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mathlib-fp 1.9.0 qualification

Completion-gate evidence

Gate	Reproducible evidence
End-to-end workflow	Example 22: 5x5 Poisson triplets → CSR → Matrix Market → CSR → IC(0) → CG; 13 stored entries, one iteration, three products, confirmed true residual, endpoint solution 1
Four-scalar storage/operators	`TestSparseMatrices`, `TestIterativeSolvers`, `TestStructuredSolvers`, and `TestPartialEigensystems`; all five iterative methods, operator adjoints, preconditioner families, and direct-factor families execute through named scalar facades
Complete outcomes	Iterative success/limit/cancel/breakdown; invalid preconditioner structure; band/sparse singularity; spectral validation
No dense-scale allocation	portable constructor regression whose hypothetical dense product exceeds `High(SizeInt)`, 20,000-dimensional matrix-free solve, and 100,000-entry sparse/200,000-dimensional matrix-free benchmark rows below
Reuse/aliasing/mutation/failure atomicity	sequential/concurrent factor and preconditioner reuse, exact in-place operation, partial-view rejection, source snapshots, atomic validation/construction failures, and atomic workspace ownership/recovery
Interchange	text real/complex and four-scalar binary round trips; malformed index, duplicate, explicit zero, version, kind, checksum, truncation, nonzero-limit, and per-axis dimension-limit rejection
Migration/API freeze	example 23 runs dense/sparse solves, fitting, interpolation, optimization, DSP, and statistics; schema-2 snapshot distinguishes owners/overloads and the generated reference contains every exact declaration
Documentation audit	`check_doc_examples.py` inventories 225 Pascal fences and compiles/runs all 15 self-contained programs; every 1.9 release-facing Pascal fence must be self-contained; 59 pages, capability data, release notes, examples, and declarations reconcile

Numerical contracts exercised

Workflow	Published check
CSR/CSC/triplets	strict canonical ordering, deterministic duplicate sum, zero policy, shape/index/finite validation, transpose/conjugate transpose and arithmetic
Structured storage	compact diagonal/tridiagonal/band products agree with dense values
Operator adapters	sparse/structured/dense/matrix-free ordinary and adjoint products agree with direct references
Preconditioners	diagonal/IC(0)/ILU(0) application plus missing diagonal, non-Hermitian, and pivot failures
Krylov solvers	all five methods execute for all four scalars; square true-residual and inconsistent-LSQR normal-residual convergence; refresh/progress, result statuses, aliasing, atomic failure, and workspace reuse
Direct factors	pivoted tridiagonal multiple RHS; no-pivot band singularity; sparse natural-order fill/pivot; real/complex single/double

| Partial spectra | deterministic selected pairs and `||A*v-lambda*v||_2`; general Arnoldi and Hermitian Lanczos; target/shape rejection |

| Interchange | canonical round trip plus corrupt/malformed/nonzero-limit/dimension-limit rejection before result publication |

Fixture tolerances are precision- and algorithm-specific checks in the linked test source, not universal worst-case guarantees.

Large sparse and matrix-free evidence

Observed locally with FPC 3.2.2, Win64 x86-64, -B -O3 -FcUTF8, on 2026-07-31. GetTickCount64 timing and GetHeapStatus.TotalAllocated sampling are machine-specific. Logical slots are derived from public matrix, preconditioner, input/output, and prepared workspace capacities. They exclude small object/interface headers.

Case	Shape / retained matrix data	Initial / 20 warmed solves	Iterations / products per solve	Final true residual	Warmed peak / retained heap delta	Approximate retained storage
CSR diagonal + exact sparse diagonal preconditioner + CG	100,000²; 100,000 nonzeros	125 ms / 2,109 ms	1 / 3	`0.0` confirmed	0 / 0 bytes	3,300,041 scalar/index slots; initial sampled heap increase 26,404,352 bytes
Matrix-free scaled identity + CG	200,000²; 0 retained operator values	172 ms / 3,484 ms	1 / 3 (action count 63 including warm-up and repeats)	`0.0` confirmed	0 / 0 bytes	5,800,041 scalar slots; initial sampled heap increase 46,404,000 bytes

Both report dense_shape_elements_allocated=0. Their storage is linear in vector length/nonzeros; a full dense binary64 allocation would require 80 GB and 320 GB respectively. The stable regression suite separately uses dimension 20,000, where a dense matrix alone would require 3.2 GB, and passes within linear workspace storage. Constructor coverage also uses a portable shape whose hypothetical dense byte count exceeds High(SizeInt) while each axis remains a representable vector; this prevents a dense-product address-space check from reappearing on matrix-free paths.

