feat: ui rework and gear generator

lib/model/gear_configurator.dart

@@ -0,0 +1,91 @@
+import 'package:abawo_bt_app/model/gear_ratio_codec.dart';
+
+enum GearRetentionMode { keepHighest, keepAll }
+
+class GearConfiguratorCalculation {
+  const GearConfiguratorCalculation({
+    required this.ratios,
+    required this.discardedBelowRange,
+    required this.discardedAboveRange,
+    required this.duplicateCount,
+    required this.truncatedCount,
+  });
+
+  final List<double> ratios;
+  final int discardedBelowRange;
+  final int discardedAboveRange;
+  final int duplicateCount;
+  final int truncatedCount;
+}
+
+GearConfiguratorCalculation calculateGearRatios({
+  required List<int> chainrings,
+  required List<int> sprockets,
+  required GearRetentionMode mode,
+  int maxRatios = 32,
+}) {
+  final sortedChainrings = List<int>.from(chainrings)..sort();
+  final sortedSprockets = List<int>.from(sprockets)..sort((a, b) => b - a);
+
+  var discardedBelowRange = 0;
+  var discardedAboveRange = 0;
+  var duplicateCount = 0;
+  final encoded = <int>{};
+  final ratios = <double>[];
+
+  void addRatio(double ratio) {
+    if (ratio < gearRatioMin) {
+      discardedBelowRange++;
+      return;
+    }
+    if (ratio > gearRatioMax) {
+      discardedAboveRange++;
+      return;
+    }
+
+    final raw = encodeGearRatioByte(ratio);
+    if (!encoded.add(raw)) {
+      duplicateCount++;
+      return;
+    }
+    ratios.add(decodeGearRatioByte(raw));
+  }
+
+  switch (mode) {
+    case GearRetentionMode.keepAll:
+      for (final chainring in sortedChainrings) {
+        for (final sprocket in sortedSprockets) {
+          addRatio(chainring / sprocket);
+        }
+      }
+      break;
+    case GearRetentionMode.keepHighest:
+      var threshold = double.negativeInfinity;
+      for (final chainring in sortedChainrings) {
+        final beforeLength = ratios.length;
+        for (final sprocket in sortedSprockets) {
+          final ratio = chainring / sprocket;
+          if (ratio >= threshold) {
+            addRatio(ratio);
+          }
+        }
+        if (ratios.length > beforeLength) {
+          threshold = ratios.reduce((a, b) => a > b ? a : b);
+        }
+      }
+      break;
+  }
+
+  ratios.sort();
+  final truncatedCount =
+      ratios.length > maxRatios ? ratios.length - maxRatios : 0;
+  final limited = ratios.take(maxRatios).toList(growable: false);
+
+  return GearConfiguratorCalculation(
+    ratios: limited,
+    discardedBelowRange: discardedBelowRange,
+    discardedAboveRange: discardedAboveRange,
+    duplicateCount: duplicateCount,
+    truncatedCount: truncatedCount,
+  );
+}