{
  "schemaVersion": 1,
  "slug": "cube-root-calculator",
  "category": "math",
  "kind": "implementation",
  "independentValidation": false,
  "implementationHash": "7e4a24cb95633f7ba19f5b3984a9867d2a15334c3adf1c8444faefa7707474a4",
  "provenance": "Generated from the calculation contract used by the published page. Publication is not external validation.",
  "sourceFiles": [
    "data/calculators/cube-root-calculator.json",
    "src/engine.js"
  ],
  "runtimeSource": "/sources/engine.txt",
  "runtimeHash": "5c888d8898afbdee36267bb9977829e1e2ac568f6677c8ee87469c139864645c",
  "scope": "The compute function records implemented equations, constants, lookup tables and custom rules. Inputs record defaults and allowed values; outputs record precision and units. Defaults are examples, not recommendations. General background references are not evidence for this specific algorithm.",
  "publishedFormula": {
    "formula": "∛v = sgn(v) × |v|^(1/3)",
    "vars": [
      [
        "v",
        "Input number"
      ],
      [
        "n",
        "Degree of the n-th root"
      ]
    ],
    "note": "Cube roots support negative values. An even-degree real root of a negative value is undefined and is returned as unavailable."
  },
  "externalEvidence": null,
  "contract": {
    "compute": "const v=Number(value),r=Number(root),empty={cubeRoot:null,cubed:null,nthRoot:null};if(!Number.isFinite(v)||!Number.isInteger(r)||r<2||r>100)return{...empty,__error:'inputError'};const sign=v<0?-1:1;return{cubeRoot:sign*Math.pow(Math.abs(v),1/3),cubed:v*v*v,nthRoot:v<0&&r%2===0?null:sign*Math.pow(Math.abs(v),1/r),__error:v<0&&r%2===0?'inputError':undefined};",
    "inputs": [
      {
        "name": "value",
        "type": "number",
        "default": 27,
        "min": -1000000000000000,
        "max": 1000000000000000,
        "step": 0.0001,
        "requiredValue": true
      },
      {
        "name": "root",
        "type": "number",
        "default": 3,
        "min": 2,
        "max": 100,
        "step": 1,
        "requiredValue": true
      }
    ],
    "outputs": [
      {
        "name": "cubeRoot",
        "precision": 6,
        "unit": "",
        "showWhen": {
          "root": [
            "3"
          ]
        },
        "trimTrailingZeros": true
      },
      {
        "name": "nthRoot",
        "precision": 6,
        "unit": "",
        "optional": true,
        "showWhen": {
          "root": [
            "2",
            "4",
            "5",
            "6",
            "7",
            "8",
            "9",
            "10",
            "11",
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            "59",
            "60",
            "61",
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            "65",
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            "95",
            "96",
            "97",
            "98",
            "99",
            "100"
          ]
        },
        "trimTrailingZeros": true
      },
      {
        "name": "cubed",
        "precision": 6,
        "unit": "",
        "trimTrailingZeros": true
      }
    ],
    "interpret": null
  }
}