,
-        distribution: Dictionary, from_year: float, to_year: float) -> void:
+func produce_for_period(previous: Dictionary, target: Dictionary, quantities: Dictionary, distribution: Dictionary, from_year: Variant, to_year: Variant) -> void:
     var basic: Dictionary = {}
     var automatic: Dictionary = {}
     for id in quantities:
         var entity: OwniverseEntity = world.catalog.entities[id]
-        var object_years: float = world.batches.object_years(previous, id, quantities[id], from_year, to_year)
-        var auto_share: float = clampf(entity.auto, 0.0, 1.0)
         var products: Dictionary = yearly_products(entity)
+        if products.is_empty(): continue
+        var object_years: Variant = world.batches.object_years(previous, id, quantities[id], from_year, to_year)
+        var auto_share: Variant = E.clamp_value(entity.auto, 0, 1)
         for product in products:
-            var amount: float = object_years * products[product] * WorldParameters.production(previous, entity)
-            basic[product] = basic.get(product, 0.0) + amount * (1.0 - auto_share)
-            automatic[product] = automatic.get(product, 0.0) + amount * auto_share
+            var amount: Variant = E.multiply(E.multiply(object_years, products[product]), WorldParameters.production(previous, entity))
+            basic[product] = E.add(basic.get(product, 0), E.multiply(amount, (E.subtract(1, auto_share))))
+            automatic[product] = E.add(automatic.get(product, 0), E.multiply(amount, auto_share))
     # Basic and automatic output each retain their unproduced remainder.
-    if not target.has("resource_remainders"):
+    if (not target.has("resource_remainders")):
         target.resource_remainders = {"basic": {}, "automatic": {}}
     var pending: Dictionary = target.resource_remainders
     var requests: Dictionary = {}
     for id in basic:
-        pending.basic[id] = pending.basic.get(id, 0.0) + basic[id]
-        pending.automatic[id] = pending.automatic.get(id, 0.0) + automatic[id]
+        pending.basic[id] = E.add(pending.basic.get(id, 0), basic[id])
+        pending.automatic[id] = E.add(pending.automatic.get(id, 0), automatic[id])
     var totals: Dictionary = {}
     for channel in ["basic", "automatic"]:
         for id in pending[channel]:
-            totals[id] = maxf(0.0, pending.basic.get(id, 0.0) + pending.automatic.get(id, 0.0))
+            totals[id] = E.maximum(0, E.add(pending.basic.get(id, 0), pending.automatic.get(id, 0)))
     for id in totals:
-        if id == "S" or id == "H":
-            requests[id] = floorf(totals[id])
-    var funded: Dictionary = QuantityMath.allocate_whole(requests, floorf(maxf(0.0, previous.energy)))
+        if (E.eq(id, "S") or E.eq(id, "H")):
+            requests[id] = E.floor_value(totals[id])
+    var funded: Dictionary = QuantityMath.allocate_whole(requests, E.floor_value(E.maximum(0, previous.energy)))
     automatic = {}
     target.energy = previous.energy
     for id in totals:
-        var amount: float = floorf(totals[id])
-        if id == "S" or id == "H":
-            amount = funded.get(id, 0.0)
-            target.energy -= amount
+        var amount: Variant = E.floor_value(totals[id])
+        if (E.eq(id, "S") or E.eq(id, "H")):
+            amount = funded.get(id, 0)
+            target.energy = E.subtract(target.energy, amount)
         # Split the actual whole output, retaining the allocation error for next time.
-        var auto_ratio: float = clampf(pending.automatic.get(id, 0.0) / totals[id], 0.0, 1.0) if totals[id] > 0.0 else 0.0
-        var auto_amount: float = floorf(amount * auto_ratio)
-        pending.automatic[id] = pending.automatic.get(id, 0.0) - auto_amount
-        pending.basic[id] = pending.basic.get(id, 0.0) - (amount - auto_amount)
+        var auto_ratio: Variant = (E.clamp_value(E.divide(pending.automatic.get(id, 0), totals[id]), 0, 1) if E.gt(totals[id], 0) else 0)
+        var auto_amount: Variant = E.floor_value(E.multiply(amount, auto_ratio))
+        pending.automatic[id] = E.subtract(pending.automatic.get(id, 0), auto_amount)
+        pending.basic[id] = E.subtract(pending.basic.get(id, 0), (E.subtract(amount, auto_amount)))
         automatic[id] = auto_amount
         amount = world.ledger.credit(target, id, amount)
         world.batches.append_batch(target, id, amount, from_year, to_year)
@@ -60,22 +61,22 @@ func produce_for_period(previous: Dictionary, target: Dictionary, quantities: Di
     # Keep unused automatic resources across cycles; they are part of free amounts.
     var budget: Dictionary = previous.get("auto_resources", {}).duplicate(true)
     for id in automatic:
-        budget[id] = budget.get(id, 0.0) + automatic[id]
+        budget[id] = E.add(budget.get(id, 0), automatic[id])
     for id in budget:
-        budget[id] = minf(maxf(0.0, budget[id]), world.ledger.available(target, id))
+        budget[id] = E.minimum(E.maximum(0, budget[id]), world.ledger.available(target, id))
     target.auto_resources = budget
-    produce_brown_dwarfs(target, automatic.get("H", 0.0), from_year, to_year)
+    produce_brown_dwarfs(target, automatic.get("H", 0), from_year, to_year)
     budget = ordinary_star_budget(target)
 
     # One common multiplier preserves the initial count ratios, even under scarcity.
     var candidates: Dictionary = {}
     for id in distribution:
         var entity: OwniverseEntity = world.catalog.entities[id]
-        if entity.group_as != "Star":
+        if E.ne(entity.group_as, "Star"):
             continue
         var has_cost: bool = false
         for resource in entity.cost:
-            if entity.cost[resource] > 0.0:
+            if E.gt(entity.cost[resource], 0):
                 has_cost = true
         if has_cost:
             candidates[id] = distribution[id]
@@ -85,88 +86,87 @@ func produce_for_period(previous: Dictionary, target: Dictionary, quantities: Di
     var costs: Dictionary = {}
     var needs: Dictionary = {}
     for id in candidates:
-        if auto_capacity(target, world.catalog.entities[id], budget) <= 0.0:
+        if E.le(auto_capacity(target, world.catalog.entities[id], budget), 0):
             continue
         for resource in world.catalog.entities[id].cost:
-            var cost: float = maxf(0.0, world.catalog.entities[id].cost[resource]) * candidates[id]
-            costs[resource] = costs.get(resource, 0.0) + cost
-            needs[resource] = needs.get(resource, 0.0) + cost
+            var cost: Variant = E.multiply(E.maximum(0, world.catalog.entities[id].cost[resource]), candidates[id])
+            costs[resource] = E.add(costs.get(resource, 0), cost)
+            needs[resource] = E.add(needs.get(resource, 0), cost)
         for resource in world.catalog.entities[id].bind:
-            needs[resource] = needs.get(resource, 0.0) + maxf(0.0, world.catalog.entities[id].bind[resource]) * candidates[id]
-    var scale: float = INF
+            needs[resource] = E.add(needs.get(resource, 0), E.multiply(E.maximum(0, world.catalog.entities[id].bind[resource]), candidates[id]))
+    var scale: Variant = INF
     for resource in costs:
-        if costs[resource] > 0.0:
-            scale = minf(scale, budget.get(resource, 0.0) / costs[resource])
+        if E.gt(costs[resource], 0):
+            scale = E.minimum(scale, E.divide(budget.get(resource, 0), costs[resource]))
     for resource in needs:
-        if needs[resource] > 0.0:
-            scale = minf(scale, world.ledger.available(target, resource) / needs[resource])
+        if E.gt(needs[resource], 0):
+            scale = E.minimum(scale, E.divide(world.ledger.available(target, resource), needs[resource]))
     var concrete_needs: Dictionary = world.ledger.expand_requirements(target, needs)
     for resource in concrete_needs:
-        if concrete_needs[resource] > 0.0:
-            scale = minf(scale, world.ledger.available(target, resource) / concrete_needs[resource])
-    if not is_finite(scale) or scale <= 0.0:
+        if E.gt(concrete_needs[resource], 0):
+            scale = E.minimum(scale, E.divide(world.ledger.available(target, resource), concrete_needs[resource]))
+    if ((not E.finite(scale)) or E.le(scale, 0)):
         return
     # Rare types are served first; signed count deficits compensate later cycles.
-    if not target.has("auto_star_deficits"):
+    if (not target.has("auto_star_deficits")):
         target.auto_star_deficits = {}
     var deficits: Dictionary = target.auto_star_deficits
     var order: Array = candidates.keys()
-    order.sort_custom(func(a: String, b: String) -> bool:
-        return candidates[a] < candidates[b] if candidates[a] != candidates[b] else a < b)
+    order.sort_custom(func ( a : String , b : String ) -> bool : return (E.lt(candidates[a], candidates[b]) if E.ne(candidates[a], candidates[b]) else E.lt(a, b)))
     var created: Dictionary = {}
-    var metallicity: float = world.environment.stellar_environment(target).metallicity
-    var total_created: float = 0.0
+    var metallicity: Variant = world.environment.stellar_environment(target).metallicity
+    var total_created: Variant = 0
     for id in order:
         var entity: OwniverseEntity = world.catalog.entities[id]
-        var step: float = world.production.production_step(entity)
-        if not is_finite(step):
+        var step: Variant = world.production.production_step(entity)
+        if (not E.finite(step)):
             continue
-        var quota: float = maxf(0.0, candidates[id] * scale + deficits.get(id, 0.0))
-        var desired: float = floorf(quota / step) * step
-        var actual: float = minf(desired, auto_capacity(target, entity, budget))
-        if actual <= 0.0:
+        var quota: Variant = E.maximum(0, E.add(E.multiply(candidates[id], scale), deficits.get(id, 0)))
+        var desired: Variant = E.multiply(E.floor_value(E.divide(quota, step)), step)
+        var actual: Variant = E.minimum(desired, auto_capacity(target, entity, budget))
+        if E.le(actual, 0):
             continue
-        if not world.production.try_production(target, entity, actual, true):
+        if (not world.production.try_production(target, entity, actual, true)):
             continue
         budget = ordinary_star_budget(target)
         created[id] = actual
-        total_created += actual
+        total_created = E.add(total_created, actual)
     for id in candidates:
         # Credit only actual production, so retained resources aren't counted twice.
-        deficits[id] = deficits.get(id, 0.0) + candidates[id] * total_created - created.get(id, 0.0)
+        deficits[id] = E.subtract(E.add(deficits.get(id, 0), E.multiply(candidates[id], total_created)), created.get(id, 0))
     for id in created:
         world.ledger.credit(target, id, created[id])
         world.batches.append_batch(target, id, created[id], from_year, to_year)
         world.stellar.create_planets(target, id, created[id], from_year, to_year, metallicity)
 
 
-func produce_brown_dwarfs(target: Dictionary, new_hydrogen: float, from_year: float, to_year: float) -> void:
-    if not world.catalog.entities.has("HBD"):
+func produce_brown_dwarfs(target: Dictionary, new_hydrogen: Variant, from_year: Variant, to_year: Variant) -> void:
+    if (not world.catalog.entities.has("HBD")):
         return
     var entity: OwniverseEntity = world.catalog.entities.HBD
-    var cost: float = entity.cost.get("H", 0.0)
-    if cost <= 0.0:
+    var cost: Variant = entity.cost.get("H", 0)
+    if E.le(cost, 0):
         return
-    var quota: float = target.auto_star_deficits.get("HBD", 0.0) + maxf(0.0, new_hydrogen) * 0.001 / cost
-    var fuel: float = maxf(0.0, target.auto_star_deficits.get("HBD_fuel", 0.0))
-    var available: float = minf(target.auto_resources.get("H", 0.0), world.ledger.available(target, "H"))
-    quota = minf(quota, (available + fuel) / cost)
-    var expected: float = maxf(0.0, snappedf(quota, 1e-9))
-    var amount: float = floorf(expected)
+    var quota: Variant = E.add(target.auto_star_deficits.get("HBD", 0), E.mul_div(E.maximum(0, new_hydrogen), E.of("0.001"), cost))
+    var fuel: Variant = E.maximum(0, target.auto_star_deficits.get("HBD_fuel", 0))
+    var available: Variant = E.minimum(target.auto_resources.get("H", 0), world.ledger.available(target, "H"))
+    quota = E.minimum(quota, E.divide((E.add(available, fuel)), cost))
+    var expected: Variant = E.maximum(0, quota)
+    var amount: Variant = E.floor_value(expected)
     # Do not retry a fractional chance on frames with no new automatic fuel.
-    if new_hydrogen > 0.0 and expected > amount:
-        var random_state: float = target.auto_star_deficits.get("HBD_random", 1234567.0)
-        random_state = fmod(random_state * 48271.0, 2147483647.0)
+    if (E.gt(new_hydrogen, 0) and E.gt(expected, amount)):
+        var random_state: Variant = target.auto_star_deficits.get("HBD_random", 1234567)
+        random_state = E.remainder(E.multiply(random_state, 48271), E.of("2147483647.0"))
         target.auto_star_deficits.HBD_random = random_state
-        if random_state / 2147483647.0 < expected - amount:
-            amount += 1.0
-    amount = minf(amount, floorf(snappedf((available + fuel) / cost, 1e-9)))
-    var charge: float = ceilf(maxf(0.0, snappedf(amount * cost - fuel, 1e-9)))
-    if amount > 0.0 and charge <= available:
+        if E.lt(E.divide(random_state, E.of("2147483647.0")), E.subtract(expected, amount)):
+            amount = E.add(amount, 1)
+    amount = E.minimum(amount, E.floor_value(E.divide((E.add(available, fuel)), cost)))
+    var charge: Variant = E.ceil_value(E.maximum(0, E.subtract(E.multiply(amount, cost), fuel)))
+    if (E.gt(amount, 0) and E.le(charge, available)):
         world.ledger.take_available(target, "H", charge)
-        target.auto_resources.H = maxf(0.0, target.auto_resources.get("H", 0.0) - charge)
-        target.auto_star_deficits.HBD_fuel = maxf(0.0, snappedf(fuel + charge - amount * cost, 1e-9))
-        quota -= amount
+        target.auto_resources.H = E.maximum(0, E.subtract(target.auto_resources.get("H", 0), charge))
+        target.auto_star_deficits.HBD_fuel = E.maximum(0, E.subtract(E.add(fuel, charge), E.multiply(amount, cost)))
+        quota = E.subtract(quota, amount)
         world.ledger.credit(target, "HBD", amount)
         world.batches.append_batch(target, "HBD", amount, from_year, to_year)
     target.auto_star_deficits.HBD = quota
@@ -175,52 +175,51 @@ func produce_brown_dwarfs(target: Dictionary, new_hydrogen: float, from_year: fl
 func ordinary_star_budget(target: Dictionary) -> Dictionary:
     var budget: Dictionary = target.auto_resources.duplicate()
     if world.catalog.entities.has("HBD"):
-        var reserved: float = maxf(0.0, target.auto_star_deficits.get("HBD", 0.0) * world.catalog.entities.HBD.cost.get("H", 0.0) - target.auto_star_deficits.get("HBD_fuel", 0.0))
-        budget.H = maxf(0.0, budget.get("H", 0.0) - reserved)
+        var reserved: Variant = E.maximum(0, E.subtract(E.multiply(target.auto_star_deficits.get("HBD", 0), world.catalog.entities.HBD.cost.get("H", 0)), target.auto_star_deficits.get("HBD_fuel", 0)))
+        budget.H = E.maximum(0, E.subtract(budget.get("H", 0), reserved))
     return budget
 
