calculus.hpp

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//==================================================================================================
/// \file
/// This header-file is part of module \alib_expressions of the \aliblong.
///
/// Copyright 2013-2026 A-Worx GmbH, Germany.
/// Published under #"mainpage_license".
//==================================================================================================
ALIB_EXPORT namespace alib {  namespace expressions {
 
/// This inner namespace of module \alib_expressions_nl contains the implementations
/// of built-in compiler plug-ins.
///
/// In addition, helper-class #"%Calculus" is defined here, which is the foundation for most of
/// the built-in functionality.
///
/// It is strongly recommended to use this helper-class for the creation of custom compiler plug-ins
/// instead of deriving such from class #"CompilerPlugin" directly.
///
/// \note Sibling \alib module \alib_filetree, provides a compiler plug-in dedicated to file and
///       directory trees.
namespace plugins {
 
 
//==================================================================================================
/// ## 1. Introduction ##
/// This struct specializes #"%CompilerPlugin" and provides generic approaches and the
/// implementation of variants of the method
/// #"CompilerPlugin::TryCompilation(CIUnaryOp&);CompilerPlugin::TryCompilation".
/// Consequently, this is the base type of most built-in compiler plug-ins, and is strongly
/// recommended to consider this struct as the preferred base when implementing custom plug-ins.
///
/// The class implements virtual, overloaded methods
/// - #"CompilerPlugin::TryCompilation(CIFunction&)",
/// - #"CompilerPlugin::TryCompilation(CIUnaryOp&)",
/// - #"CompilerPlugin::TryCompilation(CIBinaryOp&)", and
/// - #"CompilerPlugin::TryCompilation(CIAutoCast&)".
///
/// For each <em>AST</em> node type to compile, this class holds a vector or a hash map to store
/// all information needed for compilation.
///
/// The simple schema of using this class is:
/// 1. Derive a custom type from this class.
/// 2. Create constant value objects and native C++ callback functions.
/// 3. Create constant (\c constexpr) tables with all compilation information.
/// 4. In the constructor of the derived class, feed the tables into to this struct, using the
///    corresponding helper methods.
///
/// \note
///   Sample code and detailed explanations are given with user manual section
///   #"alib_expressions_cpcc_calculus"
///   and tutorial section
///   #"alib_expressions_tut_ffext"
///
/// <p>
/// \note
///   The name "Calculus" seems a little overstated, we admit.
///
/// ## 2. Choose Anonymous Namespaces ##
///
/// A good design pattern is to put the callback functions, constant values and compilation information
/// tables into an anonymous namespace at the start of the compilation unit (.cc or .cpp file) of
/// your custom plug-in. This way, the linker is not bothered with the function and object names,
/// which solely are referenced by their address and never need to get linked to other units.
///
/// Just after this anonymous namespace, the implementation of the constructor of the custom
/// plug-in should be placed. As explained above, its duty is to fill the vector/hash map using
/// the right combination of operator or function argument types, as well as providing a proper
/// #"alib_expressions_prereq_sb;sample box" that corresponds to the type of the
/// output parameter of the native function.
///
/// When implementing a custom plug-in, it may be helpful to have a look at the source code of
/// the built-in plug-ins provided with module \alib_expressions.
/// You will see that these implementations are quite straight forward and use some 'handy' local
/// preprocessor macros that may be copied and used for custom implementations.
///
/// ## 3. Implementing Identifiers and Functions ##
/// While parent class #"%CompilerPlugin" does not make any direct distinction between functions
/// that are always returning a constant value and those that don't, this class does.
/// Arguably such functions are always parameterless, hence identifiers. Samples for such constants
/// are \b "PI" or \b "True".<br>
/// Such constant identifiers are supported by populating the table #"ConstantIdentifiers" which is
/// a \c std::vector of elements of type #"%ConstantIdentifierEntry".
/// For details on each "table column", refer to the documentation of the fields of
/// #"Calculus;ConstantIdentifierEntry".
///
/// Non-constant identifiers and functions are supported by populating the table
/// #".Functions", which is a \c std::vector of elements of type #"%FunctionEntry".
/// For details on each "table column", refer to the documentation of the fields of
/// #"Calculus;FunctionEntry".
///
/// Some notes:
/// - It can be specified if function names are case-sensitive and whether they might be abbreviated.
/// - The list of arguments (their types) accepted by a function is to be provided as a
///   \c std::vector of #"alib_expressions_prereq_sb;sample boxes". It is
///   recommended to define such vectors once per unique function "signature" in the anonymous
///   namespace section of the compilation unit and fill its contents once in the constructor of the
///   custom plug-in. Such vectors can then be reused for each function that shares the same
///   signature.
/// - Variadic functions are supported by adding a final \e nulled #"%Box" to the argument list.
///   All sample argument types before this box are mandatory, but an arbitrary number of arguments
///   of likewise arbitrary types may be followed. It is also allowed to add just that one \e nulled
///   #"%Box" to the signature vector, which leads to functions that accept just any number of any
///   type of argument, including zero arguments.
/// - With debug-builds, besides the callback function pointer, the C++ name of the callback
///   function is to be provided. For this, macro #"CALCULUS_CALLBACK" is defined.
///   The macro creates a stringified version of the given function pointer, separated by a comma.
/// - Flag #"FunctionEntry::IsCTInvokable"
///   is a boolean value
///   that denotes whether a function can be evaluated at compile-time in the case that all of the
///   parameters given in the expression are constant.
///   If so, this struct will do the invocation at compile-time and return the constant result value
