Enhancing Z3's Multi-Precision Capabilities for Advanced Mathematical Computations

[yihong1120]

Dear Z3 Maintainers,

I trust this message finds you in good spirits. I am writing to propose an enhancement to the Z3 theorem prover that I believe could significantly benefit users engaged in advanced mathematical computations, particularly those requiring robust multi-precision capabilities.

While Z3 already offers commendable support for multi-precision arithmetic, there is an opportunity to expand its functionality to better cater to complex use cases that demand higher precision and performance. Specifically, I suggest the following enhancements:

1. Integration with GMP: Although Z3 includes its own multi-precision arithmetic, the GNU Multiple Precision Arithmetic Library (GMP) is renowned for its performance and extensive feature set. Offering an option to leverage GMP could improve the efficiency of Z3 in scenarios where computational intensity is paramount.

2. Benchmarking Precision and Performance: Establishing a comprehensive suite of benchmarks to compare the performance of Z3's native multi-precision arithmetic against GMP and other libraries. This would not only provide valuable insights into the current capabilities but also guide future optimisations.

3. Precision Scaling: Implementing a dynamic precision scaling mechanism that adjusts the level of precision in real-time, based on the requirements of the computation at hand. This could enhance the solver's efficiency by using higher precision only when necessary.

4. Documentation and Examples: Expanding the documentation to include guidance on best practices for utilising multi-precision arithmetic within Z3. Additionally, providing examples that demonstrate the application of these practices in real-world scenarios would be immensely beneficial.

I am keen to engage in a dialogue regarding these suggestions and explore how we might collaborate to bring these enhancements to fruition. I believe that by bolstering Z3's multi-precision capabilities, we can open the door to more sophisticated applications and research opportunities.

Thank you for considering my proposal. I eagerly await your thoughts and hope to contribute to the ongoing development of Z3.

Best regards,
yihong1120

[NikolajBjorner]

Take a look at the readme file regarding availability of GMP: https://github.com/z3prover/z3?tab=readme-ov-file#dependencies