In this post, we explore how low‑level implementation details—like loop ordering and data layout—can dramatically change performance on real hardware, even when the algorithmic complexity remains the same. Using a cycle‑accurate simulator, we compare three variants of 64 × 64 matrix multiplication (ijk, ikj, and blocked) under different cache configurations, then dive into pointer‑chasing microbenchmarks to illustrate the effects of spatial locality, compulsory/capacity/conflict misses, and how data structures like linked lists fare in practice.
All data and graphs are available here: https://docs.google.com/spreadsheets/d/1GkAadkYI23Ly6zkF_IDtUQqkVuRqSxlpfwma6S_5OrM/edit?gid=504022095#gid=504022095.
1. Matrix Multiplication Benchmarks
1.1. Cache‑Disabled Performance
We first ran each multiply variant with the simulator’s cache turned off (cycle limit = 8 M). The cycle counts:
Variant Cycles Relative Rank
ikj 6,349,534 Fastest
ijk 6,611,614 Middle
blocked 7,273,233 Slowest
The **ikj **loop ordering outperforms the others because it has only three nested loops and it visits memory in strides that incur less loop‑overhead. The blocked version incurs extra overhead from six nested loops—necessary for partitioning the matrices into 8×8 subblocks—but without a cache, this bookkeeping dominates runtime.
1.2. Cache‑Enabled Performance
Next, we enabled a realistic cache model ([A=4, B=32 bytes, C=512 bytes, d=100 cycles]) and increased the cycle limit to 40 M:
Variant Cycles New Rank
blocked 16,150,761 Fastest
ikj 19,832,938 Middle
ijk 36,283,399 Slowest
Now, blocking shines: each 8×8 chunk fits in the cache, letting us reuse data before eviction. The ikj variant remains competitive due to row‑major, stride‑1 accesses on both B and C, while ijk suffers from poor spatial locality on B, triggering frequent 100‑cycle DRAM penalties.
**2. Finding the Most Inefficient Configuration
**By fixing [C=512 B, d=100 cycles] and sweeping associativity 𝐴 and block size 𝐵, we identified that the worst performance occurs at A=1, B=512—a direct‑mapped, single‑line cache. Under this setup, every access to a new block evicts the only cache line, resulting in near‑constant misses:
gemm_block: 85,130,199 cycles
gemm_ijk: 84,468,580 cycles
gemm_ikj: 84,206,500 cycles
As block size increases, the number of cache sets decreases, causing even more evictions and a linear rise in cycle count (see graph below).
3. Pointer‑Chasing Microbenchmarks
3.1. Setup
We compared two initialization patterns for pointer arrays of size
2^𝑛
Fast init: Sequential chain (0→1→2→…→0), maximizing spatial locality
Slow init: Strided chain (stride = 128 elements), causing conflict and capacity misses
Using [C=512 B, d=10 cycles], we varied
𝑛∈[6,18] and recorded cycles and miss rates for both.
3.2. Slowdown Curve
The slowdown (slow cycles / fast cycles) remains ≈1 until n=7, then spikes to ≈3 at n=8 and plateaus thereafter:
n=8 is the tipping point: each pointer chase jumps by 1024 bytes, twice the cache block size (512 B), so every access misses.
Beyond n=8, the cache is thrashing on the slow init, while the fast init still benefits from prefetching entire cache lines.
3.3. Miss‑Type Analysis
Fast init: Mostly compulsory misses on first touches; reuse in cache avoids further misses.
Slow init: Suffers from conflict (direct‑mapped evictions) and capacity misses once the working set exceeds the single cache line.
4. Practical Takeaways for Data Structures
Although Big‑O treats arrays and linked lists both as O(n) for traversal, real‑world performance differs drastically:
- Array Lists: Contiguous memory → Exploitable spatial locality → Few misses → High bandwidth
- Linked Lists: Pointer hops → Random accesses → Cache thrashing → Latency‑bound
Similarly, tree or graph traversals can incur massive penalties if nodes are scattered in memory. Thus, memory layout matters almost as much as algorithmic steps.
Conclusion
These experiments highlight that loop ordering, blocking, and pointer patterns can swing performance by orders of magnitude on real machines. Understanding cache behavior—miss types, associativity, block sizes—is crucial when optimizing high‑performance code. By combining simulation data with graph‑driven insights, we gain a deeper appreciation for why certain algorithms beat others in practice, regardless of identical Big‑O footprints
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