fix: remove allocations in P3 scheme

[haakon-e]

Purpose

This pull request introduces several improvements and refactorings to the P3 microphysics scheme and its related utilities, focusing on code clarity, numerical stability, and performance benchmarking. The most significant changes are grouped below by theme.

P3 Scheme Refactoring and Utility Improvements

• Added the get_bounded_thresholds utility to consistently clamp and sanitize particle size thresholds, and refactored related functions (integral_bounds, get_segments) to use this for more robust interval handling. This improves the reliability of segment and bounds calculations for particle distributions. [1] [2]
• Refactored particle property functions (ice_mass, ice_density, get_∂mass_∂D_coeffs, ∂ice_mass_∂D, ϕᵢ) to accept explicit arguments or state objects rather than variadic arguments, improving type stability and readability. [1] [2] [3] [4]

Numerical Integration and Terminal Velocity

• Improved numerical integration routines by adding input validation (returning zero for invalid bounds) and using unrolled_sum for efficient summation in particle_terminal_velocity, enhancing both correctness and performance. [1] [2] [3] [4]

Consistency and Readability Updates

• Standardized unit conversion factors in ice nucleation routines for clarity (e.g., using 1000 and 1_000_000 instead of scientific notation). [1] [2]
• Various code style improvements in test and benchmark files, including argument formatting and variable naming for clarity and maintainability. [1] [2] [3] [4] [5] [6] [7]

Testing and Benchmarking Enhancements

• Expanded and updated performance benchmarks to cover new and refactored P3 routines, including state construction, distribution parameter calculation, terminal velocities, and ice nucleation/melt processes. Also added type stability checks in test cases. [1] [2] [3]

These changes collectively improve the robustness, maintainability, and test coverage of the P3 microphysics codebase.

[haakon-e]

This change is part of the following stack:

• fix: limiting behavior of 2M and P3 PSDs #617
  • feat: chebyshev-gauss quadrature instead of quadgk #618
    • fix: bulk_liquid_ice_collision_sources issues #619
      • feat: ice terminal velocity function aliases #620
        • fix: remove allocations in P3 scheme #621 ◀

_{Change managed by git-spice.}

[codecov]

Codecov Report

❌ Patch coverage is 94.28571% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 92.79%. Comparing base (37b9712) to head (f834e76).
⚠️ Report is 3 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #621      +/-   ##
==========================================
+ Coverage   91.65%   92.79%   +1.14%     
==========================================
  Files          48       48              
  Lines        1953     1957       +4     
==========================================
+ Hits         1790     1816      +26     
+ Misses        163      141      -22     

Components	Coverage Δ
src	93.98% <94.28%> (+1.19%)	⬆️
ext	69.47% <ø> (ø)

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[haakon-e]

Adding UnrolledUtilities and the unrolled_sum statement is needed for inference on julia 1.10 only. This is a small package with no dependencies, so it should be fine. Further, it is a dependency of ClimaCore, so the addition doesn't matter from the perspective of ClimaAtmos/KiD anyways. If we ever drop support for julia 1.10, then this could potentially be revisited.

[haakon-e]

This arises from fixing the type instability here