 
-func auto_capacity(source: Dictionary, entity: OwniverseEntity, budget: Dictionary) -> float:
-    var capacity: float = INF
+func auto_capacity(source: Dictionary, entity: OwniverseEntity, budget: Dictionary) -> Variant:
+    var capacity: Variant = INF
     var needs: Dictionary = {}
     for resource in entity.cost:
-        var cost: float = maxf(0.0, entity.cost[resource])
+        var cost: Variant = E.maximum(0, entity.cost[resource])
         needs[resource] = cost
-        if cost > 0.0:
-            capacity = minf(capacity, floorf(budget.get(resource, 0.0) / cost))
+        if E.gt(cost, 0):
+            capacity = E.minimum(capacity, E.floor_value(E.divide(budget.get(resource, 0), cost)))
     for resource in entity.bind:
-        needs[resource] = needs.get(resource, 0.0) + maxf(0.0, entity.bind[resource])
+        needs[resource] = E.add(needs.get(resource, 0), E.maximum(0, entity.bind[resource]))
     for resource in needs:
-        if needs[resource] > 0.0:
-            capacity = minf(capacity, floorf(world.ledger.available(source, resource) / needs[resource]))
+        if E.gt(needs[resource], 0):
+            capacity = E.minimum(capacity, E.floor_value(E.divide(world.ledger.available(source, resource), needs[resource])))
     var concrete: Dictionary = world.ledger.expand_requirements(source, needs)
     for resource in concrete:
-        if concrete[resource] > 0.0:
-            capacity = minf(capacity, floorf(world.ledger.available(source, resource) / concrete[resource]))
-    var step: float = world.production.production_step(entity)
-    return floorf(capacity / step) * step if is_finite(capacity) and is_finite(step) else 0.0
+        if E.gt(concrete[resource], 0):
+            capacity = E.minimum(capacity, E.floor_value(E.divide(world.ledger.available(source, resource), concrete[resource])))
+    var step: Variant = world.production.production_step(entity)
+    return (E.multiply(E.floor_value(E.divide(capacity, step)), step) if (E.finite(capacity) and E.finite(step)) else 0)
 
 
-func produce_newborn_lifetime(target: Dictionary, id: String, count: float,
-        born_from: float, born_to: float, to_year: float, before_batches: Array,
-        remaining_object_years: float = NAN) -> void:
+func produce_newborn_lifetime(target: Dictionary, id: String, count: Variant, born_from: Variant, born_to: Variant, to_year: Variant, before_batches: Array, remaining_object_years: Variant = NAN) -> void:
     var products: Dictionary = yearly_products(world.catalog.entities[id])
-    if products.is_empty() or count <= 0.0:
+    if (products.is_empty() or E.le(count, 0)):
         return
-    var object_years: float = remaining_object_years if is_finite(remaining_object_years) else count * maxf(0.0, to_year - (born_from + born_to) * 0.5)
+    var object_years: Variant = (remaining_object_years if E.finite(remaining_object_years) else E.multiply(count, E.maximum(0, E.subtract(to_year, E.multiply((E.add(born_from, born_to)), E.of("0.5"))))))
     var previous_amounts: Dictionary = {}
-    for old: Dictionary in before_batches:
-        var start: float = old.get("created_from", -INF)
-        if not previous_amounts.has(start):
-            previous_amounts[start] = old.amount
-    for batch: Dictionary in target.batches.get(id, []):
-        var added: float = batch.amount - previous_amounts.get(batch.get("created_from", INF), 0.0)
-        object_years -= maxf(0.0, added) * world.batches.expired_years(to_year, batch.start_year, batch.end_year)
-    object_years = maxf(0.0, object_years)
+    for old : Dictionary in before_batches:
+        var start: Variant = old.get("created_from", E.neg(INF))
+        if (not previous_amounts.has(str(start))):
+            previous_amounts[str(start)] = old.amount
+    for batch : Dictionary in target.batches.get(id, []):
+        var added: Variant = E.subtract(batch.amount, previous_amounts.get(str(batch.get("created_from", INF)), 0))
+        object_years = E.subtract(object_years, E.multiply(E.maximum(0, added), world.batches.expired_years(to_year, batch.start_year, batch.end_year)))
+    object_years = E.maximum(0, object_years)
     for resource in products:
-        var output: float = object_years * products[resource] * WorldParameters.production(target, world.catalog.entities[id])
-        if resource in ["H", "S"]:
-            output = minf(output, target.energy)
-        var actual: float = world.ledger.credit(target, resource, output)
-        if resource in ["H", "S"]:
-            target.energy = maxf(0.0, target.energy - actual)
+        var coefficient: Variant = E.multiply(products[resource], WorldParameters.production(target, world.catalog.entities[id]))
+        var output: Variant = E.multiply(object_years, coefficient)
+        if E.contains(["H", "S"], resource):
+            output = E.minimum(output, target.energy)
+        var actual: Variant = world.ledger.credit(target, resource, output)
+        if E.contains(["H", "S"], resource):
+            target.energy = E.maximum(0, E.subtract(target.energy, actual))

world/owniverse/civilization_evolution.gd

@@ -1,4 +1,5 @@
 extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const QuantityMath = preload("res://world/owniverse/quantity_math.gd")
 
@@ -7,95 +8,100 @@ const WorldParameters = preload("res://world/owniverse/world_parameters.gd")
 const ETHICS = State.ETHICS
 const OPPOSITE = {"m": "l", "l": "m", "w": "d", "d": "w", "c": "b", "b": "c"}
 
-static func total(pop: Dictionary) -> float:
+static func total(pop: Dictionary) -> Variant:
     return QuantityMath.sum(pop)
 
 static func add(to: Dictionary, from: Dictionary) -> void:
-    for key in from: to[key] = to.get(key, 0.0) + from[key]
+    for key in from: to[key] = E.add(to.get(key, 0), from[key])
 
-static func take(world, pop: Dictionary, count: float) -> Dictionary:
+static func take(world, pop: Dictionary, count: Variant) -> Dictionary:
     var taken: Dictionary = QuantityMath.allocate_whole(pop, count)
-    for key in taken: pop[key] -= taken[key]
+    for key in taken: pop[key] = E.subtract(pop[key], taken[key])
     return taken
 
-static func rate(target: Dictionary, key: String, count: float, probability: float) -> float:
-    if not target.has("civilization_remainders"): target.civilization_remainders = {}
+static func rate(target: Dictionary, key: String, count: Variant, probability: Variant) -> Variant:
+    if (not target.has("civilization_remainders")): target.civilization_remainders = {}
     return QuantityMath.accumulate_rate(target.civilization_remainders, key, count, probability)
 
 # Fixed-size largest-remainder apportionment with saved signed rounding errors.
 # Runtime depends on the number of branches, never the number of civilizations.
-static func split(target: Dictionary, key: String, count: float, weights: Dictionary) -> Dictionary:
-    if count <= 0.0 or QuantityMath.sum(weights) <= 0.0: return {}
-    if not target.has("civilization_remainders"): target.civilization_remainders = {}
+static func split(target: Dictionary, key: String, count: Variant, weights: Dictionary) -> Dictionary:
+    if E.le(count, 0): return {}
+    if (not target.has("civilization_remainders")): target.civilization_remainders = {}
     return QuantityMath.split(target.civilization_remainders, key, count, weights)
 
-static func drift(target: Dictionary, key: String, pop: Dictionary, rows: Dictionary,
-        diplomacy: bool = false, colony: bool = false) -> Dictionary:
+static func drift(target: Dictionary, key: String, pop: Dictionary, rows: Dictionary, diplomacy: bool = false, colony: bool = false) -> Dictionary:
     var weights: Dictionary = {}
     for ethic in pop:
-        var influence: float = float(rows[ethic].diplomacy_rate) if diplomacy else 1.0
+        var influence: Variant = (E.of(rows[ethic].diplomacy_rate) if diplomacy else 1)
+        var contribution: Variant = E.multiply(pop[ethic], influence)
         for other in ETHICS:
-            var weight: float = 9.0 if colony else 1.0
-            if other == ethic: weight = 960.0 if colony else 196.0
-            elif other == OPPOSITE[ethic]: weight = 4.0 if colony else 0.0
-            weights[other] = weights.get(other, 0.0) + pop[ethic] * influence * weight
-    if total(weights) <= 0.0: return pop.duplicate()
+            var weight: Variant = (9 if colony else 1)
+            if E.eq(other, ethic): weight = (960 if colony else 196)
+            elif E.eq(other, OPPOSITE[ethic]): weight = (4 if colony else 0)
+            weights[other] = E.add(weights.get(other, 0), E.multiply(contribution, weight))
+    if E.le(total(weights), 0): return pop.duplicate()
     return split(target, key, total(pop), weights)
 
 static func emit(plan: Dictionary, destination: String, pop: Dictionary) -> void:
-    if not plan.outputs.has(destination): plan.outputs[destination] = {}
+    if (not plan.outputs.has(destination)): plan.outputs[destination] = {}
     add(plan.outputs[destination], pop)
 
 static func fall(target: Dictionary, plan: Dictionary, rules: Dictionary, pop: Dictionary) -> void:
     for ethic in pop:
+        if E.le(pop[ethic], 0): continue
         var weights: Dictionary = {}
         for term in str(rules[plan.id].ethics[ethic].fall).split("^", false):
             var pair: PackedStringArray = term.split(":")
-            weights[pair[0]] = float(pair[1])
-        if weights.is_empty(): weights[rules[plan.id].previous] = 1.0
-        var shares: Dictionary = split(target, "fall:" + plan.id + ":" + ethic, pop[ethic], weights)
+            weights[pair[0]] = E.of(pair[1])
+        if weights.is_empty(): weights[rules[plan.id].previous] = 1
+        var shares: Dictionary = split(target, E.add(E.add(E.add("fall:", plan.id), ":"), ethic), pop[ethic], weights)
         for stage in shares: emit(plan, stage, {ethic: shares[stage]})
 
-static func progress(world, target: Dictionary, rules: Dictionary, budget: Dictionary,
-        plan: Dictionary, pop: Dictionary) -> Dictionary:
+static func progress(world, target: Dictionary, rules: Dictionary, budget: Dictionary, plan: Dictionary, pop: Dictionary) -> Dictionary:
     var successor: String = rules[plan.id].next
-    var admitted: float = State.admit_transition(budget, rules, plan.id, successor, total(pop))
+    var admitted: Variant = State.admit_transition(budget, rules, plan.id, successor, total(pop))
     var accepted: Dictionary = take(world, pop, admitted)
     emit(plan, successor, accepted)
     return pop
 
-static func new_plan(id: String, year: float) -> Dictionary:
-    return {"id": id, "from": year, "to": -INF, "amount": 0.0, "outputs": {}}
+static func new_plan(id: String, year: Variant) -> Dictionary:
+    return {"id": id, "from": year, "to": E.neg(INF), "amount": 0, "outputs": {}}
 
-static func consume_untriggered(world, target: Dictionary, plan: Dictionary, pop: Dictionary, count: float, year: float) -> Dictionary:
-    var old_total: float = total(pop)
+static func consume_untriggered(world, target: Dictionary, plan: Dictionary, pop: Dictionary, count: Variant, year: Variant) -> Dictionary:
+    var old_total: Variant = total(pop)
     var removed: Dictionary = take(world, pop, count)
-    var actual: float = total(removed)
-    if actual > 0.0:
-        world.batches.scale_batches(target, plan.id, (old_total - actual) / old_total)
-        plan.amount += actual
-        plan.to = maxf(plan.to, year)
+    var actual: Variant = total(removed)
+    if E.gt(actual, 0):
+        world.batches.scale_batches(target, plan.id, E.divide((E.subtract(old_total, actual)), old_total))
+        plan.amount = E.add(plan.amount, actual)
+        plan.to = E.maximum(plan.to, year)
     return removed
 
