[decimal] Use Chudnovsky with binary splitting to calculate pi #95
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This pull request introduces significant improvements to the
BigDecimallibrary by optimizing the calculation of π (pi) for high precision and documenting the performance characteristics of different algorithms. The main changes include replacing Machin's formula with the Chudnovsky algorithm for faster computation, introducing binary splitting for efficiency, and adding internal notes on time complexity and algorithm results.Optimizations for π Calculation:
src/decimojo/bigdecimal/constants.mojo: Replaced Machin's formula with the Chudnovsky algorithm for π calculation, leveraging binary splitting for higher precision and faster computation. Added caching logic to store precomputed values for precision ≤ 1024.src/decimojo/bigdecimal/constants.mojo: Introduced helper functionspi_chudnovsky_binary_split,chudnovsky_split, andcompute_m_k_rationalto implement the Chudnovsky algorithm efficiently.Documentation Updates:
docs/internal_notes.md: Added a section describing time complexity and performance results for π calculation using Machin's formula and the Chudnovsky algorithm.Code Cleanup:
src/decimojo/bigdecimal/constants.mojo: Removed redundant code related to Machin's formula for π, including unused variables and outdated comments.