Set up clang format & tidy and format all the files

.clang-format

@@ -41,14 +41,13 @@ BreakBeforeBinaryOperators: None
 BreakBeforeTernaryOperators: true
 BreakConstructorInitializers: BeforeColon
 BreakInheritanceList: BeforeColon
-ColumnLimit: 80
+ColumnLimit: 120
 CompactNamespaces: false
 ContinuationIndentWidth: 4
 Cpp11BracedListStyle: true
 DerivePointerAlignment: false  
 EmptyLineBeforeAccessModifier: LogicalBlock
 FixNamespaceComments: true
-IncludeBlocks: Preserve
 IndentCaseLabels: true
 IndentPPDirectives: None
 IndentWidth: 4
@@ -80,3 +79,17 @@ SpacesInSquareBrackets: false
 Standard: c++17
 TabWidth: 4
 UseTab: Never
+QualifierAlignment: Left
+SortIncludes: true
+IncludeBlocks: Regroup
+IncludeCategories:
+  # Classes own header is always priority 0
+  # System C/C++ headers in <> with extension.
+  - Regex:           '<([A-Za-z0-9.\Q/-_\E])+.h.*>'
+    Priority:        1
+  # System Headers in <> without extension.
+  - Regex:           '<([A-Za-z0-9.\Q/-_\E])+>'
+    Priority:        2
+  # c Headers in "" with extension.
+  - Regex:           '"([A-Za-z0-9.\Q/-_\E])+"'
+    Priority:        3