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perf(math): build matrix results without zero-filling them first - #349

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Oct 5, 2026
Merged

perf(math): build matrix results without zero-filling them first#349
gabrielfrasantos merged 2 commits into
mainfrom
ccr-90fcd432-u9pqe7

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@gabrielfrasantos gabrielfrasantos commented Oct 5, 2026 •
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Summary

math::Matrix's operators now build the matrices they return without zero-filling them first. This follows up #348: without its O3 pragmas, a consumer that builds at -O2 paid for every zeroed result with a memset call. The RLS update, and every other user of these operators, keeps its matrix expressions.

This replaces the PR's first version, which rewrote the RLS covariance update as a hand-written element loop. That worked around Matrix instead of fixing it, and the loop lost the covariance's exact symmetry under -ffast-math (see below).

Why

Each operator that returns a new matrix (+, -, the matrix and scalar *, Transpose, GetBlock, GetColumn) declared Matrix result;, value-initialised through data = {}, and then wrote every element. At O3 the loops were unrolled and the zeroing removed as dead stores. At -O2 the loops stay rolled and the zeroing survives. For a 3×3 result it is a 36-byte memset call, and the Arm GNU toolchain's newlib-nano memset stores one byte at a time, about 150 instructions per call.

e-foc runs an RLS update in the control interrupt during mechanical identification. Its covariance update, (covariance - Px * Px.Transpose() * denominatorInv) * lambdaInverse, builds four 3×3 temporaries. e-foc's SIL scenario that times the control interrupt through a full calibration (embedded-pro/e-foc#333) measures the slowest execution, in cycles of the emulated 25 MHz clock (one cycle is five instructions retired):

e-foc firmware arm-none-eabi-gcc 15.2.1 (Arm GNU, as in CI) 13.2.1 (Ubuntu)
e-foc main (pragmas, O3) 237 236
e-foc#333 with this repository's main (-O2) 377, over the scenario's 360 limit; the four memset calls are 596 of its 1 892 instructions 274
e-foc#333 with this PR 250–251, no memset 236

Ubuntu's newlib-nano memset stores 16 bytes per iteration, so the same dead zeroing cost less there. CI uses the Arm GNU toolchain, so CI failed the scenario and a local run did not.

Change

  • Matrix gains a private constructor taking a private tag; it leaves the elements uninitialised. The listed operators build their results with it, since each writes every element. All Matrix specialisations are friends, so an operator can build a result of another shape.
  • The default and initializer-list constructors zero-fill explicitly, so Matrix m; and a partly listed matrix keep their zeros. Identity() still starts from zeros.
  • The matrix product, a friend function of its left operand's class, calls a private member, Multiply, that builds the result in place, as Transpose, GetBlock and GetColumn do. MSVC (C2248) does not let a friend function of one specialisation use another specialisation's private constructor; GCC and Clang did. A static helper returning the uninitialised result was tried and rejected: GCC folds that argument-less constexpr call into a zero-filled constant, and the memset calls came back (377 cycles again).
  • RecursiveLeastSquares is unchanged from main.

Tests

  • New: operators_write_every_element_of_their_result evaluates the outer product, sum, difference, scalar product, GetBlock and GetColumn in constant expressions. A compiler that checks for uninitialised subobjects rejects any of them that leaves an element unwritten.
    • Clang does: with operator+ changed to skip its last element, the test fails to compile ("subobject '_M_elems' is not initialized").
    • GCC 13 and 15 accept the same code, so the check runs in CI's macOS job, which builds with AppleClang.
  • Existing: DefaultConstructorZeroInitializes and PartialInitializerListZeroFillsRemainder cover the zero-fill that remains.

The first version

It computed P(i,j) and P(j,i) in separate iterations. With -ffast-math, GCC 15 hoisted denominatorInv·Px(i) out of the column loop and fused the subtraction, so the two elements rounded differently. Under the online mechanical estimator's forgetting factor (λ = 0.9995) that asymmetry grows by 1/λ per update, and e-foc's CI read REQ-CAL-014's online friction 71 % off the plant (limit 30 %). The matrix expression computes the outer product Px·Pxᵀ first, and Px(i)·Px(j) = Px(j)·Px(i) exactly, so the covariance stays symmetric, as on main.

Validation

  • clang-format 18 reports nothing on the changed files.
  • host-single-Debug (GCC 13): the build is clean with no warnings, and ctest passes 14/14.
  • The same suite built with Clang 18: no warnings, and ctest passes 14/14.
  • qemu-cortex-m4: the build succeeds, and ctest passes 15/15. Its only warnings are newlib's stub notices (_open, _gettimeofday, _getentropy "is not implemented"), as on main.
  • e-foc#333 at 0e6a2fc, which pins this PR's head:
    • With arm-none-eabi-gcc 15.2.1, the full SIL suite passes 135/135.
    • The control-loop timing scenarios pass 7/7. The full calibration measures 250 to 251 cycles, and the closed-loop rows 99–106.
    • The REQ-CAL-014 scenarios pass 7/7 in two runs, and three more on the first commit alone. The teknic inertia reads 6.775·10⁻⁶ (once 6.774·10⁻⁶), as on main.
    • With 13.2.1, the timing scenarios pass 7/7, and the full calibration measures 236 cycles.
    • The firmware built with 15.2.1 makes no memset call in RecursiveLeastSquares<float, 3>::Update or in either e-foc function that inlines it.