-static func prepare(world, target: Dictionary, expired: Dictionary, year: float, budget: Dictionary, rules: Dictionary) -> Dictionary:
-    State.reconcile(world, target, rules)
-    var remaining: Dictionary = target.ethics.duplicate(true)
+static func prepare(world, target: Dictionary, expired: Dictionary, year: Variant, budget: Dictionary, rules: Dictionary, physical: Dictionary = {}, budget_timer: RefCounted = null) -> Dictionary:
+    var profile_started: int = world.profile_start()
+    State.reconcile(world, target, rules, physical)
+    var remaining: Dictionary = target.ethics.duplicate()
+    var copied: Dictionary = {}
     var plans: Dictionary = {}
     var colonies: Array = []
     var collateral: Dictionary = {}
     var modifiers: Dictionary = WorldParameters.life_modifiers(target)
-    var order: float = WorldParameters.value(target, "Order")
-    if not target.has("civilization_stats"): target.civilization_stats = {}
+    var order: Variant = WorldParameters.value(target, "Order")
+    if (not target.has("civilization_stats")): target.civilization_stats = {}
     var ids: Array = expired.keys()
     ids.sort()
     for id in ids:
-        if not rules.has(id) or expired[id].is_empty(): continue
+        if budget_timer != null and not await budget_timer.pause(): return {}
+        if ((not rules.has(id)) or expired[id].is_empty()): continue
         var plan: Dictionary = new_plan(id, year)
         plans[id] = plan
-        for part: Dictionary in expired[id]:
-            plan.amount += part.amount
-            plan.from = minf(plan.from, part.from)
-            plan.to = maxf(plan.to, part.to)
+        for part : Dictionary in expired[id]:
+            plan.amount = E.add(plan.amount, part.amount)
+            plan.from = E.minimum(plan.from, part.from)
+            plan.to = E.maximum(plan.to, part.to)
+        remaining[id] = remaining[id].duplicate()
+        copied[id] = true
         var triggered: Dictionary = take(world, remaining[id], plan.amount)
         var successes: Dictionary = {}
         var failures: Dictionary = {}
@@ -103,126 +109,147 @@ static func prepare(world, target: Dictionary, expired: Dictionary, year: float,
         var settlers: Dictionary = {}
         for ethic in triggered:
             var row: Dictionary = rules[id].ethics[ethic]
-            var p: float = maxf(0.0, float(row.progress) * modifiers.progress)
-            var d: float = maxf(0.0, float(row.degradation) * modifiers.degradation)
-            var scale: float = maxf(1.0, p + d)
-            var pro: float = rate(target, id + ":" + ethic + ":pro", triggered[ethic], p / scale)
-            var deg: float = rate(target, id + ":" + ethic + ":deg", triggered[ethic], d / scale)
+            var p: Variant = E.maximum(0, E.multiply(E.of(row.progress), modifiers.progress))
+            var d: Variant = E.maximum(0, E.multiply(E.of(row.degradation), modifiers.degradation))
+            var scale: Variant = E.maximum(1, E.add(p, d))
+            var pro: Variant = rate(target, E.add(E.add(E.add(id, ":"), ethic), ":pro"), triggered[ethic], E.divide(p, scale))
+            var deg: Variant = rate(target, E.add(E.add(E.add(id, ":"), ethic), ":deg"), triggered[ethic], E.divide(d, scale))
             var bounded: Dictionary = QuantityMath.allocate_whole({"pro": pro, "deg": deg}, triggered[ethic])
-            if rules[id].fights: warriors[ethic] = rate(target, id + ":" + ethic + ":war", triggered[ethic], minf(1.0, float(row.war) * modifiers.war))
-            if rules[id].colonizes: settlers[ethic] = rate(target, id + ":" + ethic + ":col", triggered[ethic], minf(1.0, float(row.colonization) * modifiers.colonization))
+            if rules[id].fights: warriors[ethic] = rate(target, E.add(E.add(E.add(id, ":"), ethic), ":war"), triggered[ethic], E.minimum(1, E.multiply(E.of(row.war), modifiers.war)))
+            if rules[id].colonizes: settlers[ethic] = rate(target, E.add(E.add(E.add(id, ":"), ethic), ":col"), triggered[ethic], E.minimum(1, E.multiply(E.of(row.colonization), modifiers.colonization)))
             successes[ethic] = bounded.pro
             failures[ethic] = bounded.deg
-            triggered[ethic] -= bounded.pro + bounded.deg
+            triggered[ethic] = E.subtract(triggered[ethic], E.add(bounded.pro, bounded.deg))
+        var profile_transitions: int = world.profile_start()
         add(triggered, progress(world, target, rules, budget, plan, successes))
         fall(target, plan, rules, failures)
+        world.profile_end("civilization_transitions", profile_transitions)
         if rules[id].fights:
-            for ethic in warriors: warriors[ethic] = minf(warriors[ethic], triggered[ethic])
-            var wars: float = minf(total(warriors), floorf((total(triggered) + total(remaining[id])) / 2.0))
+            var profile_wars: int = world.profile_start()
+            for ethic in warriors: warriors[ethic] = E.minimum(warriors[ethic], triggered[ethic])
+            var wars: Variant = E.minimum(total(warriors), E.floor_value(E.divide((E.add(total(triggered), total(remaining[id]))), 2)))
             warriors = QuantityMath.allocate_whole(warriors, wars)
-            for ethic in warriors: triggered[ethic] -= warriors[ethic]
-            var outcomes: Dictionary = split(target, id + ":wars", wars, {"deg": 1.0, "pro25": 2.0, "pro50": 3.0, "pro75": 3.0})
-            var win_expected: float = outcomes.get("pro25", 0.0) * 0.25 + outcomes.get("pro50", 0.0) * 0.5 + outcomes.get("pro75", 0.0) * 0.75
-            var loss_expected: float = outcomes.get("deg", 0.0) * 2.0 + outcomes.get("pro25", 0.0) + outcomes.get("pro50", 0.0) * 1.5 + outcomes.get("pro75", 0.0) * 2.0
-            var winners: Dictionary = take(world, warriors, rate(target, id + ":wins", win_expected, 1.0))
-            var attackers_lost: Dictionary = take(world, warriors, rate(target, id + ":attackers_lost", outcomes.get("deg", 0.0) / order, 1.0))
+            for ethic in warriors: triggered[ethic] = E.subtract(triggered[ethic], warriors[ethic])
+            var outcomes: Dictionary = split(target, E.add(id, ":wars"), wars, {"deg": 1, "pro25": 2, "pro50": 3, "pro75": 3})
+            var win_expected: Variant = E.add(E.add(E.multiply(outcomes.get("pro25", 0), E.of("0.25")), E.multiply(outcomes.get("pro50", 0), E.of("0.5"))), E.multiply(outcomes.get("pro75", 0), E.of("0.75")))
+            var loss_expected: Variant = E.add(E.add(E.add(E.multiply(outcomes.get("deg", 0), 2), outcomes.get("pro25", 0)), E.multiply(outcomes.get("pro50", 0), E.of("1.5"))), E.multiply(outcomes.get("pro75", 0), 2))
+            var winners: Dictionary = take(world, warriors, rate(target, E.add(id, ":wins"), win_expected, 1))
+            var attackers_lost: Dictionary = take(world, warriors, rate(target, E.add(id, ":attackers_lost"), E.divide(outcomes.get("deg", 0), order), 1))
             add(triggered, progress(world, target, rules, budget, plan, winners))
             fall(target, plan, rules, attackers_lost)
-            var losses: float = minf(rate(target, id + ":loss", loss_expected / order, 1.0), total(triggered) + total(remaining[id]))
+            var losses: Variant = E.minimum(rate(target, E.add(id, ":loss"), E.divide(loss_expected, order), 1), E.add(total(triggered), total(remaining[id])))
             var sides: Dictionary = QuantityMath.allocate_whole({"due": total(triggered), "later": total(remaining[id])}, losses)
             var victims: Dictionary = take(world, triggered, sides.due)
             add(victims, consume_untriggered(world, target, plan, remaining[id], sides.later, year))
             fall(target, plan, rules, victims)
             add(triggered, warriors)
-            var damage: float = rate(target, id + ":collateral", (outcomes.get("pro50", 0.0) * 10.0 + outcomes.get("pro75", 0.0) * 30.0) / order, 1.0)
-            collateral[rules[id].previous] = collateral.get(rules[id].previous, 0.0) + damage
-            target.civilization_stats.wars = target.civilization_stats.get("wars", 0.0) + wars
+            var damage: Variant = rate(target, E.add(id, ":collateral"), E.divide((E.add(E.multiply(outcomes.get("pro50", 0), 10), E.multiply(outcomes.get("pro75", 0), 30))), order), 1)
+            collateral[rules[id].previous] = E.add(collateral.get(rules[id].previous, 0), damage)
+            target.civilization_stats.wars = E.add(target.civilization_stats.get("wars", 0), wars)
+            world.profile_end("wars", profile_wars)
         emit(plan, id, triggered)
-        if total(settlers) > 0.0: colonies.append({"stage": rules[id].colony, "source": id, "population": settlers})
+        if E.gt(total(settlers), 0): colonies.append({"stage": rules[id].colony, "source": id, "population": settlers})
     # Collateral is applied after all stages planned their own attempts.
     for id in collateral:
-        if not rules.has(id): continue
-        if not plans.has(id): plans[id] = new_plan(id, year)
+        if (not rules.has(id)): continue
+        if not copied.has(id):
+            remaining[id] = remaining[id].duplicate()
+            copied[id] = true
+        if (not plans.has(id)): plans[id] = new_plan(id, year)
         var plan: Dictionary = plans[id]
         var retry: Dictionary = plan.outputs.get(id, {})
-        var amount: float = minf(collateral[id], total(retry) + total(remaining[id]))
+        var amount: Variant = E.minimum(collateral[id], E.add(total(retry), total(remaining[id])))
         var sides: Dictionary = QuantityMath.allocate_whole({"due": total(retry), "later": total(remaining[id])}, amount)
         var victims: Dictionary = take(world, retry, sides.due)
         add(victims, consume_untriggered(world, target, plan, remaining[id], sides.later, year))
         fall(target, plan, rules, victims)
-        target.civilization_stats.collateral = target.civilization_stats.get("collateral", 0.0) + total(victims)
+        target.civilization_stats.collateral = E.add(target.civilization_stats.get("collateral", 0), total(victims))
     var incoming: Dictionary = {}
     var planetary: Dictionary = {}
     for id in plans:
+        if budget_timer != null and not await budget_timer.pause(): return {}
         var plan: Dictionary = plans[id]
         var products: Dictionary = {}
         for destination in plan.outputs:
             var pop: Dictionary = plan.outputs[destination]
             if rules.has(destination):
-                if destination != "Ct":
-                    pop = drift(target, id + ":" + destination + ":drift", pop, rules[id].ethics, destination == id and rules[id].diplomacy)
-                if not incoming.has(destination): incoming[destination] = {}
+                if E.ne(destination, "Ct"):
+                    var profile_drift: int = world.profile_start()
+                    pop = drift(target, E.add(E.add(E.add(id, ":"), destination), ":drift"), pop, rules[id].ethics, (E.eq(destination, id) and rules[id].diplomacy))
+                    world.profile_end("ethics_drift", profile_drift)
+                if (not incoming.has(destination)): incoming[destination] = {}
                 add(incoming[destination], pop)
             products[destination] = total(pop)
-            if State.is_space_civilization(id, rules) and world.catalog.entities[destination].group_as == "Planet":
-                planetary[destination] = planetary.get(destination, 0.0) + total(pop)
-        expired[id] = [{"amount": plan.amount, "from": plan.from, "to": maxf(plan.from, plan.to), "products": products}]
+            if (State.is_space_civilization(id, rules) and E.eq(world.catalog.entities[destination].group_as, "Planet")):
+                planetary[destination] = E.add(planetary.get(destination, 0), total(pop))
+        expired[id] = [{"amount": plan.amount, "from": plan.from, "to": E.maximum(plan.from, plan.to), "products": products}]
+    world.profile_end("civilization_prepare", profile_started)
     return {"remaining": remaining, "incoming": incoming, "planetary": planetary, "colonies": colonies}
 
-static func finish(world, target: Dictionary, transaction: Dictionary, year: float, rules: Dictionary) -> void:
+static func finish(world, target: Dictionary, transaction: Dictionary, year: Variant, rules: Dictionary, budget_timer: RefCounted = null) -> void:
+    var profile_started: int = world.profile_start()
     target.ethics = transaction.remaining
     for id in transaction.incoming:
-        if not target.ethics.has(id): target.ethics[id] = {}
+        if (not target.ethics.has(id)): target.ethics[id] = {}
         add(target.ethics[id], transaction.incoming[id])
     # Space civilizations that fall back to planetary stages need a stellar host.
     var physical: Dictionary = world.ledger.physical_amounts(target)
     var hosts: Dictionary = {}
     for id in physical:
-        if world.catalog.entities[id].event_group == "DwStar" and physical[id] > 0.0: hosts[id] = physical[id]
+        if (E.eq(world.catalog.entities[id].event_group, "DwStar") and E.gt(physical[id], 0)): hosts[id] = physical[id]
     for id in transaction.planetary:
-        var shares: Dictionary = split(target, "return:" + id, minf(transaction.planetary[id], target.amount.get(id, 0.0)), hosts)
+        var shares: Dictionary = split(target, E.add("return:", id), E.minimum(transaction.planetary[id], target.amount.get(id, 0)), hosts)
         for owner in shares:
-            if not target.binds.has(owner): target.binds[owner] = {}
-            target.binds[owner][id] = target.binds[owner].get(id, 0.0) + shares[owner]
-            target.amount[id] -= shares[owner]
-    colonize(world, target, transaction.colonies, year, rules)
-    State.reconcile(world, target, rules)
-    var worship: float = 0.0
+            if (not target.binds.has(owner)): target.binds[owner] = {}
+            target.binds[owner][id] = E.add(target.binds[owner].get(id, 0), shares[owner])
+            target.amount[id] = E.subtract(target.amount[id], shares[owner])
+    if budget_timer != null:
+        await colonize(world, target, transaction.colonies, year, rules, physical, budget_timer)
+        if budget_timer.cancelled: return
+    else:
+        colonize(world, target, transaction.colonies, year, rules, physical)
+    State.reconcile(world, target, rules, physical if transaction.colonies.is_empty() else {})
+    var worship: Variant = 0
     for id in rules:
-        if not rules[id].worships: continue
-        for ethic in target.ethics[id]: worship += target.ethics[id][ethic] * float(rules[id].ethics[ethic].worship)
+        if (not rules[id].worships): continue
+        for ethic in target.ethics[id]: worship = E.add(worship, E.multiply(target.ethics[id][ethic], E.of(rules[id].ethics[ethic].worship)))
     target.civilization_stats.worship = worship
+    world.profile_end("civilization_finish", profile_started)
 
-static func colonize(world, target: Dictionary, colonies: Array, year: float, rules: Dictionary) -> void:
-    var physical: Dictionary = world.ledger.physical_amounts(target)
+static func colonize(world, target: Dictionary, colonies: Array, year: Variant, rules: Dictionary, physical: Dictionary = {}, budget_timer: RefCounted = null) -> void:
+    if colonies.is_empty(): return
+    var profile_colonies: int = world.profile_start()
+    if physical.is_empty(): physical = world.ledger.physical_amounts(target)
     var stock: Dictionary = {}
-    for id in ["GG", "AB", "RP", "HP"]: stock[id] = physical.get(id, 0.0)
+    for id in ["GG", "AB", "RP", "HP"]: stock[id] = physical.get(id, 0)
     var requests: Dictionary = {}
     for i in colonies.size(): requests[str(i)] = total(colonies[i].population)
     var granted: Dictionary = QuantityMath.allocate_whole(requests, total(stock))
     for i in colonies.size():
+        if budget_timer != null and not await budget_timer.pause(): return
         var colony: Dictionary = colonies[i]
         var population: Dictionary = QuantityMath.allocate_whole(colony.population, granted[str(i)])
-        population = drift(target, colony.source + ":colonies", population, rules[colony.source].ethics, false, true)
-        var count: float = total(population)
+        population = drift(target, E.add(colony.source, ":colonies"), population, rules[colony.source].ethics, false, true)
+        var count: Variant = total(population)
         var targets: Dictionary = QuantityMath.allocate_whole(stock, count)
         for id in targets:
-            var amount: float = targets[id]
-            if amount <= 0.0: continue
-            var slots: Dictionary = {"": target.amount.get(id, 0.0)}
-            for owner in target.binds: slots[owner] = target.binds[owner].get(id, 0.0)
+            var amount: Variant = targets[id]
+            if E.le(amount, 0): continue
+            var slots: Dictionary = {"": target.amount.get(id, 0)}
+            for owner in target.binds: slots[owner] = target.binds[owner].get(id, 0)
             var taken: Dictionary = QuantityMath.allocate_whole(slots, amount)
-            world.batches.scale_batches(target, id, 1.0 - amount / stock[id])
-            stock[id] -= amount
+            world.batches.scale_batches(target, id, E.subtract(1, E.divide(amount, stock[id])))
+            stock[id] = E.subtract(stock[id], amount)
             for owner in taken:
-                if taken[owner] <= 0.0: continue
-                if owner == "": target.amount[id] -= taken[owner]
-                else: target.binds[owner][id] -= taken[owner]
-                var created: float = world.ledger.credit(target, colony.stage, taken[owner])
-                if owner != "":
-                    target.amount[colony.stage] -= created
-                    target.binds[owner][colony.stage] = target.binds[owner].get(colony.stage, 0.0) + created
+                if E.le(taken[owner], 0): continue
+                if E.eq(owner, ""): target.amount[id] = E.subtract(target.amount[id], taken[owner])
+                else: target.binds[owner][id] = E.subtract(target.binds[owner][id], taken[owner])
+                var created: Variant = world.ledger.credit(target, colony.stage, taken[owner])
+                if E.ne(owner, ""):
+                    target.amount[colony.stage] = E.subtract(target.amount[colony.stage], created)
+                    target.binds[owner][colony.stage] = E.add(target.binds[owner].get(colony.stage, 0), created)
             world.batches.append_batch(target, colony.stage, amount, year, year)
-        if not target.ethics.has(colony.stage): target.ethics[colony.stage] = {}
+        if (not target.ethics.has(colony.stage)): target.ethics[colony.stage] = {}
         add(target.ethics[colony.stage], population)
-        target.civilization_stats.colonies = target.civilization_stats.get("colonies", 0.0) + count
+        target.civilization_stats.colonies = E.add(target.civilization_stats.get("colonies", 0), count)
+    world.profile_end("colonization", profile_colonies)

world/owniverse/civilization_state.gd

@@ -1,237 +1,230 @@
 extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const QuantityMath = preload("res://world/owniverse/quantity_math.gd")
 
 const ETHICS = ["m", "l", "w", "d", "c", "b"]
 
 static func is_space_civilization(id: String, rules: Dictionary) -> bool:
-    return rules.has(id) and str(rules[id].home) != ""
+    return (rules.has(id) and E.ne(str(rules[id].home), ""))
 
