{
  "software": "gnumeric",
  "function": "COTPI",
  "review_date": "2026-10-12",
  "validation_method": "Independent Python numeric and limited database-criteria models; not a native application or a general spreadsheet parser. Error tokens model documented rules only.",
  "native_application_execution": false,
  "hugo_compiled": false,
  "passed": 9,
  "total": 9,
  "scope": "Explicit examples only, not every input or application version. Expected error tokens are documented rules, not observed native error outputs.",
  "official_references": [
    "https://gnome.pages.gitlab.gnome.org/gnumeric/manual/CATEGORY_Mathematics.html#gnumeric-function-COTPI",
    "https://gnome.pages.gitlab.gnome.org/gnumeric-web/announcements/1.12/gnumeric-1.12.22.html"
  ],
  "examples": [
    {
      "case_id": 165,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A2)",
      "operation": "cotpi",
      "args": [
        0.125
      ],
      "expected": 2.4142135624,
      "native_executed": false,
      "model_result": 2.414213562373095,
      "passed": true
    },
    {
      "case_id": 166,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A3)",
      "operation": "cotpi",
      "args": [
        0.25
      ],
      "expected": 1,
      "native_executed": false,
      "model_result": 1.0000000000000002,
      "passed": true
    },
    {
      "case_id": 167,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A4)",
      "operation": "cotpi",
      "args": [
        0.5
      ],
      "expected": 0,
      "native_executed": false,
      "model_result": 6.123233995736766e-17,
      "passed": true
    },
    {
      "case_id": 168,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A5)",
      "operation": "cotpi",
      "args": [
        -0.25
      ],
      "expected": -1,
      "native_executed": false,
      "model_result": -1.0000000000000002,
      "passed": true
    },
    {
      "case_id": 169,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A6)",
      "operation": "cotpi",
      "args": [
        0.75
      ],
      "expected": -1,
      "native_executed": false,
      "model_result": -0.9999999999999999,
      "passed": true
    },
    {
      "case_id": 170,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A7)",
      "operation": "cotpi",
      "args": [
        0
      ],
      "expected": "undefined mathematically",
      "native_executed": false,
      "model_result": "undefined mathematically",
      "passed": true
    },
    {
      "case_id": 171,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=COTPI(A8)",
      "operation": "cotpi",
      "args": [
        1
      ],
      "expected": "undefined mathematically",
      "native_executed": false,
      "model_result": "undefined mathematically",
      "passed": true
    },
    {
      "case_id": 172,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=B2*COTPI(A2)",
      "operation": "cotpi",
      "args": [
        0.125
      ],
      "expected": 9.6568542495,
      "native_executed": false,
      "multiplier": 4,
      "model_result": 9.65685424949238,
      "passed": true
    },
    {
      "case_id": 173,
      "software": "gnumeric",
      "function": "COTPI",
      "source_path": "content/gnumeric/functions/cotpi.md",
      "formula": "=B2*COTPI(A2)",
      "operation": "cotpi",
      "args": [
        0.25
      ],
      "expected": 4,
      "native_executed": false,
      "multiplier": 4,
      "model_result": 4.000000000000001,
      "passed": true
    }
  ]
}