# Optimizing C++/Print Version

Optimizing C++/Cover

# Introduction

One of the main reason for preferring C++ over simpler, higher-level programming languages is that C++ allows the development of complex software in a way that makes more efficient use of hardware resources than when using these other languages. The language does not guarantee efficient code automatically, but provides a toolchest that aids programmers in the pursuit of efficiency. Sloppy C++ code may be no more efficient than higher-level implementations of the same algorithms, but a good C++ programmer with knowledge of the language can write software that is efficient from the first cut and then optimize the code further. This book provides techniques for writing efficient code and for optimizing existing software.
Often, there is no single solution to a programming problem that is optimal for all cases. Thus, optimization generally does not mean writing optimally performing software; rather, it means incrementally changing (refactoring) software to increase its performance, bringing it closer to the optimum.
Such optimization requires that the software source is written in a sufficiently modular way that performance critical parts can be isolated. With suitably written code, it then requires the use of tools, libraries, knowledge and time to change those parts in a way that increases the overall execution speed of the software.
Nowadays, many optimizations are already performed by compilers and are no longer the programmer's burden. This book discusses higher-level optimizations that present-day compilers are not (yet) able to perform.
This book is aimed at readers already familiar with the C++ language, who want to use it to develop high performance application software or software libraries.
Almost all of the optimization techniques presented are platform independent and, therefore, there will be few references to specific operating systems, processor architectures or compilers. However, some of the presented techniques may be ineffective or inapplicable in some combinations of operating system/processor/compiler.

# Optimization life cycle

The construction of an efficient application should adhere to the following development process:
* Design. Firstly, the algorithms and data structures are designed in a way that makes sense for the application logic and that is reasonably efficient, but without considering optimization. When designing a widely used data structure the optimal implementation of which is not obvious (for example, it is debated whether it is better to use an array or a linked list), an abstract structure is defined for which the implementation may be changed at the optimization stage.
* Implementation. Secondly, the code that implements the designed algorithms is written, following guidelines to avoid inefficient operations and encapsulating operations that are likely to require optimization.
* Functional testing. The resulting software is then tested to increase the probability that it doesn't have crippling defects.
* Optimization (aka Tuning). After having completed the development of a correctly working application, the optimization stage begins, with the following sub-stages:
** Performance testing. Commands with inadequate performance are detected. These are commands that, when processing typical data, require more resources (CPU time, storage space, etc) than are available.
** Profiling (aka Performance analysis). For every command with inadequate performance, a profiler is used to determine which portions of code are the so-called bottlenecks for that command. Bottlenecks are parts of code where a disproportionate amount of time is spent or memory space is allocated.
** Algorithmic optimization. For each bottleneck, optimization techniques are applied that are largely independent of the programming language and totally independent of the platform. Such techniques can be found in algorithm theory textbooks. This optimization involves attempting to reduce the number of executed machine cycles. In particular it involves reducing the number of calls to costly routines or transforming expensive operations into equivalent but less costly operations. For example, the quick sort sorting algorithm is chosen instead of the selection sort algorithm. If this makes the program fast enough, the optimization stage is complete.
** Platform independent optimization. For each bottleneck, optimization techniques are applied that depend upon the programming language and its standard library but that are independent of both the software and hardware platforms. For example, integer operations are used instead of floating point operations or a more appropriate container class is chosen from those available in the standard library. If this makes the program fast enough, the optimization stage is complete.
** Software platform dependent optimization. For each bottleneck, optimization techniques are applied that depend upon both the programming language and the software platform but that are independent of the hardware platform. For example, compiler options, pragma compiler directives, language extensions, non-standard libraries, direct calls to the operating system are exploited. If this makes the program fast enough, the optimization stage is complete.
** Hardware platform dependent optimization. For each bottleneck, optimization techniques that depend upon the hardware platform are applied. This can involve using machine instructions that are specific to a processor family or using more generally available high level features that are particularly advantageous on some processor types.
This development process follows two criteria:
* Principle of diminishing returns. Optimizations that yield big results with little effort should be applied first, as this minimizes the time needed to reach the performance goals.
* Principle of diminishing portability. It is better to apply optimizations applicable to several platforms first, as they remain applicable on changing platform and are more understandable to other programmers.
In the rare case of software that must be used with several compilers and several operating systems but just one processor architecture, the stages 4.5 and 4.6 should be swapped.
This stage sequence is not meant to be a one-way sequence, in which once one stage is reached, the preceding stage is no longer used. In fact, every stage may succeed or fail. If a stage succeeds, the next stage is applied, while if a stage fails, the previous stage is repeated, in a sort of backtracking algorithm.
In addition, a partial performance test should be performed after every optimization attempt, just to check whether the attempt was useful and, if so, to check whether more optimizations are needed.
Finally, after having completed the optimization, both the functional testing and the complete performance testing must be repeated to guarantee that the newly optimized version of the software is still functionally correct and has suitable performance.
This book is about only three of the above stages:
* Stage 2, specifically the usage of the C++ language, in the chapter "Writing efficient code".
* Some general techniques for stage 4.3, with examples in C++, in chapter "General optimization techniques".
* Stage 4.4, specifically the usage of the C++ language, in the chapter "Code optimization".

## Conventions

By object, it is meant an allocated region of memory. In particular, a piece of data associated to a variable of a fundamental type (like bool, double, unsigned long, or a pointer) is an object, as it is such the data structure associated to an instance of a class. With every variable an object is associated, whose size is given by the sizeof C++ operator, but an object could have no variable associated with it, or several variables associated with it. For example, a pointer is an object, but it can point to another object; this pointed object is not associated with any variable. On the other hand, in the following code, both the variable a and the variable b are associated with the same object:
Arrays, structs, and class instances are objects which, if not empty, contain sub-objects. Therefore, they will be called aggregate objects.
We say that an object owns another object when the destruction of the former object causes the destruction of the latter. For example, a non-empty vector object typically contains a pointer to a buffer containing all the elements; the destruction of the vector causes the destruction of such buffer, and therefore we say that this buffer is owned by the vector object.
Some optimizations are useful only for short data sequences, others for longer sequences. Later on, the following classification will be used for objects sizes:
* Tiny: No more than 8 bytes. It fits in one or two 32-bit registers or in one 64-bit register.
* Small: More than 8 bytes, but no more than 64 bytes. It doesn't fit in a processor register, but it fits in a processor data cache line, and it can be wholly referenced by very compact machine instructions using an offset from the start address.
* Medium: More than 64 bytes, but no more than 4096 bytes. It doesn't fit in a processor data cache line, and it cannot be wholly referenced by compact machine instructions, but it fits in the processor first-level data cache, it fits in a virtual memory page, and it fits in a mass storage cluster of blocks.
* Large: More than 4096 bytes. It doesn't fit in the processor first-level data cache, it doesn't fit in a single virtual memory page, and it doesn't fit in a single mass storage cluster of blocks.
For example, an array of doubles is considered tiny only if it contains exactly one element, small if it has 2 to 8 elements, medium if it has 9 to 512 numbers, large if it has more than 512 of them.
Because there are very different hardware architectures, the given numbers are only an indication. Though, such numbers are rather realistic, and can be taken as serious criteria to develop software covering the main architectures in a rather efficient way.
Writing Efficient Code

# Writing efficient code

In this chapter, guidelines are presented for the avoidance of inefficient operations and for the preparation of source code for a possible optimization stage - all without jeopardizing code safety or maintainability.
Following these guidelines might result in no overall performance gain. But equally there is unlikely to be a performance loss. The guidelines can therefore be applied without worrying about their impact on performance. It is advisable always to follow these guidelines, even in code portions that have no particular efficiency requirements.
* Performance improving features
* Performance worsening features
* Constructions and destructions
* Allocations and deallocations
* Memory access
* Thread usage

# Performance improving features

Some features of the C++ language, if properly used, allow to increase the speed of the resulting software.
In this section guidelines to exploit such features are presented.

### The most efficient types

When defining an object to store an integer number, use the int or the unsigned int type, except when a longer type is needed; when defining an object to store a character, use the char type, except when the wchar_t type is needed; and when defining an object to store a floating point number, use the double type, except when the long double type is needed. If the resulting aggregate object is of medium or large size, replace each integer type with the smallest integer type that is long enough to contain it (but without using bit-fields) and replace the floating point types with the float type, except when greater precision is needed.
The int and unsigned int types are, by definition, the most efficient ones available on the platform that can hold at least a 16-bit range. If you only need 8-bit width and are compiling for an 8-bit processor then char might be more efficient, but otherwise one of the int types is likely to be the most efficient type you can use.
The double type is two to three times less efficient than the float type, but it has greater precision.
Some processor types handle signed char objects more efficiently, while others handle unsigned char objects more efficiently. Therefore, both in C and in C++, the char type, which differs from the signed char type, was defined as the most efficient character type for the target processor.
The char type can contain only small character sets; typically up to a maximum of 255 distinct characters. To handle bigger character sets, you should use the wchar_t type, although that is less efficient.
In the case of numbers contained in a medium or large aggregate object or in a collection that will be probably be of medium or large size, it is better to minimize the size in bytes of the aggregate object or collection. This can be done by replacing primitives larger than word size with those that are word size for the processor. A short actually takes up the same amount of memory as word size even though the field size of a short is less.
Bit-fields can also be used to minimize the size of aggregate objects, but as their handling is slower this can be counterproductive. Therefore, postpone their introduction until the optimization stage.

