{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "division",
    "version": "1.0.5",
    "title": "Division Calculator",
    "formula_family": "division",
    "capability_id": "math.divide",
    "verification_revision": "2026-09-08.exact-contract"
  },
  "profile": "core",
  "status": "VERIFIED",
  "runner": {
    "name": "cvp-runner",
    "version": "1.0.0"
  },
  "environment": {
    "runtime": "node",
    "runtime_version": "20.19.2",
    "numeric_model": "IEEE-754 binary64",
    "os": "darwin"
  },
  "suite": {
    "id": "division",
    "version": "1.0.5",
    "uri": "https://www.calculatorx.com/evidence/math.divide/1.0.5.json",
    "verification_revision": "2026-09-08.exact-contract"
  },
  "obligation_set": [
    "CVP-PROV-01",
    "CVP-MODEL-01",
    "CVP-SCOPE-01",
    "CVP-UNIT-01",
    "CVP-REF-01",
    "CVP-GOLD-01",
    "CVP-BND-01",
    "CVP-INV-01",
    "CVP-NUM-01",
    "CVP-COV-01",
    "CVP-CONTRACT-01",
    "CVP-DEP-01",
    "CVP-ART-01",
    "CVP-PROD-01",
    "CVP-PROP-01",
    "CVP-META-01",
    "CVP-ROUND-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "ECMAScript Language Specification",
        "kind": "standard",
        "reference": "Number.prototype.toFixed ( fractionDigits )",
        "url": "https://tc39.es/ecma262/#sec-number.prototype.tofixed"
      },
      {
        "label": "ECMAScript Language Specification",
        "kind": "standard",
        "reference": "Number type (IEEE-754 binary64)",
        "url": "https://tc39.es/ecma262/#sec-ecmascript-language-types-number-type"
      },
      {
        "label": "IEEE Std 754-2019",
        "kind": "standard",
        "reference": "IEEE Standard for Floating-Point Arithmetic",
        "url": "https://standards.ieee.org/ieee/754/6210/"
      },
      {
        "label": "Division theorem (Euclidean division)",
        "kind": "other",
        "reference": "For integers a and b > 0 there exist unique q, r with a = bq + r and 0 ≤ r < b",
        "url": "https://proofwiki.org/wiki/Division_Theorem"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Division a÷b and Euclidean long division"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath 1.4.1 divide (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*",
        "engine": {
          "name": "divide-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "rounding": "round-to-nearest-binary64",
          "backend": "python",
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
          "seed": "20260907",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/math-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-math-o3.py",
          "public_checker": "/developers/cvp/reproduce/check-math-o3-rest.py"
        }
      },
      {
        "class": "O3",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O3 table vs IUT value; ≤2 ULP on tabulated vectors only, not the whole domain. Distinct from legacy Evidence case-level tol.",
        "engine": {
          "name": "divide-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "rounding": "round-to-nearest-binary64",
          "backend": "python",
          "generator_version": "1.0.0",
          "generator_sha256": "3453ec60bd03738a1f1f3723baed7e617ff49466452efab1844fe68b8f654cea",
          "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
          "seed": "20260907",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/math-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-math-o3.py",
          "public_checker": "/developers/cvp/reproduce/check-math-o3-rest.py"
        }
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module divide oracle — independent a÷b and BigInt Euclidean long division",
        "engine": {
          "name": "divide-reference",
          "precision_bits": 53,
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP quotient comparison and exact long q,r vs IUT",
        "engine": {
          "name": "divide-reference",
          "precision_bits": 53,
          "independent_of_iut": true,
          "same_runtime_as_iut": true
        }
      }
    ],
    "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node /) for tabulated quotient vectors, and Python int divmod for tabulated long-division q,r. O2 is a live oracle for identities and shares V8 binary64 with the IUT unless noted otherwise."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "a ÷ b quotient; long mode Euclidean q,r with a = bq + r, 0 ≤ r < b"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "quotient or long integer division"
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "dimensionless"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O3 mpmath a/b and Python int divmod + O2 live identities (O2 shares V8 binary64 with the IUT)"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "25/25 legacy golden; 10/10 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "9/9 boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "9 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "≤2 ULP vs O3 applies to the published tabulated quotient vectors (1/3, 100/7, 1.005/1, 1/1e-300, (2^53−1)/7). Long-division vectors are exact integer q,r (Python int divmod). This is not a whole-domain guarantee. Legacy Evidence `tol` is not this policy."
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Declared partitions: quotient-normal, quotient-rounding, quotient-boundary, long-normal, long-large-integer, long-boundary, invalid-domain. Counts alone are not the claim."
