Prevent AVB signing from using _RESERVED_SIZE

When AVB is enabled with PRODUCT_USE_DYNAMIC_PARTITION_SIZE, AVB
metadata (e.g., hash tree, fec metadata) will consume _RESERVED_SIZE,
resulting in smaller reserved size in file system (e.g., ext4).

Adding additional space for AVB signing and keep the _RESERVED_SIZE only
for file system. This is done by adding a function to binary search an
optimal partition size for a given image size (disk usage + _RESERVED_SIZE).

Bug: 112322265
Test: Build aosp_arm64-userdebug, calculate the running time of
      AVBCalcMinPartitionSize() is about 0.3-0.4 seconds.
Test: python -m unittest test_build_image
Change-Id: I8f0051b57701d6fbba6a9db3756dd194066c74b8

tools/releasetools/test_build_image.py

@@ -15,11 +15,15 @@
 #
 
 import filecmp
+import math
 import os.path
+import random
 import unittest
 
 import common
-from build_image import CheckHeadroom, RunCommand, SetUpInDirAndFsConfig
+from build_image import (
+    AVBCalcMinPartitionSize, BLOCK_SIZE,
+    CheckHeadroom, RunCommand, SetUpInDirAndFsConfig)
 
 
 class BuildImageTest(unittest.TestCase):
@@ -28,6 +32,13 @@ class BuildImageTest(unittest.TestCase):
   EXT4FS_OUTPUT = (
       "Created filesystem with 2777/129024 inodes and 515099/516099 blocks")
 
+  def setUp(self):
+    # To test AVBCalcMinPartitionSize(), by using 200MB to 2GB image size.
+    #   -  51200 = 200MB * 1024 * 1024 / 4096
+    #   - 524288 = 2GB * 1024 * 1024 * 1024 / 4096
+    self._image_sizes = [BLOCK_SIZE * random.randint(51200, 524288) + offset
+                         for offset in range(BLOCK_SIZE)]
+
   def tearDown(self):
     common.Cleanup()
 
@@ -176,3 +187,51 @@ class BuildImageTest(unittest.TestCase):
     self.assertIn('fs-config-system\n', fs_config_data)
     self.assertIn('fs-config-root\n', fs_config_data)
     self.assertEqual('/', prop_dict['mount_point'])
+
+  def test_AVBCalcMinPartitionSize_LinearFooterSize(self):
+    """Tests with footer size which is linear to partition size."""
+    for image_size in self._image_sizes:
+      for ratio in 0.95, 0.56, 0.22:
+        expected_size = common.RoundUpTo4K(int(math.ceil(image_size / ratio)))
+        self.assertEqual(
+            expected_size,
+            AVBCalcMinPartitionSize(image_size, lambda x: int(x * ratio)))
+
+  def test_AVBCalcMinPartitionSize_SlowerGrowthFooterSize(self):
+    """Tests with footer size which grows slower than partition size."""
+
+    def _SizeCalculator(partition_size):
+      """Footer size is the power of 0.95 of partition size."""
+      # Minus footer size to return max image size.
+      return partition_size - int(math.pow(partition_size, 0.95))
+
+    for image_size in self._image_sizes:
+      min_partition_size = AVBCalcMinPartitionSize(image_size, _SizeCalculator)
+      # Checks min_partition_size can accommodate image_size.
+      self.assertGreaterEqual(
+          _SizeCalculator(min_partition_size),
+          image_size)
+      # Checks min_partition_size (round to BLOCK_SIZE) is the minimum.
+      self.assertLess(
+          _SizeCalculator(min_partition_size - BLOCK_SIZE),
+          image_size)
+
+  def test_AVBCalcMinPartitionSize_FasterGrowthFooterSize(self):
+    """Tests with footer size which grows faster than partition size."""
+
+    def _SizeCalculator(partition_size):
+      """Max image size is the power of 0.95 of partition size."""
+      # Max image size grows less than partition size, which means
+      # footer size grows faster than partition size.
+      return int(math.pow(partition_size, 0.95))
+
+    for image_size in self._image_sizes:
+      min_partition_size = AVBCalcMinPartitionSize(image_size, _SizeCalculator)
+      # Checks min_partition_size can accommodate image_size.
+      self.assertGreaterEqual(
+          _SizeCalculator(min_partition_size),
+          image_size)
+      # Checks min_partition_size (round to BLOCK_SIZE) is the minimum.
+      self.assertLess(
+          _SizeCalculator(min_partition_size - BLOCK_SIZE),
+          image_size)