CVP reproduce

math.cos

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: 1.0.5
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 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros.

Last O3 run 18 / 18
Max error observed 0 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 cos 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.cos
REST check: POST https://www.calculatorx.com/api/v1/calc/cos 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.

ID	Kind	Inputs	Expected (f64)	Actual	Status
`o3-cos-0`	angle	`{"theta":0,"unit":"deg"}`	1 1.000000000000000000000000000000000000000	1	PASS
`o3-cos-30`	angle	`{"theta":30,"unit":"deg"}`	0.8660254037844386 0.8660254037844386467637231707529361834714	0.8660254037844386	PASS
`o3-cos-45`	angle	`{"theta":45,"unit":"deg"}`	0.7071067811865476 0.7071067811865475244008443621048490392848	0.7071067811865476	PASS
`o3-cos-60`	angle	`{"theta":60,"unit":"deg"}`	0.5 0.5000000000000000000000000000000000000000	0.5	PASS
`o3-cos-90`	angle	`{"theta":90,"unit":"deg"}`	0 0.0	0	PASS
`o3-cos-180`	angle	`{"theta":180,"unit":"deg"}`	-1 -1.000000000000000000000000000000000000000	-1	PASS
`o3-cos-33.3`	angle	`{"theta":33.3,"unit":"deg"}`	0.8358073613682703 0.8358073613682702857094153628941470787928	0.8358073613682703	PASS
`o3-cos-12.5`	angle	`{"theta":12.5,"unit":"deg"}`	0.9762960071199334 0.9762960071199333659708864896054275771653	0.9762960071199334	PASS
`o3-cos--30`	angle	`{"theta":-30,"unit":"deg"}`	0.8660254037844386 0.8660254037844386467637231707529361834714	0.8660254037844386	PASS
`o3-cos-15`	angle	`{"theta":15,"unit":"deg"}`	0.9659258262890683 0.9659258262890682867497431997288973676339	0.9659258262890683	PASS
`o3-cos-rand-00`	random-interior	`{"theta":-9.559773420915008,"unit":"deg"}`	0.9861128800941029 0.9861128800941028652908262453963846876746	0.9861128800941029	PASS
`o3-cos-rand-01`	random-interior	`{"theta":41.753348731435835,"unit":"deg"}`	0.7460184554083706 0.7460184554083705867088104707357776419516	0.7460184554083706	PASS
`o3-cos-rand-02`	random-interior	`{"theta":16.403990518301725,"unit":"deg"}`	0.9592943077850056 0.9592943077850055966326827207755255900343	0.9592943077850056	PASS
`o3-cos-rand-03`	random-interior	`{"theta":-24.075726536102593,"unit":"deg"}`	0.9130070852711516 0.9130070852711515531889422578244704191104	0.9130070852711516	PASS
`o3-cos-rand-04`	random-interior	`{"theta":-25.105708884075284,"unit":"deg"}`	0.9055265277845048 0.9055265277845048629611810932764418743549	0.9055265277845048	PASS
`o3-cos-rand-05`	random-interior	`{"theta":43.52653187233955,"unit":"deg"}`	0.7250555379109475 0.7250555379109474598894102059111360381079	0.7250555379109475	PASS
`o3-cos-rand-06`	random-interior	`{"theta":24.071603268384933,"unit":"deg"}`	0.9130364404111473 0.9130364404111472886583069181110995588040	0.9130364404111473	PASS
`o3-cos-rand-07`	random-interior	`{"theta":9.037105715833604,"unit":"deg"}`	0.9875868238749216 0.9875868238749215616683168383263587344341	0.9875868238749216	PASS