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CVP reproduce

math.log

Independent re-run pack: fixed input vectors, O3 expected values, oracle version, commands, and the last result summary. This is how a reader moves from “CalculatorX says it passed” to “I can reproduce why it passed.”

Reproduce JSON CVP Manifest O3 table Generator REST checker Calculator

Identity

Calculation version, protocol version, and evidence revision are distinct.

Calculation version
1.1.5
CVP protocol
1.0.0-proposed · proposed
Evidence revision
2026-09-08.xcal
Oracle
O3 · mpmath 1.4.1 · 80 dps
Generator
math-mpmath-o3 · seed 20260907
Table SHA-256
efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee

Numerical claim

O3 PASS is a tabulated-vector claim, not a whole-domain proof.

≤2 ULP vs O3 applies to the 14 published tabulated common-log vectors (log₁₀ of 1, 10, 100, 0.1, 2, 1000 plus 8 seeded random x = 10^(u·6−2) in about [0.01, 10⁴]). It is not a guarantee over all bases, the whole positive reals, or unlisted neighborhoods of 0 and 1.

  • Last O3 run 14 / 14
  • Max error observed 0.5588572521476642 ULP
  • Threshold ≤ 2 ULP

Commands

Regenerate the table from the public generator. Independent REST check needs only this page's reproduce.json plus stdlib Python — no repo clone and no mpmath. The CVP runner remains a maintainer command.

Regenerate O3 table
python3 generate-math-o3.py after downloading the public generator next to the table
Repo maintainer path
python3 scripts/lib/cvp/oracles/generate-math-o3.py
Independent REST check
python3 check-math-o3-rest.py log10 after downloading check-math-o3-rest.py next to math-o3-tables.json (or pass --reproduce reproduce.json)
Re-run CVP
npm run cvp:run -- --capability math.log
REST check
POST https://www.calculatorx.com/api/v1/calc/log with a tabulated input from the table below

Re-running the generator without changing seed or inputs should reproduce table SHA-256 efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee. Compare each expected_f64 to the production result within the declared ULP threshold.

Tabulated vectors

Every O3 vector used for the ≤2 ULP claim. Expected values come from the published mpmath table, not from the implementation under test.

IDKindInputsExpected (f64)ActualULPStatus
o3-log10-1p0interior{"x":1,"base":"10"}0
0.0
00PASS
o3-log10-10p0interior{"x":10,"base":"10"}1
1.000000000000000000000000000000000000000
10PASS
o3-log10-100p0interior{"x":100,"base":"10"}2
2.000000000000000000000000000000000000000
20PASS
o3-log10-0p1interior{"x":0.1,"base":"10"}-1
-1.000000000000000000000000000000000000000
-10PASS
o3-log10-2p0interior{"x":2,"base":"10"}0.3010299956639812
0.3010299956639811952137388947244930267682
0.30102999566398120PASS
o3-log10-1000p0interior{"x":1000,"base":"10"}3
3.000000000000000000000000000000000000000
30PASS
o3-log10-rand-00random-interior{"x":2.801182637514798,"base":"10"}0.4473414258100093
0.4473414258100092739585058723437655146953
0.447341425810009240.5588572521476642PASS
o3-log10-rand-01random-interior{"x":253.04877701188164,"base":"10"}2.4032042426988482
2.403204242698848223231576019138293834216
2.40320424269884820PASS
o3-log10-rand-02random-interior{"x":908.8372887797552,"base":"10"}2.958486137446016
2.958486137446016072265429607028576161399
2.9584861374460160PASS
o3-log10-rand-03random-interior{"x":35.83770308093714,"base":"10"}1.5543401669710875
1.554340166971087454833292639408778144528
1.55434016697108750PASS
o3-log10-rand-04random-interior{"x":0.303973263679299,"base":"10"}-0.5171646135859191
-0.5171646135859191150297526899882842741670
-0.51716461358591910PASS
o3-log10-rand-05random-interior{"x":97.26995949052845,"base":"10"}1.9879787350073457
1.987978735007345707853397117325222524152
1.98797873500734570PASS
o3-log10-rand-06random-interior{"x":52.516519905953444,"base":"10"}1.720295939128846
1.720295939128845924988783693898778952831
1.7202959391288460PASS
o3-log10-rand-07random-interior{"x":1033.9184358911507,"base":"10"}3.0144862793385983
3.014486279338598281718400946709428234484
3.01448627933859830PASS