### Function-objects

Instead of passing a function pointer as an argument to a function, pass a function-object (or, if using the C++11 standard, a lambda expression).
For example, if you have the following array of structures:
… and you want to sort it by the b field, you could define the following comparison function:
… and pass it to the standard sort algorithm:
However, it is probably more efficient to define the following function-object class (aka functor):
… and pass a temporary instance of it to the standard sort algorithm:
Function-objects are usually expanded inline and are therefore as efficient as in-place code, while functions passed by pointers are rarely inlined. Lambda expressions are implemented as function-objects, so they have the same performance.

### qsort and bsearch functions

Instead of the qsort and bsearch C standard library functions, use the std::sort and std::lower_bound C++ standard library functions.
The former two functions require a function pointer as an argument, whereas the latter two may take a function-object argument (or, using the C++11 standard, a lambda expression). Pointers to functions are often not expanded inline and are therefore less efficient than function-objects, which are almost always inlined.

### Encapsulated collections

Encapsulate (using a class) a collection that is accessible from several compilation units.
At design time, it is difficult to decide which data structure will have optimal performance when the software is used. At optimization time, performance can be measured and it can be seen whether changes to the container type result in improvements, for example changing from std::vector to std::list. Such implementation changes can however propagate to users of the code.
If a collection is private to one compilation unit, implementation changes will only impact the source code of that unit and encapsulation of the collection is unnecessary. If, however, the collection is not private (in other words, it is directly accessible from other compilation units) an implementation change could result in extensive change being necessary. To make such optimization feasible, therefore, encapsulate the collection in a class whose interface does not change when the container implementation is changed.
STL containers already use this principle, but certain operations are still available only for some containers (like operator, existing for std::vector, but not for std::list).

### STL container usage

When using an STL container, if several equivalent expressions have the same performance, choose the more general expression.
For instance, call a.empty instead of a.size == 0, call iter != a.end instead of iter < a.end, and call distance(iter1, iter2) instead of iter2 - iter1. The former expressions are valid for every container type, while the latter are valid only for some. The former are also no less efficient than the latter and may even be more efficient. For example, to get the size of a linked list the list must be traversed, whereas to see that it is empty is a constant time operation.
Unfortunately, it is not always possible to write code that is equally correct and efficient for every type of container. Nevertheless, decreasing the number of statements that are dependent on the container type will decrease the number of statements that must be changed if the type of the container is later changed.

### Choice of the default container

When choosing a variable-length container, if in doubt, choose a vector.
For a data-set with a small number of elements, vector is the most efficient variable-length container for any operation.
For larger collections, other containers may become more efficient for certain operations, but vector still has the lowest space overhead (as long as there is no excess capacity) and the greatest locality of reference.

### Inlined functions

If your compiler allows whole program optimization and automatic inline-expansion of functions, use such options and do not declare any functions inline. If such compiler features are not available, declare suitable functions as inline in a header; suitable functions contain no more than three lines of code and have no loops.
Inline function-expansion avoids the function call overhead. The overhead grows as the number of function arguments increases. In addition, since inline code is near to the caller code, it has better locality of reference. And because the intermediate code generated by the compiler for inlined functions is merged with the caller code, it can be optimized more easily by the compiler.
Expanding inline a tiny function, such as a function containing only a simple assignment or a simple return statement, can result in a decrease in the size of the generated machine code.
Conversely, every time a function containing substantial code is inlined the machine code is duplicated and the total size of the program increases. Increasing the size of the program also will likely decrease the performance of your instruction cache, increasing latency.
Inlined code is more difficult to profile. If a non-inlined function is a bottleneck, it can be found by the profiler. But if the same function is inlined wherever it is called, its run-time is scattered among many functions and the bottleneck cannot be detected by the profiler.
For functions containing substantial amounts of code, only performance critical ones should be declared inline during optimization.

### Symbols representation

To represent internal symbols, use enumerations instead of strings.
For example, instead of the following code:
use the following code:
An enumeration is implemented as an integer. Compared to an integer, a string occupies more space and is slower to copy and compare. (In addition, using strings instead of integers to represent internal state may introduce string comparison errors in code that deals with multiple locales.)

### if and switch statements

If you have to compare an integer value with a set of constant values, instead of a sequence of if statements, use a switch statement.
For example, instead of the following code:
write the following code:
Compilers may exploit the regularity of switch statements to apply some optimizations, in particular if the guideline "Case values for switch statements" in this section is applied.

### Case values of switch statements

As constants for switch statements cases, use compact sequences of values, that is, sequences with no gaps or with few small gaps.
When compiling a switch statement whose case values comprise most of the values in an integer interval, instead of generating a sequence of if statements, an optimizing compiler will generate a jump-table. The table is an array containing the start address of the code for each case. When executing the switch statement, the table is used to jump to the code associated with the case number.
For example, the following C++ code:
probably generates machine code corresponding to the following pseudo-code:
Instead, the following C++ code:
probably generates machine code corresponding to the following code:
For so few cases, there is probably little difference between the two situations, but as the case count increases, the former code becomes more efficient, as it performs only one computed goto instead of a sequence of branches.

### Case order in switch statement

In switch statements, put typical cases first.
If the compiler does not use a jump-table, cases are evaluated in order of appearance; therefore, fewer comparisons are performed for the more frequent cases.

### Grouping function arguments

In a loop that calls a function with more arguments than there are registers, consider passing a struct or object instead.
For example, instead of the following code:
consider writing the following:
If all function arguments can be placed directly into processor registers, the arguments can be passed and manipulated quickly. If there are more arguments than available registers, those arguments that could not be placed into registers will be pushed onto the stack at the start of every function call and removed from the stack at the end of the call. If a structure or object is passed, a register may be used and after initialization of the structure or object, only those parts of the structure or object that change between successive calls must be updated.
Compilers vary in the number of registers used for function arguments. Relying on the number used by any particular compiler version is unwise. Assuming that 4 registers are used is reasonable.

### Use of container member functions

To search for an element in a container, use a container member function instead of an STL algorithm.
If a container provides a member function that duplicates a generic STL algorithm it is because the member function is more efficient.
For example, to search a std::set object, you can use the std::find generic algorithm, or the std::set::find member function. The former has linear complexity (O(n)), while the latter has logarithmic complexity (O(log(n))).

### Search in sorted sequences

To search a sorted sequence, use the std::lower_bound, std::upper_bound, std::equal_range, or std::binary_search generic algorithms.
Given that all the cited algorithms use a logarithmic complexity (O(log(n))) binary search, they are faster than the std::find algorithm, which uses a linear complexity (O(n)) sequential scan.

### static member functions

In every class, declare every member function that does not access the non-static members of the class as static .
In other words, declare all the member functions that you can as static.
In this way, the implicit this argument is not passed.

# Performance worsening features

When compared to C, C++ has some features that worsen efficiency if used inappropriately.
Some of these features are nevertheless quite efficient and can be used liberally when useful. However, their increased cost should be avoided when the feature is not needed.
Other features are instead quite inefficient and so should be used sparingly.
In this section, guidelines are presented for the avoidance of C++ features that worsen performance.

### The throw operator

Call the throw operator only when you want to notify a user of the failure of the current command.
Raising an exception has a very high cost when compared to a function call. It requires thousands of processor cycles. If an exception is raised only when a message is displayed on the user interface or written into a log file, there is a guarantee that it will not be performed too often without notice.
In contrast, if exceptions are made part of an algorithm, even if initially thought to be rare they may end up being performed too frequently.

### virtual member functions

Define the destructor as virtual if and only if the class contains at least one other virtual member function or if the class might be derived from (i.e. the class is intended for use as a base class). With the exception of destructors, do not declare functions as virtual unless you intend to override them.
Classes that have virtual member functions occupy more storage space than those without. Instances of classes having at least one virtual member function occupy more space (typically, a pointer and possibly some padding) and their construction requires more time (typically, to set the pointer) than instances of classes without virtual member functions.
In addition, every virtual member function has a slower call time than an identical non-virtual member function.

### virtual inheritance

Use virtual inheritance only when several classes must share the representation of a common base class.
For example, consider the following class definitions:
With such definitions, every C class object contains two distinct class A objects, one inherited from the B1 base class, and the other from the B2 class.
This is no problem if class A has no non-static member variables.
If, instead, class A contains some member variables and you mean that such member variables are unique for every class C instance, you must use virtual inheritance, in the following way:
This situation is the only case when virtual derivation is necessary.
The member functions of the class A are somewhat slower to call on a C class object if virtual inheritance is used.

### Templates of polymorphic classes

Do not define templates of polymorphic classes.
In other words, don't use the "template" and the "virtual" keywords in the same class definition.
Every time a class template is instantiated a copy is made of all member functions used. If such classes contain virtual functions, even their vtable and RTTI data is replicated. This data bloats the code.

### Use of automatic deallocators

Use a memory manager based on garbage-collection or a kind of reference-counted smart-pointer (like shared_ptr in the Boost library) only if you can prove its expediency for the specific case.
Garbage collection, or automatic reclamation of unreferenced memory, allows the programmer to leave out calls for memory deallocation and prevents memory leaks. However, one must implement garbage collection through a non-standard library since these features are not included in C++. In addition, code using garbage collection typically executes more slowly than code using explicit deallocation (when the delete operator is explicitly called). In addition, when the garbage collector runs the rest of the program doesn't. This makes execution of the program less deterministic.
The C++98 standard library contains only one kind of smart-pointer, auto_ptr, that is quite efficient. Other smart-pointers provided by non-standard libraries, such as Boost, will be provided by the C++11 standard library. Smart-pointers rely upon reference-counting but are less efficient than simple pointers. For example, shared_ptr is the standard Boost smart pointer. However, if the thread-safe version of Boost is used, the library has very poor performance for creation, destruction and copying of these pointers as it must guarantee mutual exclusion for these operations.
Usually, you should try to assign every dynamically allocated object to a single owner at design time. When such an assignment is difficult, for example if several objects tend to bounce the responsibility to destroy the object, it becomes expedient to use a reference-counted smart-pointer to handle the object.

