Скачать или смотреть Understanding Why % is Not Equal to pow() in Python

Discover why the `%` operator and `pow()` function yield different results in Python when calculating large integers, and learn how to resolve the issue.
---
This video is based on the question https://stackoverflow.com/q/67427384/ asked by the user 'Cobra_Fast' ( https://stackoverflow.com/u/522479/ ) and on the answer https://stackoverflow.com/a/67427396/ provided by the user 'Charles Dupont' ( https://stackoverflow.com/u/14185009/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: Why is ** % not equal to pow()?

Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l...
The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license.

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
Why is % Not Equal to pow() in Python?

When working with large integers in Python, you might run into some unexpected behavior between common arithmetic operators and functions. One such instance is when using the modulo operator (%) alongside the power function (pow()). Let's explore this problem to understand why they can yield different results, especially when you're operating on large numbers.

The Problem: Discrepancy Between % and pow()

You may have encountered a scenario where you had large integers and you tried to compute them using the modulo operator with exponentiation. For instance, consider the following code:

[[See Video to Reveal this Text or Code Snippet]]

When you run this code, you may encounter an AssertionError, indicating that result and a * pow(b, c, d) are not the same. This raises an important question: Why are these two calculations different and which one is correct?

Understanding the Discrepancy

The main reason for the discrepancy comes down to operator precedence and the specific calculations that are being performed. In the original implementation, the expression result = a * (b ** c) % d is executed in a particular order:

Calculate b ** c (power).

Multiply the result by a.

Finally apply the modulo d.

However, note that this sequence might not yield the same result as using the pow() function, which can handle modular arithmetic more efficiently.

The Solution: Adding Parentheses

To resolve the discrepancy, you need to clarify the order of operations in your calculation. Specifically, you should first compute the exponentiation and then apply the modulo before performing the multiplication with a. Here’s the corrected code implementation:

[[See Video to Reveal this Text or Code Snippet]]

By adding parentheses to ensure that ((b ** c) % d) is evaluated first, you will align the results of both operations, and the assertion will hold true.

Conclusion

When dealing with operations on large integers in Python, always be mindful of operator precedence and the importance of parentheses for clarity and correctness. The pow() function can handle modular operations in a way that might differ from what you get using the % operator directly with large numbers. With this understanding and the correct parenthesis placement, you can ensure that your calculations yield the expected results every time.

By taking the time to analyze how Python evaluates expressions, you can avoid common pitfalls and write more reliable code. Happy coding!