Add function for computing package trend

app/lib/service/download_counts/package_trends.dart

@@ -0,0 +1,87 @@
+// Copyright (c) 2025, the Dart project authors.  Please see the AUTHORS file
+// for details. All rights reserved. Use of this source code is governed by a
+// BSD-style license that can be found in the LICENSE file.
+
+const analysisWindowDays = 30;
+
+/// Calculates the relative daily growth rate of a package's downloads.
+///
+/// Given a list with total daily downloads ([totalDownloads]), where the most
+/// recent day's data is at index 0, this function analyzes the downloads trend
+/// over the last ([analysisWindowDays]) days to determine how fast a package is
+/// growing relative to its own current download volume.
+///
+/// A positive value indicates an upward trend in downloads, while a negative
+/// value indicates a downward trend. The magnitude represents the growth (or
+/// decline) rate normalized by the average daily downloads, allowing for
+/// comparison across packages of different popularity. For example, a slope of
+/// +10 downloads/day is more significant for a package with 100 average daily
+/// downloads (10% relative growth) than for a package with 10000 average daily
+/// downloads (0.1% relative growth).
+double computeRelativeGrowthRate(List<int> totalDownloads) {
+  final List<int> data;
+  if (totalDownloads.length < analysisWindowDays) {
+    data = [
+      ...totalDownloads,
+      ...List.filled(analysisWindowDays - totalDownloads.length, 0)
+    ];
+  } else {
+    data = totalDownloads;
+  }
+
+  final recentDownloads = data.sublist(0, analysisWindowDays);
+
+  final averageRecentDownloads =
+      recentDownloads.reduce((prev, element) => prev + element) /
+          recentDownloads.length;
+
+  // We reverse the recentDownloads list for regression, since the first entry
+  // is the newest point in time. By reversing, we pass the data in
+  // chronological order.
+  final growthRate =
+      calculateLinearRegressionSlope(recentDownloads.reversed.toList());
+
+  // Normalize slope by average downloads to represent relative growth.
+  // This measures how much the download count is growing relative to its
+  // current volume.
+  return growthRate / averageRecentDownloads;
+}
+
+/// Computes the slope of the best-fit line for a given list of data points
+/// [yValues] using the method of least squares (linear regression).
+///
+/// The function assumes that the [yValues] are equally spaced in time and are
+/// provided in chronological order
+///
+/// The slope `b` is calculated using the formula: `b = (N * sum(xy) - sum(x) *
+/// sum(y)) / (N * sum(x^2) - (sum(x))^2)` where `N` is the number of data
+/// points.
+///
+/// Returns `0.0` if the slope cannot be determined reliably (e.g., if there are
+/// fewer than 2 data points, or if the denominator in the slope formula is
+/// effectively zero).
+double calculateLinearRegressionSlope(List<num> yValues) {
+  double sumX = 0, sumY = 0, sumXY = 0, sumXX = 0;
+  final n = yValues.length;
+
+  // Slope is undefined or 0 for fewer than 2 points.
+  if (n < 2) {
+    return 0.0;
+  }
+
+  for (int x = 0; x < n; x++) {
+    final y = yValues[x];
+    sumX += x;
+    sumY += y;
+    sumXY += x * y;
+    sumXX += x * x;
+  }
+
+  final double denominator = (n * sumXX - sumX * sumX);
+
+  // If the denominator is very close to zero, the slope is unstable/undefined.
+  if (denominator.abs() < 1e-9) {
+    return 0.0;
+  }
+  return (n * sumXY - sumX * sumY) / denominator;
+}

app/test/service/download_counts/package_trends_test.dart

@@ -0,0 +1,96 @@
+// Copyright (c) 2025, the Dart project authors.  Please see the AUTHORS file
+// for details. All rights reserved. Use of this source code is governed by a
+// BSD-style license that can be found in the LICENSE file.
+
+import 'package:pub_dev/service/download_counts/package_trends.dart';
+import 'package:test/test.dart';
+
+void main() {
+  group('calculateLinearRegressionSlope', () {
+    test('correctly calculates slope for chronological data', () {
+      expect(calculateLinearRegressionSlope([10.0, 20.0, 30.0]), 10.0);
+      expect(calculateLinearRegressionSlope([30.0, 20.0, 10.0]), -10.0);
+      expect(calculateLinearRegressionSlope([10.0, 10.0, 10.0]), 0);
+    });
+
+    test('return 0.0 if denominator is very small', () {
+      expect(calculateLinearRegressionSlope([]), 0.0);
+      expect(calculateLinearRegressionSlope([10.0]), 0.0);
+    });
+  });
+
+  group('computeRelativeGrowthRate', () {
+    test('returns 0.0 for stable downloads meeting threshold', () {
+      final downloads = List<int>.generate(analysisWindowDays, (i) => 2000);
+      expect(computeRelativeGrowthRate(downloads), 0.0);
+    });
+
+    test('calculates positive relative growth rate for positive trend', () {
+      // Input list (newest first):  [1645, 1635, ..., 1355] (30 values)
+      // Average = 1500 for the first 30 values. Slope: 10.
+      final downloads =
+          List<int>.generate(analysisWindowDays * 2, (i) => 1645 - (i * 10));
+      final expectedRate = 10.0 / 1500.0;
+      expect(computeRelativeGrowthRate(downloads), expectedRate);
+    });
+
+    test('calculates negative relative growth rate for negative trend', () {
+      // Input list (newest first):  [1355, 1365, ..., 1645]
+      // Average = 1500. Slope: -10.
+      final downloads =
+          List<int>.generate(analysisWindowDays, (i) => 1355 + (i * 10));
+      final expectedRate = -10.0 / 1500.0;
+      expect(computeRelativeGrowthRate(downloads), expectedRate);
+    });
+
+    test(
+        'calculates positive relative growth for data barely meeting threshold',
+        () {
+      // Input list (newest first): [1016, 1015, ..., 987]
+      // Average: 1001.5. Slope: 1.
+      final downloads =
+          List<int>.generate(analysisWindowDays, (i) => 1016 - i * 1);
+      final expectedRate = 1.0 / 1001.5;
+      expect(computeRelativeGrowthRate(downloads), closeTo(expectedRate, 1e-9));
+    });
+
+    test('should handle fluctuating data with a slight positive overall trend',
+        () {
+      // Newest first. Average 1135.
+      final downloads = <int>[
+        1300,
+        1250,
+        1280,
+        1230,
+        1260,
+        1210,
+        1240,
+        1190,
+        1220,
+        1170,
+        1200,
+        1150,
+        1180,
+        1130,
+        1160,
+        1110,
+        1140,
+        1090,
+        1120,
+        1070,
+        1100,
+        1050,
+        1080,
+        1030,
+        1060,
+        1010,
+        1040,
+        990,
+        1020,
+        970
+      ];
+      final expectedRate = 683250.0 / 67425.0 / 1135.0;
+      expect(computeRelativeGrowthRate(downloads), expectedRate);
+    });
+  });
+}