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "1/1 contract checks"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine divide; Node binary64"
    },
    "CVP-ART-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "release_integrity.status=verified · evidence_digest=CVP verification fingerprint v2 (canonical inputs, expected/actual/status, policy, versions; independent of generated_at) · evidence_bundle_sha256=legacy Evidence JSON bytes · production_sha256=bound production attestation report"
    },
    "CVP-PROD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "CURRENT · site report pass · local checks pass · attestation_id=00c818a77ba026c2d6aa3f7402680cd2dac2a40a816209600bc3c3fcd0b8921c · CURRENT · Public schema 1.0.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.5 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20"
    },
    "CVP-DIM-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "Unitless core calculator — no physical dimension algebra"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "8/8 property"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "2/2 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "2/2 round-trips"
    },
    "CVP-XCAL-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "No related calculator in the same formula family / no related-identity peers declared — control not in obligation set"
    },
    "CVP-IFACE-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session."
    },
    "CVP-ORACLE-01": {
      "result": "PASS",
      "applicability": "higher_assurance",
      "notes": "O3 9/9 tabulated vectors vs IUT · ≤2 ULP vs O3 applies to the published tabulated quotient vectors (1/3, 100/7, 1.005/1, 1/1e-300, (2^53−1)/7). Long-division vectors are exact integer q,r (Python int divmod). This is not a whole-domain guarantee."
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "expert_reviewed=false"
    }
  },
  "tests": {
    "golden": {
      "passed": 10,
      "total": 10,
      "failed": 0,
      "case_ids": [
        "g-div-20-4",
        "g-div-1-3",
        "g-div-100-7",
        "g-div-1p005",
        "g-div-tiny",
        "g-div-max-safe",
        "g-div-long-100-7",
        "g-div-long-past-safe",
        "g-div-long-huge",
        "g-div-long-48"
      ]
    },
    "boundary": {
      "passed": 9,
      "total": 9,
      "failed": 0,
      "case_ids": [
        "div-zero",
        "long-reject-decimal",
        "long-reject-negative",
        "long-div-zero",
        "quotient-reject-unsafe-int",
        "decimals-out-of-range",
        "long-reject-neg10",
        "long-too-long",
        "boundary-div-zero"
      ]
    },
    "invalid": {
      "passed": 9,
      "total": 9,
      "failed": 0,
      "case_ids": [
        "div-zero",
        "long-reject-decimal",
        "long-reject-negative",
        "long-div-zero",
        "quotient-reject-unsafe-int",
        "decimals-out-of-range",
        "long-reject-neg10",
        "long-too-long",
        "boundary-div-zero"
      ]
    },
    "property": {
      "passed": 8,
      "total": 8,
      "failed": 0,
      "case_ids": [
        "prop-div-self",
        "prop-div-one",
        "prop-tofixed-1p005",
        "prop-max-safe-not-math-exact",
        "prop-euclid-normal",
        "prop-euclid-zero-rem",
        "prop-euclid-past-safe",
        "prop-euclid-48"
      ],
      "definition_ids": [
        "a-over-a",
        "a-over-one",
        "tofixed-half-away",
        "ieee-not-math-exact",
        "euclid-division"
      ]
    },
    "round_trip": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "rt-20-4",
        "rt-15-3"
      ]
    },
    "metamorphic": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "meta-scale-num",
        "meta-scale-den"
      ],
      "definition_ids": [
        "scale-numerator",
        "scale-denominator"
      ]
    },
    "contract": {
      "passed": 1,
      "total": 1,
      "failed": 0
    },
    "cross_interface": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "iface-div",
        "iface-div-long"
      ]
    },
    "o3": {
      "passed": 9,
      "total": 9,
      "failed": 0,
      "case_ids": [
        "o3-div-1-3",
        "o3-div-100-7",
        "o3-div-1p005",
        "o3-div-tiny",
        "o3-div-max-safe",
        "o3-div-long-100-7",
        "o3-div-long-past-safe",
        "o3-div-long-huge",
        "o3-div-long-48"
      ],
      "generator_id": "math-mpmath-o3",
      "seed": "20260907",
      "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee",
      "max_error_ulp": 0,
      "reproduce": "python3 generate-math-o3.py",
      "table_url": "/developers/cvp/reproduce/math-o3-tables.json",
      "generator_url": "/developers/cvp/reproduce/generate-math-o3.py",
      "claim_scope": "≤2 ULP vs O3 applies to the published tabulated quotient vectors (1/3, 100/7, 1.005/1, 1/1e-300, (2^53−1)/7). Long-division vectors are exact integer q,r (Python int divmod). This is not a whole-domain guarantee.",
      "reproduce_url": "https://www.calculatorx.com/evidence/math.divide/reproduce"
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "quotient-normal",
        "description": "Quotient mode, ordinary finite values",
        "exercised": true,
        "case_count": 15
      },
      {
        "id": "quotient-rounding",