///   instead of the function call.<br>
///   Most built-in functions are compile-time invokable. For example, most mathematical functions
///   like \c log(Float) or \c sin(Float) can be evaluated at compile-time (again, only in the case
///   that the given parameters are constant). The reason is that
///   these functions are independent of custom scope data.
///   In contrast to this, custom functions, especially even parameterless identifiers usually are
///   dependent on scope information and thus often cannot be evaluated at compile-time.
///
/// ## 4. Implementing Operators ##
///
/// ### 4.1 Unary And Binary Operators ###
/// Apart from some specialities for binary operators documented in the next section, this class
/// treats unary and binary the same.
/// Wherever a second operator argument's type is requested, in the case of unary operators, static
/// type specifier #"Types::Void;*" is to be given.
///
/// The compilation of unary and binary operators is supported by populating the hash map
/// #"Operators".
/// For feeding the map with entries, the following convenience types and methods are provided:
/// - #"AddOperator"<br>
///   This function adds compilation information for a single operator to the field #"Operators".
///
/// - #"OperatorTableEntry"<br>
///   This is a type definition that allows defining tables with compilation information on
///   operators. It is recommended to create such tables as \c constexpr data in an anonymous
///   namespace of the compilation unit.
///
/// - #".AddOperators"<br>
///   This is a pair of overloaded functions. One of them is templated and just used to deduce
///   the length of the given table of static data. This table is then fed as a pointer, together
///   with the table's size to the second method, which in turn feeds the table entries into
///   field #".Operators".
///
/// In other words: Method #".AddOperator" defines a single operator, while #".AddOperators" defines
/// "bulk" data on operators which is defined in a static table.
/// For details of the functions and types, consult the corresponding documentation.
///
/// As documented in user manual section
/// #"alib_expressions_operators_aliases",
/// module \alib_expressions_nl supports the use of alias operators.
/// This is reflected by this class with:
///
/// - #".OperatorAliases"<br>
///   A hash map that collects information about unary and binary operator aliases.
///
/// - #".AddOperatorAlias"<br>
///   This function adds information about an operator alias to field #".OperatorAliases".
///
/// - #".OperatorAliasTableEntry"
///   A type definition that allows defining tables with information about operator aliases.
///   It is recommended to create such tables as \c constexpr data in an anonymous
///   namespace of the compilation unit.
///
/// - AddOperatorAliases<br>
///   This is a pair of overloaded functions. One of them is templated and just used to deduce
///   the length of the given table of static data. This table is then fed as a pointer, together
///   with the table size to the second method, which in turn feeds the table entries into
///   field #".OperatorAliases".
///
///
/// ### 4.2 Specifics For Binary Operators ###
///
/// #### Aliasing '==' With '=': ####
/// With the use of this class it is \e not necessary to define alias <c>'='</c> for binary
/// operator <c>'=='</c>, because this alias replacement is internally always made for any
/// combination of argument types, when compilation flag
/// #"Compilation::AliasEqualsOperatorWithAssignOperator;*" is set in field
/// #"Compiler::CfgCompilation;*".
///
/// #### Aliasing Bitwise Boolean Operators: ####
/// In contrast to the above, compilation flag #"Compilation::AllowBitwiseBooleanOperators;*"
/// affects only built-in type \e boolean - just as the flag's name suggests.
/// The flag is therefore tested only in derived plug-in #"plugins::Arithmetics;*".
/// In other words: to allow, for example, operator <c>'&'</c> to be used as an alias for operator
/// <c>'&&'</c> defined on custom types, this has to be explicitly added as a set alias definitions
/// for each combination of types in question.
///
/// #### Support For Compile-Time Optimization: ####
/// For binary operators, this class provides a mechanism to provide information on possible
/// compile-time optimizations.
/// Samples of possible binary operator optimizations are given in documentation of struct
/// #"CompilerPlugin::CIBinaryOp;*".
///
/// The following fields and methods are provided:
///
/// - #".BinaryOperatorOptimizations"<br>
///   A hash-map that collects information about possible optimizations of binary operators
///   when either of the operands are a specific constant value.
///
/// - #".BinaryOpOptimizationsTableEntry"<br>
///   A type definition that allows feeding tables (arrays of this type) with information about
///   binary operator optimizations.
///   It is recommended to create such tables as \c constexpr data in an anonymous
///   namespace of the compilation unit.
///
/// - #".AddBinaryOpOptimizations"<br>
///   A pair of overloaded functions. One of them is templated and just used to deduce
///   the length of the given table of static data. This table is then fed as a pointer, together
///   with the table size to the second method, which in turn feeds the table entries into
///   hash map #".BinaryOperatorOptimizations".
///
/// # Reference Documentation #
//==================================================================================================
struct Calculus   : public CompilerPlugin {
    /// Boolean to denote if a callback function allows compile-time invocation.
    /// If \c true, on constant function input (either from expression string literals or sub-expressions
    /// that have been optimized to constant input) the program can be optimized by invoking the
    /// #"CallbackDecl" already at compile-time.
    ///
    /// This flag is set for most built-in functions, e.g., arithmetic calculations, but usually
    /// cannot be set custom callbacks, as those usually rely on custom scope objects which are
    /// available only at evaluation-time.
    ///
    /// \note
    ///   This type is used with helper-class #"plugins::Calculus;*" but exposed
    ///   as a namespace type for convenience, together with constants #".CTI" and
    ///   #".ETI"
    ///
    using CTInvokable= bool;
 
