The Associativity of Floating-Point Arithmetic
Floating-point arithmetic is widely employed in scientific computing, yet a peculiar question arises: Is it associative for addition and multiplication? This seemingly simple query harbors hidden complexities.
In the realm of floating-point addition, associativity is not always guaranteed. A striking example is the following code:
cout << ((0.7 + 0.2 + 0.1) == 1) << endl; //output is 0 cout << ((0.7 + 0.1 + 0.2) == 1) << endl; //output is 1
To our astonishment, these two statements produce different results. Why is this so?
The explanation lies in the limitations of floating-point representation. Floating-point numbers are stored as an approximation of the actual value, introducing a degree of imprecision. When adding multiple floating-point values, the order of operations matters due to accumulated errors and rounding.
As the referenced standard paper, "What Every Computer Scientist Should Know about Floating Point Arithmetic," aptly states:
"Due to roundoff errors, the associative laws of algebra do not necessarily hold for floating-point numbers."
The above is the detailed content of Is Floating-Point Arithmetic Associative?. For more information, please follow other related articles on the PHP Chinese website!

Hot AI Tools

Undress AI Tool
Undress images for free

Undresser.AI Undress
AI-powered app for creating realistic nude photos

AI Clothes Remover
Online AI tool for removing clothes from photos.

Clothoff.io
AI clothes remover

Video Face Swap
Swap faces in any video effortlessly with our completely free AI face swap tool!

Hot Article

Hot Tools

Notepad++7.3.1
Easy-to-use and free code editor

SublimeText3 Chinese version
Chinese version, very easy to use

Zend Studio 13.0.1
Powerful PHP integrated development environment

Dreamweaver CS6
Visual web development tools

SublimeText3 Mac version
God-level code editing software (SublimeText3)

Hot Topics

Yes, function overloading is a polymorphic form in C, specifically compile-time polymorphism. 1. Function overload allows multiple functions with the same name but different parameter lists. 2. The compiler decides which function to call at compile time based on the provided parameters. 3. Unlike runtime polymorphism, function overloading has no extra overhead at runtime, and is simple to implement but less flexible.

C has two main polymorphic types: compile-time polymorphism and run-time polymorphism. 1. Compilation-time polymorphism is implemented through function overloading and templates, providing high efficiency but may lead to code bloating. 2. Runtime polymorphism is implemented through virtual functions and inheritance, providing flexibility but performance overhead.

Yes, polymorphisms in C are very useful. 1) It provides flexibility to allow easy addition of new types; 2) promotes code reuse and reduces duplication; 3) simplifies maintenance, making the code easier to expand and adapt to changes. Despite performance and memory management challenges, its advantages are particularly significant in complex systems.

C destructorscanleadtoseveralcommonerrors.Toavoidthem:1)Preventdoubledeletionbysettingpointerstonullptrorusingsmartpointers.2)Handleexceptionsindestructorsbycatchingandloggingthem.3)Usevirtualdestructorsinbaseclassesforproperpolymorphicdestruction.4

Polymorphisms in C are divided into runtime polymorphisms and compile-time polymorphisms. 1. Runtime polymorphism is implemented through virtual functions, allowing the correct method to be called dynamically at runtime. 2. Compilation-time polymorphism is implemented through function overloading and templates, providing higher performance and flexibility.

People who study Python transfer to C The most direct confusion is: Why can't you write like Python? Because C, although the syntax is more complex, provides underlying control capabilities and performance advantages. 1. In terms of syntax structure, C uses curly braces {} instead of indentation to organize code blocks, and variable types must be explicitly declared; 2. In terms of type system and memory management, C does not have an automatic garbage collection mechanism, and needs to manually manage memory and pay attention to releasing resources. RAII technology can assist resource management; 3. In functions and class definitions, C needs to explicitly access modifiers, constructors and destructors, and supports advanced functions such as operator overloading; 4. In terms of standard libraries, STL provides powerful containers and algorithms, but needs to adapt to generic programming ideas; 5

C polymorphismincludescompile-time,runtime,andtemplatepolymorphism.1)Compile-timepolymorphismusesfunctionandoperatoroverloadingforefficiency.2)Runtimepolymorphismemploysvirtualfunctionsforflexibility.3)Templatepolymorphismenablesgenericprogrammingfo

C polymorphismisuniqueduetoitscombinationofcompile-timeandruntimepolymorphism,allowingforbothefficiencyandflexibility.Toharnessitspowerstylishly:1)Usesmartpointerslikestd::unique_ptrformemorymanagement,2)Ensurebaseclasseshavevirtualdestructors,3)Emp