        "description": "Quotient display rounding / repeating binary64",
        "exercised": true,
        "case_count": 14
      },
      {
        "id": "quotient-boundary",
        "description": "Quotient range edges: zero dividend, max safe integer, tiny divisor, unsafe integer tokens",
        "exercised": true,
        "case_count": 8
      },
      {
        "id": "long-normal",
        "description": "Long division ordinary integers, zero and non-zero remainder",
        "exercised": true,
        "case_count": 9
      },
      {
        "id": "long-large-integer",
        "description": "Long division integers larger than 2^53−1",
        "exercised": true,
        "case_count": 7
      },
      {
        "id": "long-boundary",
        "description": "Long division 48-digit product bound and INTEGER_TOO_LONG",
        "exercised": true,
        "case_count": 5
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs (division by zero, domain, range)",
        "exercised": true,
        "case_count": 9
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64 a/b (quotient); exact BigInt Euclidean q,r (long)",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Quotient ieee_value ≤2 ULP vs O3/O2. Long quotient/remainder are exact integer identity (0 ULP). Declared a priori.",
      "declared_before_evaluation": true
    },
    "legacy_regression_notes": "Legacy Evidence JSON may record case-level tol (e.g. 1e-8). That is a regression epsilon, not the CVP ≤2 ULP acceptance policy. CVP records list reference, actual, error_ulp, and the a-priori ULP threshold.",
    "claim_scope": "≤2 ULP vs O3 applies to the published tabulated quotient vectors (1/3, 100/7, 1.005/1, 1/1e-300, (2^53−1)/7). Long-division vectors are exact integer q,r (Python int divmod). This is not a whole-domain guarantee.",
    "max_error_observed": 0,
    "records": [
      {
        "id": "g-div-20-4",
        "reference": {
          "mode": "quotient",
          "a": 20,
          "b": 4,
          "value": 5,
          "ieee_value": 5,
          "decimal_places": 8,
          "decimal_value": "5",
          "exact": true,
          "display_exact": true
        },
        "actual": {
          "mode": "quotient",
          "a": 20,
          "b": 4,
          "value": 5,
          "ieee_value": 5,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "5",
          "exact": true,
          "display_exact": true,
          "exact_value": "20/4",
          "integer_quotient": 5,
          "remainder": 0
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-1-3",
        "reference": {
          "mode": "quotient",
          "a": 1,
          "b": 3,
          "value": 0.3333333333333333,
          "ieee_value": 0.3333333333333333,
          "decimal_places": 8,
          "decimal_value": "0.33333333",
          "exact": false,
          "display_exact": false
        },
        "actual": {
          "mode": "quotient",
          "a": 1,
          "b": 3,
          "value": 0.3333333333333333,
          "ieee_value": 0.3333333333333333,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "0.33333333",
          "exact": false,
          "display_exact": false,
          "exact_value": "1/3",
          "integer_quotient": 0,
          "remainder": 1
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-100-7",
        "reference": {
          "mode": "quotient",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "decimal_places": 8,
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false
        },
        "actual": {
          "mode": "quotient",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false,
          "exact_value": "100/7",
          "integer_quotient": 14,
          "remainder": 2
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-1p005",
        "reference": {
          "mode": "quotient",
          "a": 1.005,
          "b": 1,
          "value": 1.005,
          "ieee_value": 1.005,
          "decimal_places": 2,
          "decimal_value": "1",
          "exact": true,
          "display_exact": false
        },
        "actual": {
          "mode": "quotient",
          "a": 1.005,
          "b": 1,
          "value": 1.005,
          "ieee_value": 1.005,
          "decimal_places": 2,
          "precision": 2,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "1",
          "exact": true,
          "display_exact": false,
          "exact_value": null,
          "integer_quotient": null,
          "remainder": null
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-tiny",
        "reference": {
          "mode": "quotient",
          "a": 1,
          "b": 1e-300,
          "value": 9.999999999999999e+299,
          "ieee_value": 9.999999999999999e+299,
          "decimal_places": 8,
          "decimal_value": "9.999999999999999e+299",
          "exact": false,
          "display_exact": true
        },
        "actual": {
          "mode": "quotient",
          "a": 1,
          "b": 1e-300,
          "value": 9.999999999999999e+299,
          "ieee_value": 9.999999999999999e+299,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "9.999999999999999e+299",
          "exact": false,
          "display_exact": true,
          "exact_value": null,
          "integer_quotient": null,
          "remainder": null