 
    /// Used for values of #".CTInvokable" flags.<br>
    /// The use of this constant makes code more readable.
    static constexpr CTInvokable  CTI  = true;
 
    /// Used for values of #".CTInvokable" flags to denote that a callback function
    /// is only invokable at evaluation-time.<br>
    /// The use of this constant makes code more readable.
    static constexpr CTInvokable  ETI  = false;
 
    /// This class uses monotonic allocation, which is well supported by the common way how this
    /// type is used.
    MonoAllocator          allocator;
 
    /// Constructor.
    /// @param name      Assigned to the field #"CompilerPlugin::Name;*".
    /// @param compiler  The compiler we will get attached to
    /// @param pPriority The priority of this plugin.
    Calculus( const NString& name, Compiler& compiler, CompilePriorities pPriority )
    : CompilerPlugin( name, compiler, pPriority )
    , allocator                  (ALIB_DBG("Calculus",) 4)
    , Operators                  (allocator)
    , OperatorAliases            (allocator)
    , BinaryOperatorOptimizations(allocator)
    { ALIB_DBG( allocator.DbgName= NCString(allocator, name).Buffer(); ) }
 
    /// Virtual destructor.
    virtual        ~Calculus()                                                           override {}
 
 
  //################################################################################################
  // Constant Identifiers, Identifiers and Functions
  //################################################################################################
 
    /// An entry of field #"Calculus::ConstantIdentifiers".
    /// Describes how the identifier is recognized and the constant value to return for it.
    struct ConstantIdentifierEntry {
        /// The name, minimum length and letter case sensitivity of the function to recognize.
        Token                       Descriptor;
 
        /// The constant result.
        Box                         Result;
    };
 
    /// List of identifiers that return constant values to be compiled by this plug-in.
    std::vector<ConstantIdentifierEntry>   ConstantIdentifiers;
 
    /// An entry of field #"Calculus::Functions". Describes how the function is recognized and
    /// the callback function and return type for it.
    struct FunctionEntry {
        /// The name, minimum length and letter case sensitivity of the function to recognize.
        Token                       Descriptor;
 