🤖 Generated with Claude Code

https://claude.ai/code/session_01HKhRVwu8yvxdKJgNo17oNc

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✅⚠️MegaLinter analysis: Success with warnings

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⚠️ SPELL / lychee - 23 errors 
📝 Summary
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🔗 Unique.........436
✅ Successful.....532
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🔀 Redirected.....152
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[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/12 (at 221:8) | Rejected status code: 404 Not Found
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[ERROR] file://doc/filters/solvers/DiscreteAlgebraicRiccatiEquation.md (at 134:3) | File not found. Check if file exists and path is correct

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[403] https://developer.arm.com/documentation/100166/latest/ (at 472:3) | Rejected status code: 403 Forbidden
[403] https://developer.arm.com/documentation/dui0473/latest (at 474:3) | Rejected status code: 403 Forbidden

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[ERROR] file:///releases/latest (at 38:14) | File not found. Check if file exists and path is correct
[404] https://embedded-pro.github.io/embedded-dsp-control/ (at 37:1) | Rejected status code: 404 Not Found

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[ERROR] file://roadmap/filters/passive/ExponentialMovingAverage/implementation.md (at 24:1) | File not found. Check if file exists and path is correct

Hint: Followed 152 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
Hint: You can configure accepted/rejected response codes with `-a` or `--accept`
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doc/filters/active/UnscentedKalmanFilter.md:11:401 error MD013/line-length Line length [Expected: 400; Actual: 468]
doc/filters/active/UnscentedKalmanFilter.md:149:65 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/filters/active/UnscentedKalmanFilter.md:149:153 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
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doc/solvers/README.md:16:163 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/solvers/README.md:17:163 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/solvers/README.md:18:167 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/solvers/README.md:19:184 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/solvers/README.md:20:184 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/solvers/RungeKuttaIntegrators.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 509]
doc/solvers/SpectralRadius.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 665]
doc/windowing/window.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 415]
README.md:1 error MD041/first-line-heading/first-line-h1 First line in a file should be a top-level heading [Context: "[![Quality Gate Status](https:..."]
README.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 442]
README.md:19:327 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:20:211 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:21:303 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:22:250 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:23:446 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:25:140 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:26:174 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:27:363 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:28:158 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:29:205 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
roadmap/math/SE3Transform/implementation.md:7 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/implementation.md:21 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/implementation.md:35 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/tests.md:7 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/tests.md:16 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/README.md:11 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]

(Truncated to last 20000 characters out of 24106)

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@gabrielfrasantos gabrielfrasantos mentioned this pull request Oct 5, 2026
Merged
@claude
perf(math): build matrix results without zero-filling them first
e5ea80d 
Every Matrix operator that returns a new matrix value-initialised its
result (data = {}) and then overwrote every element. Without the O3
pragmas #348 removed, a consumer that builds at -O2 keeps those loops
rolled, so the zeroing survives. For a 3x3 result it is a memset call,
and the Arm GNU toolchain's newlib-nano memset stores one byte at a
time.

e-foc runs an RLS update in the control interrupt during mechanical
identification. Its covariance update, (P - g g^T / d) / lambda,
builds four 3x3 temporaries. In e-foc's SIL scenario that times the
control interrupt through a full calibration, the slowest execution
rose from 237 to 377 cycles of the emulated 25 MHz clock
(arm-none-eabi-gcc 15.2.1). The four memset calls were 596 of its 1892
instructions.

- Matrix gains a private constructor that leaves the elements
  uninitialised. operator+, operator-, the matrix and scalar products,
  Transpose, GetBlock and GetColumn build their results with it, since
  each writes every element.
- The default and initializer-list constructors still zero-fill, so a
  default-constructed or partly listed matrix keeps its zeros.
- A test evaluates those operators in constant expressions, so a
  compiler that checks (Clang does, GCC does not) rejects an operator
  that leaves an element unwritten.

The RLS update keeps its matrix expression and now makes no memset
calls. The same scenario peaks at 250 cycles.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HKhRVwu8yvxdKJgNo17oNc
@gabrielfrasantos gabrielfrasantos changed the title perf(estimators): update the RLS covariance in place perf(math): build matrix results without zero-filling them first Oct 5, 2026
@claude
fix(math): build the matrix product's result in a member function
b54894a 
The matrix product is a friend function of its left operand's Matrix
specialisation. It built its result, a Matrix of another shape, with
that shape's private constructor. GCC and Clang allowed it, but MSVC
rejects it (C2248): friendship goes to the Matrix specialisations, not
to their friend functions.

The operator now calls a private member function, Multiply, which
builds the result in place, as Transpose, GetBlock and GetColumn
already do. Members of every Matrix specialisation are friends of the
others, so every compiler accepts it.

A static helper that returned the uninitialised result was not used:
GCC folds such an argument-less constexpr call into a zero-filled
constant, which brings back the memset calls.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HKhRVwu8yvxdKJgNo17oNc
@sonarqubecloud

sonarqubecloud Bot commented Oct 5, 2026

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Quality Gate Passed Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
100.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

@gabrielfrasantos
gabrielfrasantos merged commit e36d52a into main Oct 5, 2026
11 checks passed
@gabrielfrasantos
gabrielfrasantos deleted the ccr-90fcd432-u9pqe7 branch October 5, 2026 15:49
@embedded-releaser-app embedded-releaser-app Bot mentioned this pull request Oct 4, 2026
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2 participants

@gabrielfrasantos @claude