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-max-safe",
        "reference": {
          "mode": "quotient",
          "a": 9007199254740991,
          "b": 7,
          "value": 1286742750677284.5,
          "ieee_value": 1286742750677284.5,
          "decimal_places": 8,
          "decimal_value": "1286742750677284.5",
          "exact": false,
          "display_exact": true
        },
        "actual": {
          "mode": "quotient",
          "a": 9007199254740991,
          "b": 7,
          "value": 1286742750677284.5,
          "ieee_value": 1286742750677284.5,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "1286742750677284.5",
          "exact": false,
          "display_exact": true,
          "exact_value": "9007199254740991/7",
          "integer_quotient": 1286742750677284,
          "remainder": 3
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-long-100-7",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "quotient": 14,
          "remainder": 2,
          "decimal_places": 8,
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "quotient": 14,
          "remainder": 2,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false,
          "exact_value": "100/7",
          "work": "Long division: 100 ÷ 7\n\n      14\n  7 ) 100\n\nStep-by-step:\n  1. Take 1: 7 goes 0 times → 0 × 7 = 0; 1 − 0 = 1\n  2. Take 10: 7 goes 1 time → 1 × 7 = 7; 10 − 7 = 3\n  3. Take 30: 7 goes 4 times → 4 × 7 = 28; 30 − 28 = 2\n\nQuotient = 14\nRemainder = 2\nCheck: 7 × 14 + 2 = 100"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-long-past-safe",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993",
          "b": 1,
          "value": null,
          "ieee_value": null,
          "quotient": "9007199254740993",
          "remainder": 0,
          "decimal_places": 8,
          "decimal_value": null,
          "exact": true,
          "display_exact": null
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993",
          "b": 1,
          "value": null,
          "ieee_value": null,
          "quotient": "9007199254740993",
          "remainder": 0,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": null,
          "exact": true,
          "display_exact": null,
          "exact_value": "9007199254740993/1",
          "work": "Long division: 9007199254740993 ÷ 1\n\n      9007199254740993\n  1 ) 9007199254740993\n\nStep-by-step:\n  1. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  2. Take 0: 1 goes 0 times → 0 × 1 = 0; 0 − 0 = 0\n  3. Take 0: 1 goes 0 times → 0 × 1 = 0; 0 − 0 = 0\n  4. Take 7: 1 goes 7 times → 7 × 1 = 7; 7 − 7 = 0\n  5. Take 1: 1 goes 1 time → 1 × 1 = 1; 1 − 1 = 0\n  6. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  7. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  8. Take 2: 1 goes 2 times → 2 × 1 = 2; 2 − 2 = 0\n  9. Take 5: 1 goes 5 times → 5 × 1 = 5; 5 − 5 = 0\n  10. Take 4: 1 goes 4 times → 4 × 1 = 4; 4 − 4 = 0\n  11. Take 7: 1 goes 7 times → 7 × 1 = 7; 7 − 7 = 0\n  12. Take 4: 1 goes 4 times → 4 × 1 = 4; 4 − 4 = 0\n  13. Take 0: 1 goes 0 times → 0 × 1 = 0; 0 − 0 = 0\n  14. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  15. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  16. Take 3: 1 goes 3 times → 3 × 1 = 3; 3 − 3 = 0\n\nQuotient = 9007199254740993\nRemainder = 0\nCheck: 1 × 9007199254740993 + 0 = 9007199254740993"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-long-huge",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993123456789",
          "b": 7,
          "value": null,
          "ieee_value": null,
          "quotient": "1286742750677284731922398",
          "remainder": 3,
          "decimal_places": 8,
          "decimal_value": null,
          "exact": false,
          "display_exact": null
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993123456789",
          "b": 7,
          "value": null,
          "ieee_value": null,
          "quotient": "1286742750677284731922398",
          "remainder": 3,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": null,
          "exact": false,
          "display_exact": null,
          "exact_value": "9007199254740993123456789/7",
          "work": "Long division: 9007199254740993123456789 ÷ 7\n\n      1286742750677284731922398\n  7 ) 9007199254740993123456789\n\nStep-by-step:\n  1. Take 9: 7 goes 1 time → 1 × 7 = 7; 9 − 7 = 2\n  2. Take 20: 7 goes 2 times → 2 × 7 = 14; 20 − 14 = 6\n  3. Take 60: 7 goes 8 times → 8 × 7 = 56; 60 − 56 = 4\n  4. Take 47: 7 goes 6 times → 6 × 7 = 42; 47 − 42 = 5\n  5. Take 51: 7 goes 7 times → 7 × 7 = 49; 51 − 49 = 2\n  6. Take 29: 7 goes 4 times → 4 × 7 = 28; 29 − 28 = 1\n  7. Take 19: 7 goes 2 times → 2 × 7 = 14; 19 − 14 = 5\n  8. Take 52: 7 goes 7 times → 7 × 7 = 49; 52 − 49 = 3\n  9. Take 35: 7 goes 5 times → 5 × 7 = 35; 35 − 35 = 0\n  10. Take 4: 7 goes 0 times → 0 × 7 = 0; 4 − 0 = 4\n  11. Take 47: 7 goes 6 times → 6 × 7 = 42; 47 − 42 = 5\n  12. Take 54: 7 goes 7 times → 7 × 7 = 49; 54 − 49 = 5\n  13. Take 50: 7 goes 7 times → 7 × 7 = 49; 50 − 49 = 1\n  14. Take 19: 7 goes 2 times → 2 × 7 = 14; 19 − 14 = 5\n  15. Take 59: 7 goes 8 times → 8 × 7 = 56; 59 − 56 = 3\n  16. Take 33: 7 goes 4 times → 4 × 7 = 28; 33 − 28 = 5\n  17. Take 51: 7 goes 7 times → 7 × 7 = 49; 51 − 49 = 2\n  18. Take 22: 7 goes 3 times → 3 × 7 = 21; 22 − 21 = 1\n  19. Take 13: 7 goes 1 time → 1 × 7 = 7; 13 − 7 = 6\n  20. Take 64: 7 goes 9 times → 9 × 7 = 63; 64 − 63 = 1\n  21. Take 15: 7 goes 2 times → 2 × 7 = 14; 15 − 14 = 1\n  22. Take 16: 7 goes 2 times → 2 × 7 = 14; 16 − 14 = 2\n  23. Take 27: 7 goes 3 times → 3 × 7 = 21; 27 − 21 = 6\n  24. Take 68: 7 goes 9 times → 9 × 7 = 63; 68 − 63 = 5\n  25. Take 59: 7 goes 8 times → 8 × 7 = 56; 59 − 56 = 3\n\nQuotient = 1286742750677284731922398\nRemainder = 3\nCheck: 7 × 1286742750677284731922398 + 3 = 9007199254740993123456789"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "g-div-long-48",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "100000000000000000000000000000000000000000000000",