        /// A pointer to list of pointers to sample boxes that describe the function signature.
        /// If \c nullptr, then the function does not accept parameters (aka is an identifier).
        ///
        /// To denote variadic parameters (similar to C/C++ ellipsis operator \c "..." ), either
        /// \c nullptr or a #"alib_boxing_more_void_void;void box" may be given as the last
        /// array element. All prior provided boxes represent mandatory arguments, while the
        /// function accepts an arbitrary number of arguments of arbitrary types in addition.
        ///
        /// The length of this list is given with field #".SignatureLength".
        ///
        /// \see Macro #"CALCULUS_SIGNATURE" which is recommended to be used to pass both
        ///      fields (this and #".SignatureLength"). The macro accepts a C++ array of #"%Box"* and
        ///      deducts the array's length from the declaration type of the given array.
        Box**                       Signature;
 
        /// See #".Signature" for more information.
        size_t                      SignatureLength;
 
        /// Callback function to add to the program. If \c nullptr, field #".ResultType" is
        /// used as both: a constant value added to the program and the result type!
        CallbackDecl                Callback;
 
 
        #if ALIB_DEBUG
        /// The C++ name of the callback function (only available with debug-builds of the
        /// library. Use preprocessor macro #"CALCULUS_CALLBACK" to provide this field
        /// together with field #".Callback". The macro selects to prune the name string
        /// in release compilations.
        const char*             DbgCallbackName;
        #endif
 
        /// The result type given as a pointer to a #"alib_expressions_prereq_sb;sample box".
        ///
        /// \note
        ///   If #".Callback" is \c nullptr, this box changes its meaning from being just a sample that
        ///   provides the return type of the callback function, to being the 'real' constant
        ///   result value that the function represents. However, it is preferable, to
        ///   implement such constant functions using field
        ///   #"Calculus::ConstantIdentifiers"
        Box*                        ResultType;
 
        /// Denotes, if the callback function is allowed to be invoked on the
        /// #"expressions::Scope" object used at compile-time.
        /// This scope object is of the same (eventually custom) type as the one for evaluation,
        /// however the evaluation-specific data is not set.
        /// If allowed, such invocation is performed, if all function arguments are constant and
        /// instead of the function, the result is returned.
        CTInvokable                 IsCTInvokable;
    };
 
    /// List of functions to be compiled by this plug-in.
    std::vector<FunctionEntry>      Functions;
 
    /// Searches in vectors #".Functions" and #".ConstantIdentifiers" for an entry matching \p{name}
    /// and, if found, adds either a constant value or a callback function to \p{ciFunction}.
    ///
    /// This plug-in corrects abbreviated and letter case differences in functions within
    /// in/out parameter #"CIFunction::Name".
    ///
    /// @param[in,out]  ciFunction  The compilation result.
    /// @return \c true if an entry was found in #".Functions" and a corresponding command
    ///         was added to \p{ciFunction}. \c false otherwise.
    ALIB_DLL
    virtual bool    TryCompilation( CIFunction& ciFunction )                               override;
 
  //################################################################################################
  // Operators
  //################################################################################################
  protected:
 
    /// Key type for operator hash maps #"Calculus::Operators" and #"Calculus::OperatorAliases".
    struct OperatorKey {
        const String           op;          ///< A string defining the operator.
        const std::type_info&  lhs;         ///< Left-hand side type.
        const std::type_info&  rhs;         ///< Right-hand side type. For unary operators
                                            ///< equals to <c>typeid(void)</c>.
 
        /// Hash functor for operator hash map.
        struct Hash {
            /// Calculates a hash code for objects of type #"%OperatorKey".
            /// @param src The node to hash.
            /// @return The hash code.
            std::size_t operator()(const OperatorKey& src)                                   const {
                return      src.op.Hashcode()
                         +  4026031ul * src.lhs.hash_code()
                         +  8175383ul * src.rhs.hash_code();
            }
 
        };
 
        /// Equality functor for operator hash map.
        struct EqualTo {
            /// Compares two objects of type #"%OperatorKey".
            /// @param left  The left-hand side object.
            /// @param right The left-hand side object.
            /// @return The result of the comparison.
            bool        operator()(const OperatorKey& left, const OperatorKey& right )       const {
                return     left.op       == right.op
                        && left.lhs      == right.lhs
                        && left.rhs      == right.rhs;
            }
        };
    };
 
 
  public:
 
