117: Chapter 117 The Ultimate Weapon

The second diagram was the toolchain diagram of MPS-Kernel v0.2.

The game between software and underlying microkernels officially began in the fifth year of the Wasteland.

Jiang Lin did not touch sort5 again.

That problem had already been demonstrated in Chen Qiming's office.

The stunning half-hour in the office only solved the most basic question in the academic world: "Can this path work in theory?"

What the ninth year of the Wasteland had to solve was: "Can this system truly be scaled up?"

Reality was always relentless.

The first version of the attempted scalable searcher met with a grand, total collapse in the sixth year.

The reason for the system's collapse was neither that the zero-one validator's proof speed was too slow, nor that the hardware cost model he built was inaccurate enough.

Rather, before the candidate instructions even had time to queue up to enter the validator, the frontend generator had already expanded the state space to a black-hole level that a workstation's memory simply could not bear due to combinatorial explosion.

sort8 could barely finish running by squeezing the I/O of the swap file.

But once it touched median9, the state tree began to distort and deform.

When he tried to expand a top-k small kernel, even with added constraints, the garbage candidate code spit out by the generator completely filled several terabyte-level enterprise hard drives within a few hours, pierced the swap partition, caused the logging system to report errors, and ultimately killed the process via the OOM killer, freezing the workstation in a continuous I/O avalanche.

This failure not only did not make Jiang Lin depressed, but instead excited him.

Pei Li's judgment was precise.

What truly stood in front of MPS-Kernel was not a certain obscure piece of code, but the unstoppable laws of mathematics.

State space explosion.

In the eighth year, Jiang Lin decisively pressed the delete key in the code base, erasing the traditional old route of brute-force exhaustive enumeration of instruction sequences.

The core object of the search was changed by him from specific code to abstract semantic equivalence classes.

He no longer let the generator act like a fool enumerating every possible register allocation or instruction order.

Instead, he introduced equivalence graphs—that is, e-graph style representations—coupled with canonical hashing, symmetry reduction, and dominance-relation pruning.

Under the same set of mathematical input-output semantics, candidate sequences that could be proven to differ only in register naming, independent instruction reordering, redundant intermediate values, or local equivalent rewriting would be folded into the same state node.

What the generator spit out was no longer lines of C code or assembly.

Rather, it was a huge state graph.

Each node no longer represented a specific piece of code, but a set of normalized intermediate states with identical input-output semantics.

Each edge truly corresponded to a substantive, actionable underlying primitive transformation or machine instruction transformation.

The search space, in the eighth year of the Wasteland, was forcefully suppressed from a Physics sense for the first time.

In the eleventh year, to further combat the consumption of time, Jiang Lin added an evidence caching mechanism to the bottom layer of the system.

In the past, whenever a search encountered a similar structure, the system had to call the Z3 solver again to prove it.

Now, all verified equivalent states had their proof processes serialized and stored permanently.

The proofs of local primitives could be reused like building blocks.

The correctness proofs of underlying subnetworks could directly serve as prerequisite evidence for components of larger-scale networks.

MPS-Kernel began to undergo a metamorphosis.

It no longer resembled a clumsy searcher that pushed from the beginning to the end every time, but began to resemble an intelligent proving machine with memory that automatically accumulated intermediate theorems.

In the thirteenth year, Jiang Lin slashed through the huge and chaotic proving system, clearly splitting it into three layers.

Layer one: the abstract primitive layer.

Microkernels such as sorting, selection, rank finding, median, and top-k were first defined impeccably in pure mathematical semantics.

What was the input data distribution?

What were the sorting stability requirements of the output?

Were duplicate values allowed in the array?

Did the algorithm boundaries have a sentinel mechanism?

Most importantly, special value processing for integer comparisons, non-numbers in floating-point operations, and signed zeros had to be clearly shunted at this layer.

Layer two: the source code and intermediate representation layer.

Reaching this layer, whether it was C code, LLVM IR, or manually written intrinsic inline functions, was absolutely not allowed to be glossed over with a light sentence saying it looked equivalent.

The notorious undefined behaviors in the C language standard, undefined behaviors of signed integer overflows, modular wrapping semantics of unsigned integers, truncation rules during conversions of integers of different widths, NaN propagation in floating-point comparisons, positive and negative zero sorting, rounding modes, exception flags, and different platforms' handling of denormalized numbers all had to be ruthlessly torn apart and kneaded by mathematical logic at this layer, ensuring that the IR remained consistent with the upper-layer abstract semantics within the declared semantic subset.