### The volatile modifier

Only variables that are changed asynchronously by hardware devices should be defined volatile.
The usage of the volatile modifier prevents the compiler from locating a variable in a register, even for a short time. This guarantees that all devices see the same variable, but slows down operations that access the variable.
volatile does not guarantee that other threads will see the same values, as it does not force the compiler to generate the necessary memory barrier and lock instructions. Therefore, read and write access to a volatile value may be made out of order even on the same CPU (important in the case of interrupts and signals) and especially out of order across the memory cache and bus to other CPUs. You must use a proper thread or atomic memory API or write machine code to guarantee the proper order of operations for safe threading.

# Constructions and destructions

Construction and destruction of an object requires time, especially if the object owns other objects.
This section will provide guidelines for decreasing the number of object constructions and corresponding destructions.

### Variable scope

Declare variables as late as possible.
To do so, the programmer must declare all variables in the most local scope. By doing so, the variable is neither constructed nor destructed if that scope is never reached. Postponing declaration as far as possible within a scope means that should there be an early exit before the declaration (using a return or break or continue statement) the object associated to the variable is neither constructed nor destructed.
It is often the case that at the beginning of a routine no appropriate value is available with which to initialize a variable. The variable is therefore initialized with a default value and a later assignment sets the correct value when it becomes available. If, instead, the variable is defined only when an appropriate value is available, the object is initialized with this value and no subsequent assignment is necessary. This is advised by the guideline "Initializations" in this section.

### Initializations

Use initializations instead of assignments. In particular, in constructors, use initialization lists.
For example, instead of writing:
write:
Even if a class instance (s in the first example above) is not explicitly initialized, it is nevertheless automatically initialized by the default constructor.
To call the default constructor followed by an assignment with a value may be less efficient than to call only a constructor with the same value.

### Increment/decrement operators

Use prefix increment (++) or decrement (--) operators instead of the corresponding postfix operators if the expression value is not used.
If the incremented object is a primitive type, there is no difference between prefix and postfix operators. However, if it is a composite object, the postfix operator causes the creation of a temporary object, while the prefix operator does not.
Because every object that is a primitive type may become a composite object in the future, it is better to use the prefix operator whenever possible, especially when writing generic (templatized) code that operates on iterators.
Use the postfix operator only when the variable is in a larger expression and must be incremented only after the expression is evaluated.

### Assignment composite operators

Use the assignment composite operators (like in a += b) instead of simple operators combined with assignment operators (like in a = a + b).
For example, instead of the following code:
write the following code:
Typically, a simple operator creates a temporary object. In the example, the operator + creates temporary strings whose creation and destruction require much time.
On the contrary, the equivalent code using the += operator does not create temporary objects.

### Function argument passing

When you pass an object x of type T as argument to a function, use the following criterion:
* If x is an input-only argument,
** if x may be null,
*** pass it by pointer to constant (const T* x),
** otherwise, if T is a fundamental type or an iterator or a function-object,
*** pass it by value (T x) or by constant value (const T x),
** otherwise,
*** pass it by reference to constant (const T& x),
* otherwise, i.e. if x is an output-only or input/output argument,
** if x may be null,
*** pass it by pointer to non-constant (T* x),
** otherwise,
*** pass it by reference to non-constant (T& x).
Pass by reference is more efficient than pass by pointer as it facilitates variable elimination by the compiler and because the callee need not check whether the reference is valid or null. However, where the argument can be missing, it is more efficient to pass a NULL pointer, than to pass a reference to a possibly dummy object and a boolean indicating whether the reference is valid.
For objects that may be contained in one or two registers, pass by value is more efficient than pass by reference (or equally efficient). This applies to tiny objects, such as the fundamental types, iterators and function-objects. For larger objects, pass by reference is more efficient than pass by value, as with the latter, the object must be copied onto the stack.
A composite object that is currently fast to copy might be passed efficiently by value. However, unless the object is an iterator or a function-object (which are assumed always to copy efficiently), this technique is risky. Future changes to the object might increase its size and make it more expensive to copy. For example, if an object of class Point contains only two floats, it could be efficiently passed by value; but if in the future a third float is added, or if the two floats become two doubles, it could become more efficient pass by reference.

### explicit declaration

Declare as explicit all constructors that receive only one argument, except for the copy constructors of concrete classes.
Non-explicit constructors may be called automatically by the compiler when it performs an automatic (implicit) type conversion. The execution of such constructors may take much time.
If such conversion is made compulsorily explicit, and if a new class name is not specified in the code, the compiler could choose another overloaded function, avoiding to call the costly constructor, or it could generate an error, so forcing the programmer to choose another way to avoid the constructor call.
For copy constructors of concrete classes a distinction must be made to allow their pass by value. For abstract classes, even copy constructors may be declared explicit, as, by definition, abstract classes cannot be instantiated and so objects of such type should never be passed by value.

### Conversion operators

Declare conversion operators only to keep compatibility with an obsolete library (in C++11, declare them explicit).
Conversion operators allow implicit conversions and so incur in the same problem as implicit constructors described in the guideline "explicit declaration" in this section.
If such conversions are needed, provide instead an equivalent member function, as it may only be called explicitly.
The only acceptable remaining usage for conversion operators is when a new library must coexist with an older similar library. In such a case, it may be convenient to have operators that automatically convert objects from the old library into the corresponding types of the new library and vice versa.

### The Pimpl idiom

Use the Pimpl idiom only when you want to make the rest of the program independent from the implementation of a class.
The Pimpl idiom (meaning Pointer to implementation) consists of storing in an object only a pointer to a data structure containing all the useful information about the object.
The main advantage of the idiom is that it speeds up incremental compilation of code by making it less likely that a small change in the source code causes the need to recompile a large number of code lines.
This idiom also makes some operations more efficient, such as a swap of two objects. In general, however, it slows down every access to the object data because of the added level of indirection and causes an additional memory allocation each time such an object is created or copied. It should not, therefore, be used for classes whose public member functions are called frequently.

### Iterators and function objects

Ensure that custom iterators and function objects are tiny and do not allocate dynamic memory.
STL algorithms pass such objects by value. Therefore, if their copy is not extremely efficient, STL algorithms are slowed down.
If an iterator or function object for some reason needs an elaborate internal state, allocate it dynamically and use a shared pointer. For example, say you want to implement an STL-compliant 32-bit Random Number Generator on top of the Linux/OpenBSD /dev/urandom device:
In this case, the use of a pointer was actually necessary because the ifstream class is non-copyable: its copy constructor is declared private. This example uses the boost::shared_ptr smart pointer; for more speed, intrusive reference counting could be used.

# Allocations and deallocations

Dynamic memory allocation and deallocation are very slow operations when compared to automatic memory allocation and deallocation. In other words, the heap is much slower than the stack.
In addition, dynamic allocation has a per-allocation overhead, causes virtual memory fragmentation, and causes bad data locality of reference, with the ensuing bad usage of both the processor data cache and virtual memory space.
Dynamic memory allocation/deallocation was performed in the C language using the malloc and free standard library functions. In C++, although these functions are still available, the new, new, delete, and delete operators are normally used.
An obvious way to decrease the allocation count is to decrease the number of constructed objects and for that you should refer to the section "Constructions and destructions" in this chapter.
Here we concentrate on guidelines for decreasing the allocation count for a given number of new operator calls.

### Fixed length arrays

If a static or non-large array has compile-time constant length, instead of a vector object, use a C-language array, std::array, or an array object from the Boost library.
vectors store data in a dynamically allocated buffer, whereas arrays allocate data inside the object itself. This avoids repeated allocations/deallocations of dynamic memory and favors data locality.
If the array is large, such advantages are diminished and it becomes more important to avoid using too much stack space.

### Allocating many small objects

If you have to allocate many objects of the same size, use a block allocator.
A block allocator (aka pool allocator) allocates medium to large memory blocks and provides a service to allocate/deallocate smaller, fixed-size blocks. It allows high allocation/deallocation speed, low memory fragmentation and efficient use of data caches and of virtual memory.
In particular, an allocator of this kind can greatly improve the performance of the std::list, std::set, std::multiset, std::map, and std::multimap standard containers.
If your standard library implementation does not already use a block allocator for such containers, you should get one and specify it as a template parameter of instances of such container templates. Boost provides two customizable block allocators, pool_allocator and fast_pool_allocator. Other pool allocator libraries can be found on the World Wide Web. Always measure first to find the fastest allocator for the job at hand.

### Appending elements to a collection

When you have to append elements to a collection, use push_back to append a single element, use insert to append a sequence of elements, and use back_inserter to cause an STL algorithm to append elements to a sequence.
The push_back functions guarantees an amortized linear time, as, in case of vectors, it increases the capacity exponentially.
The back_inserter class calls the push_back function internally.
The insert function allows a whole sequence to be inserted in an optimized way and therefore a single insert call is faster than many calls to push_back.

# Memory access

This section presents guidelines for improving main-memory access performance by exploiting features of the processor caches and of secondary memory swapping by the operating system virtual memory manager.