    /// Hash map assigning combinations of (unary and binary) operators and its argument types to a
    /// tuple providing information about a callback function.
    ///
    /// The tuple stored, contains the function pointer and the functions' return type.
    /// A third member of type #".CTInvokable" indicates whether the callback function is allowed to be
    /// invoked on the #"expressions::Scope" object used at compile-time.
    /// This scope object is of the same (eventually custom) type as the one for evaluation, however
    /// the evaluation-specific data is not set. In other words, the third tuple member denotes
    /// if during program compilation the function might be invoked when the operator's argument(s)
    /// are constant.
    ///
    /// A fourth tuple member of type #"^String" is available only with debug-builds
    /// and receives the name of the callback function.
    ///
    /// \note
    ///   This map, similar to map #".OperatorAliases" is best to be filled using corresponding
    ///   \e add-methods #AddOperator and #AddOperators.<br>
    ///   Usually this is done once in the constructor of derived classes.
    HashMap<MonoAllocator,
            OperatorKey,
            std::tuple<CallbackDecl, Box, CTInvokable  ALIB_DBG( , const char* ) >,
            OperatorKey::Hash,
            OperatorKey::EqualTo> Operators;
 
    /// Hash map assigning combinations of alias versions of operators and their argument types to
    /// the original operator.
    ///
    /// \note
    ///   This map, similar to map #Operators is best to be filled using corresponding
    ///   \e add-methods #AddOperatorAlias and #AddOperatorAliases.<br>
    ///   Usually this is done once in the constructor of derived classes.
    HashMap<MonoAllocator,
            OperatorKey,
            String,
            OperatorKey::Hash,
            OperatorKey::EqualTo> OperatorAliases;
 
 
    /// Entry of input tables (arrays) used with methods #AddOperators to perform bulk-loading of
    /// compile definition data into map #Operators.<br>
    /// The tuple elements are:
    /// - The operator to compile.
    /// - The type of the first argument of the operator.
    /// - The type of the right-hand side argument of the operator.
    ///   For unary operators, value #"Types::Void;*" is to be provided.
    /// - The callback function. Set to \c nullptr if operator evaluates constant.
    /// - The C++ name of the callback function. (This tuple element is only available in debug
    ///   compilations of the library.)
    /// - The result type sample box, respectively, if \b callback is \c nullptr, the constant
    ///   result value.
    /// - Flag to denote if the callback function allows compile-time invocation and thus on constant
    ///   input the program can be optimized. This is true e.g., for arithmetic functions, but usually
    ///   not for custom operators that rely on scope objects available only at evaluation time.
    using OperatorTableEntry=      const std::tuple< String, Type, Type,
                                                     CallbackDecl,
                                                     ALIB_DBG(const char* ,)
                                                     Type, CTInvokable>;
 
   /// Entry of input tables (arrays) used with method #AddOperatorAliases to perform bulk-loading
   /// of operator alias definition data into map #OperatorAliases.<br>
   /// The tuple elements are:
   /// - The alias operator.
   /// - The type of first argument of the operator.
   /// - The type of the right-hand side argument of the operator.
   ///   For unary operators, value #"Types::Void;*" is to be provided.
   /// - The operator that gets aliased.
    using OperatorAliasTableEntry= const std::tuple<String, Type, Type, String>;
 
 
 
    #if DOXYGEN
    //==============================================================================================
    /// Adds an entry to the operator definition map #Operators.
    ///
    /// \see
    ///    If multiple operators are to be defined, consider the use of #AddOperators, which is a
    ///    variant of this method that allows effective bulk loading.
    ///
    /// @param op              The operator.
    /// @param lhsType         The type of the first argument that the operator is defined for.
    /// @param rhsType         The type of the right-hand side argument that the operator is defined
    ///                        for.
    ///                        For unary operators, value #"Types::Void;*" is to be
    ///                        provided.
    /// @param callback        The callback function to execute.
    /// @param dbgCallbackName The name of the C++ name of the callback function.
    ///                        \note This parameter is available (and to be passed) only in debug
    ///                        version of the library.
    /// @param cti             See #CTInvokable for the meaning of this flag.
    /// @param resultType      The result type of the callback function.
    //==============================================================================================
    void AddOperator     ( const String& op, Type lhsType, Type rhsType, CallbackDecl callback,
                       #if ALIB_DEBUG
                           const char*   dbgCallbackName,
                       #endif
                           Type resultType,
                           CTInvokable   cti     );
    #else // clang would complain about the doxing of parameter dbgCallbackName
    ALIB_DLL
    void AddOperator     ( const String& op, Type lhsType, Type rhsType, CallbackDecl callback,
                       #if ALIB_DEBUG
                           const char*   dbgCallbackName,
                       #endif
                           Type resultType,
                           CTInvokable   cti     );
    #endif
 