Layer three: the machine code layer.

This was the realm closest to the metal.

The finally generated binary instruction sequence had to be able to reversely connect back to the upper-layer semantics.

Whether it was the high-efficiency conditional move cmov, vector blending blend, pminsd used for packed minimum finding, or even a few combinations of logic instructions that seemed to take a detour to avoid pipeline hazards, they all had to be automatically provided with strict logical equivalence proofs by the system.

Pei Li's tricky question about scaling in the office did not receive an engineering answer piled up by Jiang Lin with code amidst the yellow sand of the Wasteland until this year.

The zero-one validator was never the end point; it was merely the first link in a sturdy proof chain leading to the industrialization of microkernels.

In the nineteenth year, Jiang Lin welcomed another huge challenge.

Rewriting the cost evaluation backend.

The cost model of the old version was ridiculously naive; it only gave a cold ranking based on static instruction cycles.

First place: theoretically looked the fastest.

Second place: looked a bit slower.

But on a real Von Neumann architecture machine, silicon wafers were not clean mathematical paper; they were full of the agitation and uncertainty of the Physics world.

L1/L2 cache hit rates fluctuated with context.

The operating system's thread scheduling could trigger interrupts at any time.

The CPU's turbo frequency mechanism dynamically changed the operating frequency due to the accumulation of heat.

Different processing batch sizes completely changed the throughput bottlenecks of the pipeline.

The exact same seemingly perfect instruction cleverly avoided the congestion of execution ports on machine A, but upon reaching machine B, it might crash headfirst into the penalty trap of a branch predictor failure.

Therefore, Jiang Lin completely overthrew the old backend.

The new backend no longer output pale and powerless single-point scores.

For each candidate microkernel, what it output was three sets of three-dimensional evaluations.

Theoretical cost: Pure static calculation based on the micro-architecture model.

Measured distribution: Candidate microkernels had to undergo tens of thousands of repeated tests under various cache hot and cold states, various batch lengths, various code warm-up methods, and even various forced frequency-locking conditions to plot the probability density distribution graph of execution time.

Robustness score: Measures the code's anti-interference ability under harsh hardware noise.

What was ultimately retained by MPS-Kernel was definitely not a champion that happened to win by luck in a specific benchmark run.

Rather, it was an iron-blooded candidate whose performance baseline could still steadily lead other schemes after excluding all hardware environmental noise windows.

In the twenty-fourth year, the workstation fan let out a continuous roar, and MPS-Kernel finally generated the first true batch of evidence cards.

Each evidence card corresponded to a rigorously tempered microkernel package.

This was no longer a cold piece of code, but the irrefutable resume archive of a piece of code.

[Kernel_ID: Median]

[Abstract_Semantics: strict weak ordering, NaN unified sinking, +0/-0 normalized according to declaration rules]

[Source_IR_Proof: No UB overflow, IR isomorphism verification passed]

[Binary_Equivalence: Within the declared semantic domain, SMT counterexample search UNSAT]

[ISA: x86-64, AVX2 extension]

[Microarchitecture_Assumption: L1D hot cache path; attached with cold cache downgrade curve]

[Cost_Model: Port contention delay analysis report]

[Benchmark_Distribution: Latency distribution, P50/P95/P99 and long-tail sample graphs]

[Robustness_Score: Performance lower-bound stability within 99.9% sample windows]

[Fallback_Path: Scalar downgrade fallback path when AVX fails]

In the thirty-first year, Jiang Lin pushed the entire massive toolchain to version v0.2.

It was already able to extremely stably process a batch of small kernels that far crossed the boundary of sort5: sort8, rank8, median9, and top-k problems under specific memory-alignment-constrained scenarios.

These things were still not huge in modern software engineering with millions of lines of code at every turn, but they were enough to cross the boundary of that demonstration in the office.

It proved to the world that MPS-Kernel was by no means a potted landscape that could only display beautiful mathematical structures on toy problems like sort5.

It already possessed the potential to advance toward a truly automated tool for producing industrial-grade microkernels, leveraging semantic equivalence class searching, a three-layer logical proof chain, and a multi-dimensional robustness cost model.

In the thirty-fifth year of the Wasteland, Jiang Lin drew the final version of the second diagram.

Title: [MPS-Kernel v0.2: Semantic Equivalence Class Search — Proof-Carrying Chain — Robust Cost Backend]

This would be an ultimate weapon.