### Memory access order

Access memory in increasing addresses order. In particular:
* scan arrays in increasing order;
* scan multi-dimensional arrays using the rightmost index for innermost loops;
* in class constructors and in assignment operators (operator=), access member variables in the order of declaration.
Data caches optimize memory access in increasing sequential order.
When a multi-dimensional array is scanned, the innermost loop should iterate on the last index, the innermost-but-one loop should iterate on the last-but-one index, and so on. In such a way, it is guaranteed that array cells are processed in the same order in which they are arranged in memory. For example, the following code is optimized:

### Memory alignment

Keep the compiler default memory alignment.
By default, compilers use an alignment criterion for fundamental types, for which objects may have only memory addresses that are a multiple of particular factors. Such criterion guarantees top performance, but it may add paddings (or holes) between successive objects.
If it is necessary to avoid such paddings for some structures, use the pragma directive only around such structure definitions.

### Grouping functions in compilation units

Define in the same compilation unit all the member functions of a class, all the friend functions of the class, and all the member functions of friend classes of the class, except when the resulting file becomes unwieldy because of its size.
In this way, both the machine code resulting from the compilation of the functions and the static data defined in the classes and functions will have adjacent addresses. In addition, even compilers that do not perform whole program optimization may optimize calls among these functions.

### Grouping variables in compilation units

Define every global variable in the compilation unit in which it is used most often.
In this way, such variables will have addresses near to each other and to the static variables defined in such compilation units. In addition, even compilers that do not perform whole program optimization may optimize accesses to such variables from the functions that use them most often.

### Private functions and variables in compilation units

Declare in an anonymous namespace the variables and functions that are global to a compilation unit, but that are not used by other compilation units.
In the C language and also in C++, such variables and functions may be declared static. However, in modern C++, the use of static global variables and functions is not recommended and should be replaced by variables and functions declared in an anonymous namespace.
In both cases, the compiler is notified that such identifiers will never be used by other compilation units. This allows compilers that do not perform whole program optimization to optimize the use of such variables and functions.

# Thread usage
### Worker thread

In an interactive application, whenever you must perform an operation that can take more than few seconds, assign the operation to a worker thread having a lower priority than normal.
In this way, the main thread is ready to handle new user commands and by assigning the worker thread a lower priority, the user interface remains responsive.
Strictly speaking, this guideline does not improve the speed of the application, only its responsiveness. However, this is perceived by users as an improvement in speed.

### Multiple worker threads

In a multicore system, if you can split a CPU-intensive operation across several threads, use as many worker threads as there are processor cores.
In this way, every core can process a worker thread. If more worker threads are assigned than there are cores, the result will be heavy thread-switching, thus reducing execution speed. The main thread does not affect operational speed as it is mostly inactive.
This recipe does not hold for I/O-bound tasks; scheduling threads that are all waiting for the same disk only causes overhead. But one thread can compute while another is reading from disk, so two threads can perform useful work in some I/O-bound programs. Similarly, two threads can sometimes make better use of a full-duplex network link than one can.

### Use of multi-threaded libraries

If you are developing a single-threaded application, don't use libraries designed only for multi-threaded applications.
The techniques used to make a library thread-safe may have memory and time overheads. If you don't use threads, avoid paying their costs.

### Creation of multi-threaded libraries

If you are developing a library, handle its use by multi-threaded applications correctly, but also optimize for cases where it is used by single-threaded applications.
The techniques used to make a library thread-safe may have memory and time overheads. If the users of your library don't use threads, avoid forcing your users to pay the cost of threads.

### Mutual exclusion

Use mutual exclusion primitives only when several threads access the same data concurrently and at least one of these accesses is for writing.
Mutual exclusion primitives have an overhead.
If you are sure that, in a given period, no thread is writing in a memory area, there is no need to synchronize read accesses for such area.
General Optimization Techniques

# General optimization techniques

In this section we present some common techniques for algorithmic optimization. These techniques should mostly be independent of the programming language, software or hardware platform. When optimizing, always start by considering different algorithms before resorting to lower-level optimizations in order to retain generality, maintainability and portability in your code.
Some of the proposed techniques will have an implementation in C++.
* Input/Output
* Memoization
* Sorting
* Other techniques

# Output
### Store text files in a compressed format

Disk have much less bandwidth than processors. By (de)compressing on the fly, the CPU can speed up I/O.
Text files tend to compress well. Be sure to pick a fast compression library, though; zlib/gzip is very fast, bzip2 less so. The Boost Iostreams library contains Gzip filters that can be used to read from a compressed file as if it were a normal file:
Even if this is not faster than "raw" I/O (e.g. if you have a fast solid state disk), it still saves disk space.
Often the data stored as a compressed text file uses less space on disk than the same data represented in a binary format, even after that binary data is compressed.

### Binary format

Instead of storing data in text mode, store them in a binary format.
On average, binary numbers occupy less space than formatted numbers, and so it is faster to transfer them from memory to disk or vice versa. Also, if the data is transferred in the same format used by the processor there is no need of costly conversions from text format to binary format or vice versa.
Some disadvantages of using a binary format are that data is not human-readable and that the format may be dependent on the processor architecture.

### Open files

Instead of opening and closing an often needed file every time you access it, open it only the first time you access it, and close it when you are finished using it.
To close and reopen a disk file takes time. Therefore, if you need to access a file often, you can avoid this overhead by opening the file only one time before accessing it, keeping it open by hoisting its handle wrapper to an external scope, and closing it when you are done.

### I/O buffers

Instead of doing many I/O operations on single small or tiny objects, do I/O operations on a 4 KB buffer containing many objects.
Even if the run-time support I/O operations are buffered, the overhead of many I/O functions costs more than copying the objects into a buffer.
Larger buffers do not have a good locality of reference.

### Memory-mapped file

Except in a critical section of a real-time system, if you need to access most parts of a binary file in a non-sequential fashion, instead of accessing it repeatedly with seek operations, or loading it all in an application buffer, use a memory-mapped file, if your operating system provides such feature.
When you have to access most parts of a binary file in a non-sequential fashion, there are two standard alternative techniques:
* Open the file without reading its contents; and every time a data is demanded, jump to the data position using a file positioning operation (aka seek), and read that data from the file.
* Allocate a buffer as large as the whole file, open the file, read its contents into the buffer, close the file; and every time a data is demanded, search the buffer for it.
Using a memory-mapped file, with respect to the first technique, every positioning operation is replaced by a simple pointer assignment, and every read operation is replaced by a simple memory-to-memory copy. Even assuming that the data is already in disk cache, both memory-mapped files operations are much faster than the corresponding file operations, as the latter require as many system calls.
With respect to the technique of pre-loading the whole file into a buffer, using a memory-mapped file has the following advantages:
* When file reading system calls are used, data is usually transferred first into the disk cache and then in the process memory, while using a memory-mapped file the system buffer containing the data loaded from disk is directly accessed, thus saving both a copy operation and the disk cache space. The situation is analogous for output operations.
* When reading the whole file, the program is stuck for a significant time period, while using a memory-mapped file such time period is scattered through the processing, as long as the file is accessed.
* If some sessions need only a small part of the file, a memory-mapped file loads only those parts.
* If several processes have to load in memory the same file, the memory space is allocated for every process, while using a memory-mapped file the operating system keeps in memory a single copy of the data, shared by all the processes.
* When memory is scarce, the operating system has to write out to the swap disk area even the parts of the buffer that haven't been changed, while the unchanged pages of a memory-mapped file are just discarded.
Yet, usage of memory-mapped files is not appropriate in a critical portion of a real-time system, as access to data has a latency that depends on the fact that the data has already been loaded in system memory or is still only on disk.
The C++ standard does not define a memory mapping interface and in fact the C interfaces differ per platform. The Boost Iostreams library fills the gap by providing a portable, RAII-style interface to the various OS implementations. A similar, leaner, open-source library is cpp-mmf.

# Memoization

Memoization techniques (aka caching techniques) are based on the principle that if you must repeatedly compute a pure function, that is a referentially transparent function (aka mathematical function), for the same argument, and if such computation requires significant time, you can save time by storing the result of the first evaluation and retrieve that result the other times.

### Look-up table

If you often have to call a pure function that has a small integer interval as domain, pre-compute (at compile time or at program start-up time) all the values of the function for every value of the domain and put them in a static array called lookup table. When you need the value of the function for a particular value of the domain, read the corresponding value of such array.
For example, to compute the square root of an integer between 0 and 9, the following function is faster:
Array access is very fast, mainly if the accessed cell is in processor data cache. Therefore, if the lookup table is not large, almost surely its access is faster than the function to evaluate.
If the lookup table is large, it may be no more efficient, for the memory footprint, for the time to pre-compute all the values, if it doesn't fit the processor data cache. But if the function to evaluate is slow, it is called many times and you can afford to use much memory, consider using a lookup table up to several hundreds of kilobytes. It is rarely efficient to exceed one megabyte.

### One-place cache

If you often have to call a pure function with the same arguments, the first time the function is called save the arguments and the result in static variables. When the function is called again, compare the new arguments with the saved ones; if they match, return the saved result, otherwise compute the result and store the new arguments and the new result.
For example, instead of the following function:
you can use this function:
Notice that, for faster processing it isn't necessary that the function be called with the same arguments for the entire program session. It is enough that it is called some times with the same arguments, then some other times with other arguments. In such cases, the computation is performed only when the arguments change.
Obviously, instead of increasing the speed, this technique may decrease it if the function is called with almost always changing arguments or if the comparison between the new arguments and the old ones requires more time than the computation of the function itself.
Notice that if you use static variables this function is not thread-safe and cannot be recursive. If this function must be called concurrently by several threads, it is necessary to replace the static variables with variables that are distinct for every thread.
Notice also that in the example it is assumed that the function has zero value when both arguments are zero. Failing this, you should choose another solution, such as one of the following:
* Initialize the variable result with the value that corresponds to all-zero arguments.
* Initialize the variables prev_x and prev_y with values that will never be passed as arguments.
* Add a static flag indicating whether the static variables keep valid values and check that flag at every call.