 # Preserve any existing ethics. New populations start equally distributed;
 # reductions (including blasts) are proportional and never leave negative counts.
-static func reconcile(world, target: Dictionary, rules: Dictionary) -> void:
-    if not target.has("ethics"):
+static func reconcile(world, target: Dictionary, rules: Dictionary, physical: Dictionary = {}) -> void:
+    if (not target.has("ethics")):
         target.ethics = {}
-    var physical: Dictionary = world.ledger.physical_amounts(target)
+    if physical.is_empty():
+        physical = world.ledger.physical_amounts(target)
     for id in rules:
-        var count: float = physical.get(id, 0.0)
+        var count: Variant = physical.get(id, 0)
         var current: Dictionary = target.ethics.get(id, {})
-        var total: float = 0.0
+        var total: Variant = 0
         for ethic in ETHICS:
-            current[ethic] = maxf(0.0, current.get(ethic, 0.0))
-            total += current[ethic]
-        if total > count:
+            current[ethic] = E.maximum(0, current.get(ethic, 0))
+            total = E.add(total, current[ethic])
+        if E.gt(total, count):
             current = QuantityMath.allocate_whole(current, count)
-        elif total < count:
-            var missing: float = count - total
-            var base: float = floorf(missing / ETHICS.size())
-            var rest: int = int(missing - base * ETHICS.size())
+        elif E.lt(total, count):
+            var missing: Variant = E.subtract(count, total)
+            var base: Variant = E.floor_value(E.divide(missing, ETHICS.size()))
+            var rest: int = E.integer(E.subtract(missing, E.multiply(base, ETHICS.size())))
             for i in ETHICS.size():
-                current[ETHICS[i]] += base + (1.0 if i < rest else 0.0)
+                current[ETHICS[i]] = E.add(current[ETHICS[i]], E.add(base, ((1 if E.lt(i, rest) else 0))))
         target.ethics[id] = current
 
 static func detach_space_civilizations(target: Dictionary, rules: Dictionary) -> void:
-    for held: Dictionary in target.binds.values():
+    for held : Dictionary in target.binds.values():
         for id in held:
             if is_space_civilization(id, rules):
-                target.amount[id] = target.amount.get(id, 0.0) + held[id]
-                held[id] = 0.0
+                target.amount[id] = E.add(target.amount.get(id, 0), held[id])
+                held[id] = 0
 
 # A shared budget per stellar family, including stars bound into structures.
 # Reservations affect capacity, not the physical stock or its production.
-static func stellar_budget(world, target: Dictionary, rules: Dictionary) -> Dictionary:
-    var physical: Dictionary = world.ledger.physical_amounts(target)
+static func stellar_budget(world, target: Dictionary, rules: Dictionary, physical: Dictionary = {}) -> Dictionary:
+    if physical.is_empty():
+        physical = world.ledger.physical_amounts(target)
+    var layout: Dictionary = world.catalog.civilization_layout(rules)
     var capacity: Dictionary = {}
-    for id in physical:
-        var entity = world.catalog.entities[id]
-        for home in ["DwStar", "GiStar", "WD", "NS", "MGT", "BH"]:
-            if entity.event_group == home or entity.count_as == home or id == home:
-                capacity[home] = capacity.get(home, 0.0) + physical[id]
-    capacity["SMBH"] = maxf(0.0, target.amount.get("SMBH", 0.0))
-    for held: Dictionary in target.binds.values():
-        capacity["SMBH"] += maxf(0.0, held.get("SMBH", 0.0))
+    for id in layout.star_homes:
+        for home in layout.star_homes[id]:
+            capacity[home] = E.add(capacity.get(home, 0), physical.get(id, 0))
+    capacity["SMBH"] = E.maximum(0, target.amount.get("SMBH", 0))
+    for held : Dictionary in target.binds.values():
+        capacity["SMBH"] = E.add(capacity["SMBH"], E.maximum(0, held.get("SMBH", 0)))
     var populations: Dictionary = {}
     var requested: Dictionary = {}
     for id in rules:
-        if not is_space_civilization(id, rules):
+        if (not is_space_civilization(id, rules)):
             continue
-        populations[id] = physical.get(id, 0.0)
+        populations[id] = physical.get(id, 0)
         var home: String = rules[id].home
-        requested[home] = requested.get(home, 0.0) + populations[id] * maxf(1.0, rules[id].stars)
+        requested[home] = E.add(requested.get(home, 0), E.multiply(populations[id], E.maximum(1, rules[id].stars)))
     var free: Dictionary = {}
     for home in capacity:
-        free[home] = maxf(0.0, capacity[home] - requested.get(home, 0.0))
-    return {"capacity": capacity, "requested": requested, "free": free, "populations": populations, "habitats": habitat_budget(world, target, rules)}
+        free[home] = E.maximum(0, E.subtract(capacity[home], requested.get(home, 0)))
+    return {"capacity": capacity, "requested": requested, "free": free, "populations": populations, "habitats": habitat_budget(world, target, rules, physical)}
 
 # Account for the source's existing reservation when changing stages. A failed
 # transition retains its population at the source, rather than losing objects.
-static func admit_transition(budget: Dictionary, rules: Dictionary, source: String,
-        destination: String, requested: float) -> float:
-    if source == destination or not is_space_civilization(destination, rules):
+static func admit_transition(budget: Dictionary, rules: Dictionary, source: String, destination: String, requested: Variant) -> Variant:
+    if (E.eq(source, destination) or (not is_space_civilization(destination, rules))):
         return requested
     var home: String = rules[destination].home
-    var cost: float = maxf(1.0, rules[destination].stars)
+    var cost: Variant = E.maximum(1, rules[destination].stars)
     var old_home: String = ""
-    var old_cost: float = 0.0
+    var old_cost: Variant = 0
     if is_space_civilization(source, rules):
         old_home = rules[source].home
-        old_cost = maxf(1.0, rules[source].stars)
+        old_cost = E.maximum(1, rules[source].stars)
     # Existing overcapacity is handled by the separate population policy.
-    if budget.requested.get(home, 0.0) > budget.capacity.get(home, 0.0):
-        return 0.0
-    var net_cost: float = cost - old_cost if old_home == home else cost
-    var admitted: float = floorf(maxf(0.0, requested))
-    if net_cost > 0.0:
-        admitted = minf(admitted, floorf(budget.free.get(home, 0.0) / net_cost))
+    if E.gt(budget.requested.get(home, 0), budget.capacity.get(home, 0)):
+        return 0
+    var net_cost: Variant = (E.subtract(cost, old_cost) if E.eq(old_home, home) else cost)
+    var admitted: Variant = E.floor_value(E.maximum(0, requested))
+    if E.gt(net_cost, 0):
+        admitted = E.minimum(admitted, E.floor_value(E.divide(budget.free.get(home, 0), net_cost)))
     if budget.has("habitats"):
         var housing: Dictionary = budget.habitats
         var new_req: Dictionary = housing.requirements.get(destination, {})
         var old_req: Dictionary = housing.requirements.get(source, {})
-        if not new_req.is_empty():
-            var net_units: float = new_req.units - (old_req.units if old_req.get("id", "") == new_req.id else 0.0)
-            if net_units > 0.0:
-                var free_units: float = maxf(0.0, housing.capacity.get(new_req.id, 0.0) - housing.requested.get(new_req.id, 0.0))
-                admitted = minf(admitted, floorf(free_units / net_units))
-        if not old_req.is_empty(): housing.requested[old_req.id] = maxf(0.0, housing.requested.get(old_req.id, 0.0) - admitted * old_req.units)
-        if not new_req.is_empty(): housing.requested[new_req.id] = housing.requested.get(new_req.id, 0.0) + admitted * new_req.units
-    if old_home != "":
-        budget.requested[old_home] = maxf(0.0, budget.requested.get(old_home, 0.0) - admitted * old_cost)
-        budget.free[old_home] = maxf(0.0, budget.capacity.get(old_home, 0.0) - budget.requested[old_home])
-    budget.requested[home] = budget.requested.get(home, 0.0) + admitted * cost
-    budget.free[home] = maxf(0.0, budget.capacity.get(home, 0.0) - budget.requested[home])
+        if (not new_req.is_empty()):
+            var net_units: Variant = E.subtract(new_req.units, ((old_req.units if E.eq(old_req.get("id", ""), new_req.id) else 0)))
+            if E.gt(net_units, 0):
+                var free_units: Variant = E.maximum(0, E.subtract(housing.capacity.get(new_req.id, 0), housing.requested.get(new_req.id, 0)))
+                admitted = E.minimum(admitted, E.floor_value(E.divide(free_units, net_units)))
+        if (not old_req.is_empty()): housing.requested[old_req.id] = E.maximum(0, E.subtract(housing.requested.get(old_req.id, 0), E.multiply(admitted, old_req.units)))
+        if (not new_req.is_empty()): housing.requested[new_req.id] = E.add(housing.requested.get(new_req.id, 0), E.multiply(admitted, new_req.units))
+    if E.ne(old_home, ""):
+        budget.requested[old_home] = E.maximum(0, E.subtract(budget.requested.get(old_home, 0), E.multiply(admitted, old_cost)))
+        budget.free[old_home] = E.maximum(0, E.subtract(budget.capacity.get(old_home, 0), budget.requested[old_home]))
+    budget.requested[home] = E.add(budget.requested.get(home, 0), E.multiply(admitted, cost))
+    budget.free[home] = E.maximum(0, E.subtract(budget.capacity.get(home, 0), budget.requested[home]))
     return admitted
 
 # Resolve shortages from the most advanced stages downwards. This gives existing
 # advanced populations priority and lets a demotion cascade in the same cycle.
-static func enforce_capacity(world, target: Dictionary, rules: Dictionary, year: float) -> void:
+static func enforce_capacity(world, target: Dictionary, rules: Dictionary, year: Variant) -> void:
+    var profile_started: int = world.profile_start()
     detach_space_civilizations(target, rules)
-    reconcile(world, target, rules)
-    var budget: Dictionary = stellar_budget(world, target, rules)
+    var physical: Dictionary = world.ledger.physical_amounts(target)
+    reconcile(world, target, rules, physical)
+    var budget: Dictionary = stellar_budget(world, target, rules, physical)
     var remaining: Dictionary = budget.capacity.duplicate()
     var remaining_homes: Dictionary = budget.habitats.capacity.duplicate()
-    var stages: Array = []
-    for id in rules:
-        if is_space_civilization(id, rules):
-            stages.append(id)
-    stages.sort()
-    for index in range(stages.size() - 1, -1, -1):
+    var stages: Array = world.catalog.civilization_layout(rules).stages
+    var changed: bool = false
+    for index in range(E.subtract(stages.size(), 1), E.neg(1), E.neg(1)):
         var id: String = stages[index]
+        var count: Variant = target.amount.get(id, 0)
+        if E.le(count, 0): continue
         var home: String = rules[id].home
-        var cost: float = maxf(1.0, rules[id].stars)
-        var count: float = target.amount.get(id, 0.0)
-        var supported: float = minf(count, floorf(remaining.get(home, 0.0) / cost))
+        var cost: Variant = E.maximum(1, rules[id].stars)
+        var supported: Variant = E.minimum(count, E.floor_value(E.divide(remaining.get(home, 0), cost)))
         var requirement: Dictionary = budget.habitats.requirements.get(id, {})
-        if not requirement.is_empty():
-            supported = minf(supported, floorf(remaining_homes.get(requirement.id, 0.0) / requirement.units))
-            remaining_homes[requirement.id] = maxf(0.0, remaining_homes.get(requirement.id, 0.0) - supported * requirement.units)
-        remaining[home] = maxf(0.0, remaining.get(home, 0.0) - supported * cost)
-        var excess: float = count - supported
-        if excess <= 0.0:
+        if (not requirement.is_empty()):
+            supported = E.minimum(supported, E.floor_value(E.divide(remaining_homes.get(requirement.id, 0), requirement.units)))
+            remaining_homes[requirement.id] = E.maximum(0, E.subtract(remaining_homes.get(requirement.id, 0), E.multiply(supported, requirement.units)))
+        remaining[home] = E.maximum(0, E.subtract(remaining.get(home, 0), E.multiply(supported, cost)))
+        var excess: Variant = E.subtract(count, supported)
+        if E.le(excess, 0):
             continue
-        var previous: String = stages[index - 1] if index > 0 else "C1.9"
-        world.batches.scale_batches(target, id, supported / count)
+        changed = true
+        var previous: String = (stages[E.subtract(index, 1)] if E.gt(index, 0) else "C1.9")
+        world.batches.scale_batches(target, id, E.divide(supported, count))
         target.amount[id] = supported
         world.ledger.credit(target, previous, excess)
         world.batches.append_batch(target, previous, excess, year, year)
         var removed: Dictionary = QuantityMath.allocate_whole(target.ethics[id], excess)
-        if not target.ethics.has(previous):
+        if (not target.ethics.has(previous)):
             target.ethics[previous] = {}
         for ethic in ETHICS:
-            target.ethics[id][ethic] -= removed[ethic]
-            target.ethics[previous][ethic] = target.ethics[previous].get(ethic, 0.0) + removed[ethic]
-        if previous == "C1.9":
+            target.ethics[id][ethic] = E.subtract(target.ethics[id][ethic], removed[ethic])
+            target.ethics[previous][ethic] = E.add(target.ethics[previous].get(ethic, 0), removed[ethic])
+        if E.eq(previous, "C1.9"):
             var stars: Dictionary = {}
-            var physical: Dictionary = world.ledger.physical_amounts(target)
-            for star in physical:
-                if world.catalog.entities[star].event_group == "DwStar" and physical[star] > 0.0:
-                    stars[star] = physical[star]
+            var current_physical: Dictionary = world.ledger.physical_amounts(target)
+            for star in current_physical:
+                if (E.eq(world.catalog.entities[star].event_group, "DwStar") and E.gt(current_physical[star], 0)):
+                    stars[star] = current_physical[star]
             var weights: Dictionary = QuantityMath.normalize_distribution(stars)
             # Worlds are aggregates: a star may host several inhabited planets.
-            var assigned: float = 0.0
+            var assigned: Variant = 0
             var owners: Array = weights.keys()
             owners.sort()
             for i in owners.size():
                 var owner: String = owners[i]
-                var amount: float = floorf(excess * weights[owner]) if i + 1 < owners.size() else excess - assigned
-                assigned += amount
-                if not target.binds.has(owner):
+                var amount: Variant = (E.floor_value(E.multiply(excess, weights[owner])) if E.lt(E.add(i, 1), owners.size()) else E.subtract(excess, assigned))
+                assigned = E.add(assigned, amount)
+                if (not target.binds.has(owner)):
                     target.binds[owner] = {}
-                target.binds[owner][previous] = target.binds[owner].get(previous, 0.0) + amount
-                target.amount[previous] -= amount
-    reconcile(world, target, rules)
-    assign_homes(world, target, rules)
+                target.binds[owner][previous] = E.add(target.binds[owner].get(previous, 0), amount)
+                target.amount[previous] = E.subtract(target.amount[previous], amount)
+    if changed:
+        physical = world.ledger.physical_amounts(target)
+        reconcile(world, target, rules, physical)
+    assign_homes(world, target, rules, physical)
+    world.profile_end("enforce_capacity", profile_started)
 
 # Unity's structure chain: direct Claim resets the required structure count;
 # intervening stages require ten times more units of the preceding structure.
-static func habitat_budget(world, target: Dictionary, rules: Dictionary) -> Dictionary:
-    var physical: Dictionary = world.ledger.physical_amounts(target)
-    var structures: Array = []
+static func habitat_budget(world, target: Dictionary, rules: Dictionary, physical: Dictionary = {}) -> Dictionary:
+    if physical.is_empty():
+        physical = world.ledger.physical_amounts(target)
+    var layout: Dictionary = world.catalog.civilization_layout(rules)
+    var structures: Array = layout.structures
     var capacity: Dictionary = {}
-    for id in world.catalog.entities:
-        if world.catalog.entities[id].claim != "":
-            structures.append(id)
-            capacity[id] = physical.get(id, 0.0)
-    structures.sort_custom(func(a, b):
-        var left: float = world.catalog.entities[a].civ_bonus
-        var right: float = world.catalog.entities[b].civ_bonus
-        return left > right if left != right else str(a) < str(b))
-    var stages: Array = []
-    for id in rules:
-        if is_space_civilization(id, rules): stages.append(id)
-    stages.sort()
-    var requirements: Dictionary = {}
-    var anchors: Dictionary = {}
-    var anchor: String = ""
-    var units: float = 1.0
-    for id in stages:
-        var direct: String = ""
-        for structure in structures:
-            if world.catalog.entities[structure].claim == id: direct = structure
-        if direct != "":
-            anchor = direct
-            units = 1.0
-        else:
-            units *= 10.0
-        anchors[id] = anchor
-        if id.begins_with("C3.") or id.begins_with("C4."):
-            requirements[id] = {"id": anchor, "units": units}
+    for id in structures: capacity[id] = physical.get(id, 0)
+    var requirements: Dictionary = layout.requirements
+    var anchors: Dictionary = layout.anchors
     var requested: Dictionary = {}
     for id in requirements:
         var req: Dictionary = requirements[id]
-        requested[req.id] = requested.get(req.id, 0.0) + physical.get(id, 0.0) * req.units
+        requested[req.id] = E.add(requested.get(req.id, 0), E.multiply(physical.get(id, 0), req.units))
     return {"capacity": capacity, "requested": requested, "requirements": requirements, "structures": structures, "anchors": anchors}
 
