⚡️ Speed up method Algorithms.fibonacci by 84%

[codeflash-ai]

📄 84% (0.84x) speedup for Algorithms.fibonacci in code_to_optimize/java/src/main/java/com/example/Algorithms.java

⏱️ Runtime : 34.3 milliseconds → 18.6 milliseconds (best of 8 runs)

📝 Explanation and details

Runtime improvement (primary): The optimized version reduces the measured runtime from 34.3 ms to 18.6 ms (reported "84%" speedup). The main benefit is a much lower execution time for computing Fibonacci numbers.

What changed (specific optimizations):

• Replaced the naive recursive Fibonacci (exponential time, many repeated calls) with an iterative fast-doubling algorithm.
• Implemented the fast-doubling formulas:
  • c = F(2k) = F(k) * (2*F(k+1) - F(k))
  • d = F(2k+1) = F(k)^2 + F(k+1)^2
    and used them in a bitwise loop that processes bits of n from most-significant to least-significant.
• Used Integer.numberOfLeadingZeros to find the highest significant bit and a simple for-loop over bits (no recursion or extra allocations).
• Kept arithmetic in primitive long operations (shifts, multiplies, adds) and avoided function call overhead.

Why this is faster (how it reduces runtime):

• Algorithmic complexity: naive recursion is O(φ^n) (exponential) due to repeated subcomputations. Fast doubling computes Fibonacci in O(log n) steps. Changing complexity from exponential to logarithmic yields massive savings for all but the smallest n.
• Eliminates recursion and repeated work: recursion creates many stack frames and repeated recomputation; the iterative fast-doubling does each step once.
• Lower overhead per step: the optimized code uses a tight loop with a few integer multiplications and additions per bit, which is far cheaper than millions of method calls and the associated control-flow overhead.
• Bitwise iteration: scanning only the needed bits (highestBit downwards) means the loop does ~log2(n) iterations rather than n or worse; Integer.numberOfLeadingZeros is a cheap native operation to find that range.
• Better CPU locality and fewer allocations: no allocation or deep stacks, so better cache and lower GC pressure.

Key behavior and dependency changes:

• Behavior (return values and overflow semantics) is preserved for non-negative n — n <= 1 still returns n, result type remains long. No external dependencies were introduced.
• Space usage improved from O(n) recursion depth (or large implicit stack during recursion) to O(1) additional space.

Impact on workloads / hot paths:

• This is a win in any code path that computes Fibonacci for moderate-to-large n or does many calls (e.g., in loops, services, or batch jobs). If this function sits in a hot path, the O(log n) vs exponential improvement compounds significantly across many calls.
• For very small n (0 or 1) the difference is negligible; the optimized version still has minimal overhead and remains appropriate.
• Because the optimized code uses only primitive ops, it plays well in tight loops and concurrent contexts where reducing per-call overhead is important.

Test-case suitability (based on observed runtimes):

• Big wins for test cases with larger n (where recursion cost explodes).
• Repeated or batched calls to fibonacci(n) show much larger end-to-end gains.
• No functional tests were required to change; correctness for n <= 1 and typical positive n remains the same.

Summary: The main reason the optimized code was accepted is a clear runtime benefit — it switches from an exponential, recursion-heavy implementation to a fast-doubling iterative algorithm that runs in O(log n) time and O(1) space. That structural change is the source of the observed ~84% speedup and will reduce CPU time dramatically for realistic inputs and hot-path usage.

✅ Correctness verification report:

Test	Status
⚙️ Existing Unit Tests	✅ 16 Passed
🌀 Generated Regression Tests	🔘 None Found
⏪ Replay Tests	🔘 None Found
🔎 Concolic Coverage Tests	🔘 None Found
📊 Tests Coverage	Coverage data not available

⚙️ Click to see Existing Unit Tests

To edit these changes git checkout codeflash/optimize-Algorithms.fibonacci-ml15qwne and push.