{
  "capability_id": "math.sin",
  "calculation_version": "1.0.5",
  "protocol_version": "1.0.0-proposed",
  "protocol_document_status": "proposed",
  "verification_revision": "2026-09-08.xcal",
  "oracle": {
    "class": "O3",
    "library": "mpmath 1.4.1",
    "mpmath_dps": 80,
    "backend": "python",
    "rounding": "round-to-nearest-binary64",
    "generator_id": "math-mpmath-o3",
    "generator_version": "1.0.0",
    "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
    "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
    "seed": "20260907",
    "independent_of_iut": true
  },
  "claim_scope": "≤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.",
  "commands": {
    "regenerate_table": "python3 generate-math-o3.py",
    "regenerate_table_repo": "python3 scripts/lib/cvp/oracles/generate-math-o3.py",
    "independent_rest": "python3 check-math-o3-rest.py sin",
    "run_cvp": "npm run cvp:run -- --capability math.sin",
    "rest_example": "POST https://www.calculatorx.com/api/v1/calc/sin"
  },
  "public_files": {
    "table": "/developers/cvp/reproduce/math-o3-tables.json",
    "table_url": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
    "generator": "/developers/cvp/reproduce/generate-math-o3.py",
    "generator_url": "https://www.calculatorx.com/developers/cvp/reproduce/generate-math-o3.py",
    "checker": "/developers/cvp/reproduce/check-math-o3-rest.py",
    "checker_url": "https://www.calculatorx.com/developers/cvp/reproduce/check-math-o3-rest.py",
    "manifest": "/evidence/math.sin/1.0.5.cvp.json",
    "this_file": "/evidence/math.sin/reproduce.json"
  },
  "result_summary": {
    "passed": 18,
    "total": 18,
    "failed": 0,
    "max_error_ulp": 1,
    "threshold_ulp": 2,
    "max_threshold_ulp": 2
  },
  "vectors": [
    {
      "id": "o3-sin-0",
      "kind": "angle",
      "inputs": {
        "theta": 0,
        "unit": "deg"
      },
      "expected_f64": 0,
      "expected_decimal": "0.0",
      "actual": 0,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-30",
      "kind": "angle",
      "inputs": {
        "theta": 30,
        "unit": "deg"
      },
      "expected_f64": 0.5,
      "expected_decimal": "0.5000000000000000000000000000000000000000",
      "actual": 0.5,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-45",
      "kind": "angle",
      "inputs": {
        "theta": 45,
        "unit": "deg"
      },
      "expected_f64": 0.7071067811865476,
      "expected_decimal": "0.7071067811865475244008443621048490392848",
      "actual": 0.7071067811865476,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-60",
      "kind": "angle",
      "inputs": {
        "theta": 60,
        "unit": "deg"
      },
      "expected_f64": 0.8660254037844386,
      "expected_decimal": "0.8660254037844386467637231707529361834714",
      "actual": 0.8660254037844386,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-90",
      "kind": "angle",
      "inputs": {
        "theta": 90,
        "unit": "deg"
      },
      "expected_f64": 1,
      "expected_decimal": "1.000000000000000000000000000000000000000",
      "actual": 1,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-180",
      "kind": "angle",
      "inputs": {
        "theta": 180,
        "unit": "deg"
      },
      "expected_f64": 0,
      "expected_decimal": "0.0",
      "actual": 0,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-33.3",
      "kind": "angle",
      "inputs": {
        "theta": 33.3,
        "unit": "deg"
      },
      "expected_f64": 0.5490228179981317,
      "expected_decimal": "0.5490228179981317020573893264846730203889",
      "actual": 0.5490228179981317,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-12.5",
      "kind": "angle",
      "inputs": {
        "theta": 12.5,
        "unit": "deg"
      },
      "expected_f64": 0.21643961393810288,
      "expected_decimal": "0.2164396139381028797595536696179407286734",
      "actual": 0.21643961393810288,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin--30",
      "kind": "angle",
      "inputs": {
        "theta": -30,
        "unit": "deg"
      },
      "expected_f64": -0.5,
      "expected_decimal": "-0.5000000000000000000000000000000000000000",
      "actual": -0.5,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-15",
      "kind": "angle",
      "inputs": {
        "theta": 15,
        "unit": "deg"
      },
      "expected_f64": 0.25881904510252074,
      "expected_decimal": "0.2588190451025207623488988376240483283491",
      "actual": 0.25881904510252074,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-00",
      "kind": "random-interior",
      "inputs": {
        "theta": -9.598528663627803,
        "unit": "deg"
      },
      "expected_f64": -0.16674342661408253,
      "expected_decimal": "-0.1667434266140825400165235493924631897422",
      "actual": -0.16674342661408253,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-01",
      "kind": "random-interior",
      "inputs": {
        "theta": 32.682972215116024,
        "unit": "deg"
      },
      "expected_f64": 0.5399902072681445,
      "expected_decimal": "0.5399902072681445090193751406915325740786",
      "actual": 0.5399902072681444,
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-02",
      "kind": "random-interior",
      "inputs": {
        "theta": 47.93316328432411,
        "unit": "deg"
      },
      "expected_f64": 0.7423637652930208,
      "expected_decimal": "0.7423637652930208699180874271455931674612",
      "actual": 0.7423637652930208,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-03",
      "kind": "random-interior",
      "inputs": {
        "theta": -27.777363127097487,
        "unit": "deg"
      },
      "expected_f64": -0.4660371166518522,
      "expected_decimal": "-0.4660371166518522197866704209282503599691",
      "actual": -0.4660371166518522,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-04",
      "kind": "random-interior",
      "inputs": {
        "theta": 8.247665339149535,
        "unit": "deg"
      },
      "expected_f64": 0.1434522960336174,
      "expected_decimal": "0.1434522960336173950259165395225344990107",
      "actual": 0.1434522960336174,
      "error_ulp": 0,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-05",
      "kind": "random-interior",
      "inputs": {
        "theta": -31.244554836302996,
        "unit": "deg"
      },
      "expected_f64": -0.5186920083835915,
      "expected_decimal": "-0.5186920083835914760820430319334533766172",
      "actual": -0.5186920083835914,
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-06",
      "kind": "random-interior",
      "inputs": {
        "theta": -19.03209995944053,
        "unit": "deg"
      },
      "expected_f64": -0.3260978300997276,
      "expected_decimal": "-0.3260978300997275695045617815597839966177",
      "actual": -0.32609783009972754,
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    },
    {
      "id": "o3-sin-rand-07",
      "kind": "random-interior",
      "inputs": {
        "theta": 17.42180953733623,
        "unit": "deg"
      },
      "expected_f64": 0.2994040004795209,
      "expected_decimal": "0.2994040004795209001749731976252296054391",
      "actual": 0.29940400047952087,
      "error_ulp": 1,
      "threshold_ulp": 2,
      "ok": true
    }
  ]
}