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Discover the reasons behind the unexpected slowness of gmpy2 in complex exponentiation and how it stacks up against mpmath.
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Why is gmpy2 Slow at Complex Exponentiation Compared to mpmath?

If you are a Python developer working with complex numbers, you might have come across a peculiar issue: the complex exponentiation operator in gmpy2 tends to be slower than its counterpart in mpmath. This observation can be surprising, especially since mpmath is written in Python and typically thought to be slower than libraries implemented in C. In this post, we will explore why gmpy2 experiences this performance issue and provide insights into potential causes and solutions.

Understanding the Performance Discrepancy

The observation was brought to light when a developer compared the exponentiation performance using gmpy2 and mpmath. Here’s how their testing setup looked, yielding some unexpected results:

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

The developer experienced significant performance differences:

gmpy2 took around 87 seconds to compute complex exponentiation for a1 ** a2.

In contrast, mpmath completed the same operation in just 51 seconds.

As can be seen, mpmath was not only faster, but also provided a remarkable performance for simpler operations. Specifically, exponentiation by an integer was executed more than 40% faster in mpmath than in gmpy2. This raised questions about why such a performance gap existed.

Investigating the Core Issues

Library Versions Matter

The tests revealed differences in library versions and configurations. The following versions were in use during testing:

gmpy2 version: 2.0.8 and 2.1.0 beta

The underlying libraries had older versions in the initial tests compared to newer releases in the later tests.

Argument Handling Changes

Significant changes had been made in argument handling between versions. For example:

Performance improvements were noted for operations like mpc ** int (integer exponentiation) in newer versions.

However, mpc ** mpc (complex exponentiation with complex numbers) experienced a slight performance regression.

Dependency on System Configuration

The performance of gmpy2 can also vary based on where it is run (e.g., Windows vs. WSL). Better versions of gmpy2 were noted to be slightly faster on certain setups, which indicates that compiling the library under suitable conditions can yield better performance.

Solutions and Optimization Insights

Upgrade to the Latest Versions: Always ensure that you are using the latest version of gmpy2 and the underlying libraries (GMP, MPFR, MPC), as they may contain crucial optimizations and bug fixes related to performance.

Profile Your Code: Use profiling tools to identify bottlenecks in your code. This will help you understand if the slowness is inherent to gmpy2 or due to how it is being used in your application.

Test in Different Environments: Performance can vary across different systems and libraries. Running your tests in multiple environments might give you a clearer picture of gmpy2's performance characteristics.

Engage with Community Optimizations: Being an open-source library, engaging with the community or maintaining the library can provide insights into upcoming optimizations or even contribute to fixing specific performance issues.

Monitor Updates: Keep an eye on ongoing development for gmpy2, which aims to maintain compatibility with new versions of its dependencies and enhance performance.

In summary, while gmpy2 has its strengths, it's crucial to stay informed about its version and the environment to leverage optimized performance effectively. Continuous improvements are being made to address the performance gaps identified in complex operations.

Conclusion

The performance of gmpy2 in complex exponentiation operations, particularly compared to mpmath, stems from multiple factors, including library versions,