          "b": 3,
          "value": null,
          "ieee_value": null,
          "quotient": "33333333333333333333333333333333333333333333333",
          "remainder": 1,
          "decimal_places": 8,
          "decimal_value": null,
          "exact": false,
          "display_exact": null
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "100000000000000000000000000000000000000000000000",
          "b": 3,
          "value": null,
          "ieee_value": null,
          "quotient": "33333333333333333333333333333333333333333333333",
          "remainder": 1,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": null,
          "exact": false,
          "display_exact": null,
          "exact_value": "100000000000000000000000000000000000000000000000/3",
          "work": "Long division: 100000000000000000000000000000000000000000000000 ÷ 3\n\n      33333333333333333333333333333333333333333333333\n  3 ) 100000000000000000000000000000000000000000000000\n\nStep-by-step:\n  1. Take 1: 3 goes 0 times → 0 × 3 = 0; 1 − 0 = 1\n  2. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  3. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  4. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  5. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  6. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  7. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  8. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  9. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  10. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  11. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  12. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  13. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  14. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  15. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  16. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  17. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  18. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  19. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  20. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  21. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  22. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  23. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  24. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  25. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  26. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  27. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  28. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  29. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  30. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  31. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  32. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  33. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  34. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  35. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  36. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  37. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  38. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  39. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  40. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  41. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  42. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  43. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  44. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  45. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  46. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  47. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  48. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n\nQuotient = 33333333333333333333333333333333333333333333333\nRemainder = 1\nCheck: 3 × 33333333333333333333333333333333333333333333333 + 1 = 100000000000000000000000000000000000000000000000"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-1-3",
        "reference": {
          "mode": "quotient",
          "a": 1,
          "b": 3,
          "value": 0.3333333333333333,
          "ieee_value": 0.3333333333333333,
          "decimal_places": 8,
          "decimal_value": "0.33333333",
          "exact": false,
          "display_exact": false
        },
        "actual": {
          "mode": "quotient",
          "a": 1,
          "b": 3,
          "value": 0.3333333333333333,
          "ieee_value": 0.3333333333333333,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "0.33333333",
          "exact": false,
          "display_exact": false,
          "exact_value": "1/3",
          "integer_quotient": 0,
