canonical-data.json

{
  "exercise": "rational-numbers",
  "comments": [
    " The canonical data assumes mathematically correct real   ",
    " numbers. The testsuites should consider rounding errors  ",
    " instead of testing for exact values for any non-integer  ",
    " tests.                                                   ",
    " Rational numbers r are represented as arrays [a, b] so   ",
    " that r = a/b.                                            "
  ],
  "cases": [
    {
      "description": "Arithmetic",
      "cases": [
        {
          "description": "Addition",
          "cases": [
            {
              "uuid": "0ba4d988-044c-4ed5-9215-4d0bb8d0ae9f",
              "description": "Add two positive rational numbers",
              "property": "add",
              "input": {
                "r1": [1, 2],
                "r2": [2, 3]
              },
              "expected": [7, 6]
            },
            {
              "uuid": "88ebc342-a2ac-4812-a656-7b664f718b6a",
              "description": "Add a positive rational number and a negative rational number",
              "property": "add",
              "input": {
                "r1": [1, 2],
                "r2": [-2, 3]
              },
              "expected": [-1, 6]
            },
            {
              "uuid": "92ed09c2-991e-4082-a602-13557080205c",
              "description": "Add two negative rational numbers",
              "property": "add",
              "input": {
                "r1": [-1, 2],
                "r2": [-2, 3]
              },
              "expected": [-7, 6]
            },
            {
              "uuid": "6e58999e-3350-45fb-a104-aac7f4a9dd11",
              "description": "Add a rational number to its additive inverse",
              "property": "add",
              "input": {
                "r1": [1, 2],
                "r2": [-1, 2]
              },
              "expected": [0, 1]
            }
          ]
        },
        {
          "description": "Subtraction",
          "cases": [
            {
              "uuid": "47bba350-9db1-4ab9-b412-4a7e1f72a66e",
              "description": "Subtract two positive rational numbers",
              "property": "sub",
              "input": {
                "r1": [1, 2],
                "r2": [2, 3]
              },
              "expected": [-1, 6]
            },
            {
              "uuid": "93926e2a-3e82-4aee-98a7-fc33fb328e87",
              "description": "Subtract a positive rational number and a negative rational number",
              "property": "sub",
              "input": {
                "r1": [1, 2],
                "r2": [-2, 3]
              },
              "expected": [7, 6]
            },
            {
              "uuid": "a965ba45-9b26-442b-bdc7-7728e4b8d4cc",
              "description": "Subtract two negative rational numbers",
              "property": "sub",
              "input": {
                "r1": [-1, 2],
                "r2": [-2, 3]
              },
              "expected": [1, 6]
            },
            {
              "uuid": "0df0e003-f68e-4209-8c6e-6a4e76af5058",
              "description": "Subtract a rational number from itself",
              "property": "sub",
              "input": {
                "r1": [1, 2],
                "r2": [1, 2]
              },
              "expected": [0, 1]
            }
          ]
        },
        {
          "description": "Multiplication",
          "cases": [
            {
              "uuid": "34fde77a-75f4-4204-8050-8d3a937958d3",
              "description": "Multiply two positive rational numbers",
              "property": "mul",
              "input": {
                "r1": [1, 2],
                "r2": [2, 3]
              },
              "expected": [1, 3]
            },
            {
              "uuid": "6d015cf0-0ea3-41f1-93de-0b8e38e88bae",
              "description": "Multiply a negative rational number by a positive rational number",
              "property": "mul",
              "input": {
                "r1": [-1, 2],
                "r2": [2, 3]
              },
              "expected": [-1, 3]
            },
            {
              "uuid": "d1bf1b55-954e-41b1-8c92-9fc6beeb76fa",
              "description": "Multiply two negative rational numbers",
              "property": "mul",
              "input": {
                "r1": [-1, 2],
                "r2": [-2, 3]
              },
              "expected": [1, 3]
            },
            {
              "uuid": "a9b8f529-9ec7-4c79-a517-19365d779040",
              "description": "Multiply a rational number by its reciprocal",
              "property": "mul",
              "input": {
                "r1": [1, 2],
                "r2": [2, 1]
              },
              "expected": [1, 1]
            },
            {
              "uuid": "d89d6429-22fa-4368-ab04-9e01a44d3b48",
              "description": "Multiply a rational number by 1",
              "property": "mul",
              "input": {
                "r1": [1, 2],
                "r2": [1, 1]
              },
              "expected": [1, 2]
            },
            {