The warmed measurements use GetHeapStatus.TotalAllocated, sampled by the iteration monitor and after every solve from a post-warm-up baseline. The benchmark fails above 65,536 bytes. This catches retained or vector-scale transient growth; it is not a count of every short-lived RTL allocation between sample points.

Reproduce:


fpc -B -O3 -FcUTF8 -Fusrc -FUbenchmarks/lib/qualification \

  -FEbenchmarks/lib/qualification benchmarks/BenchmarkRunner.lpr

benchmarks/lib/qualification/BenchmarkRunner.exe

The benchmark reports measurements; CI compiles it for bit-rot protection and does not enforce machine timing thresholds.

Release verification commands


fpc -B -FcUTF8 -Fusrc -FUtests/lib/normal -FEtests/lib/normal tests/TestRunner.lpr

tests/lib/normal/TestRunner.exe -a --format=plain

fpc -B -O3 -FcUTF8 -Fusrc -FUtests/lib/release -FEtests/lib/release tests/TestRunner.lpr

tests/lib/release/TestRunner.exe -a --format=plain

fpc -B -Ci -Cr -Co -Ct -gl -gh -FcUTF8 -Fusrc -FUtests/lib/checked -FEtests/lib/checked tests/TestRunner.lpr

tests/lib/checked/TestRunner.exe -a --format=plain

build-examples.ps1

lazbuild --build-all packages/lazarus/mathlib_fp.lpk

python tools/test_api_snapshot.py

python tools/test_doc_examples.py

python tools/check_docs.py

python tools/check_doc_examples.py

python tools/build_docs.py --output build-temp/docs-site/1.9.0

The final observed matrix is recorded after the commands complete:

Path	Result
Win64 normal	930 tests, 0 errors, 0 failures
Win64 `-O3`	930 tests, 0 errors, 0 failures
Win64 checked/heap-traced	930 tests, 0 errors, 0 failures; 295,567 blocks allocated/freed and 0 unfreed
Win32 `-O2`	Native i386 FPC 3.2.2: 930 tests, 0 errors, 0 failures; final GitHub Actions pull-request and push jobs passed
Linux x86-64	Final GitHub Actions pull-request and push jobs passed
Examples	24 compiled and ran successfully on Win64
Lazarus package	Package 1.9 built successfully for Win64 and Win32
Documentation/API snapshot	Static checks pass for 59 pages, 24 indexed examples, 281 required entry names, and 2,880 exact owner/signature-aware declaration rows; 15 self-contained Pascal fragments compile and run
Representative benchmark	Compiled and ran at `-O3`; large results above
Clean checksummed archive	197 source files checksummed and extracted into an isolated directory; normal, `-O3`, checked/heap-traced, documentation, all examples, Win64 package, and benchmark gates repeated successfully

The required Linux and Windows GitHub Actions pull-request and push workflows passed on the final portability-correction commit. The Win32 and Linux results are remote CI evidence and are not represented as local runs.

Dependency and remaining-gap audit

The new stable units use only repository code and Free Pascal RTL/FCL units. They do not load third-party DLLs, invoke programs, contact a service/network, require a licence key, or hide a dense/vendor fallback.

The stable boundary does not include distributed/out-of-core/GPU execution, parallel/SIMD sparse kernels, fill-reducing sparse ordering, advanced sparse direct methods, block/flexible Krylov or algebraic multigrid, LSQR preconditioning, shift-invert/interior/generalized/Schur/polynomial spectral families, or unrelated deferred DSP/statistics/state-space/ODE/optimisation families. These exact gaps are machine-readable in capabilities.json.