          "remainder": 1
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-100-7",
        "reference": {
          "mode": "quotient",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "decimal_places": 8,
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false
        },
        "actual": {
          "mode": "quotient",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false,
          "exact_value": "100/7",
          "integer_quotient": 14,
          "remainder": 2
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-1p005",
        "reference": {
          "mode": "quotient",
          "a": 1.005,
          "b": 1,
          "value": 1.005,
          "ieee_value": 1.005,
          "decimal_places": 2,
          "decimal_value": "1",
          "exact": true,
          "display_exact": false
        },
        "actual": {
          "mode": "quotient",
          "a": 1.005,
          "b": 1,
          "value": 1.005,
          "ieee_value": 1.005,
          "decimal_places": 2,
          "precision": 2,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "1",
          "exact": true,
          "display_exact": false,
          "exact_value": null,
          "integer_quotient": null,
          "remainder": null
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-tiny",
        "reference": {
          "mode": "quotient",
          "a": 1,
          "b": 1e-300,
          "value": 9.999999999999999e+299,
          "ieee_value": 9.999999999999999e+299,
          "decimal_places": 8,
          "decimal_value": "9.999999999999999e+299",
          "exact": false,
          "display_exact": true
        },
        "actual": {
          "mode": "quotient",
          "a": 1,
          "b": 1e-300,
          "value": 9.999999999999999e+299,
          "ieee_value": 9.999999999999999e+299,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "9.999999999999999e+299",
          "exact": false,
          "display_exact": true,
          "exact_value": null,
          "integer_quotient": null,
          "remainder": null
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-max-safe",
        "reference": {
          "mode": "quotient",
          "a": 9007199254740991,
          "b": 7,
          "value": 1286742750677284.5,
          "ieee_value": 1286742750677284.5,
          "decimal_places": 8,
          "decimal_value": "1286742750677284.5",
          "exact": false,
          "display_exact": true
        },
        "actual": {
          "mode": "quotient",
          "a": 9007199254740991,
          "b": 7,
          "value": 1286742750677284.5,
          "ieee_value": 1286742750677284.5,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "1286742750677284.5",
          "exact": false,
          "display_exact": true,
          "exact_value": "9007199254740991/7",
          "integer_quotient": 1286742750677284,
          "remainder": 3
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-long-100-7",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "quotient": 14,
          "remainder": 2,
          "decimal_places": 8,
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": 100,
          "b": 7,
          "value": 14.285714285714286,
          "ieee_value": 14.285714285714286,
          "quotient": 14,
          "remainder": 2,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": "14.28571429",
          "exact": false,
          "display_exact": false,
          "exact_value": "100/7",
          "work": "Long division: 100 ÷ 7\n\n      14\n  7 ) 100\n\nStep-by-step:\n  1. Take 1: 7 goes 0 times → 0 × 7 = 0; 1 − 0 = 1\n  2. Take 10: 7 goes 1 time → 1 × 7 = 7; 10 − 7 = 3\n  3. Take 30: 7 goes 4 times → 4 × 7 = 28; 30 − 28 = 2\n\nQuotient = 14\nRemainder = 2\nCheck: 7 × 14 + 2 = 100"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-long-past-safe",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993",
          "b": 1,
          "value": null,
          "ieee_value": null,
          "quotient": "9007199254740993",
          "remainder": 0,
          "decimal_places": 8,
          "decimal_value": null,
          "exact": true,
          "display_exact": null
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993",
          "b": 1,
          "value": null,
          "ieee_value": null,
          "quotient": "9007199254740993",
          "remainder": 0,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": null,
          "exact": true,
          "display_exact": null,
          "exact_value": "9007199254740993/1",
          "work": "Long division: 9007199254740993 ÷ 1\n\n      9007199254740993\n  1 ) 9007199254740993\n\nStep-by-step:\n  1. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  2. Take 0: 1 goes 0 times → 0 × 1 = 0; 0 − 0 = 0\n  3. Take 0: 1 goes 0 times → 0 × 1 = 0; 0 − 0 = 0\n  4. Take 7: 1 goes 7 times → 7 × 1 = 7; 7 − 7 = 0\n  5. Take 1: 1 goes 1 time → 1 × 1 = 1; 1 − 1 = 0\n  6. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  7. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  8. Take 2: 1 goes 2 times → 2 × 1 = 2; 2 − 2 = 0\n  9. Take 5: 1 goes 5 times → 5 × 1 = 5; 5 − 5 = 0\n  10. Take 4: 1 goes 4 times → 4 × 1 = 4; 4 − 4 = 0\n  11. Take 7: 1 goes 7 times → 7 × 1 = 7; 7 − 7 = 0\n  12. Take 4: 1 goes 4 times → 4 × 1 = 4; 4 − 4 = 0\n  13. Take 0: 1 goes 0 times → 0 × 1 = 0; 0 − 0 = 0\n  14. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  15. Take 9: 1 goes 9 times → 9 × 1 = 9; 9 − 9 = 0\n  16. Take 3: 1 goes 3 times → 3 × 1 = 3; 3 − 3 = 0\n\nQuotient = 9007199254740993\nRemainder = 0\nCheck: 1 × 9007199254740993 + 0 = 9007199254740993"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-long-huge",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993123456789",
