⚡️ Speed up method Algorithms.fibonacci by 31%

[codeflash-ai]

📄 31% (0.31x) speedup for Algorithms.fibonacci in code_to_optimize/java/src/main/java/com/example/Algorithms.java

⏱️ Runtime : 5.92 milliseconds → 4.52 milliseconds (best of 5 runs)

📝 Explanation and details

The optimized code achieves a 30% runtime improvement by replacing the exponential-time recursive Fibonacci algorithm with an iterative fast-doubling algorithm that runs in O(log n) time complexity instead of O(2^n).

Key Changes:

1. Algorithm replacement: The naive recursive approach makes exponential function calls (e.g., fibonacci(30) triggers over 2 million calls), while the fast-doubling method uses bit manipulation to traverse only the binary representation of n, requiring just log₂(n) iterations.

2. Elimination of call stack overhead: The recursive version creates deep call stacks with significant overhead for parameter passing and return value management. The iterative approach uses only local variables (a, b, c, d) with no function call overhead.

3. Fast-doubling technique: This algorithm leverages the mathematical property that F(2k) and F(2k+1) can be computed from F(k) and F(k+1) using simple arithmetic. By processing n's bits from most significant to least significant, it "doubles" the index at each step and conditionally adds 1, building up to F(n) efficiently.

4. Cache-friendly computation: Uses only primitive long operations with no object allocations, keeping all data in CPU registers for maximum performance.

Why This Optimization Matters:

The improvement is most dramatic for larger Fibonacci numbers. While both implementations handle small values (n ≤ 1) identically, the exponential growth of recursive calls makes the original version impractical for n > 40, whereas the optimized version handles even n = 90 (near the long overflow limit) in microseconds. The 30% speedup observed suggests the test cases include moderate-sized n values where the logarithmic advantage becomes significant while still being small enough that the recursive version completes in reasonable time.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	✅ 12 Passed
🌀 Generated Regression Tests	🔘 None Found
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	No coverage data found for fibonacci

⚙️ Click to see Existing Unit Tests

To edit these changes git checkout codeflash/optimize-Algorithms.fibonacci-mlbced70 and push.