 
    /// Templated helper method. Deduces the array size of the given table and passes it
    /// to #"AddOperators(OperatorTableEntry*" table, size_t length).
    ///
    /// @tparam TCapacity Implicitly deferred size of the array provided.
    /// @param  table     The table containing operator compilation information.
    template<size_t TCapacity>
    void AddOperators    ( OperatorTableEntry (&table) [TCapacity]  )
    { AddOperators( &table[0], TCapacity ); }
 
    /// Loads all entries of the given table into hash map #Operators.
    ///
    /// Note, that usually, the given table is a constexpr array located in an anonymous namespace
    /// of a compilation unit.<br>
    /// It can be passed as a reference to templated helper method, which defers the length of the
    /// table implicitly.
    ///
    /// @param  table     The table containing operator compilation information.
    /// @param  length    The table containing operator compilation information.
    ALIB_DLL
    void AddOperators    ( OperatorTableEntry* table, size_t length );
 
    /// Adds an alias operator to hash table #OperatorAliases.
    ///
    /// \see
    ///    If multiple alias operators are to be defined, consider the use of #AddOperatorAliases,
    ///    which is a variant of this method that allows effective bulk loading.
    ///
    /// @param alias    The alias for operator \p{op}.
    /// @param lhsType  The left-hand side argument type that the operator is defined for.
    /// @param rhsType  The right-hand side argument type that the operator is defined for.
    /// @param op       The operator aliased by \p{alias}.
    void AddOperatorAlias  ( const String& alias, Type lhsType, Type rhsType, const String& op );
 
    /// Templated helper method. Deduces the array size of the given table and passes it
    /// to #"AddOperatorAliases(OperatorAliasTableEntry*" table, size_t length).
    ///
    /// @tparam TCapacity Implicitly deferred size of the array provided.
    /// @param  table     The table containing operator compilation information.
    template<size_t TCapacity>
    void AddOperatorAliases( OperatorAliasTableEntry (&table) [TCapacity]  )
    { AddOperatorAliases( &table[0], TCapacity ); }
 
    /// Loads all entries of the given table into hash map #OperatorAliases.
    ///
    /// Note, that usually, the given table is a constexpr array located in an anonymous namespace
    /// of a compilation unit.<br>
    /// It can be passed as a reference to templated helper method, which defers the length of the
    /// table implicitly.
    ///
    /// @param  table     The table containing operator compilation information.
    /// @param  length    The table containing operator compilation information.
    void AddOperatorAliases( OperatorAliasTableEntry* table, size_t length );
 
 
  //################################################################################################
  // Binary operator optimizations
  //################################################################################################
  protected:
 
    /// Key type for operator hash maps #Operators and OperatorAliases.
    struct BinOpOptKey {
        const String           op;        ///< The operator to optimize.
        lang::Side             constSide; ///< Denotes a left- or right-hand side optimization.
        const Box              constVal;  ///< The type and value of the constant argument.
        const std::type_info&  other;     ///< The type of the non-constant argument.
 
        /// Hash functor for operator hash map.
        struct Hash {
            /// Calculates a hash code for objects of type #"%OperatorKey".
            /// @param src The node to hash.
            /// @return The hash code.
            std::size_t operator()(const BinOpOptKey& src)                                   const {
                return  (   std::hash<String>()(src.op)
                          +  6949ul * std::hash<Box>()(src.constVal)
                          + 14033ul * src.other.hash_code()
                        ) ^ ( src.constSide == lang::Side::Left ? size_t( 0)
                                                                : size_t(-1) );
            }
        };
 
        /// Equality functor for operator hash map.
        struct EqualTo {
            /// Compares two objects of type #"%OperatorKey".
            /// @param lhs The left-hand side object.
            /// @param rhs The left-hand side object.
            /// @return The result of the comparison.
            bool        operator()(const BinOpOptKey& lhs, const BinOpOptKey& rhs )          const {
                return     lhs.op       == rhs.op
                        && lhs.constSide== rhs.constSide
                        && lhs.constVal == rhs.constVal
                        && lhs.other    == rhs.other;
            }
        };
    };
 
  public:
    /// Hash map storing optimization information for binary operators where either argument is
    /// constant.<br>
    /// This map may be filled with #AddBinaryOpOptimizations, which is usually done in the.
    /// constructor of derived classes.
    ///
    /// The stored element of type #"%Box" may contain either, a constant result value that replaces
    /// the binary operator (as in <c> x || true</c>) or be a \e nulled box, which indicates that
    /// the result equals the non-constant argument (as in <c>x && true</c>).
    HashMap <MonoAllocator,
             BinOpOptKey, Box,
             BinOpOptKey::Hash,
             BinOpOptKey::EqualTo>                              BinaryOperatorOptimizations;
 