          "b": 7,
          "value": null,
          "ieee_value": null,
          "quotient": "1286742750677284731922398",
          "remainder": 3,
          "decimal_places": 8,
          "decimal_value": null,
          "exact": false,
          "display_exact": null
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "9007199254740993123456789",
          "b": 7,
          "value": null,
          "ieee_value": null,
          "quotient": "1286742750677284731922398",
          "remainder": 3,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": null,
          "exact": false,
          "display_exact": null,
          "exact_value": "9007199254740993123456789/7",
          "work": "Long division: 9007199254740993123456789 ÷ 7\n\n      1286742750677284731922398\n  7 ) 9007199254740993123456789\n\nStep-by-step:\n  1. Take 9: 7 goes 1 time → 1 × 7 = 7; 9 − 7 = 2\n  2. Take 20: 7 goes 2 times → 2 × 7 = 14; 20 − 14 = 6\n  3. Take 60: 7 goes 8 times → 8 × 7 = 56; 60 − 56 = 4\n  4. Take 47: 7 goes 6 times → 6 × 7 = 42; 47 − 42 = 5\n  5. Take 51: 7 goes 7 times → 7 × 7 = 49; 51 − 49 = 2\n  6. Take 29: 7 goes 4 times → 4 × 7 = 28; 29 − 28 = 1\n  7. Take 19: 7 goes 2 times → 2 × 7 = 14; 19 − 14 = 5\n  8. Take 52: 7 goes 7 times → 7 × 7 = 49; 52 − 49 = 3\n  9. Take 35: 7 goes 5 times → 5 × 7 = 35; 35 − 35 = 0\n  10. Take 4: 7 goes 0 times → 0 × 7 = 0; 4 − 0 = 4\n  11. Take 47: 7 goes 6 times → 6 × 7 = 42; 47 − 42 = 5\n  12. Take 54: 7 goes 7 times → 7 × 7 = 49; 54 − 49 = 5\n  13. Take 50: 7 goes 7 times → 7 × 7 = 49; 50 − 49 = 1\n  14. Take 19: 7 goes 2 times → 2 × 7 = 14; 19 − 14 = 5\n  15. Take 59: 7 goes 8 times → 8 × 7 = 56; 59 − 56 = 3\n  16. Take 33: 7 goes 4 times → 4 × 7 = 28; 33 − 28 = 5\n  17. Take 51: 7 goes 7 times → 7 × 7 = 49; 51 − 49 = 2\n  18. Take 22: 7 goes 3 times → 3 × 7 = 21; 22 − 21 = 1\n  19. Take 13: 7 goes 1 time → 1 × 7 = 7; 13 − 7 = 6\n  20. Take 64: 7 goes 9 times → 9 × 7 = 63; 64 − 63 = 1\n  21. Take 15: 7 goes 2 times → 2 × 7 = 14; 15 − 14 = 1\n  22. Take 16: 7 goes 2 times → 2 × 7 = 14; 16 − 14 = 2\n  23. Take 27: 7 goes 3 times → 3 × 7 = 21; 27 − 21 = 6\n  24. Take 68: 7 goes 9 times → 9 × 7 = 63; 68 − 63 = 5\n  25. Take 59: 7 goes 8 times → 8 × 7 = 56; 59 − 56 = 3\n\nQuotient = 1286742750677284731922398\nRemainder = 3\nCheck: 7 × 1286742750677284731922398 + 3 = 9007199254740993123456789"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      },
      {
        "id": "o3-div-long-48",
        "reference": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "100000000000000000000000000000000000000000000000",
          "b": 3,
          "value": null,
          "ieee_value": null,
          "quotient": "33333333333333333333333333333333333333333333333",
          "remainder": 1,
          "decimal_places": 8,
          "decimal_value": null,
          "exact": false,
          "display_exact": null
        },
        "actual": {
          "mode": "long",
          "integer_engine": "bigint",
          "a": "100000000000000000000000000000000000000000000000",
          "b": 3,
          "value": null,
          "ieee_value": null,
          "quotient": "33333333333333333333333333333333333333333333333",
          "remainder": 1,
          "decimal_places": 8,
          "precision": 8,
          "rounding": "IEEE-754 binary64 a/b, then Number.prototype.toFixed(n) (round half away from 0 on that binary64 value). Display may strip trailing zeros. Not decimal arbitrary-precision.",
          "decimal_value": null,
          "exact": false,
          "display_exact": null,
          "exact_value": "100000000000000000000000000000000000000000000000/3",
          "work": "Long division: 100000000000000000000000000000000000000000000000 ÷ 3\n\n      33333333333333333333333333333333333333333333333\n  3 ) 100000000000000000000000000000000000000000000000\n\nStep-by-step:\n  1. Take 1: 3 goes 0 times → 0 × 3 = 0; 1 − 0 = 1\n  2. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  3. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  4. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  5. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  6. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  7. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  8. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  9. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  10. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  11. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  12. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  13. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  14. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  15. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  16. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  17. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  18. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  19. