[WIP] Start implementation of optimized binary search method

[Copilot]

Cloud agent has begun work on Start implementation and will update this pull request as work progresses.

Original prompt

Start implementation

The user has attached the following file paths as relevant context:

• AGENTS.md

[Chronological Review: The conversation began with the user requesting a more efficient method for performing binary search in their Fortran code, specifically in relation to the function #sym:GetReionizationOptDepth. The user then suggested avoiding Romberg integration entirely, proposing to leverage the monotonic nature of the integral being matched. The user subsequently requested to start the implementation of this new approach.]

[Intent Mapping:

1. "This does binary search, where each #sym:GetReionizationOptDepth also does binary search. Smarter way to do this?" - User is seeking a more efficient binary search method.
2. "No smart method using the factor that trying to match the value of an integral? (which must be monotonic here), e.g. skipping romberg entirely?" - User is suggesting an alternative approach to avoid Romberg integration.
3. "Start implementation" - User is ready to begin coding the proposed solution.]

[Technical Inventory:

• Fortran: The programming language being used for the implementation.
• Binary Search: The algorithm being optimized.
• Romberg Integration: A numerical integration method that the user wishes to avoid.]

[Code Archaeology:

• Files discussed:
  • reionization.f90: Related to the user's binary search implementation.
  • recfast.f90: Another file mentioned in the context of the user's requests.
  • subroutines.f90: The current file the user is working on.]

[Progress Assessment:

• Completed Tasks: User has articulated the need for a more efficient binary search method and proposed avoiding Romberg integration.
• Partially Complete Work: The implementation of the new method has been initiated but not yet completed.]

[Context Validation: All necessary context for continuing the work on the binary search optimization is captured, including the user's intent to avoid Romberg integration and the readiness to start implementation.]

[Recent Commands Analysis:

• Last Agent Commands: The user requested to "Start implementation."
• Tool Results Summary: No specific tool results were generated from this command as it was a directive to begin coding.
• Pre-Summary State: The agent was actively preparing to assist the user in implementing the new binary search method when the token budget was exceeded.
• Operation Context: The commands executed were directly related to the user's goal of optimizing the binary search process in their Fortran code.]

1. Conversation Overview: - Primary Objectives: - "This does binary search, where each #sym:GetReionizationOptDepth also does binary search. Smarter way to do this?" - "No smart method using the factor that trying to match the value of an integral? (which must be monotonic here), e.g. skipping romberg entirely?" - "Start implementation" - Session Context: The user is focused on optimizing binary search in their Fortran code, specifically avoiding Romberg integration. - User Intent Evolution: The user moved from identifying a problem with the current implementation to proposing a new approach and expressing readiness to implement it.

2. Technical Foundation:

• Fortran: The programming language used for the project.
• Binary Search: The algorithm being optimized for efficiency.
• Romberg Integration: A numerical method that the user wishes to bypass.

3. Codebase Status:

• File Name: subroutines.f90
  • Purpose: Contains subroutines relevant to the user's binary search implementation.
  • Current State: User is preparing to implement a new binary search method.
  • Key Code Segments: Not specified yet as implementation has not started.
  • Dependencies: Related to other files like reionization.f90 and recfast.f90.

4. Problem Resolution:

• Issues Encountered: Inefficiencies in the current binary search implementation.
• Solutions Implemented: User has proposed a new method to optimize the search process.
• Debugging Context: No ongoing troubleshooting mentioned; focus is on implementation.
• Lessons Learned: The user recognizes the monotonic nature of the integral as a factor for optimization.

5. Progress Tracking:

• Completed Tasks: User has articulated the need for optimization and proposed a new method.
• Partially Complete Work: Implementation of the new method is pending.
• Validated Outcomes: No features confirmed working yet as implementation has not begun.

6. Active Work State:

• Current Focus: User is ready to implement a new binary search method.
• Recent Context: User has expressed a desire to start coding the proposed solution.
• Working Code: No specific code snippets discussed recently.
• Immediate Context: User is focused on implementing a more efficient binary search method.

7. Recent Operations:

• Last Agent Commands: "Start implementation"
• Tool Results Summary: No specific results as this was a directive to begin coding.
• Pre-Summary State: The ag...

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