    /// Entry of arrays used with methods #AddBinaryOpOptimizations to perform bulk-loading of
    /// optimization data to hash map #BinaryOperatorOptimizations.<br>
    /// The tuple element's meanings are:
    /// - The operator to optimize.
    /// - Denotes if an optimization applies if the left-hand side or right-hand side argument
    ///   is constant.
    /// - The type and value of the constant argument.
    /// - The type of the non-constant argument.
    /// - Either, a constant result value that replaces the binary operator
    ///   (as in <c> x || true</c>) or a \e nulled box, which indicates that the result equals the
    ///   non-constant argument (as in <c>x && true</c>).
    using BinaryOpOptimizationsTableEntry= const std::tuple<String, lang::Side, Type, const Box&, const Box&>;
 
 
    /// Templated helper method. Deduces the array size of the given table and passes it
    /// to #"AddBinaryOpOptimizations(BinaryOpOptimizationsTableEntry*", size_t).
    ///
    /// @tparam TCapacity Implicitly deferred size of the array provided.
    /// @param  table     The table containing operator compilation information.
    template<size_t TCapacity>
    void AddBinaryOpOptimizations( BinaryOpOptimizationsTableEntry (&table) [TCapacity] )
    { AddBinaryOpOptimizations( &table[0], TCapacity ); }
 
    /// Loads all entries of the given table into hash map #BinaryOperatorOptimizations.
    ///
    /// Note, that usually, the given table is a constexpr array located in an anonymous namespace
    /// of a compilation unit.<br>
    /// It can be passed as a reference to templated helper method, which defers the length of the
    /// table implicitly.
    ///
    /// @param  table     The table containing operator compilation information.
    /// @param  length    The table containing operator compilation information.
    ALIB_DLL
    void AddBinaryOpOptimizations( BinaryOpOptimizationsTableEntry* table, size_t length );
 
    /// Searches in #Operators for an entry matching the combination of
    /// #"CIUnaryOp::Operator"
    /// and the argument type of operand found with iterator
    /// #"CompilationInfo::ArgsBegin".
    /// (The second argument type of the key of the hash map #Operators is set to
    /// #"Types::Void;*").
    /// If found, the corresponding callback function and result type are added the \p{CIUnaryOp}.
    ///
    /// Before the search, it is checked whether the given operator is an alias for another
    /// operator. Operator aliases might be defined by filling map #OperatorAliases in the
    /// constructor of the derived types.
    /// If so, the corrected operator is returned with in/out parameter
    /// #"CIUnaryOp::Operator".
    ///
    /// @param    ciUnaryOp    The compilation result.
    /// @return \c true if an entry was found in #Operators and a corresponding command was added to
    ///         \p{ciUnaryOp}. \c false otherwise.
    ALIB_DLL
    virtual bool    TryCompilation( CIUnaryOp& ciUnaryOp )                                 override;
 
 
    /// Searches in #Operators for an entry matching the combination of #"CIBinaryOp::Operator"
    /// and the argument types of operands found with argument iterators
    /// #"CompilationInfo::ArgsBegin"
    /// and
    /// #"CompilationInfo::ArgsBegin".
    /// If found, the corresponding callback function and result type are added the \p{CIBinaryOp}.
    ///
    /// Before the search, it is checked whether the given operator is an alias for another
    /// operator. Operator aliases might be defined by filling map #OperatorAliases in the
    /// constructor of the derived types.
    /// If so, the corrected operator is returned with in/out parameter
    /// #"CIBinaryOp::Operator".
    ///
    /// @param  ciBinaryOp  The compilation info struct.
    /// @return \c true if an entry was found in #Operators and a corresponding command was added
    ///         to \p{ciBinaryOp}. \c false otherwise.
    ALIB_DLL
    virtual bool    TryCompilation( CIBinaryOp& ciBinaryOp )                               override;
 
 
  //################################################################################################
  // Auto-Casts
  //################################################################################################
 
