{
  "capability_id": "math.ln",
  "tool_id": "ln",
  "engine": "ln",
  "calculation_version": "1.0.4",
  "generated_at": "2026-09-16T22:03:43.776Z",
  "engine_build": "2026-09-10",
  "test_count": 23,
  "passed": 23,
  "failed": 0,
  "tests_summary": {
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      "total": 11,
      "passed": 11
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    "boundary": {
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      "passed": 12
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    "property": {
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  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
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      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
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  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
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  "page": "https://www.calculatorx.com/calc/math/ln",
  "api": "https://www.calculatorx.com/api/v1/calc/ln",
  "schema_input": "https://www.calculatorx.com/schemas/math.ln.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.ln.output.json",
  "assumptions": [
    "Real arithmetic; argument x > 0. Base is e, not 10.",
    "On many calculators log means log₁₀; in some programming languages log(x) means ln(x).",
    "Published engine is y = ln(x). A legacy y query parameter is ignored and stripped from the address bar. Inverse x = e^y is Antilog with base e."
  ],
  "limitations": [
    "Real ln only: x > 0 → INVALID_ARGUMENT when x ≤ 0",
    "Missing x → MISSING_REQUIRED_INPUT; non-finite → INVALID_NUMBER"
  ],
  "boundary_conditions": [
    "Missing x returns MISSING_REQUIRED_INPUT.",
    "x ≤ 0 returns INVALID_ARGUMENT (real ln is undefined).",
    "x = 1 returns 0 (exact). The token e and the binary64 constant Math.E return 1 with the exact display flag; Math.E is a rounded approximation of the mathematical constant e, not an exact representation.",
    "0 < x < 1 yields a negative result (for example ln(0.5) = −ln(2)).",
    "For every finite x > 0 in binary64, y = ln(x) is finite (about −744 < y < 710). Domain errors use INVALID_ARGUMENT; the engine does not return Infinity for valid positive finite inputs."
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  "sources": [
    {
      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "section": "Logarithm, Exponential, Powers",
      "url": "https://dlmf.nist.gov/4",
      "supports": "Natural logarithm as the inverse of the exponential; ln(x)=y ⇔ e^y=x",
      "kind": "reference"
    },
    {
      "title": "NIST DLMF §4.2",
      "section": "Logarithm: definitions and inverse of the exponential",
      "url": "https://dlmf.nist.gov/4.2",
      "supports": "e^(ln x) = x and ln(e^y) = y for real x > 0",
      "kind": "reference"
    },
    {
      "title": "CalculatorX mathematical conventions",
      "section": "Natural logarithm base e; real argument x > 0",
      "supports": "This page is ln only. Common log is the Log calculator; inverse is Antilog with base e.",
      "kind": "definition"
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  "fingerprint": "sha256:61a83a4f0bd289e5279485b0066d05c06eede305d63e15a9444869c77b4fed0e",
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        "value": 0,
        "verification": {
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          "passed": true
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        "exact": true
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      "tol": 0
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        "value": 1,
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        "exact": true
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      "tol": 1e-12
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      "tol": 1e-12
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      "tol": 1e-12
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      "tol": 1e-12
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      "tol": 1e-12
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      "tol": 1e-12
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      "id": "ln-half",
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          "value": 0.5,
          "passed": true
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      "tol": 1e-12
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