              "uuid": "0d95c8b9-1482-4ed7-bac9-b8694fa90145",
              "description": "Multiply a rational number by 0",
              "property": "mul",
              "input": {
                "r1": [1, 2],
                "r2": [0, 1]
              },
              "expected": [0, 1]
            }
          ]
        },
        {
          "description": "Division",
          "cases": [
            {
              "uuid": "1de088f4-64be-4e6e-93fd-5997ae7c9798",
              "description": "Divide two positive rational numbers",
              "property": "div",
              "input": {
                "r1": [1, 2],
                "r2": [2, 3]
              },
              "expected": [3, 4]
            },
            {
              "uuid": "7d7983db-652a-4e66-981a-e921fb38d9a9",
              "description": "Divide a positive rational number by a negative rational number",
              "property": "div",
              "input": {
                "r1": [1, 2],
                "r2": [-2, 3]
              },
              "expected": [-3, 4]
            },
            {
              "uuid": "1b434d1b-5b38-4cee-aaf5-b9495c399e34",
              "description": "Divide two negative rational numbers",
              "property": "div",
              "input": {
                "r1": [-1, 2],
                "r2": [-2, 3]
              },
              "expected": [3, 4]
            },
            {
              "uuid": "d81c2ebf-3612-45a6-b4e0-f0d47812bd59",
              "description": "Divide a rational number by 1",
              "property": "div",
              "input": {
                "r1": [1, 2],
                "r2": [1, 1]
              },
              "expected": [1, 2]
            }
          ]
        }
      ]
    },
    {
      "description": "Absolute value",
      "cases": [
        {
          "uuid": "5fee0d8e-5955-4324-acbe-54cdca94ddaa",
          "description": "Absolute value of a positive rational number",
          "property": "abs",
          "input": {
            "r": [1, 2]
          },
          "expected": [1, 2]
        },
        {
          "uuid": "3cb570b6-c36a-4963-a380-c0834321bcaa",
          "description": "Absolute value of a positive rational number with negative numerator and denominator",
          "property": "abs",
          "input": {
            "r": [-1, -2]
          },
          "expected": [1, 2]
        },
        {
          "uuid": "6a05f9a0-1f6b-470b-8ff7-41af81773f25",
          "description": "Absolute value of a negative rational number",
          "property": "abs",
          "input": {
            "r": [-1, 2]
          },
          "expected": [1, 2]
        },
        {
          "uuid": "5d0f2336-3694-464f-8df9-f5852fda99dd",
          "description": "Absolute value of a negative rational number with negative denominator",
          "property": "abs",
          "input": {
            "r": [1, -2]
          },
          "expected": [1, 2]
        },
        {
          "uuid": "f8e1ed4b-9dca-47fb-a01e-5311457b3118",
          "description": "Absolute value of zero",
          "property": "abs",
          "input": {
            "r": [0, 1]
          },
          "expected": [0, 1]
        },
        {
          "uuid": "4a8c939f-f958-473b-9f88-6ad0f83bb4c4",
          "description": "Absolute value of a rational number is reduced to lowest terms",
          "property": "abs",
          "input": {
            "r": [2, 4]
          },
          "expected": [1, 2]
        }
      ]
    },
    {
      "description": "Exponentiation of a rational number",
      "cases": [
        {
          "uuid": "ea2ad2af-3dab-41e7-bb9f-bd6819668a84",
          "description": "Raise a positive rational number to a positive integer power",
          "property": "exprational",
          "input": {
            "r": [1, 2],
            "n": 3
          },
          "expected": [1, 8]
        },
        {
          "uuid": "8168edd2-0af3-45b1-b03f-72c01332e10a",
          "description": "Raise a negative rational number to a positive integer power",
          "property": "exprational",
          "input": {
            "r": [-1, 2],
            "n": 3
          },
          "expected": [-1, 8]
        },
        {
          "uuid": "c291cfae-cfd8-44f5-aa6c-b175c148a492",
          "description": "Raise a positive rational number to a negative integer power",
          "property": "exprational",
          "input": {
            "r": [3, 5],
            "n": -2
          },
          "expected": [25, 9]
        },
        {
          "uuid": "45cb3288-4ae4-4465-9ae5-c129de4fac8e",
          "description": "Raise a negative rational number to an even negative integer power",
          "property": "exprational",
          "input": {
            "r": [-3, 5],
            "n": -2
          },
          "expected": [25, 9]
        },
        {
          "uuid": "2d47f945-ffe1-4916-a399-c2e8c27d7f72",
          "description": "Raise a negative rational number to an odd negative integer power",
          "property": "exprational",
          "input": {
            "r": [-3, 5],
            "n": -3
          },
          "expected": [-125, 27]
        },
        {
          "uuid": "e2f25b1d-e4de-4102-abc3-c2bb7c4591e4",