-static func assign_homes(world, target: Dictionary, rules: Dictionary) -> void:
-    var budget: Dictionary = habitat_budget(world, target, rules)
-    var used: Dictionary = {}
-    target.civilization_homes = {}
-    var stages: Array = budget.anchors.keys()
-    stages.sort()
-    stages.reverse()
-    for id in stages:
-        var left: float = target.amount.get(id, 0.0)
-        var homes: Dictionary = {}
-        var allowed: bool = budget.anchors[id] == ""
-        for structure in budget.structures:
-            if structure == budget.anchors[id]: allowed = true
-            if not allowed or budget.capacity[structure] <= 0.0: continue
-            var amount: float = left
-            if world.catalog.entities[structure].claim == id:
-                amount = minf(amount, maxf(0.0, budget.capacity[structure] - used.get(structure, 0.0)))
-                used[structure] = used.get(structure, 0.0) + amount
-            if amount > 0.0: homes[structure] = amount
-            left -= amount
-            if left <= 0.0: break
-        target.civilization_homes[id] = homes
+# A structure's direct reservation belongs only to its Claim stage. Other
+# stages do not debit it, so each stage's placement can be calculated alone.
+static func stage_homes(world, target: Dictionary, id: String, layout: Dictionary, capacity: Dictionary = {}) -> Dictionary:
+    var left: Variant = target.amount.get(id, 0)
+    var homes: Dictionary = {}
+    if E.le(left, 0): return homes
+    var allowed: bool = layout.anchors[id] == ""
+    for structure in layout.structures:
+        if structure == layout.anchors[id]: allowed = true
+        if not allowed: continue
+        var stock: Variant = capacity.get(structure, 0) if not capacity.is_empty() else world.ledger.physical_amount(target, structure)
+        if E.le(stock, 0): continue
+        var amount: Variant = left
+        if world.catalog.entities[structure].claim == id:
+            amount = E.minimum(amount, stock)
+        if E.gt(amount, 0): homes[structure] = amount
+        left = E.subtract(left, amount)
+        if E.le(left, 0): break
+    return homes
 
-static func effective_span(world, target: Dictionary, id: String, rules: Dictionary) -> float:
-    if not rules.has(id): return world.catalog.entities[id].lifespan
-    var base: float = rules[id].span
-    if not is_space_civilization(id, rules): return base
-    assign_homes(world, target, rules)
-    var population: float = target.amount.get(id, 0.0)
-    if population <= 0.0: return base
-    var weighted: float = population
-    for home in target.civilization_homes.get(id, {}):
-        weighted += target.civilization_homes[id][home] * (maxf(0.0, world.catalog.entities[home].civ_bonus) - 1.0)
-    return base * population / weighted if weighted > 0.0 else base
+static func assign_homes(world, target: Dictionary, rules: Dictionary, physical: Dictionary = {}) -> void:
+    var profile_started: int = world.profile_start()
+    var layout: Dictionary = world.catalog.civilization_layout(rules)
+    var capacity: Dictionary = {}
+    for structure in layout.structures:
+        capacity[structure] = world.ledger.physical_amount(target, structure) if physical.is_empty() else physical.get(structure, 0)
+    target.civilization_homes = {}
+    for index in range(layout.stages.size() - 1, -1, -1):
+        var id: String = layout.stages[index]
+        target.civilization_homes[id] = stage_homes(world, target, id, layout, capacity)
+    world.profile_end("assign_homes", profile_started)
+
+
+static func effective_span(world, target: Dictionary, id: String, rules: Dictionary) -> Variant:
+    if (not rules.has(id)): return world.catalog.entities[id].lifespan
+    var base: Variant = rules[id].span
+    if (not is_space_civilization(id, rules)): return base
+    var population: Variant = target.amount.get(id, 0)
+    if E.le(population, 0): return base
+    var homes: Dictionary = stage_homes(world, target, id, world.catalog.civilization_layout(rules))
+    target.civilization_homes[id] = homes
+    var weighted: Variant = population
+    for home in homes:
+        weighted = E.add(weighted, E.multiply(homes[home], (E.subtract(E.maximum(0, world.catalog.entities[home].civ_bonus), 1))))
+    return (E.mul_div(base, population, weighted) if E.gt(weighted, 0) else base)

world/owniverse/entity_catalog.gd

@@ -1,4 +1,5 @@
 extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
 ## Definitions and their indexes only: no population, batches or UI state.
 ## Definitions are Nodes owned by the caller, as before this extraction.
 
@@ -8,7 +9,10 @@ var event_groups: Dictionary[String, Array] = {}
 var automatic_producers: Array = []
 var unlockable_entities: Array = []
 var _group_members: Dictionary = {}
+var index_revision: int = 0
 var _indexed_entity_count: int = -1
+var _civilization_layout: Dictionary = {}
+var _civilization_rules: Dictionary = {}
 
 ## Populate an empty catalog; replacement uses a new catalog to preserve ownership.
 func load_definitions(rows: Dictionary) -> void:
@@ -28,6 +32,8 @@ func load_definitions(rows: Dictionary) -> void:
 
 ## Call explicitly after modifying group_as without changing the entity count.
 func rebuild_group_index() -> void:
+    index_revision += 1
+    _civilization_layout.clear()
     _group_members.clear()
     for id in entities:
         var group: String = entities[id].group_as
@@ -45,3 +51,47 @@ func is_group(id: String) -> bool:
 func members(id: String) -> Array:
     if not is_group(id): return [id]
     return _group_members.get(id, []).duplicate()
+
+## Definition-only cache. Rebuild indexes after changing claims or bonuses;
+## invalidate this layout after changing stage homes in an existing rules table.
+func invalidate_civilization_layout() -> void:
+    _civilization_layout.clear()
+
+func civilization_layout(rules: Dictionary) -> Dictionary:
+    _ensure_group_index()
+    if not _civilization_layout.is_empty() and is_same(_civilization_rules, rules):
+        return _civilization_layout
+    _civilization_rules = rules
+    var structures: Array = []
+    for id in entities:
+        if entities[id].claim != "": structures.append(id)
+    structures.sort_custom(func(a, b): return E.gt(entities[a].civ_bonus, entities[b].civ_bonus) if E.ne(entities[a].civ_bonus, entities[b].civ_bonus) else str(a) < str(b))
+    var stages: Array = []
+    for id in rules:
+        if str(rules[id].home) != "": stages.append(id)
+    stages.sort()
+    var anchors: Dictionary = {}
+    var requirements: Dictionary = {}
+    var anchor: String = ""
+    var units: Variant = 1
+    for id in stages:
+        var direct: String = ""
+        for structure in structures:
+            if entities[structure].claim == id: direct = structure
+        if direct != "":
+            anchor = direct
+            units = 1
+        else:
+            units = E.multiply(units, 10)
+        anchors[id] = anchor
+        if id.begins_with("C3.") or id.begins_with("C4."):
+            requirements[id] = {"id": anchor, "units": units}
+    var star_homes: Dictionary = {}
+    for id in entities:
+        var homes: Array = []
+        for home in ["DwStar", "GiStar", "WD", "NS", "MGT", "BH"]:
+            if entities[id].event_group == home or entities[id].count_as == home or id == home:
+                homes.append(home)
+        if not homes.is_empty(): star_homes[id] = homes
+    _civilization_layout = {"structures": structures, "stages": stages, "anchors": anchors, "requirements": requirements, "star_homes": star_homes}
+    return _civilization_layout

world/owniverse/evolution_coordinator.gd

@@ -1,4 +1,5 @@
 extends "res://world/owniverse/simulation_module.gd"
+const E = preload("res://world/owniverse/math/exact.gd")
 const CivilizationEvolution = preload("res://world/owniverse/civilization_evolution.gd")
 const CivilizationState = preload("res://world/owniverse/civilization_state.gd")
 const SimulationTime = preload("res://world/owniverse/simulation_time.gd")
@@ -12,138 +13,176 @@ func initialize_life_batches() -> void:
     for id in world.catalog.entities:
         if world.catalog.entities[id].life_rule.is_empty():
             continue
-        var tracked: float = 0.0
-        for batch: Dictionary in world.state.batches.get(id, []):
-            tracked += batch.amount
-        world.batches.append_batch(world.state, id, maxf(0.0, physical.get(id, 0.0) - tracked), world.state.time.datetime, world.state.time.datetime)
+        var tracked: Variant = 0
+        for batch : Dictionary in world.state.batches.get(id, []):
+            tracked = E.add(tracked, batch.amount)
+        world.batches.append_batch(world.state, id, E.maximum(0, E.subtract(physical.get(id, 0), tracked)), world.state.time.datetime, world.state.time.datetime)
 
 
-func evolute_to_datetime(datetime: float) -> void:
+func run_frame(clock: Dictionary, budget: RefCounted) -> void:
+    var _keep_alive: RefCounted = self
+    await evolute_to_datetime(clock.datetime, clock, budget)
+    if not budget.cancelled and world != null: world.finish_frame()
+
+func evolute_to_datetime(datetime: Variant, clock: Dictionary = {}, budget: RefCounted = null) -> void:
+    var _keep_alive: RefCounted = self
     # Reconcile only when simulation advances.
     # Fractional frame updates cannot change capacity or populations.
-    var processed_year: float = SimulationTime.processed_year(datetime)
-    if processed_year > world.state.time.year:
+    var processed_year: Variant = SimulationTime.processed_year(datetime)
+    if E.gt(processed_year, world.state.time.year):
+        var profile_initialize: int = world.profile_start()
         initialize_life_batches()
+        world.profile_end("initialize", profile_initialize)
     var previous: Dictionary = world.state
     var next: Dictionary = previous.duplicate_deep()
     next.version = SimulationTime.STATE_VERSION
-    next.speed = clampi(int(previous.speed), 1, Global.SPEED_LIMIT)
-    next.speed_in_year = pow(10.0, next.speed - 1)
-    var from_year: float = previous.time.year
-    var to_year: float = processed_year
-    if to_year > from_year:
+    next.speed = clampi(E.integer(previous.speed), 1, Global.SPEED_LIMIT)
+    next.speed_in_year = E.power(10, E.subtract(next.speed, 1))
+    var from_year: Variant = previous.time.year
+    var to_year: Variant = processed_year
+    if E.gt(to_year, from_year):
         var quantities: Dictionary = world.ledger.physical_amounts(previous)
         var distribution: Dictionary = QuantityMath.normalize_distribution(quantities)
         next.distribution = distribution
 
+        var profile_production: int = world.profile_start()
         world.automatic.produce_for_period(previous, next, quantities, distribution, from_year, to_year)
-        evolve_batches(next, to_year)
+        world.profile_end("production", profile_production)
+        var profile_generations: int = world.profile_start()
+        if budget != null:
+            await evolve_batches(next, to_year, budget)
+            if budget.cancelled: return
+        else:
+            evolve_batches(next, to_year)
+        world.profile_end("generations", profile_generations)
         world.ledger.refresh_groups(next)
         world.ledger.clamp_auto_resources(next)
-        WorldParameters.advance(previous, next, Global.CivilizationRules, to_year - from_year)
-    next.time = {"datetime": datetime, "year": to_year}
+        var profile_trends: int = world.profile_start()
+        WorldParameters.advance(previous, next, Global.CivilizationRules, E.subtract(to_year, from_year))
+        world.profile_end("trends", profile_trends)
+    next.time = clock if not clock.is_empty() else {"datetime": datetime, "year": to_year}
 
     # Publish only after every phase has finished; previous stays untouched.
-    world.state = next
-    if to_year > from_year:
+    world.state = E.bound_state(next)
+    if E.gt(to_year, from_year):
         world.presentation.refresh(world.state, world.catalog)
 
 
-func evolve_batches(target: Dictionary, to_year: float) -> void:
+func evolve_batches(target: Dictionary, to_year: Variant, budget: RefCounted = null) -> void:
+    var _keep_alive: RefCounted = self
     # A long cycle may contain several generations; preserve actual birth intervals.
     var completed: Dictionary = {}
-    while evolve_batch_generation(target, to_year, completed):
-        pass
+    while await evolve_batch_generation(target, to_year, completed, budget):
+        if budget != null and not await budget.pause(): return
 
 
-func evolve_batch_generation(target: Dictionary, to_year: float, completed: Dictionary = {}) -> bool:
+func evolve_batch_generation(target: Dictionary, to_year: Variant, completed: Dictionary = { }, budget: RefCounted = null) -> bool:
+    var _keep_alive: RefCounted = self
     # Apply direct completions at the original next-generation boundary, so
     # binding transfers, the blast environment and capacity checks keep order.
+    if budget != null and not await budget.pause(): return false
     var completed_now: Dictionary = completed.duplicate(true)
     completed.clear()
     var quantities: Dictionary = world.ledger.physical_amounts(target)
     var expired: Dictionary = {}
     var preview: Dictionary = {"batches": {}}
     for id in target.batches:
-        if world.catalog.entities.has(id) and world.catalog.entities[id].destroy_level > 0:
+        if (world.catalog.entities.has(id) and E.gt(world.catalog.entities[id].destroy_level, 0)):
             preview.batches[id] = target.batches[id].duplicate(true)
     for id in target.batches.keys():
-        if not world.catalog.entities.has(id) or world.catalog.entities[id].destroy_level <= 0:
+        if ((not world.catalog.entities.has(id)) or E.le(world.catalog.entities[id].destroy_level, 0)):
             continue
-        var dying: float = 0.0
-        for part: Dictionary in completed_now.get(id, []):
-            dying += part.amount
-        for part: Dictionary in world.batches.withdraw_batches(preview, id, to_year):
-            dying += part.amount
-        if quantities.get(id, 0.0) > 0.0:
-            world.stellar.destroy_planets(target, id, dying / quantities[id], world.catalog.entities[id].destroy_level)
+        var dying: Variant = 0
+        for part : Dictionary in completed_now.get(id, []):
+            dying = E.add(dying, part.amount)
+        for part : Dictionary in world.batches.withdraw_batches(preview, id, to_year):
+            dying = E.add(dying, part.amount)
+        if E.gt(quantities.get(id, 0), 0):
+            world.stellar.destroy_planets(target, id, E.divide(dying, quantities[id]), world.catalog.entities[id].destroy_level)
     quantities = world.ledger.physical_amounts(target)
     # Withdraw all types before creating successors: iteration order cannot affect them.
     for id in target.batches.keys():
         if world.catalog.entities.has(id):
-            expired[id] = completed_now.get(id, []) + world.batches.withdraw_batches(target, id, to_year)
+            expired[id] = E.add(completed_now.get(id, []), world.batches.withdraw_batches(target, id, to_year))
     var has_expired: bool = false
-    for parts: Array in expired.values():
-        if not parts.is_empty():
+    for parts : Array in expired.values():
+        if (not parts.is_empty()):
             has_expired = true
             break
-    if not has_expired:
+    if (not has_expired):
         return false
     var fractions: Dictionary = {}
     var outputs: Dictionary = {}
-    var star_budget: Dictionary = CivilizationState.stellar_budget(world, target, Global.CivilizationRules)
-    var civilization_transaction: Dictionary = CivilizationEvolution.prepare(world, target, expired, to_year, star_budget, Global.CivilizationRules)
+    var current_quantities: Dictionary = quantities
+    var star_budget: Dictionary = CivilizationState.stellar_budget(world, target, Global.CivilizationRules, current_quantities)
+    var civilization_transaction: Dictionary = await CivilizationEvolution.prepare(world, target, expired, to_year, star_budget, Global.CivilizationRules, current_quantities, budget)
+    if budget != null and budget.cancelled: return false
     for id in expired:
-        var total: float = 0.0
-        for part: Dictionary in expired[id]:
-            total += part.amount
-        fractions[id] = clampf(total / quantities[id], 0.0, 1.0) if quantities.get(id, 0.0) > 0.0 else 0.0
+        if budget != null and not await budget.pause(): return false
+        var total: Variant = 0
+        for part : Dictionary in expired[id]:
+            total = E.add(total, part.amount)
+        fractions[id] = (E.clamp_value(E.divide(total, quantities[id]), 0, 1) if E.gt(quantities.get(id, 0), 0) else 0)
         var combined: Dictionary = {}
-        for part: Dictionary in expired[id]:
-            if not part.has("products"):
+        for part : Dictionary in expired[id]:
+            if (not part.has("products")):
                 part.products = world.stellar.evolution_products(target, world.catalog.entities[id], part.amount)
             for successor in part.products.keys():
                 if Global.CivilizationRules.has(id):
                     continue
-                var requested: float = part.products[successor]
-                var admitted: float = CivilizationState.admit_transition(star_budget, Global.CivilizationRules, id, successor, requested)
+                var requested: Variant = part.products[successor]
+                var admitted: Variant = CivilizationState.admit_transition(star_budget, Global.CivilizationRules, id, successor, requested)
                 part.products[successor] = admitted
-                if admitted < requested:
-                    part.products[id] = part.products.get(id, 0.0) + requested - admitted
+                if E.lt(admitted, requested):
+                    part.products[id] = E.subtract(E.add(part.products.get(id, 0), requested), admitted)
             for successor in part.products:
-                combined[successor] = combined.get(successor, 0.0) + part.products[successor]
+                combined[successor] = E.add(combined.get(successor, 0), part.products[successor])
         outputs[id] = {}
-        if total > 0.0:
+        if E.gt(total, 0):
             for successor in combined:
-                outputs[id][successor] = combined[successor] / total
+                outputs[id][successor] = E.divide(combined[successor], total)
 
