Why Does Double Precision Appear to Have More Decimal Places Than Its Advertised 15?-C++-php.cn

Home

Backend Development

C++

Why Does Double Precision Appear to Have More Decimal Places Than Its Advertised 15?

Patricia Arquette

Dec 06, 2024 pm 08:40 PM

Why Does Double Precision Appear to Have More Decimal Places Than Its Advertised 15?

Double Precision and Decimal Place Accuracy

In computer programming, the double precision data type is often assumed to have an approximate precision of 15 decimal places. However, certain number representations, such as 1.0/7.0, seem to have more precision when represented internally within the variable. This article will explore why this occurs and why the precision is often described as around 15 decimal places.

Internal Representation

An IEEE double has 53 significant bits, approximately equaling 15.95 decimal digits. To account for rounding, the implementation sets the precision (DBL_DIG) to 15. This provides nearly an extra decimal digit of precision beyond what's implied by DBL_DIG.

Output Precision

When displaying a double, compilers usually round the value based on the precision. For example, 1.0/7.0, when displayed with "%.17g," has 17 digit accuracy. However, if "%.64g" is used, no significant digits appear beyond the expected 15-digit precision.

Conclusion

Double precision numbers have an internal representation that allows for around 15.95 decimal digits of precision. However, due to rounding, the displayed precision is typically set to 15 decimal places. This explanation helps clarify why certain exact numbers, like 1.0/7.0, appear to have more precision internally but still conform to the estimated 15-digit precision when displayed.

The above is the detailed content of Why Does Double Precision Appear to Have More Decimal Places Than Its Advertised 15?. For more information, please follow other related articles on the PHP Chinese website!

Statement

The content of this article is voluntarily contributed by netizens, and the copyright belongs to the original author. This site does not assume corresponding legal responsibility. If you find any content suspected of plagiarism or infringement, please contact admin@php.cn

C# vs. C : History, Evolution, and Future ProspectsApr 19, 2025 am 12:07 AM

The history and evolution of C# and C are unique, and the future prospects are also different. 1.C was invented by BjarneStroustrup in 1983 to introduce object-oriented programming into the C language. Its evolution process includes multiple standardizations, such as C 11 introducing auto keywords and lambda expressions, C 20 introducing concepts and coroutines, and will focus on performance and system-level programming in the future. 2.C# was released by Microsoft in 2000. Combining the advantages of C and Java, its evolution focuses on simplicity and productivity. For example, C#2.0 introduced generics and C#5.0 introduced asynchronous programming, which will focus on developers' productivity and cloud computing in the future.

C# vs. C : Learning Curves and Developer ExperienceApr 18, 2025 am 12:13 AM

There are significant differences in the learning curves of C# and C and developer experience. 1) The learning curve of C# is relatively flat and is suitable for rapid development and enterprise-level applications. 2) The learning curve of C is steep and is suitable for high-performance and low-level control scenarios.

C# vs. C : Object-Oriented Programming and FeaturesApr 17, 2025 am 12:02 AM

There are significant differences in how C# and C implement and features in object-oriented programming (OOP). 1) The class definition and syntax of C# are more concise and support advanced features such as LINQ. 2) C provides finer granular control, suitable for system programming and high performance needs. Both have their own advantages, and the choice should be based on the specific application scenario.

From XML to C : Data Transformation and ManipulationApr 16, 2025 am 12:08 AM

Converting from XML to C and performing data operations can be achieved through the following steps: 1) parsing XML files using tinyxml2 library, 2) mapping data into C's data structure, 3) using C standard library such as std::vector for data operations. Through these steps, data converted from XML can be processed and manipulated efficiently.

C# vs. C : Memory Management and Garbage CollectionApr 15, 2025 am 12:16 AM

C# uses automatic garbage collection mechanism, while C uses manual memory management. 1. C#'s garbage collector automatically manages memory to reduce the risk of memory leakage, but may lead to performance degradation. 2.C provides flexible memory control, suitable for applications that require fine management, but should be handled with caution to avoid memory leakage.

Beyond the Hype: Assessing the Relevance of C TodayApr 14, 2025 am 12:01 AM

C still has important relevance in modern programming. 1) High performance and direct hardware operation capabilities make it the first choice in the fields of game development, embedded systems and high-performance computing. 2) Rich programming paradigms and modern features such as smart pointers and template programming enhance its flexibility and efficiency. Although the learning curve is steep, its powerful capabilities make it still important in today's programming ecosystem.

The C Community: Resources, Support, and DevelopmentApr 13, 2025 am 12:01 AM

C Learners and developers can get resources and support from StackOverflow, Reddit's r/cpp community, Coursera and edX courses, open source projects on GitHub, professional consulting services, and CppCon. 1. StackOverflow provides answers to technical questions; 2. Reddit's r/cpp community shares the latest news; 3. Coursera and edX provide formal C courses; 4. Open source projects on GitHub such as LLVM and Boost improve skills; 5. Professional consulting services such as JetBrains and Perforce provide technical support; 6. CppCon and other conferences help careers

C# vs. C : Where Each Language ExcelsApr 12, 2025 am 12:08 AM

C# is suitable for projects that require high development efficiency and cross-platform support, while C is suitable for applications that require high performance and underlying control. 1) C# simplifies development, provides garbage collection and rich class libraries, suitable for enterprise-level applications. 2)C allows direct memory operation, suitable for game development and high-performance computing.

See all articles