Why Does Double-Precision Arithmetic Sometimes Show More Than 15 Decimal Places of Precision?-C++-php.cn

Home

Backend Development

C++

Why Does Double-Precision Arithmetic Sometimes Show More Than 15 Decimal Places of Precision?

Barbara Streisand

Nov 30, 2024 pm 07:49 PM

Why Does Double-Precision Arithmetic Sometimes Show More Than 15 Decimal Places of Precision?

Double Precision: Understanding the Extended Precision

When working with double-precision data types, it is commonly understood that the approximate precision is limited to 15 decimal places. However, certain types of numbers, such as 1.0/7.0, may display a precision of 17 decimal places when internally stored as a double.

This anomaly is attributable to the inherent design of the IEEE double data representation. Double-precision values have 53 significant bits, providing approximately 15.95 decimal digits of precision. However, the C library rounds this value down to 15, resulting in a theoretical precision of 15 decimal places. In reality, the value of DBL_DIG is set to 15 rather than 16 due to this rounding.

The significance of this extended precision is further elaborated using the nextafter() function. This function calculates the nearest representable number to a given value. When examining the value of 1.0/7.0 using this function, the output reveals three consecutive values with differing last digits: 0.14285714285714282, 0.14285714285714285, and 0.14285714285714288.

The precise value of the last displayed digit is determined by the rounding operation performed by the compiler. In this case, the digit changes by 3 with each step, indicating that the precision is approximately 16 decimal digits. Thus, while the theoretical precision of a double is 15 decimal places, the extended precision of nearly 16 digits provides greater accuracy for certain types of calculations.

The above is the detailed content of Why Does Double-Precision Arithmetic Sometimes Show More Than 15 Decimal Places of Precision?. 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

How does the C Standard Template Library (STL) work?Mar 12, 2025 pm 04:50 PM

This article explains the C Standard Template Library (STL), focusing on its core components: containers, iterators, algorithms, and functors. It details how these interact to enable generic programming, improving code efficiency and readability t

How do I use algorithms from the STL (sort, find, transform, etc.) efficiently?Mar 12, 2025 pm 04:52 PM

This article details efficient STL algorithm usage in C . It emphasizes data structure choice (vectors vs. lists), algorithm complexity analysis (e.g., std::sort vs. std::partial_sort), iterator usage, and parallel execution. Common pitfalls like

How do I handle exceptions effectively in C ?Mar 12, 2025 pm 04:56 PM

This article details effective exception handling in C , covering try, catch, and throw mechanics. It emphasizes best practices like RAII, avoiding unnecessary catch blocks, and logging exceptions for robust code. The article also addresses perf

How do I use ranges in C 20 for more expressive data manipulation?Mar 17, 2025 pm 12:58 PM

C 20 ranges enhance data manipulation with expressiveness, composability, and efficiency. They simplify complex transformations and integrate into existing codebases for better performance and maintainability.

How do I use move semantics in C to improve performance?Mar 18, 2025 pm 03:27 PM

The article discusses using move semantics in C to enhance performance by avoiding unnecessary copying. It covers implementing move constructors and assignment operators, using std::move, and identifies key scenarios and pitfalls for effective appl

How does dynamic dispatch work in C and how does it affect performance?Mar 17, 2025 pm 01:08 PM

The article discusses dynamic dispatch in C , its performance costs, and optimization strategies. It highlights scenarios where dynamic dispatch impacts performance and compares it with static dispatch, emphasizing trade-offs between performance and

How do I use rvalue references effectively in C ?Mar 18, 2025 pm 03:29 PM

Article discusses effective use of rvalue references in C for move semantics, perfect forwarding, and resource management, highlighting best practices and performance improvements.(159 characters)

How does C 's memory management work, including new, delete, and smart pointers?Mar 17, 2025 pm 01:04 PM

C memory management uses new, delete, and smart pointers. The article discusses manual vs. automated management and how smart pointers prevent memory leaks.

See all articles