     var incoming: Dictionary = world.ledger.transfer_evolution(target, fractions, outputs)
 
     var new_owners: Dictionary = {}
-    var blast_power: float = 0.0
+    var blast_power: Variant = 0
     var environment: Dictionary = world.environment.stellar_environment(target)
     for id in expired:
-        for part: Dictionary in expired[id]:
+        for part : Dictionary in expired[id]:
             for successor in part.products:
-                var amount: float = part.products[successor]
-                if successor == "blast":
-                    blast_power += amount
+                if budget != null and not await budget.pause(): return false
+                var amount: Variant = part.products[successor]
+                if E.eq(successor, "blast"):
+                    blast_power = E.add(blast_power, amount)
                     continue
-                if not world.catalog.entities.has(successor):
+                if (not world.catalog.entities.has(successor)):
                     continue
-                if successor == id and (not world.catalog.entities[id].life_rule.is_empty() or Global.CivilizationRules.has(id)):
-                    target.amount[id] = target.amount.get(id, 0.0) + amount
+                if (E.eq(successor, id) and (((not world.catalog.entities[id].life_rule.is_empty()) or Global.CivilizationRules.has(id)))):
+                    target.amount[id] = E.add(target.amount.get(id, 0), amount)
                 else:
                     amount = world.ledger.credit(target, successor, amount)
-                var before_batches: Array = target.batches.get(successor, []).duplicate(true)
-                var cutoff: float = to_year if world.stellar.uses_short_lived_fast_path(successor) else -INF
-                var integral: float = world.batches.append_batch(target, successor, amount, part.from, part.to, completed, cutoff)
-                world.automatic.produce_newborn_lifetime(target, successor, amount, part.from, part.to, to_year, before_batches, integral)
-                new_owners[successor] = new_owners.get(successor, 0.0) + amount
+                var produces: bool = not world.automatic.yearly_products(world.catalog.entities[successor]).is_empty()
+                var before_batches: Array = target.batches.get(successor, []).duplicate(true) if produces else []
+                var cutoff: Variant = (to_year if world.stellar.uses_short_lived_fast_path(successor) else E.neg(INF))
+                var profile_newborn: int = world.profile_start()
+                var integral: Variant
+                if budget != null:
+                    integral = await world.batches.append_batch(target, successor, amount, part.from, part.to, completed, cutoff, budget)
+                    if budget.cancelled: return false
+                else:
+                    integral = world.batches.append_batch(target, successor, amount, part.from, part.to, completed, cutoff)
+                if produces:
+                    world.automatic.produce_newborn_lifetime(target, successor, amount, part.from, part.to, to_year, before_batches, integral)
+                world.profile_end("newborn_batches", profile_newborn)
+                new_owners[successor] = E.add(new_owners.get(successor, 0), amount)
     world.ledger.accept_transfers(target, incoming)
     world.ledger.bind_new_owners(target, new_owners)
     world.ledger.round_object_allocations(target)
-    CivilizationEvolution.finish(world, target, civilization_transaction, to_year, Global.CivilizationRules)
+    if budget != null:
+        await CivilizationEvolution.finish(world, target, civilization_transaction, to_year, Global.CivilizationRules, budget)
+        if budget.cancelled: return false
+    else:
+        CivilizationEvolution.finish(world, target, civilization_transaction, to_year, Global.CivilizationRules)
     world.stellar.apply_blast(target, blast_power, environment)
     CivilizationState.enforce_capacity(world, target, Global.CivilizationRules, to_year)
     return true

world/owniverse/frame_budget.gd

@@ -0,0 +1,22 @@
+extends RefCounted
+## Cooperative work on the main thread. No partially calculated state is published.
+var tree: SceneTree
+var slice_usec: int = 40000
+var deadline: int
+var cancelled: bool = false
+var waiting_usec: int = 0
+
+func _init(scene_tree: SceneTree, milliseconds: int = 40):
+    tree = scene_tree
+    slice_usec = milliseconds * 1000
+    deadline = Time.get_ticks_usec() + slice_usec
+
+func pause() -> bool:
+    var keep_alive: RefCounted = self
+    if cancelled: return false
+    if Time.get_ticks_usec() >= deadline:
+        var waiting_from: int = Time.get_ticks_usec()
+        await tree.process_frame
+        keep_alive.waiting_usec += Time.get_ticks_usec() - waiting_from
+        deadline = Time.get_ticks_usec() + slice_usec
+    return not keep_alive.cancelled

world/owniverse/frame_budget.gd.uid

@@ -0,0 +1 @@
+uid://hu57pwad02sg

world/owniverse/item_description.gd

@@ -1,101 +1,90 @@
 extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
 
 const GREEN = "#40cc40"
 const RED = "#ff6060"
 const GREY = "#888888"
 const Parameters = preload("res://world/owniverse/world_parameters.gd")
 
-static func number(value: float, digits: int = 0) -> String:
-    if not is_finite(value):
-        return "—"
-    if absf(value) >= 1e5:
-        var exponent: int = int(floor(log(absf(value)) / log(10.0)))
-        return "%.4fE%+d" % [value / pow(10.0, exponent), exponent]
-    return "%.*f" % [digits, value]
+static func number(value, digits: int = 0) -> String:
+    if not E.finite(value): return "—"
+    return E.grouped(value, digits, false)
 
 static func colored(text: String, color: String) -> String:
-    return "[color=" + color + "]" + text + "[/color]"
+    return E.add(E.add(E.add(E.add("[color=", color), "]"), text), "[/color]")
 
 static func matches(world, id: String) -> Array:
     var result: Array = []
     for key in world.catalog.entities:
         var entity = world.catalog.entities[key]
-        if key == id or entity.count_as == id or entity.group_as == id:
-            if not world.catalog.is_group(key):
+        if ((E.eq(key, id) or E.eq(entity.count_as, id)) or E.eq(entity.group_as, id)):
+            if (not world.catalog.is_group(key)):
                 result.append(key)
     return result
 
 static func quantities(world, id: String) -> Dictionary:
-    var free: float = 0.0
-    var total: float = 0.0
+    var free: Variant = 0
+    var total: Variant = 0
     var physical: Dictionary = world.ledger.physical_amounts(world.state)
     for key in matches(world, id):
-        free += world.state.amount.get(key, 0.0)
-        total += physical.get(key, 0.0)
-    if id == "SMBH":
-        free = world.state.amount.get(id, 0.0)
+        free = E.add(free, world.state.amount.get(key, 0))
+        total = E.add(total, physical.get(key, 0))
+    if E.eq(id, "SMBH"):
+        free = world.state.amount.get(id, 0)
         total = free
     return {"free": free, "total": total}
 
 static func costs(world, global: Node, id: String) -> String:
-    if not world.catalog.entities.has(id):
+    if (not world.catalog.entities.has(id)):
         return ""
     var lines: PackedStringArray = []
     for requirements in [world.catalog.entities[id].cost, world.catalog.entities[id].bind]:
         for resource in requirements:
-            var required: float = requirements[resource]
-            if required < 0.0:
+            var required: Variant = requirements[resource]
+            if E.lt(required, 0):
                 continue
-            var available: float = floorf(world.ledger.available(world.state, resource))
+            var available: Variant = E.floor_value(world.ledger.available(world.state, resource))
             var name: String = str(global.get_template(resource, "Entity", "Name").get("text", resource))
-            lines.append(colored(name + ": " + number(required) + " (" + number(available) + ")", GREEN if available >= required else RED))
+            lines.append(colored(E.add(E.add(E.add(E.add(E.add(name, ": "), number(required)), " ("), number(available)), ")"), (GREEN if E.ge(available, required) else RED)))
     return "\n".join(lines)
 
-static func variables(world, global: Node, id: String, rate: float = 0.0) -> Dictionary:
+static func variables(world, global: Node, id: String, rate: Variant = 0.0) -> Dictionary:
     var counts: Dictionary = quantities(world, id)
     var show_total: bool = false
     for key in matches(world, id):
-        show_total = show_total or world.catalog.entities[key].group_as == "Planet"
-    var amount: String = number(counts.total if show_total else counts.free) if world.catalog.entities.has(id) else "—"
-    if not show_total and counts.total > counts.free:
-        amount += " " + colored("(" + number(counts.total) + ")", GREY)
-    if rate != 0.0:
-        amount += " | " + colored(("−" if rate < 0.0 else "+") + number(absf(rate), 1), RED if rate < 0.0 else GREEN)
+        show_total = (show_total or E.eq(world.catalog.entities[key].group_as, "Planet"))
+    var amount: String = (number((counts.total if show_total else counts.free)) if world.catalog.entities.has(id) else "—")
+    if ((not show_total) and E.gt(counts.total, counts.free)):
+        amount = E.add(amount, E.add(" ", colored(E.add(E.add("(", number(counts.total)), ")"), GREY)))
+    if E.ne(rate, 0):
+        amount = E.add(amount, E.add(" | ", colored(E.add((("−" if E.lt(rate, 0) else "+")), number(E.absolute(rate), 1)), (RED if E.lt(rate, 0) else GREEN))))
     var physical: Dictionary = world.ledger.physical_amounts(world.state)
-    var voids: float = 0.0
+    var voids: Variant = 0
     for key in physical:
-        voids += physical[key] * world.catalog.entities[key].voids
-    var he: float = world.state.amount.get("He", 0.0)
-    var h: float = world.state.amount.get("H", 0.0)
+        voids = E.add(voids, E.multiply(physical[key], world.catalog.entities[key].voids))
+    var he: Variant = world.state.amount.get("He", 0)
+    var h: Variant = world.state.amount.get("H", 0)
     var mixture: String = "—"
-    if he + h > 0.0:
-        mixture = "He: " + number(100.0 * he / (he + h), 2) + "% / H: " + number(100.0 * h / (he + h), 2) + "%"
+    if E.gt(E.add(he, h), 0):
+        mixture = E.add(E.add(E.add(E.add("He: ", number(E.mul_div(100, he, (E.add(he, h))), 2)), "% / H: "), number(E.mul_div(100, h, (E.add(he, h))), 2)), "%")
     var environment: Dictionary = world.environment.stellar_environment(world.state)
-    return {
-        "amount": amount, "colored costs": costs(world, global, id),
-        "lifespan": number(world.catalog.entities[id].lifespan) if world.catalog.entities.has(id) else "—",
-        "voids": number(voids), "he / h": "\n" + mixture,
-        "metallicity": number(environment.metallicity * 100.0, 2) + "%",
-        "энергия": number(world.state.energy), "плотность": number(environment.density, 6),
-        "лет в секунду": number(world.state.speed_in_year),
-        "amount1": "—", "amount2": "—", "amount3": "—", "amount4": "—",
-    }
+    return {"amount": amount, "colored costs": costs(world, global, id), "lifespan": (number(world.catalog.entities[id].lifespan) if world.catalog.entities.has(id) else "—"), "voids": number(voids), "he / h": E.add("\n", mixture), "metallicity": E.add(number(E.multiply(environment.metallicity, 100), 2), "%"), "энергия": number(world.state.energy), "плотность": number(environment.density, 6), "лет в секунду": number(world.state.speed_in_year), "amount1": "—", "amount2": "—", "amount3": "—", "amount4": "—"}
 
-static func render(world, global: Node, id: String, category: String = "Entity", rate: float = 0.0) -> String:
+static func render(world, global: Node, id: String, category: String = "Entity", rate: Variant = 0.0) -> String:
     var values: Dictionary = variables(world, global, id, rate)
-    if category == "Indicator":
-        if id == "Density":
+    if E.eq(category, "Indicator"):
+        if E.eq(id, "Density"):
             id = Parameters.density_display(world.environment.stellar_environment(world.state).density).mode
         var scales: Dictionary = {"Burnability": "Bur", "Explosiveness": "Exp", "Aggression": "Agg"}
         if scales.has(id):
-            var level: float = Parameters.value(world.state, scales[id])
-            values.amount = number(level, 1 if level != floorf(level) else 0)
-            values.scale = global.render_template(global.get_template("Scale" + str(clampi(roundi(level), 1, 19)), "Indicator", "Scale"), {})
-        if id == "Trends":
+            var level: Variant = Parameters.value(world.state, scales[id])
+            values.amount = number(level, (1 if E.ne(level, E.floor_value(level)) else 0))
+            values.scale = global.render_template(global.get_template(E.add("Scale", str(clampi(E.integer(E.round_value(level)), 1, 19))), "Indicator", "Scale"), {})
+        if E.eq(id, "Trends"):
             for trend in Parameters.TRENDS:
-                values[trend.to_lower()] = number(world.state.get("trends", {}).get(trend, 0.0) * 100.0, 2) + "%"
-        if id == "Energy":
-            values["энергия"] = number(world.state.energy) + " (" + number(clampf(world.state.energy / Parameters.INITIAL_ENERGY, 0.0, 1.0) * 100.0, 2) + "%)"
+                values[trend.to_lower()] = E.add(number(E.multiply(world.state.get("trends", {}).get(trend, 0), 100), 2), "%")
+        if E.eq(id, "Energy"):
+            values["энергия"] = E.add(E.add(E.add(number(world.state.energy), " ("), number(E.multiply(E.clamp_value(E.divide(world.state.energy, Parameters.INITIAL_ENERGY), 0, 1), 100), 2)), "%)")
     var title: String = global.render_template(global.get_template(id, category, "Name"), values)
     var body: String = global.render_template(global.get_template(id, category, "Description"), values)
-    return "[b]" + (title if title != "" else id) + "[/b]\n" + body
+    return E.add(E.add(E.add("[b]", ((title if E.ne(title, "") else id))), "[/b]\n"), body)

world/owniverse/item_presentation.gd

@@ -1,54 +1,55 @@
 extends RefCounted
+const E = preload("res://world/owniverse/math/exact.gd")
 ## Read-only projections of simulation state. No controls or simulation mutations.
 