    /// An entry of the field #AutoCasts. Defines auto-casts for custom types.
    struct AutoCastEntry {
        /// The type that is to be automatically cast.
        Box                        Type;
 
        /// List of operators that the auto-cast accepts.
        /// If \e nulled, then just any operator that is not in #OperatorsDeclined is accepted.
        std::vector<String>*        OperatorsAccepted;
 
        /// List of operators that the auto-cast does not accept. An operator should not appear
        /// in both lists, this one and list #OperatorsAccepted. However, it is does, then the
        /// operator is not accepted.
        ///
        /// A value of \c nullptr is allowed to indicate no declined operators.
        std::vector<String>*        OperatorsDeclined;
 
        /// Callback function to add to the program that performs the auto-cast.
        ///
        /// If \c nullptr is given, then an internal, predefined callback is used, which
        /// returns a value of type #"Types::Integer;*" which is generated by
        /// taking the #"Box::Data;raw value" of the argument box. This is
        /// especially useful for any boxed enum type that is to be made compatible
        /// with bitwise boolean operators (and other integral calculations and functions).
        CallbackDecl                Callback;
 
 
        #if ALIB_DEBUG
        /// The C++ name of the callback function (only available with debug-builds of the
        /// library. Use preprocessor macro #"CALCULUS_CALLBACK" to provide this field
        /// together with field #Callback. The macro selects to prune the name string
        /// in release compilations.
        ///
        /// If #Callback is set to nullptr, the name of the internal function (\e "any2int")
        /// is inserted automatically. Instead of the aforementioned macro #"CALCULUS_CALLBACK"
        /// use macro #"CALCULUS_DEFAULT_AUTOCAST" instead.
        const char*             DbgCallbackName;
        #endif
 
        /// The result type given a #"alib_expressions_prereq_sb;sample box".
        ///
        /// If field #Callback is \c nullptr to specify the use of the internal, default cast
        /// function, this field will be ignored and #"Types::Integer;*", will
        /// be set instead. Hence, in this case, this field can be specified as \c nullptr.
        Box                         ResultType;
 
        /// This is the name of the function that reverses the cast. The function is used when an
        /// expression with an auto-cast function is \e decompiled to generate compilable,
        /// optimized expression strings.
        ///
        /// \note
        ///   This method is needed only if "normalized, optimized expression strings" are
        ///   to be generated. For more information on this topic consult manual section
        ///   #"alib_expressions_details_optimizations_norm".
        ///
        /// \note
        ///   If the aforementioned feature is used, then this function name has to be
        ///   provided together with the implementation of the expression function itself,
        ///   even if the internal default cast implementation (activated by setting field
        ///   #Callback to \c nullptr) is used. The rationale is, that this library cannot
        ///   automatically convert integral types back to a custom type. This is even true
        ///   for simple enumeration types.
        String                      ReverseCastFunctionName;
    };
 
    /// List of auto-casts to be compiled by this plug-in.
    std::vector<AutoCastEntry>      AutoCasts;
 
 
    /// Searches in #AutoCasts for an entry matching the combination of
    /// #"CIAutoCast::Operator" and the type(s) that might be auto-cast.
    ///
    /// An entry in #AutoCasts might also be defined to work on just all operators.
    ///
    /// For the very frequent use case of auto-casting custom enum types to integral types, only
    /// fields
    /// #"AutoCastEntry::Type"
    /// and
    /// #"AutoCastEntry::ReverseCastFunctionName"
    /// have to be provided.
    ///
    /// \note
    ///   This method of this helper-class is not applicable if one of the following conditions apply
    ///   to a use case:
    ///   - Different auto-casts are to be applied for the first and second arguments of binary
    ///     operators.
    ///   - The custom auto-cast method is not compile-time invokable.
    ///
    /// \note
    ///   In this case, a custom implementation of this method has to be provided to fetch
    ///   these cases. The custom method might then invoke this base implementation.
    ///
    /// @param  autoCast  The compilation info struct.
    /// @return \c true if a matching entry was found in #AutoCasts and a corresponding command
    ///         was added to \p{autoCast}. \c false otherwise.
    ALIB_DLL
    virtual bool    TryCompilation(CIAutoCast& autoCast)                                   override;
};
 
}} // namespace alib[::expressions::plugin]
 
/// Type alias in namespace #"%alib".
using     Calculus=    expressions::plugins::Calculus;
 
} // namespace [alib]