### N-places cache

If you often have to call a pure function with arguments that in most cases belong to a small domain, use a static map (aka dictionary) that is initially empty. When the function is called, search the map for the function argument. If you find it, return the associated value, otherwise compute the result and insert the pair argument-result into the map.
Here is an example in which the map is implemented using an array. The same function was used for the example of the guideline "One-place cache" in this section:
Some functions, although they have a theoretically large domain, are called most often with few distinct arguments.
For example, a word processor may have many installed fonts, but in a typical document only a few fonts are used for most characters. A rendering function that has to handle the font of every character of the document will be called typically with few distinct values. For such cases, an N-places cache is preferable to a one-place cache, as in the example.
The remarks about static variables, in guideline "One-place cache" in this section, apply also to this case.
For small caches (in the example, having 8 places) the most efficient algorithm is a sequential scan on an array. To implement a larger cache, though, a search tree or a hash table could be more efficient. In addition, the cache of the example has fixed size, but it could be expedient to have a variable-size cache.
Usually, the last read element is the most likely for the next call. Therefore, as in the example, it may be expedient to save its position and to begin the search from that position.
If the cache does not expand itself indefinitely, there is the problem choosing the element to replace. Obviously, it would be better to replace the element that is the least likely to be requested by the next call. In the example, it is assumed that, among the elements in the cache, the first inserted element is the least probable for the next call. Therefore, the write scans cyclically through the array. Often, a better criterion is to replace the least recently read element instead of the least recently written element. To implement such criterion, a more complex algorithm is required.

# Sorting

The C++ Standard Template Library (STL) provides the template function sort that implements a comparison sort algorithm. Because sort is templatized, it can be used for various types of sequences holding any type of key, as long as the keys are comparable (implement the < operator). A good compiler can generate code optimized for the various kinds of sequence/key combinations.
The reference implementation of the STL uses the introsort algorithm (since the 2000 release; the GNU C++ library uses the reference implementation). This algorithm is a very fast combination of quicksort and heapsort with a specially designed selection algorithm.
The sort template function is not guaranteed to be stable. When a stable sort is required, use the stable_sort template function instead.
This section suggests alternatives to the sort and stable_sort template functions that may be faster in specific cases.

## Sorting with small ranges of keys

To sort a data set according an integer key having a small range, use the counting sort algorithm.
The counting sort algorithm has O(N+M) complexity, where N is the number of elements to sort and M is the range of the sort keys, that is the difference between the highest key and the lowest key. In case N elements are to be sorted whose key is an integer number belonging to an interval containing no more than two times N values (i.e when M <= 2 * N holds), this algorithm may be quite faster than sort. In some cases it is faster even with larger ranges.
This algorithm may be used also for a partial ordering; for example, if the keys are integers between zero and one billion, you can still sort them using only the most significant byte, so to get an order for which the formula $a_{n}<a_{n+1}+256*256*256$ holds.

### Example: sorting 8-bit integers

Say you want to sort an array of arbitrary unsigned char elements. <climits> defines constant limits for integer and char types for a specific implementation. CHAR_BIT is the number of bits in a char object. ISO C++ requires CHAR_BIT to be 8 or greater. An unsigned char may have a value in the range between 0 and UCHAR_MAX. ISO C++ requires UCHAR_MAX to be 255 (2^8-1) or greater.
Note: unsigned char must be used because char can be signed or unsigned depending on the implementation.
The counting_sort function implements the pigeonhole sort algorithm. It takes a pointer to the first element of the input array and a pointer that points one element beyond the end of the array. Why? Because we don't have to stop here.
We can generalize counting_sort to a template function that also works for string, vector<unsigned char> and other sequence types, without loss of efficiency. When doing so, we need to work with iterators rather than pointers.

## Partial sorting
### Partitioning

If you have to split a sequence according a criterion, use a partitioning algorithm, instead of a sorting one.
In STL there is the std::partition algorithm, that is faster than the std::sort algorithm, as it has O(N) complexity, instead of O(N log(N)).

### Stable partitioning and sorting

If you have to partition or sort a sequence for which equivalent entities may be swapped, don't use a stable algorithm.
In STL there is the std::stable_partition partitioning algorithm, that is slightly slower than the std::partition algorithm; and there is the std::stable_sort sorting algorithm, that is slightly slower than the std::sort algorithm.

### Order partitioning

If you have to pick out the first N elements from a sequence, or the Nth element in a sequence, use an order partitioning algorithm, instead of a sorting one.
In STL there is the std::nth_element algorithm, that, although slightly slower than the std::stable_partition algorithm, is quite faster then the std::sort algorithm, as it has O(N) complexity, instead of O(N log(N)).

### Sorting only the first N elements

If you have to sort the first N elements of a much longer sequence, use an order statistic algorithm, instead of a sorting one.
In STL there are the std::partial_sort and std::partial_sort_copy algorithms, that, although slower than the std::nth_element algorithm, are so much faster than the std::sort algorithm as the partial sequence to sort is shorter than the whole sequence.

# Other techniques
### Query cursor

Instead of defining a function that returns a collection (aka snapshot), define a function that returns an iterator (aka cursor or dynaset), with which you can generate or possibly change the required data.
This technique is particularly useful for database queries, but is applicable also to internal data structures.
Let's assume you have a collection (or a set of collections) encapsulated in a class. Such class exposes one or more member functions to extract (or filter) a subset from such collection.
A way to get it is to construct a new collection, to copy the extracted data into it, and to return such collection. In the database jargon, such collection is called snapshot.
This technique is effective but inefficient, as the allocation and copy of the snapshot takes a lot of time and a lot of storage space. In addition, it has the shortcoming that, until all the data has been extracted, you cannot proceed to process the already extracted data.
Here is an equivalent but more efficient technique.
The query function returns an iterator. In database jargon, such iterator is called cursor or dynaset. The caller uses such iterator to extract, one at a time, the data filtered, and possibly to change them.
Notice that this solution is not exactly equivalent, as if during the iterator use the collection is changed by another function call, possibly coming from another thread, it may happen that the iterator is invalidated, or just that the filtered collection do not corresponds to the specified criteria. Therefore, you can apply this technique only when you are sure that the underlying collection is not changed in any way, except by the iterator itself, during the whole life of the iterator.
This technique is independent of the programming language, as the iterator concept is an abstract design pattern.

### Binary search

If you have to do many searches in a rarely changed collection, instead of using a search tree or a hash table, you can get a speed up if you put the data in an array, sort the array, and do binary searches on it.
A binary search on an array has logarithmic complexity, like search trees, but has the advantage of compactness and locality of reference typical of arrays.
If the array is changed, this algorithm may still be competitive, as long as the changes are much less frequent than searches.
If every collection change consists in very few insertions or changes or deletions of elements, it is better to shift the array at every change operation. Instead, if a collection change is more bulky, it is better to recreate and sort the whole array.
In C++, if the array length is not a compile-time constant, use a vector.

### Singly-linked lists

If for a list you don't need bidirectional iterators, you don't need to insert elements at the end or before the current element, and you don't need to know how many elements there are in the list, use a singly-linked list, instead of a doubly-linked list.
Such container, although it has many shortcomings, occupies less space and it is faster.
Typically, the heading of a doubly-linked list contains a pointer to the head of the list, a pointer to the back, and the counter of elements, while the heading of a singly-linked list contains only a pointer to the head of the list. In addition, typically, every node of a doubly-linked list contains a pointer to the previous node and a pointer to the next node, while every node of a singly-linked list contains only a pointer to the next node. At last, every element insertion into a doubly-linked list must update four pointers and increment a counter, while every element insertion into a singly-linked list must only update two pointers.
In the C++ standard library, the std::list container is implemented by a doubly-linked list. The slist container, non-standard but available in various libraries, and the forward_list container, that will be in C++11 standard library, are implemented by singly-linked lists.
Code Optimization

# Code optimization

In this chapter some techniques, specific for C++ language, are proposed. They are to be applied only in bottlenecks, as, although they may speed up execution, they also make more complex and less maintainable the source code.
In addition, such guidelines in some cases could worsen the performance instead of improving it, and therefore their effect should be always measured before releasing them.
The optimization techniques are grouped according their goal.
* Allocations and deallocations
* Run-time support
* Instruction count
* Constructions and destructions
* Pipeline
* Memory access
* Faster operations
* Compile time optimization

# Allocations and deallocations

Even using a very efficient allocator, the allocation and deallocation operations take a significant time, and often the allocator is not very efficient.
In this section some techniques are described to decrease the total number of memory allocations, and their corresponding deallocations. They are to be applied only in bottlenecks, that is after having measured that the large number of allocations has a significant impact on performance.

### Move allocations and deallocations

Move before bottlenecks memory allocations, and after bottlenecks the matching deallocations.
Variable length dynamic memory management is much slower than automatic memory management.
Analogous optimization is to be done for operations causing allocations indirectly, as the copy of objects which, directly or indirectly, own dynamic memory.

### The reserve function

Before adding elements to a vector or to a string object, call its member function reserve with a size big enough for most cases.
If objects are repeatedly added to a vector or string object, several costly reallocations are performed. To avoid such reallocations, it is enough to initially allocate the required space.