-var pending_amounts: Dictionary[String, float] = {}
+var pending_amounts: Dictionary [ String , Variant ] = {}
 var deferred_updates: bool = false
 var dirty: bool = true
 
 func refresh(state: Dictionary, catalog, force: bool = false) -> void:
     dirty = true
-    if deferred_updates and not force:
+    if (deferred_updates and (not force)):
         return
     pending_amounts = amounts(state, catalog)
     dirty = false
 
 ## Aliases are presentation-only; group counters are not counted twice.
-static func amounts(state: Dictionary, catalog, total_produced: bool = false) -> Dictionary[String, float]:
-    var source: Dictionary = state.stats.total_amount if total_produced else state.amount
-    if not total_produced:
+static func amounts(state: Dictionary, catalog, total_produced: bool = false) -> Dictionary [ String, Variant ]:
+    var source: Dictionary = (state.stats.total_amount if total_produced else state.amount)
+    if (not total_produced):
         source = source.duplicate()
         var physical: Dictionary = {}
         for id in catalog.entities:
-            if not catalog.is_group(id):
-                physical[id] = maxf(0.0, state.amount.get(id, 0.0))
-        for bindings: Dictionary in state.binds.values():
+            if (not catalog.is_group(id)):
+                physical[id] = E.maximum(0, state.amount.get(id, 0))
+        for bindings : Dictionary in state.binds.values():
             for id in bindings:
                 if physical.has(id):
-                    physical[id] += maxf(0.0, bindings[id])
-        var planets: float = 0.0
+                    physical[id] = E.add(physical[id], E.maximum(0, bindings[id]))
+        var planets: Variant = 0
         for id in physical:
-            if catalog.entities[id].group_as == "Planet":
+            if E.eq(catalog.entities[id].group_as, "Planet"):
                 source[id] = physical[id]
-                planets += physical[id]
+                planets = E.add(planets, physical[id])
         source["Planet"] = planets
-    var result: Dictionary[String, float] = {}
+    var result: Dictionary [ String , Variant ] = {}
     for id in source:
-        result[id] = 0.0
+        result[id] = 0
     for id in source:
         # group_as counters are already sums and must not be counted a second time.
         if catalog.is_group(id):
             continue
         var item_id: String = id
-        if catalog.entities.has(id) and catalog.entities[id].count_as != "":
+        if (catalog.entities.has(id) and E.ne(catalog.entities[id].count_as, "")):
             item_id = catalog.entities[id].count_as
         # Detailed icons need their own count as well as the summary alias.
         # Aggregate only from source, never from these presentation entries.
-        if item_id != id:
-            result[id] = result.get(id, 0.0) + float(source[id])
-        result[item_id] = result.get(item_id, 0.0) + float(source[id])
+        if E.ne(item_id, id):
+            result[id] = E.add(result.get(id, 0), E.of(source[id]))
+        result[item_id] = E.add(result.get(item_id, 0), E.of(source[id]))
     for id in source:
         if catalog.is_group(id):
-            result[id] = float(source[id])
+            result[id] = E.of(source[id])
     return result
 
 
@@ -63,12 +64,12 @@ static func unlocks(state: Dictionary, catalog, locked: Array) -> Dictionary:
         var entity = catalog.entities[id]
         var eligible: bool = true
         for requirement in entity.unlock:
-            if maxf(state.stats.total_amount.get(requirement, 0.0), display_totals.get(requirement, 0.0)) < entity.unlock[requirement]:
+            if E.lt(E.maximum(state.stats.total_amount.get(requirement, 0), display_totals.get(requirement, 0)), entity.unlock[requirement]):
                 eligible = false
                 break
         if eligible:
             for item_id in [id, entity.count_as]:
-                if item_id != "" and not visible.has(item_id):
+                if (E.ne(item_id, "") and (not visible.has(item_id))):
                     visible.append(item_id)
         else:
             remaining.append(id)

world/owniverse/life_evolution.gd

@@ -1,58 +1,56 @@
 extends "res://world/owniverse/simulation_module.gd"
+const E = preload("res://world/owniverse/math/exact.gd")
 const WorldParameters = preload("res://world/owniverse/world_parameters.gd")
 const QuantityMath = preload("res://world/owniverse/quantity_math.gd")
 
-func life_products(target: Dictionary, entity: OwniverseEntity, count: float) -> Dictionary:
+func life_products(target: Dictionary, entity: OwniverseEntity, count: Variant) -> Dictionary:
     var rule: Dictionary = entity.life_rule
     var pending: Dictionary = {}
     var modifiers: Dictionary = WorldParameters.life_modifiers(target)
-    var probabilities: Dictionary = {
-        "progress": float(rule.progress) * modifiers.progress * WorldParameters.value(target, "Enlightenment"),
-        "degradation": float(rule.degradation) * modifiers.degradation,
-    }
-    var probability_sum: float = maxf(1.0, probabilities.progress + probabilities.degradation)
-    if not target.has("life_remainders"):
+    var probabilities: Dictionary = {"progress": E.multiply(E.multiply(E.of(rule.progress), modifiers.progress), WorldParameters.value(target, "Enlightenment")), "degradation": E.multiply(E.of(rule.degradation), modifiers.degradation)}
+    var probability_sum: Variant = E.maximum(1, E.add(probabilities.progress, probabilities.degradation))
+    if (not target.has("life_remainders")):
         target.life_remainders = {}
     for channel in ["progress", "degradation"]:
-        var key: String = entity.id + ":" + channel
-        var expected: float = count * probabilities[channel] / probability_sum + target.life_remainders.get(key, 0.0)
+        var key: String = E.add(E.add(entity.id, ":"), channel)
+        var expected: Variant = E.add(E.mul_div(count, probabilities[channel], probability_sum), target.life_remainders.get(key, 0))
         target.life_remainders[key] = expected
-        pending[channel] = floorf(snappedf(expected, 1.0e-12))
+        pending[channel] = E.floor_value(expected)
     var assigned: Dictionary = QuantityMath.allocate_whole(pending, count)
     for channel in assigned:
-        var key: String = entity.id + ":" + channel
-        target.life_remainders[key] = maxf(0.0, target.life_remainders[key] - assigned[channel])
-    var result: Dictionary = {entity.id: count - assigned.progress - assigned.degradation}
+        var key: String = E.add(E.add(entity.id, ":"), channel)
+        target.life_remainders[key] = E.maximum(0, E.subtract(target.life_remainders[key], assigned[channel]))
+    var result: Dictionary = {entity.id: E.subtract(E.subtract(count, assigned.progress), assigned.degradation)}
     result[rule.next] = assigned.progress
     var weights: Dictionary = {}
-    var weight_sum: float = 0.0
+    var weight_sum: Variant = 0
     for term in str(rule.fall).split("^"):
         var pair: PackedStringArray = term.split(":")
-        weights[pair[0]] = float(pair[1])
-        weight_sum += float(pair[1])
+        weights[pair[0]] = E.of(pair[1])
+        weight_sum = E.add(weight_sum, E.of(pair[1]))
     var requests: Dictionary = {}
     for id in weights:
-        var key: String = entity.id + ":fall:" + id
-        var expected: float = assigned.degradation * weights[id] / weight_sum + target.life_remainders.get(key, 0.0)
+        var key: String = E.add(E.add(entity.id, ":fall:"), id)
+        var expected: Variant = E.add(E.mul_div(assigned.degradation, weights[id], weight_sum), target.life_remainders.get(key, 0))
         target.life_remainders[key] = expected
-        requests[id] = maxf(0.0, floorf(snappedf(expected, 1.0e-12)))
+        requests[id] = E.maximum(0, E.floor_value(expected))
     var falls: Dictionary = QuantityMath.allocate_whole(requests, assigned.degradation)
-    var distributed: float = 0.0
+    var distributed: Variant = 0
     for id in falls:
-        distributed += falls[id]
-        result[id] = result.get(id, 0.0) + falls[id]
-        var key: String = entity.id + ":fall:" + id
-        target.life_remainders[key] -= falls[id]
+        distributed = E.add(distributed, falls[id])
+        result[id] = E.add(result.get(id, 0), falls[id])
+        var key: String = E.add(E.add(entity.id, ":fall:"), id)
+        target.life_remainders[key] = E.subtract(target.life_remainders[key], falls[id])
     # Fill sub-unit fall quotas deterministically, retaining signed allocation errors.
-    while distributed < assigned.degradation:
+    while E.lt(distributed, assigned.degradation):
         var selected: String = ""
-        var largest: float = -INF
+        var largest: Variant = E.neg(INF)
         for id in weights:
-            var rest: float = target.life_remainders[entity.id + ":fall:" + id]
-            if rest > largest:
+            var rest: Variant = target.life_remainders[E.add(E.add(entity.id, ":fall:"), id)]
+            if E.gt(rest, largest):
                 largest = rest
                 selected = id
-        result[selected] = result.get(selected, 0.0) + 1.0
-        target.life_remainders[entity.id + ":fall:" + selected] -= 1.0
-        distributed += 1.0
+        result[selected] = E.add(result.get(selected, 0), 1)
+        target.life_remainders[E.add(E.add(entity.id, ":fall:"), selected)] = E.subtract(target.life_remainders[E.add(E.add(entity.id, ":fall:"), selected)], 1)
+        distributed = E.add(distributed, 1)
     return result

world/owniverse/manual_production.gd

@@ -1,38 +1,40 @@
 extends "res://world/owniverse/simulation_module.gd"
+const E = preload("res://world/owniverse/math/exact.gd")
 const CivilizationState = preload("res://world/owniverse/civilization_state.gd")
 const QuantityMath = preload("res://world/owniverse/quantity_math.gd")
 
-func try_production(target: Dictionary, entity: OwniverseEntity, amount: float,
-        automatic: bool = false) -> bool:
-    if amount <= 0.0 or amount != floorf(amount):
+func try_production(target: Dictionary, entity: OwniverseEntity, amount: Variant, automatic: bool = false) -> bool:
+    if (E.le(amount, 0) or E.ne(amount, E.floor_value(amount))):
         return false
     var trial: Dictionary = target.duplicate()
     trial.amount = target.amount.duplicate()
     trial.binds = target.binds.duplicate(true)
     trial.auto_resources = target.auto_resources.duplicate()
     trial.batches = target.batches.duplicate()
+    # Physical object totals do not change while resources are withdrawn from
+    # this transaction. Keep one snapshot instead of scanning every resource.
+    var physical: Dictionary = world.ledger.physical_amounts(trial)
     var copied_batches: Dictionary = {}
     for resource in entity.cost:
-        var cost: float = roundf(maxf(0.0, entity.cost[resource]) * amount)
-        if automatic and trial.auto_resources.get(resource, 0.0) < cost:
+        var cost: Variant = E.round_value(E.multiply(E.maximum(0, entity.cost[resource]), amount))
+        if (automatic and E.lt(trial.auto_resources.get(resource, 0), cost)):
             return false
-        var before: Dictionary = world.ledger.physical_amounts(trial)
         var taken: Dictionary = world.ledger.take_available(trial, resource, cost)
-        var total: float = 0.0
+        var total: Variant = 0
         for quantity in taken.values():
-            total += quantity
-        if total != cost:
+            total = E.add(total, quantity)
+        if E.ne(total, cost):
             return false
         if automatic:
-            trial.auto_resources[resource] = maxf(0.0, trial.auto_resources.get(resource, 0.0) - cost)
+            trial.auto_resources[resource] = E.maximum(0, E.subtract(trial.auto_resources.get(resource, 0), cost))
         for id in taken:
             # Isolate only batches actually touched by this transaction.
-            if trial.batches.has(id) and not copied_batches.has(id):
+            if (trial.batches.has(id) and (not copied_batches.has(id))):
                 trial.batches[id] = trial.batches[id].duplicate(true)
                 copied_batches[id] = true
-            var factor: float = 1.0 - taken[id] / before[id] if before.get(id, 0.0) > 0.0 else 0.0
+            var factor: Variant = (E.subtract(1, E.divide(taken[id], physical[id])) if E.gt(physical.get(id, 0), 0) else 0)
             world.batches.scale_batches(trial, id, factor)
-    if not world.ledger.bind_new_owners(trial, {entity.id: amount}, true):
+    if (not world.ledger.bind_new_owners(trial, {entity.id: amount}, true)):
         return false
     world.ledger.refresh_groups(trial)
     world.ledger.clamp_auto_resources(trial)
@@ -46,72 +48,71 @@ func smbh_sources() -> Dictionary:
     var masses: Dictionary = {}
     for id in world.catalog.entities:
         var entity: OwniverseEntity = world.catalog.entities[id]
-        if entity.count_as == "BH" and entity.mass > 0.0:
-            masses[id] = floorf(maxf(0.0, world.state.amount.get(id, 0.0))) * entity.mass
+        if (E.eq(entity.count_as, "BH") and E.gt(entity.mass, 0)):
+            masses[id] = E.multiply(E.floor_value(E.maximum(0, world.state.amount.get(id, 0))), entity.mass)
     return masses
 
 
-func smbh_available() -> float:
-    var mass: float = 0.0
+func smbh_available() -> Variant:
+    var mass: Variant = 0
     for value in smbh_sources().values():
-        mass += value
-    return floorf(mass)
+        mass = E.add(mass, value)
+    return E.floor_value(mass)
 
 
-func plan_smbh(desired_amount: float) -> Dictionary:
-    var empty: Dictionary = {"amount": 0.0, "taken": {}}
-    if desired_amount <= 0.0 or not is_finite(desired_amount):
+func plan_smbh(desired_amount: Variant) -> Dictionary:
+    var empty: Dictionary = {"amount": 0, "taken": {}}
+    if (E.le(desired_amount, 0) or (not E.finite(desired_amount))):
         return empty
-    var total_mass: float = smbh_available()
-    if total_mass <= 0.0:
+    var total_mass: Variant = smbh_available()
+    if E.le(total_mass, 0):
         return empty
-    var requested: float = minf(floorf(desired_amount), total_mass)
-    if requested <= 0.0:
+    var requested: Variant = E.minimum(E.floor_value(desired_amount), total_mass)
+    if E.le(requested, 0):
         return empty
     var masses: Dictionary = smbh_sources()
     var distribution: Dictionary = QuantityMath.normalize_distribution(masses)
     var taken: Dictionary = {}
     var order: Array = []
-    var consumed_mass: float = 0.0
+    var consumed_mass: Variant = 0
     for id in distribution:
-        var expected: float = requested * distribution[id] / world.catalog.entities[id].mass
-        taken[id] = minf(floorf(expected), floorf(world.state.amount[id]))
-        consumed_mass += taken[id] * world.catalog.entities[id].mass
-        order.append({"id": id, "remainder": expected - taken[id]})
-    order.sort_custom(func(a: Dictionary, b: Dictionary) -> bool:
-        return a.remainder > b.remainder if a.remainder != b.remainder else str(a.id) < str(b.id))
+        var expected: Variant = E.mul_div(requested, distribution[id], world.catalog.entities[id].mass)
+        taken[id] = E.minimum(E.floor_value(expected), E.floor_value(world.state.amount[id]))
+        consumed_mass = E.add(consumed_mass, E.multiply(taken[id], world.catalog.entities[id].mass))
+        order.append({"id": id, "remainder": E.subtract(expected, taken[id])})
+    order.sort_custom(func ( a : Dictionary , b : Dictionary ) -> bool : return (E.gt(a.remainder, b.remainder) if E.ne(a.remainder, b.remainder) else E.lt(str(a.id), str(b.id))))
     # Consume whole BH only; all excess mass becomes SMBH, never disappears.
-    for candidate: Dictionary in order:
-        if consumed_mass >= requested:
+    for candidate : Dictionary in order:
+        if E.ge(consumed_mass, requested):
             break
         var id: String = candidate.id
-        if taken[id] < floorf(world.state.amount[id]):
-            taken[id] += 1.0
-            consumed_mass += world.catalog.entities[id].mass
-    if consumed_mass <= 0.0 or consumed_mass != floorf(consumed_mass):
+        if E.lt(taken[id], E.floor_value(world.state.amount[id])):
+            taken[id] = E.add(taken[id], 1)
+            consumed_mass = E.add(consumed_mass, world.catalog.entities[id].mass)
+    if (E.le(consumed_mass, 0) or E.ne(consumed_mass, E.floor_value(consumed_mass))):
         return empty
     return {"amount": consumed_mass, "taken": taken}
 
