# Product Requirements Document (PRD) — MemoizedFibonacci

## Revision History

| Version | Date | Author | Description |
| :--- | :--- | :--- | :--- |
| 1.0 | 2026-06-22 | Antigravity Orchestrator | Initial draft for MemoizedFibonacci feature. |

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## 1. Vision & Objectives

* **Project Summary:** The `MemoizedFibonacci` feature provides a highly optimized, high-performance utility class/module for calculating Fibonacci sequences. It leverages an advanced caching (memoization) mechanism to avoid the exponential time complexity $O(2^n)$ associated with naive recursive methods, turning sequence generation into a linear time $O(n)$ or constant-time $O(1)$ operation for subsequent lookups.
* **Problem Statement:** Standard recursive calculations of Fibonacci numbers quickly exhaust CPU resources and crash due to call stack size limits or integer overflows when $n \ge 79$ in standard floating-point representation. Naive memory caches can also grow indefinitely, leading to memory leaks in server environments.
* **Target Audience:** Core application developers, backend engineers running mathematical modeling services, and background agents requiring sequence calculations.

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## 2. Core Principles & Philosophy

* **Performance & Scalability:** Constant lookups $O(1)$ for cached values, linear complexity $O(n)$ for first-time calculations.
* **Robustness & Accuracy:** Complete support for `BigInt` calculations to prevent integer overflow beyond JS safe limit ($n > 78$).
* **Memory Safety & Self-Regulation:** Integrated Least Recently Used (LRU) cache eviction strategy to guarantee a fixed maximum memory footprint.
* **Non-Blocking Operation:** Heavy calculations ($n \ge 100,000$) must run asynchronously (chunked loops or offloaded execution) to prevent thread/event-loop blockage.

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## 3. Scope & Feature List

### In Scope
* **Multiple Calculation Modes:** Synchronous calculations for small inputs; asynchronous (non-blocking) computation for larger values.
* **Flexible Precision:** Standard JS numbers for fast calculations ($n \le 78$) and `BigInt` for arbitrarily large numbers.
* **LRU Caching Strategy:** A bounded in-memory cache that automatically evicts least recently accessed Fibonacci numbers when the maximum cache capacity is reached.
* **Cache Metrics:** Reporting of cache metrics such as hit rate, miss rate, current size, and eviction count.
* **Resource Guardrails:** Hard limits on inputs to prevent CPU exhaustion.

### Out of Scope
* **Negative/Fractional Fibonacci:** No support for negative numbers or fractional inputs (standard integer sequence only).
* **Distributed Cache integration:** No built-in Redis/Memcached integration (limited to localized, bounded memory cache with extensible hooks).

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## 4. Key Performance Indicators (KPIs)

* **Execution Time (Cached):** Sub-microsecond response time for any cached value.
* **Execution Time (Uncached):** Linear scaling $O(n)$. Computing $F(10000)$ uncached must complete in under 5 milliseconds.
* **Call Stack Safety:** Zero recursion-based Call Stack Size Exceeded errors.
* **Memory Limit:** Strict enforcement of maximum cache entries (e.g. defaults to 1,000 values), keeping peak memory consumption under 25MB even for large BigInts.

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## 5. Anti-Patterns (What NOT to do)
* Do not use recursive calls without tail call optimization or loop conversion. Recursion is forbidden for calculations.
* Do not store calculated BigInt values as standard floats since precision is lost.
* Do not allow the cache size to grow indefinitely (bounded cache is mandatory).