### Keep vectors capacity

To empty a vector<T> x object without deallocating its memory, use the statement x.resize(0);; to empty it and deallocate its memory, use the statement vector<T>.swap(x);.
To empty a vector object, there also exists the clear member function, but, the C++ standard does not specify whether or not this function preserves the allocated capacity of the vector.
While the standard does not specify if the capacity is altered, further testing points towards the capacity remaining unchanged. On top of this, C++11 has a "shrink_to_fit" function for this behavior.
If you are repeatedly filling and emptying a vector object, and thus you want to to avoid frequent reallocations, perform the emptying by calling the resize member function, which, according to the standard, preserves the capacity of the object. If instead you have finished using a large vector object, and you may not use it again or you are going to use it with substantially fewer elements, you should free the object's memory by calling the swap function on a new empty temporary vector object.

### swap function overload

For every copyable concrete class T which, directly or indirectly, owns some dynamic memory, redefine the appropriate swap functions.
In particular, add to the class public member function having the following signature:
and add the following non-member function in the same namespace that contains the class T:
and, if the class is not a class template, add also the following non-member function in the same file that contains the class T definition:
In the standard library, the swap function is called frequently by many algorithms. Such function has a generic implementation and specialized implementations for various types of the standard library.
If objects of a non-standard class are used in a standard library algorithm that calls swap on them, and the swap function is not overloaded, the generic implementation is used.
The generic implementation of the swap function causes the creation and destruction of a temporary object and the execution of two object assignments. Such operation take much time if applied to objects that own dynamic memory, as such memory is reallocated three times.
The ownership of dynamic memory may be even only indirect. For example, if a member variable is a string or a vector, or is an object that contains a string or vector object, the memory owned by these objects is reallocated every time the object that contains them is copied. Therefore, even in these cases the swap function is to be overloaded.
If the object doesn't own dynamic memory, the copy of the object is much faster, and however it is not noticeably slower than using other techniques, and so no swap overload is needed.
If the class is not copyable or abstract, the swap function must never be called on object of such type, and therefore also in these cases no swap function is to be redefined.
To speed up the function swap, you have to specialize it for your class. There are two possible ways to do that: in the same namespace of the class (that may be the global one) as an overload, or in the namespace std as a specialization of the standard template. It is advisable to define it in both ways, as, first, if it is a class template only the first way is possible, an then some compilers do not accept or accept with a warning a definition only in the first way.
The implementations of such functions must access all the members of the object, and therefore they need to call a member function, that by convention is called again swap, that does the actual work.
Such work consists in swapping all the non-static members of the two objects, typically by calling the swap function on them, without qualifying its namespace.
To put the function std::swap into the current scope, the function must begin with the statement:

# Run-time support

C++ run-time support routines obviously have a significant cost, because otherwise such behavior would have be inlined. Here techniques are presented to avoid the language features that cause an implicit call to costly run-time support routines.

### The typeid operator

Instead of using the typeid operator, use a virtual function.
Such operator may take more time than a virtual function call.

### The dynamic_cast operator

Instead of the dynamic_cast operator, use the typeid operator, or, better, a virtual function call.
Such operator may take a time noticeably longer than a virtual function call, and longer also than the typeid operator.

### Empty exception specification

Use the empty exception specification (that is, append throw to the declaration) for the functions you are sure will never throw exceptions.
In C++11 use noexcept instead.
Some compilers use such information to simplify the bookkeeping needed to handle exceptions.

### The try/catch statement

For every bottleneck, move before the bottleneck the try keywords, and after the bottleneck the matching catch clauses.
In other words, hoist try/catch statements out of bottlenecks.
The execution of a try/catch statement sometimes is free of charge, but other times causes as a slowdown. Avoid the repeated execution of such block inside bottlenecks.

### Floating point vs integer operations

If the target processor does not contain a floating point unit, replace floating point functions, constants and variables with the corresponding integer functions, constants and variables; if the target processor contains only a single precision floating point unit, replace double functions, constants and variables with their float correspondents.
Present processors for desktop or server computers contain dedicated hardware for floating point arithmetic, both at single and at double precision, and therefore such operations are almost as fast as their integer correspondents.
Instead, some processors for embedded systems do not contain dedicated hardware for floating point arithmetic, or contain hardware able to handle only single precision numbers. Therefore, in such systems, the operation that cannot be performed by hardware are emulated by very slow library functions. In such case, it is much more efficient to use integer arithmetic, or, if available in hardware, single precision floating point arithmetic.
To handle fractional numbers by using integer operations, every number is to be meant as multiplied by a scale factor. To do that, every number is multiplied by such factor at input, and is divided by the same factor at output, or vice versa.

### Number to string conversion

Use optimized functions to convert numbers to strings.
The standard functions to convert an integer number to a string or a floating point number to string are rather inefficient. To speed up such operations, use non-standard optimized function, possibly written by yourself.

### Use of cstdio functions

To perform input/output operations, instead of using the C++ streams, use the old C functions, declared in the cstdio header.
C++ I/O primitives have been designed mainly for type safety and for customization rather than for performance, and many library implementation of them turn out to be rather inefficient. In particular, the C language I/O functions fread and fwrite are more efficient than the fstream read and write member functions.
If you have to use C++ streams, use "\n" instead of std::endl since std::endl also flushes the stream.

# Instruction count

Even the language features that generate inlined code may have a significant cost, as such instruction are anyway to be executed. In this section some techniques are presented to decrease the total number of machine instructions that the processor will have to execute to perform a given operation.

### Cases order in switch statement

In switch statements, sort the cases by decreasing probability.
In the guideline "Cases order in switch statement" in section 3.1, it was already suggested to put before the most typical cases, that is those that were presumed to be more probable. As further optimization, you can count, in typical runs, the actual number of times every case is chosen, and sort the cases from the most frequent to the less frequent.

### Template integer parameters

If an integer value is a constant in the application code, but is a variable in library code, make it a template parameter.
Let's assume you are writing the following library function, in which both x and y do not have a known value when the library is developed:
Such function may be called from the following application code, in which x does not have a constant value, but y is the constant 4:
If, when you write the library, you know that the caller will surely pass a constant for the argument y, you can transform your function into the following function template:
Such function may be called from the following application code:
Such a call instantiates automatically the following function:
The latter function is faster than the former function f1, for the following reasons:
* Only one argument is passed to the function (x) instead of two (x and y).
* The multiplication by an integer constant (4) is always faster than a multiplication by an integer variable (y).
* As the constant value (4) is a power of two, the compiler, instead of performing an integer multiplication, performs a bit shift.
In general, the integer template parameters are constants for those who instantiate the template and therefore for the compiler, and constants are handled more efficiently than variables. In addition, some operations involving constants are pre-computed at compilation-time.
If, instead of a normal function, you already have a function template, it is enough to add a further parameter to that template.

### The Curiously Recurring Template Pattern

If you have to write a library abstract base class such that in every algorithm in the application code only one class derived from such base class will be used, use the Curiously Recurring Template Pattern.
Let's assume you are writing the following library base class:
In this class, the function g performs an algorithm that calls the function f as an abstract operation for the algorithm. In design patterns terminology, g is a template method design pattern. The purpose of such class is to allow to write the following application code:
In such a case, it is possible to transform the previous library code into the following:
As a consequence, the application code will become the following:
In such a way, the call to f in the function Base<Derived1>::g is statically bound to the member function Derived1::f, that is the call to such function is no more virtual, and can be inlined.
Though, let's assume you want to add the following definition:
With this technique it wouldn't be possible to define a pointer or a reference to a base class that is common to both Derived1 and Derived2, as such base classes are two unrelated types; as a consequence, this technique is not applicable when you want to allow the application code to define a container of arbitrary objects derived from the class Base.
Other limitations are:
* Base is necessarily an abstract type;
* an object of type Derived1 cannot be converted into an object of type Derived2 or vice versa;
* for every derivation of Base, all the machine code generated for Base is duplicated.

### The Strategy design pattern

If an object that implements the Strategy design pattern (aka Policy) is a constant in every algorithm of the application code, eliminate such an object, make static all its members, and add its class as a template parameter.
Let's assume you are writing the following library code, that implements the Strategy design pattern:
This library code has the purpose to allow the following application code:
In such a case, it's possible to convert the previous library code into the following:
As a consequence, the application code will become the following:
In such a way, the object-strategy is avoided, and the member functions MyStrategy::is_valid and MyStrategy::run are statically bound, that is calls to virtual functions are avoided.
Though, such solution does not allow to choose the strategy at run-time, and of course neither to change it during the object life. In addition, the algorithm code is duplicated for every instantiation of its class.

### Bitwise operators

If you have to perform boolean operations on a set of bits, put those bits in an unsigned int object, and use bitwise operators on it.
The bitwise operators (&, |, ^, <<, and >>) are translated in single fast instructions, and operate on all the bits of a register in a single instruction.

# Constructions and destructions

Often it happens that, while processing an expression, a temporary object is created, which is destroyed at the end of that expression. If such object is of a fundamental type, almost always the compiler succeeds in avoiding its creation, and anyway the creation and destruction of an object of a fundamental type are quite fast. Instead, if the object is of a composite type, its creation and destruction have an unlimited cost, as they cause the call of a constructor and the call of the destructor, that may take any time.
In this section some techniques are presented to avoid that composite temporary objects are created, and therefore that their constructors and destructors are called.