 
-func produce_smbh(desired_amount: float) -> float:
+func produce_smbh(desired_amount: Variant) -> Variant:
     var plan: Dictionary = plan_smbh(desired_amount)
-    var consumed_mass: float = plan.amount
+    var consumed_mass: Variant = plan.amount
     var taken: Dictionary = plan.taken
-    if consumed_mass <= 0.0:
-        return 0.0
+    if E.le(consumed_mass, 0):
+        return 0
     var next: Dictionary = world.state.duplicate(true)
     var physical: Dictionary = world.ledger.physical_amounts(world.state)
     for id in taken:
-        if taken[id] <= 0.0:
+        if E.le(taken[id], 0):
             continue
-        next.amount[id] -= taken[id]
-        var fraction: float = taken[id] / physical[id]
-        world.batches.scale_batches(next, id, 1.0 - fraction)
+        next.amount[id] = E.subtract(next.amount[id], taken[id])
+        var fraction: Variant = E.divide(taken[id], physical[id])
+        world.batches.scale_batches(next, id, E.subtract(1, fraction))
         # Release the consumed owners' share of any resources they held.
         for resource in next.binds.get(id, {}):
-            var released: float = next.binds[id][resource] * fraction
-            next.binds[id][resource] -= released
-            next.amount[resource] = next.amount.get(resource, 0.0) + released
+            var released: Variant = E.multiply(next.binds[id][resource], fraction)
+            next.binds[id][resource] = E.subtract(next.binds[id][resource], released)
+            next.amount[resource] = E.add(next.amount.get(resource, 0), released)
     world.ledger.credit(next, "SMBH", consumed_mass)
     world.batches.append_batch(next, "SMBH", consumed_mass, world.state.time.datetime, world.state.time.datetime)
     world.ledger.round_object_allocations(next)
@@ -122,29 +123,29 @@ func produce_smbh(desired_amount: float) -> float:
     return consumed_mass
 
 
-func produce(item_id: String, desired_amount: float) -> float:
-    if item_id == "SMBH":
+func produce(item_id: String, desired_amount: Variant) -> Variant:
+    if E.eq(item_id, "SMBH"):
         return produce_smbh(desired_amount)
     # Use special production for S and H
-    if item_id == "S" or item_id == "H":
+    if (E.eq(item_id, "S") or E.eq(item_id, "H")):
         return produce_hs(item_id, desired_amount)
-    
+
     var entity: OwniverseEntity = world.catalog.entities[item_id]
-    
-    if desired_amount <= 0:
-        return 0.0
-    
-    var max_producible = floorf(calculate_max_producible(entity, desired_amount))
+
+    if E.le(desired_amount, 0):
+        return 0
+
+    var max_producible = E.floor_value(calculate_max_producible(entity, desired_amount))
     var budget: Dictionary = CivilizationState.stellar_budget(world, world.state, Global.CivilizationRules)
     max_producible = CivilizationState.admit_transition(budget, Global.CivilizationRules, "", item_id, max_producible)
-    
-    if max_producible <= 0:
-        return 0.0
-    
-    var metallicity: float = world.environment.stellar_environment(world.state).metallicity
-    if not try_production(world.state, entity, max_producible):
-        return 0.0
-    
+
+    if E.le(max_producible, 0):
+        return 0
+
+    var metallicity: Variant = world.environment.stellar_environment(world.state).metallicity
+    if (not try_production(world.state, entity, max_producible)):
+        return 0
+
     # Add produced entities
     world.ledger.process_entity(item_id, max_producible)
     world.batches.add_entity_to_batch(item_id, max_producible, world.state.time.datetime)
@@ -154,49 +155,49 @@ func produce(item_id: String, desired_amount: float) -> float:
     return max_producible
 
 
-func produce_hs(entity_id: String, value: float) -> float:
-    if value <= 0:
-        return 0.0
-    
-    var to_produce: float = floorf(value)
-    to_produce = minf(to_produce, floorf(world.state.energy))
-    
-    if to_produce <= 0:
-        return 0.0
-    
-    world.state.energy -= to_produce
+func produce_hs(entity_id: String, value: Variant) -> Variant:
+    if E.le(value, 0):
+        return 0
+
+    var to_produce: Variant = E.floor_value(value)
+    to_produce = E.minimum(to_produce, E.floor_value(world.state.energy))
+
+    if E.le(to_produce, 0):
+        return 0
+
+    world.state.energy = E.subtract(world.state.energy, to_produce)
     world.ledger.process_entity(entity_id, to_produce)
-    
+
     return to_produce
 
 
-func production_step(entity: OwniverseEntity) -> float:
-    return QuantityMath.production_step(entity.cost.values() + entity.bind.values())
+func production_step(entity: OwniverseEntity) -> Variant:
+    return QuantityMath.production_step(E.add(entity.cost.values(), entity.bind.values()))
 
 
-func calculate_max_producible(entity: OwniverseEntity, desired_amount: float = 1.0E150) -> float:
-    if entity.id == "SMBH":
-        return plan_smbh(desired_amount).amount
+func calculate_max_producible(entity: OwniverseEntity, desired_amount: Variant = null) -> Variant:
+    if E.eq(entity.id, "SMBH"):
+        return plan_smbh(smbh_available() if desired_amount == null else desired_amount).amount
     var requirements: Dictionary = {}
     for resource in entity.cost:
-        requirements[resource] = maxf(0.0, entity.cost[resource])
+        requirements[resource] = E.maximum(0, entity.cost[resource])
     for resource in entity.bind:
-        requirements[resource] = requirements.get(resource, 0.0) + maxf(0.0, entity.bind[resource])
+        requirements[resource] = E.add(requirements.get(resource, 0), E.maximum(0, entity.bind[resource]))
     var has_requirements: bool = false
     for quantity in requirements.values():
-        if quantity > 0.0:
+        if E.gt(quantity, 0):
             has_requirements = true
             break
     # No recipe means unavailable for production, not unlimited free objects.
-    if not has_requirements:
-        return 0.0
-    var available: float = maxf(0.0, desired_amount)
+    if (not has_requirements):
+        return 0
+    var available: Variant = INF if desired_amount == null else E.maximum(0, desired_amount)
     for resource in requirements:
-        if requirements[resource] > 0.0:
-            available = minf(available, floorf(world.ledger.available(world.state, resource) / requirements[resource]))
+        if E.gt(requirements[resource], 0):
+            available = E.minimum(available, E.floor_value(E.divide(world.ledger.available(world.state, resource), requirements[resource])))
     var concrete: Dictionary = world.ledger.expand_requirements(world.state, requirements)
     for resource in concrete:
-        if concrete[resource] > 0.0:
-            available = minf(available, floorf(world.ledger.available(world.state, resource) / concrete[resource]))
-    var step: float = production_step(entity)
-    return floorf(available / step) * step if is_finite(step) else 0.0
+        if E.gt(concrete[resource], 0):
+            available = E.minimum(available, E.floor_value(E.divide(world.ledger.available(world.state, resource), concrete[resource])))
+    var step: Variant = production_step(entity)
+    return (E.multiply(E.floor_value(E.divide(available, step)), step) if E.finite(step) else 0)

world/owniverse/math/README.md

@@ -0,0 +1,43 @@
+# Числа симуляции
+
+Целые значения в диапазоне int64 хранятся как `int`. Остальные числа имеют вид
+`polarity × (sum(whole[i] × 10^(9i)) + fraction)`:
+`whole` — динамический массив целых блоков по основанию 10^9,
+`fraction` — float от 0 включительно до 1 исключительно. Числа после создания
+не изменяются. Ограничения E27 в хранении нет; размер массива растёт по необходимости.
+
+Используйте API `E.add/subtract/multiply/divide`, `E.eq/lt/le/gt/ge` и
+`E.floor_value/ceil_value/round_value`. Обычные операторы над ExactValue не работают.
+`E.integer` требует значения в диапазоне int64; `E.approx` явно преобразует
+число в float и для очень больших чисел возвращает бесконечность.
+Сравнение через E сохраняет отличие конечного большого числа от INF.
+
+Целые операции выполняются точно. Умножение и деление используют безопасные
+разряды из `big_integer.gd`; нативная арифметика применяется при отсутствии
+переполнения int64. `E.mul_div(count, numerator, denominator)` сохраняет точное
+целое частное, не превращая заранее отношение в приближённый коэффициент.
+`E.floor_sum` суммирует округлённые линейные квоты без перебора каждого окна.
+
+Дробный остаток приблизительный: при умножении и делении он преобразуется
+в десятичную дробь с 16 значащими цифрами. При сложении двух ненулевых остатков
+перенос около целой границы стабилизируется с допуском 10^-12.
+Умножение большого количества на float усиливает ошибку коэффициента;
+для известных точных отношений используйте mul_div. Целые распределения
+и сохранение числа объектов проверяются строго, без допуска.
+
+Возраст сохраняет точную целую часть. Только дробная часть переводится в
+наносекундные тики, дополнительный остаток времени переносится между кадрами.
+Синхронный диагностический API evolute отклоняет шаги от 1e27 игровых лет:
+это защита от непрактичного интервала, а не предел хранимого возраста.
+Покадровый API ограничивает одну транзакцию обычным шагом 1/60 секунды;
+остальное запрошенное время остаётся в очереди.
+
+Формат сохранения — **5**, версия состояния — **0.3.0**.
+Большие целые и числа с дробью кодируются как
+`{"$exact": [[blocks], "float bytes in hex", sign]}`.
+Байты остатка сохраняются без потери точности JSON. Миграции старых форматов нет.
+
+Проверки: `test_exact_math.gd`, `test_dynamic_math.gd`, `test_quantity_catalog.gd`,
+`test_time.gd` и `test_frame_evolution.gd`. Независимый целочисленный эталон
+покрывает числа до 220 десятичных цифр; отдельные проверки — до E1000,
+границы int64, доли, сериализацию, распределения и продолжение расчёта.

world/owniverse/math/big_integer.gd

@@ -0,0 +1,127 @@
+extends RefCounted
+## Unsigned little-endian base 10^9 arithmetic. Inputs are never mutated.
+const BASE: int = 1000000000
+
+static func trim(a: Array) -> Array:
+    while a.size() > 1 and a.back() == 0: a.pop_back()
+    return a
+
+static func parse(text: String) -> Array:
+    var result: Array = []
+    var end: int = text.length()
+    while end > 0:
+        var start: int = maxi(0, end - 9)
+        result.append(int(text.substr(start, end - start)))
+        end = start
+    return trim(result if not result.is_empty() else [0])
+
+static func decimal(a: Array) -> String:
+    var result: String = str(a.back())
+    for i in range(a.size() - 2, -1, -1): result += "%09d" % a[i]
+    return result
+
+static func compare(a: Array, b: Array) -> int:
+    if a.size() != b.size(): return 1 if a.size() > b.size() else -1
+    for i in range(a.size() - 1, -1, -1):
+        if a[i] != b[i]: return 1 if a[i] > b[i] else -1
+    return 0
+
+static func add(a: Array, b: Array) -> Array:
+    var result: Array = []
+    var carry: int = 0
+    for i in maxi(a.size(), b.size()):
+        var value: int = carry + (a[i] if i < a.size() else 0) + (b[i] if i < b.size() else 0)
+        result.append(value % BASE)
+        carry = value / BASE
+    if carry: result.append(carry)
+    return result
+
+static func subtract(a: Array, b: Array) -> Array:
+    assert(compare(a, b) >= 0, "Unsigned subtraction underflow")
+    var result: Array = []
+    var borrow: int = 0
+    for i in a.size():
+        var value: int = a[i] - borrow - (b[i] if i < b.size() else 0)
+        borrow = 1 if value < 0 else 0
+        result.append(value + BASE if borrow else value)
+    return trim(result)
+
+static func multiply(a: Array, b: Array) -> Array:
+    var result: Array = []
+    result.resize(a.size() + b.size())
+    result.fill(0)
+    for i in a.size():
+        var carry: int = 0
+        for j in b.size():
+            # < BASE^2 + 2*BASE: comfortably inside signed int64.
+            var value: int = a[i] * b[j] + result[i + j] + carry
+            result[i + j] = value % BASE
+            carry = value / BASE
+        result[i + b.size()] = carry
+    return trim(result)
+
+static func divmod(a: Array, b: Array) -> Array:
+    assert(b != [0], "Division by zero")
+    if b == [1]: return [a.duplicate(), [0]]
+    if compare(a, b) < 0: return [[0], a.duplicate()]
+    if b.size() == 1:
+        var quotient: Array = []
+        quotient.resize(a.size())
+        var carry: int = 0
+        for i in range(a.size() - 1, -1, -1):
+            var value: int = carry * BASE + a[i]
+            quotient[i] = value / b[0]
+            carry = value % b[0]
+        return [trim(quotient), [carry]]
+    # Normalize the leading divisor limb so the two-limb quotient estimate
+    # needs at most two downward corrections (Knuth's division estimate).
+    var factor: int = BASE / (b.back() + 1)
+    a = multiply(a, [factor])
+    b = multiply(b, [factor])
+    var quotient: Array = []
+    quotient.resize(a.size())
+    var remainder: Array = [0]
+    for i in range(a.size() - 1, -1, -1):
+        remainder.push_front(a[i])
+        trim(remainder)
+        var high: int = remainder[b.size()] if remainder.size() > b.size() else 0
+        var low: int = remainder[b.size() - 1] if remainder.size() >= b.size() else 0
+        var estimate: int = mini(BASE - 1, (high * BASE + low) / b.back())
+        var product: Array = multiply(b, [estimate])
+        while compare(product, remainder) > 0:
+            estimate -= 1
+            product = subtract(product, b)
+        quotient[i] = estimate
+        remainder = subtract(remainder, product)
+    return [trim(quotient), divmod(remainder, [factor])[0]]
+
+static func gcd(a: Array, b: Array) -> Array:
+    while b != [0]:
+        if b == [1]: return [1]
+        var remainder: Array = divmod(a, b)[1]
+        a = b
+        b = remainder
+    return a
+
+## Sum floor((a*i+b)/m), i=0..n-1, using Euclidean reduction.
+## All arguments are unsigned; no loop over the number of time windows.
+static func floor_sum(n: Array, m: Array, a: Array, b: Array) -> Array:
+    var result: Array = [0]
+    while n != [0]:
+        var qr: Array = divmod(a, m)
+        if qr[0] != [0]:
+            var pairs: Array = divmod(multiply(n, subtract(n, [1])), [2])[0]
+            result = add(result, multiply(pairs, qr[0]))
+        a = qr[1]
+        qr = divmod(b, m)
+        result = add(result, multiply(n, qr[0]))
+        b = qr[1]
+        var upper: Array = add(multiply(a, n), b)
+        if compare(upper, m) < 0: break
+        qr = divmod(upper, m)
+        n = qr[0]
+        b = qr[1]
+        var temporary: Array = m
+        m = a
+        a = temporary
+    return result

world/owniverse/math/big_integer.gd.uid

@@ -0,0 +1 @@
+uid://6wfbh3vq5smd