          "description": "Raise zero to an integer power",
          "property": "exprational",
          "input": {
            "r": [0, 1],
            "n": 5
          },
          "expected": [0, 1]
        },
        {
          "uuid": "431cac50-ab8b-4d58-8e73-319d5404b762",
          "description": "Raise one to an integer power",
          "property": "exprational",
          "input": {
            "r": [1, 1],
            "n": 4
          },
          "expected": [1, 1]
        },
        {
          "uuid": "7d164739-d68a-4a9c-b99f-dd77ce5d55e6",
          "description": "Raise a positive rational number to the power of zero",
          "property": "exprational",
          "input": {
            "r": [1, 2],
            "n": 0
          },
          "expected": [1, 1]
        },
        {
          "uuid": "eb6bd5f5-f880-4bcd-8103-e736cb6e41d1",
          "description": "Raise a negative rational number to the power of zero",
          "property": "exprational",
          "input": {
            "r": [-1, 2],
            "n": 0
          },
          "expected": [1, 1]
        }
      ]
    },
    {
      "description": "Exponentiation of a real number to a rational number",
      "cases": [
        {
          "uuid": "30b467dd-c158-46f5-9ffb-c106de2fd6fa",
          "description": "Raise a real number to a positive rational number",
          "property": "expreal",
          "input": {
            "x": 8,
            "r": [4, 3]
          },
          "expected": 16.0
        },
        {
          "uuid": "6e026bcc-be40-4b7b-ae22-eeaafc5a1789",
          "description": "Raise a real number to a negative rational number",
          "property": "expreal",
          "input": {
            "x": 9,
            "r": [-1, 2]
          },
          "expected": 0.3333333333333333
        },
        {
          "uuid": "9f866da7-e893-407f-8cd2-ee85d496eec5",
          "description": "Raise a real number to a zero rational number",
          "property": "expreal",
          "input": {
            "x": 2,
            "r": [0, 1]
          },
          "expected": 1.0
        },
        {
          "uuid": "da137f1c-fc94-4035-9813-94f5152a1102",
          "description": "Raise a negative real number to a rational number that has been reduced",
          "property": "expreal",
          "input": {
            "x": -1,
            "r": [1, 1]
          },
          "expected": -1.0
        },
        {
          "uuid": "9abd9332-eeab-4139-afa2-2f82efdae421",
          "description": "Raise a negative real number to a rational number that has not been reduced",
          "property": "expreal",
          "input": {
            "x": -1,
            "r": [2, 2]
          },
          "expected": -1.0
        },
        {
          "uuid": "f3734f78-91b2-4e59-905e-8c61dbf34f39",
          "description": "Fails with a negative real number if the denominator of the reduced rational number is even",
          "property": "expreal",
          "input": {
            "x": -1,
            "r": [1, 2]
          },
          "expected": {
            "error": "the result of this operation is a complex number"
          }
        }
      ]
    },
    {
      "description": "Reduction to lowest terms",
      "cases": [
        {
          "uuid": "0a63fbde-b59c-4c26-8237-1e0c73354d0a",
          "description": "Reduce a positive rational number to lowest terms",
          "property": "reduce",
          "input": {
            "r": [2, 4]
          },
          "expected": [1, 2]
        },
        {
          "uuid": "5ed6f248-ad8d-4d4e-a545-9146c6727f33",
          "description": "Reduce places the minus sign on the numerator",
          "property": "reduce",
          "input": {
            "r": [3, -4]
          },
          "expected": [-3, 4]
        },
        {
          "uuid": "f87c2a4e-d29c-496e-a193-318c503e4402",
          "description": "Reduce a negative rational number to lowest terms",
          "property": "reduce",
          "input": {
            "r": [-4, 6]
          },
          "expected": [-2, 3]
        },
        {
          "uuid": "3b92ffc0-5b70-4a43-8885-8acee79cdaaf",
          "description": "Reduce a rational number with a negative denominator to lowest terms",
          "property": "reduce",
          "input": {
            "r": [3, -9]
          },
          "expected": [-1, 3]
        },
        {
          "uuid": "c9dbd2e6-5ac0-4a41-84c1-48b645b4f663",
          "description": "Reduce zero to lowest terms",
          "property": "reduce",
          "input": {
            "r": [0, 6]
          },
          "expected": [0, 1]
        },
        {
          "uuid": "297b45ad-2054-4874-84d4-0358dc1b8887",
          "description": "Reduce an integer to lowest terms",
          "property": "reduce",
          "input": {
            "r": [-14, 7]
          },
          "expected": [-2, 1]
        },
        {
          "uuid": "a73a17fe-fe8c-4a1c-a63b-e7579e333d9e",
          "description": "Reduce one to lowest terms",
          "property": "reduce",
          "input": {
            "r": [13, 13]
          },
          "expected": [1, 1]
        }
      ]
    }
  ]
}