### Functions return value

For non-inlined functions, try to declare a return type for which an object copy moves no more than 8 bytes. If unfeasible, at least construct the result object in the return statement.
While compiling a non-inlined function, the compiler cannot know if the return value will be used, and therefore it must generate it anyway. To generate and assign an object whose copy moves no more than 8 bytes has little or no cost, but to generate and assign more complex object takes time. If the temporary object owns resources, the taken time is enormously bigger, but even without allocations, the taken time grows with the number of machine words used by such object.
However, if the object to return is constructed in the return instructions themselves, therefore without assigning such value to a variable, the language standard guarantees an optimization called Return Value Optimization, that prevents the creation of temporaries.
Some compilers succeeds to avoid creating temporaries, even when the returned object is associated to a local variable (with the so-called Named Return Value Optimization), but this is not generally guaranteed and has anyway some limitations. C++ FAQ
To check whether one of the above optimizations is applied, increment a static container in every constructor, destructor, and in assignment operators of the returned object class. In case no optimization is applied, resort to one of the following alternative techniques:
* Make void the function return type, and add to it a passed-by-reference argument, acting as return value.
* Transform the function into a constructor of the return type, taking the same function arguments.
* Make the function return an object of an auxiliary type, that steals the resources from the return object and passes them to the destination object, without copying their contents.
* Use an expression template, that is an advanced technique, part of the programming paradigm called template metaprogramming.
* If using the C++11 standard, use an rvalue reference.

### Moving declarations outside loops

If a variable is declared in the body of a loop, and an assignment to it costs less than a construction plus a destruction, move that declaration before the loop.
If the variable is declared in the body of a loop, the associated object is constructed and destructed at every iteration, while if it is outside the loop, such object is constructed and destructed only once, but is presumably assigned one more time in the body of the loop.
Though, in many cases, an assignment costs exactly as much as a pair construction+destruction, and thus in such cases there is no gain in moving the declaration outside the loop and adding an assignment inside.

### Assignment operator

In an assignment operator overload (operator=), if you are sure that it will never throw exceptions, copy every member variable, instead of using the copy&swap idiom.
The most efficient way to copy an object is to imitate an appropriate initialization list of a copy constructor, that is, first, to call the analogous member functions of the base classes, and then to copy every member variable, in declaration order.
Unfortunately, such technique is not exception-safe, that is if during this operation an exception is thrown, the destructors of some already constructed sub-objects could never be called. Therefore, if there is the chance that during the copy an exception is thrown, you must use an exception-safe technique, although it won't have optimal performance.
The most elegant exception-safe assignment technique is the one called copy&swap. It is exemplified by the following code, in which C represents the name of the class, and C a member function to define:

### Overload to avoid conversions

To avoid costly conversions, define overloaded functions for the most typical argument types.
Let's assume you wrote the following function:
whose purpose is to allows to write the following code:
But it can be used also by the following code:
And, thanks to the implicit conversion from char* to std::string, it can be used also by the following code:
Both the last two calls to the f function are inefficient, as they create a temporary non-empty std::string object.
To keep the efficiency of the first example call, you have to define also the following function overload:
In general, if a function is called by passing to it an argument of an unexpected type but that can be implicitly converted to an expected type, a temporary of the expected type is created.
To avoid such temporary object, you have to define an overload of the original function that takes an argument of the type of the actual passed object, thus avoiding the need of a conversion.

# Pipeline

The conditional jump machine language instructions (aka branches), may be generated by many C++ language features, among which there are the if-else, for, while, do-while, and switch-case statements, and by boolean and conditional expressions operators.
Modern processors handle branches efficiently only if they can predict them. In case of prediction error, the steps already done by the pipeline on the following instructions are useless and the processor must restart from the branch destination instruction.
The branch prediction is based on the previous iterations on the same instruction. If the branches follow a regular pattern, the prediction are successful.
The best cases are those in which a branch instruction has always the same effect; in such cases, the prediction is almost always correct. The worst case is that in which the branch instruction has an outcome pattern the opposite of the branch prediction behavior. As predictors usually assume reoccurrence of results, this would be a branch that outcome is always the opposite of the previous outcome. In this case the prediction is never correct and the pipeline is always interrupted. Not all processors use such prediction behavior, with some simple ones always assuming no jump will occur. The case where the branch instruction has a random outcome results in the prediction being on average correct half of the times. However random distribution means that actual results will vary from being always right to always wrong in a Gaussian shaped distribution.
In bottlenecks, the hard-to-predict branches should be avoided. If a branch is predicted very badly, even replacing it with a rather slow sequence of instructions may result in a speed up.
In this section, some techniques are presented to replace branches with equivalent instructions.

### Integer interval check

If you have to check whether an integer number i is between two integer numbers min_i and max_i included, and you are sure that min_i <= max_i, use the following expression:
In the given conditions, the above formula is equivalent to the following, more intuitive formula:
The former formula performs two differences and one comparison, while the latter formula performs no difference and two comparisons. For pipelined processors, comparisons are slower than differences, because they imply a branch.
In addition, if min_i is a constant expression with zero value, the two differences disappear.
In particular, to check whether an integer i is a valid index for an array of size elements, that is to perform array bounds checking, use the following expression:
Obviously, if the expressions are already of an unsigned type, conversions are unneeded.

### The binary look-up table

Instead of a conditional expression in which both cases are constants, use a look-up table with two-places.
If you have a statement like the following, where c and d represent constant expressions, and b represents a boolean expression:
that is equivalent to the following code:
try to replace it with the following code, equivalent but perhaps faster:
The conditional expression is compiled into a branch. If such a branch is not well predicted, it takes longer than the lookup-table.
This technique may be applied also to a sequence of conditional expressions. For example, instead of the following code:
that is equivalent to the following code:
try to see if the following code is faster:

### Early address calculation

Try to calculate the value of a pointer or iterator somewhat before when you need to access the referenced object.
For example, in a loop, the following statement:
may be a bit less efficient than the following:
In the first case, the value of the pointer or iterator is calculated just before it is used to access the referenced object, while in the second case it is computed in the previous iteration. In a pipelined processor, in the second case, the increment of the pointer may be performed simultaneously with the access of the referenced object, while in the first case the two operations must be serialized.

# Memory access

When the application accesses main memory, it implicitly uses both the various processor caches and the disk swapping mechanism by the virtual memory manager of the operating system.
Both the processor caches and the virtual memory manager process data block-wise, and therefore the software is faster if the few memory blocks contain the code and the data used by a single command. The principle that the data and the code processed by a command should reside in near regions of memory is called locality of reference.
This principle becomes even more important for performance in multi-threaded applications on multi-core systems, as if several threads running on different cores access the same cache block, the contention causes a performance degradation.
In this section techniques are proposed to optimize usage of the processor caches and of the virtual memory, by incrementing the locality of reference of code and data.

### Nearing the code

Put near in the same compilation unit all the function definitions belonging to the same bottleneck.
In such a way, the machine code generated by compiling such functions will have near addresses, and so greater code locality of reference.
Another positive consequence is that the local static data declared and used by such functions will have near addresses, and so greater data locality of reference.
Though, data used by different threads should be on different cache lines to avoid false sharing (i.e. cache lines bouncing). The recommendation made by Gerber/Bik/Smith/Tian - The Software Optimization Cookbook (page 262) is to keep this type of data spaced by at least 128 bytes apart (which is larger than any L1/2/3 cache line).

### unions

In medium or large arrays or collections, use unions.
unions allow to save memory space in variable type structures, and therefore to make them more compact.
Though, don't use them for small or tiny objects, as there are no significant space gains, and with some compilers the objects put in a union are not kept in processor registers.

### Bit-fields

If a medium or large object contains several integer numbers with a small range, transform them in bit-fields.
Bit-fields decrease the object size.
For example, instead of the following structure:
that takes up 8 bytes, you can define the following structure:
that takes up only (1 + 10 + 10 + 10 = 31 bits, 31 <= 32) 4 bytes.
For another example, instead of the following array:
that takes up 5 bytes, you can define the following structure:
that takes up only (6 + 6 + 6 + 6 + 6 = 30 bits, 30 <= 32) 4 bytes.
Though, there is a performance penalty in packing and unpacking the field. In addition, in the last example, the field can no more be accessed by index.
It should be noted that bit field behavior is not well defined so different compilers will give different results. Bit field struct members are not thread safe due to memory granularity so have undefined behavior when accessed concurrently on multi-processor platforms which can result in hard to detect faults. As such many compilers will attempt to ignore them completely.
This optimization is best used on microcontrollers. As these devices are usually single processor devices there is no problem with concurrent access. They also have very limited memory so cannot afford wasted bits. In addition, many microcontrollers have special instructions designed to improve performance of bit manipulation, eg an instruction to test if a single bit is set within a byte at an offset.

### Template code independent of parameters

If in a class template a non-trivial member function does not depend on any template parameter, define a non-member function having the same body, and replace the original function body with a call to the new function.
Let's assume you wrote the following code:
Try to replace the above code with the following:
For every instantiation of a class template that uses a function of that class template, the whole code of the function is instantiated. If a function in that class template do not depend on any template parameters, at every instantiation the function machine code is duplicated. Such code replication bloats the program.
In a class template or in a function template, a big function could have a large part that do not depend on any template parameters. In such a case, first, factor out such a code portion as a distinct function, and then apply this guideline.

# Faster operations

Some elementary operations, even being conceptually as simple as others, are much faster for the processor. A clever programmer can choose the faster instructions for the job.
Though, every optimizing compiler is already able to choose the fastest instructions for the target processor, and so some techniques are useless with some compilers.
In addition, some techniques may even worsen performance on some processors.
In this section some techniques are presented that may improve performance on some compiler/processor combinations.

