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Manual: how precision and accuracy carry through computations - #2069
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Collect what the precision PRs (#2050-#2067) established into the "Precision and Accuracy" section of the tutorial: errors in sums and products, the condition number for functions, zero values and poles, complex numbers, machine numbers, N with $MaxExtraPrecision, and SetPrecision/SetAccuracy. Every example is a doctest, and every value matches WMA 15. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This was referenced Oct 28, 2026
pytest 9.2.0 (2026-10-27) breaks pytest-benchmark 5.3.0, the latest release: every benchmark errors with "'Function' object has no attribute '_nodeid'" (ionelmc/pytest-benchmark#321). Since then the benchmark job fails on every pull request. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> (cherry picked from commit d00ed4a)
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Since pytest 9.2.0 came out (2026-10-27), the "Run performance benchmarks" job fails on every pull request, including #1989, #2032, #2069 and #2070. All 73 benchmarks error at setup: ``` AttributeError: 'Function' object has no attribute '_nodeid'. Did you mean: 'nodeid'? ``` pytest-benchmark 5.3.0, its latest release, uses a private attribute that pytest 9.2 removed: ionelmc/pytest-benchmark#321, still open. The last passing run (master, 2026-10-27 10:20) had pytest 9.1.1; the failing ones have 9.2.0. pytest-benchmark is 5.3.0 in both. This keeps pytest below 9.2 in the benchmark workflow, with a comment pointing at the upstream issue, so the pin can go once pytest-benchmark is fixed. `pyproject.toml` does not pin pytest, so the later `pip install -e .[dev,full]` keeps 9.1.x. Checked with a one-test benchmark: pytest 9.2.0 + pytest-benchmark 5.3.0 gives the same error, and pytest 9.1.1 + pytest-benchmark 5.3.0 passes. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
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LGTM - thanks! |
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How the kernel tracks the error of arbitrary-precision numbers, as WMA does: PrecisionReal's decimal precision and 64-bit value, the error rules for sums and products, condition numbers for functions, zero values, special points, complex parts, the second pass of N, and SetPrecision. Ends with how to add precision to a new function. The user-level description is in the Mathics3 Manual (Mathics3/mathics-core#2069). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Following the suggestion in #2067: this collects what the precision PRs (#2050–#2067) established into the "Precision and Accuracy" section of the Manual's tutorial.
The section keeps its introduction and gets six subsections:
0times an inexact number.Abs[x f'[x] / f[x]]; a zero value (Log[1.`20]), an inexact zero argument, andIndeterminatewhere the error covers a pole.MachinePrecision.N[expr, p]with$MaxExtraPrecision, andN[expr, {p, a}].SetPrecisionandSetAccuracy.Every example is a doctest, so the text is checked along with the code. Each value was checked against WMA 15. The internals (
PrecisionReal's stored precision and 64-bit value,condition_numbers,special_point_value, the second pass ofN) belong in the developer's guide, which is a separate repository; that will be a separate PR.docpipeline.py -s "Precision and Accuracy": 39 tests, all pass.🤖 Generated with Claude Code