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  20. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  21. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  22. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  23. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  24. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  25. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  26. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  27. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  28. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  29. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  30. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  31. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  32. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  33. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  34. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  35. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  36. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  37. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  38. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  39. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  40. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  41. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  42. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  43. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  44. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  45. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  46. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  47. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n  48. Take 10: 3 goes 3 times → 3 × 3 = 9; 10 − 9 = 1\n\nQuotient = 33333333333333333333333333333333333333333333333\nRemainder = 1\nCheck: 3 × 33333333333333333333333333333333333333333333333 + 1 = 100000000000000000000000000000000000000000000000"
        },
        "error_ulp": 0,
        "threshold_ulp": 2
      }
    ]
  },
  "interfaces": {
    "compared": [
      "ui-ssr",
      "rest",
      "mcp"
    ],
    "result": "PASS",
    "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session."
  },
  "artifacts": {
    "evidence_bundle_sha256": "e6537e5e860cd9fcd1e2218debd473c3e7ad21ec9e1e63174b147c9c00765714",
    "evidence_digest": "e5997fd9b998e67a19b72a2ce8fd476b13bc2a7ab9245887e75079f4978ce1d2",
    "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20",
    "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb",
    "production_checks": [
      {
        "id": "math.divide:output-const",
        "status": "pass",
        "detail": "output const 1.0.5 vs capability 1.0.5",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.divide:evidence-sha256",
        "status": "pass",
        "detail": "63f0d3cfbd6d",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.divide:semantic-contract",
        "status": "pass",
        "detail": "34/34",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.divide:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.5 vs origin 1.0.5",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.divide:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.divide/1.0.5/2026-09-08.exact-contract/core/e5997fd9b998",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z",
        "projection_compared": false,
        "observed_live_projection_at_attestation": "VERIFIED"
      },
      {
        "id": "math.divide:cvp-reproduce-manifest-agree",
        "status": "pass",
        "detail": "2026-09-08.exact-contract · efdad939a92a",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.divide:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Manifest",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      },
      {
        "id": "math.divide:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Manifest",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-10T02:52:51.379Z"
      }
    ]
  },
  "dependencies": [
    {
      "name": "divide-engine",
      "version": "1.0.5"
    },
    {
      "name": "divide-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "divide-o3-mpmath-table",
      "version": "math-mpmath-o3"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "00c818a77ba026c2d6aa3f7402680cd2dac2a40a816209600bc3c3fcd0b8921c",
    "attested_at": "2026-09-10T02:52:51.379Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.5"
  },
  "timestamps": {
    "verified_at": "2026-09-10T03:41:50.164Z",
    "generated_at": "2026-09-10T03:41:50.164Z"
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/math.divide/1.0.5.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.divide/1.0.5",
    "calculator": "https://www.calculatorx.com/calc/math/division",
    "schema": "https://www.calculatorx.com/developers/cvp/schema/cvp-evidence-1.0.json",
    "protocol": "https://www.calculatorx.com/developers/cvp/spec/1.0",
    "manifest": "https://www.calculatorx.com/evidence/math.divide/1.0.5.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/math.divide/1.0.5/2026-09-08.exact-contract.cvp.json",
    "reproduce": "https://www.calculatorx.com/evidence/math.divide/reproduce",
    "o3_table": "https://www.calculatorx.com/developers/cvp/reproduce/math-o3-tables.json",
    "o3_generator": "https://www.calculatorx.com/developers/cvp/reproduce/generate-math-o3.py"
  }
}