### Structure fields order

Arrange the member variables of classes and structures in such a way that the most used variables are in the first 128 bytes, and then sorted from the longest object to the shortest.
If in the following structure the msg member is used only for error messages, while the other members are used for computations:
you can speed up the computation by replacing the structure with the following one:
On some processors, the addressing of a member is more efficient if its distance from the beginning of the structure is less than 128 bytes.
In the first example, to address the d and i fields using a pointer to the beginning of the structure, an offset of at least 400 bytes is required.
Instead, in the second example, containing the same fields in a different order, the offsets to address d and i are of few bytes, and this allows to use more compact instructions.
Now, let's assume you wrote the following structure:
Because of fields alignment, it typically occupies 1 (bool) + 7 (padding) + 8 (double) + 2 (short) + 2 (padding) + 4 (int) = 24 bytes.
The following structure is obtained from the previous one by sorting the fields from the longest to the shortest:
It typically occupies 8 (double) + 4 (int) + 2 (short) + 1 (bool) + 1 (padding) = 16 bytes. The sorting minimized the paddings (or holes) caused by the alignment requirements, and so generates a more compact structure.

### Floating point to integer conversion

Exploit non-standard routines to round floating point numbers to integer numbers.
The C++ language do not provide a primitive operation to round floating point numbers. The simplest technique to convert a floating point number x to the nearest integer number n is the following statement:
Using such a technique, if x is exactly equidistant between two integers, n will be the upper integer (for example, 0.5 generates 1, 1.5 generates 2, -0.5 generates 0, and -1.5 generates -1).
Unfortunately, on some processors (in particular, the Pentium family), such expression is compiled in a very slow machine code. Some processors have specific instructions to round numbers.
In particular, the Pentium family has the instruction fistp, that, used as in the following code, gives much faster, albeit not exactly equivalent, code:
The above code rounds x to the nearest integer, but if x is exactly equidistant between two integers, n will be the nearest even integer (for example, 0.5 generates 0, 1.5 generates 2, -0.5 generates 0, and -1.5 generates -2).
If this result is tolerable or even desired, and you are allowed to use embedded assembly, then use this code. Obviously, it is not portable to other processor families.

### Integer numbers bit twiddling

Twiddle the bits of integer numbers exploiting your knowledge of their representation.
A collection of hacks of this kind is here. Some of these tricks are actually already used by some compilers, others are useful to solve rare problems, others are useful only on some platforms.

### Array cells size

Ensure that the size (resulting from the sizeof operator) of non-large cells of arrays or of vectors be a power of two, and that the size of large cells of arrays or of vectors be not a power of two.
The direct access to an array cell is performed by multiplying the index by the cell size, that is a constant. If the second factor of this multiplication is a power of two, such an operation is much faster, as it is performed as a bit shift. Analogously, in multidimensional arrays, all the sizes, except at most the first one, should be powers of two.
This sizing is obtained by adding unused fields to structures and unused cells to arrays. For example, if every cell is a 3-tuple of float objects, it is enough to add a fourth dummy float object to every cell.
Though, when accessing the cells of a multidimensional array in which the last dimension is an enough large power of two, you can drop into the data cache contention phenomenon (aka data cache conflict), that may slow down the computation by a factor of 10 or more. This phenomenon happens only when the array cells exceed a certain size, that depends on the data cache, but is about 1 to 8 KB. Therefore, in case an algorithm has to process an array whose cells have or could have as size a power of two greater or equal to 1024 bytes, first, you should detect if the data cache contention happens, in such a case you should avoid such phenomenon.
For example, a matrix of 100 x 512 float objects is an array of 100 arrays of 512 floats. Every cell of the first-level array has a size of 512 x 4 = 2048 bytes, and therefore it is at risk of data cache contention.
To detect the contention, it is enough to add an elementary cell (a float) to every last-level array, but keeping to process the same cells than before, and measure whether the processing time decrease substantially (by at least 20%). In such a case, you have to ensure that such improvement be stabilized. For that goal, you can employ one of the following techniques:
* Add one or more unused cells at the end of every last-level array. For example, the array double a[100][1024] could become double a[100][1026], even if the computation will process such an array up to the previous sizes.
* Keep the array sizes, but partition it in rectangular blocks, and process all the cells in one block at a time.

### Prefix vs. Postfix Operators

Prefer prefix operators over postfix operators.
When dealing with primitive types, the prefix and postfix arithmetic operations are likely to have identical performance. With objects, however, postfix operators can cause the object to create a copy of itself to preserve its initial state (to be returned as a result of the operation), as well as causing the side-effect of the operation. Consider the following example:
Because the postfix operators are required to return an unaltered version of the value being incremented (or decremented) — regardless of whether the result is actually being used — they will most likely make a copy. STL iterators (for example) are more efficient when altered with the prefix operators.

### Explicit inlining

If you don't use the compiler options of whole program optimization and to allow the compiler to inline any function, try to move to the header files the functions called in bottlenecks, and declare them inline.
As explained in the guideline "Inlined functions" in section 3.1, every inlined function is faster, but many inlined functions slow down the whole program.
Try to declare inline a couple of functions at a time, as long as you get significant speed improvements (at least 10%) in a single command.

### Operations with powers of two

If you have to choose an integer constant by which you have to multiply or divide often, choose a power of two.
The multiplication, division, and modulo operations between integer numbers are much faster if the second operand is a constant power of two, as in such case they are implemented as bit shifts or bit maskings.

### Integer division by a constant

When you divide an integer (that is known to be positive or zero) by a constant, convert the integer to unsigned.
If s is a signed integer, u is an unsigned integer, and C is a constant integer expression (positive or negative), the operation s / C is slower than u / C, and s % C is slower than u % C. This is most significant when C is a power of two, but in all cases, the sign must be taken into account during division.
The conversion from signed to unsigned, however, is free of charge, as it is only a reinterpretation of the same bits. Therefore, if s is a signed integer that you know to be positive or zero, you can speed up its division using the following (equivalent) expressions: (unsigned)s / C and (unsigned)s % C.

### Processors with reduced data bus

If the data bus of the target processor is smaller than the processor registers, if possible, use integer types not larger than the data bus for all the variables except for function parameters and for the most used local variables.
The types int and unsigned int are the most efficient, after they have been loaded in processor registers. Though, with some processor families, they could not be the most efficient type to access in memory.
For example, there are processors having 16-bit registers, but an 8-bit data bus, and other processors having 32-bit registers, but 16-bit data bus. For processors having the data bus smaller than the internal registers, usually the types int and unsigned int match the size of the registers.
For such systems, loading and storing in memory an int object takes a longer time than that taken by an integer not larger than the data bus.
The function arguments and the most used local variables are usually allocated in registers, and therefore do not cause memory access.

### Rearrange an array of structures as several arrays

Instead of processing a single array of aggregate objects, process in parallel two or more arrays having the same length.
For example, instead of the following code:
the following code may be faster:
Using this rearrangement, "a", "b", and "c" may be processed by array processing instructions that are significantly faster than scalar instructions. This optimization may have null or adverse results on some (simpler) architectures.
Even better is to interleave the arrays:
Remember test everything! And don't optimise prematurely.

# Tools

A list of tools to access the CPU hardware counters:
* OProfile (Linux)
* PAPI (Linux, various Unices)

# Further reading

* Calling conventions for different C++ compilers and operating systems
* Optimizing software in C++: An optimization guide for Windows, Linux and Mac platforms
* "Technical Report on C++ Performance" by Dave Abrahams et. al. 2003
* "Code optimization tips for 8-bit microcontrollers" by Steve Kolokowsky 2009
* "Getting the Least Out of Your C Compiler" by Jakob Engblom 2001 lists "some of the more common mistakes and how to avoid them, ... An important conclusion is that code that is easy for a human to understand is usually also compiler friendly, contrary to hacker tradition."
* Efficient C++: Performance Programming Techniques; Dov Bulka, David Mayhew
* Inside the C++ Object Model; Stanley B. Lippman
* What Every Programmer Should Know About Memory; Drepper, Ulrich
* The Software Optimization Cookbook; Richard Gerber, et al.
* Optimized C++ Proven Techniques for Heightened Performance; Kurt Guntheroth

# GNU Free Documentation License

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* Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice.
* Include an unaltered copy of this License.
* Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
* Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
* For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
* Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
* Delete any section Entitled "Endorsements". Such a section may not be included in the Modified version.
* Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section.
* Preserve any Warranty Disclaimers.
If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.
You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.
You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.
The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

## 5. COMBINING DOCUMENTS

You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.
The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.
In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements".

## 6. COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.
You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

## 7. AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.
If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

## 8. TRANSLATION

Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.
If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

## 9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.
However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.
Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.

## 10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.
Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Document.

## 11. RELICENSING

"Massive Multiauthor Collaboration Site" (or "MMC Site") means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A "Massive Multiauthor Collaboration" (or "MMC") contained in the site means any set of copyrightable works thus published on the MMC site.
"CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.
"Incorporate" means to publish or republish a Document, in whole or in part, as part of another Document.
An MMC is "eligible for relicensing" if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.
The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.

# How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:
    Copyright (c) YEAR YOUR NAME.
    Permission is granted to copy, distribute and/or modify this document
    under the terms of the GNU Free Documentation License, Version 1.3
    or any later version published by the Free Software Foundation;
    with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
    A copy of the license is included in the section entitled "GNU
    Free Documentation License".
If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this:
    with the Invariant Sections being LIST THEIR TITLES, with the
    Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.
If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.
If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.
* ↑ C2: PowerOfPlainText.