{ "protocol": { "name": "CVP", "version": "1.0.0-proposed" }, "document_status": "proposed", "calculator": { "id": "ln", "version": "1.0.4", "title": "Natural Log Calculator", "formula_family": "natural_logarithm", "capability_id": "math.ln", "verification_revision": "2026-09-08.xcal" }, "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": "ln", "version": "1.0.4", "uri": "https://www.calculatorx.com/evidence/math.ln/1.0.4.json", "verification_revision": "2026-09-08.xcal" }, "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-XCAL-01", "CVP-IFACE-01" ], "provenance": { "mode": "direct", "sources": [ { "label": "NIST Digital Library of Mathematical Functions, Chapter 4", "kind": "other", "reference": "Logarithm, Exponential, Powers", "url": "https://dlmf.nist.gov/4" }, { "label": "NIST DLMF §4.2", "kind": "other", "reference": "Logarithm: definitions and inverse of the exponential", "url": "https://dlmf.nist.gov/4.2" }, { "label": "CalculatorX mathematical conventions", "kind": "other", "reference": "Natural logarithm base e; real argument x > 0" } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Natural logarithm as inverse of exp" }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Precomputed mpmath 1.4.1 ln (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*", "engine": { "name": "ln-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": "ln-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 natural-log oracle — independent Math.log", "engine": { "name": "ln-reference", "precision_bits": 53, "independent_of_iut": true } }, { "class": "O2", "reference_scope": "numerical_behavior", "scope": "numerical_behavior", "label": "Same O2 module backs ≤2 ULP value comparison vs IUT", "engine": { "name": "ln-reference", "precision_bits": 53, "independent_of_iut": true } } ], "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node Math.log). O2 is a live oracle for identities and shares V8 binary64 with the IUT. O3 ≤2 ULP is a tabulated-vector claim, not a whole-domain guarantee." }, "controls": { "CVP-PROV-01": { "result": "PASS", "applicability": "required", "notes": "Sources present on evidence" }, "CVP-MODEL-01": { "result": "PASS", "applicability": "required", "notes": "y = ln(x) = log_e(x)" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "Real ln: x > 0" }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "dimensionless (unitless core)" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O3 mpmath ln table + O2 live identities" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "11/11 legacy golden; 3/3 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "12/12 boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "12 invalid-domain cases" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "≤2 ULP vs O3 applies to the 16 published tabulated natural-log vectors. It is not a guarantee over the whole positive reals or unlisted neighborhoods of 0 and 1. Legacy Evidence `tol` is not this policy." }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "3/3 declared partitions (ln, invalid-domain, xcal) · 11 golden / 12 boundary unique cases · 12 Evidence invalid-input (may overlap boundary)" }, "CVP-CONTRACT-01": { "result": "PASS", "applicability": "required", "notes": "1/1 contract checks" }, "CVP-DEP-01": { "result": "PASS", "applicability": "required", "notes": "engine ln; 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 1.0.4 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.4 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-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": "2/2 property" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "2/2 metamorphic" }, "CVP-ROUND-01": { "result": "PASS", "applicability": "applicable", "notes": "3/3 round-trips" }, "CVP-XCAL-01": { "result": "PASS", "applicability": "applicable", "notes": "12/12 cross-calculator · xcal-antilog-10 PASS vs math.antilog; xcal-antilog-2 PASS vs math.antilog; xcal-antilog-e PASS vs math.antilog; xcal-antilog-half PASS vs math.antilog; xcal-log-10 PASS vs math.log; xcal-log-2 PASS vs math.log; xcal-log-e PASS vs math.log; xcal-log-half PASS vs math.log; xcal-exponent-0 PASS vs math.exponent; xcal-exponent-1 PASS vs math.exponent; xcal-exponent-2 PASS vs math.exponent; xcal-exponent-neg1 PASS vs math.exponent; xcal-growth-na N/A (Exponential growth is listed as a related continuous-growth tool. It does not encode antilog(ln x, e)=x, log_e(x)=ln(x), or ln(e^n)=n.)" }, "CVP-IFACE-01": { "result": "PASS", "applicability": "applicable", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session." }, "CVP-ORACLE-01": { "result": "PASS", "applicability": "higher_assurance", "notes": "O3 16/16 tabulated vectors vs IUT · ≤2 ULP vs O3 applies to the 16 published tabulated natural-log vectors. It is not a guarantee over the whole positive reals or unlisted neighborhoods of 0 and 1." }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "expert_reviewed=false" } }, "tests": { "golden": { "passed": 3, "total": 3, "failed": 0, "case_ids": [ "g-ln-e", "g-ln-1", "g-ln-10" ] }, "boundary": { "passed": 12, "total": 12, "failed": 0, "case_ids": [ "x-zero", "x-neg", "empty-x", "y-only", "x-infinity", "x-nan", "x-abc", "x-whitespace", "x-null", "x-object", "x-array", "x-boolean" ] }, "invalid": { "passed": 12, "total": 12, "failed": 0, "case_ids": [ "x-zero", "x-neg", "empty-x", "y-only", "x-infinity", "x-nan", "x-abc", "x-whitespace", "x-null", "x-object", "x-array", "x-boolean" ] }, "property": { "passed": 2, "total": 2, "failed": 0, "case_ids": [ "prop-ln-1", "prop-ln-e" ], "definition_ids": [ "ln-one-is-zero", "ln-e-is-one" ] }, "round_trip": { "passed": 3, "total": 3, "failed": 0, "case_ids": [ "rt-e", "rt-1", "rt-10" ] }, "metamorphic": { "passed": 2, "total": 2, "failed": 0, "case_ids": [ "meta-power-e", "meta-power-10" ], "definition_ids": [ "ln-power" ] }, "contract": { "passed": 1, "total": 1, "failed": 0 }, "cross_interface": { "passed": 1, "total": 1, "failed": 0, "case_ids": [ "iface-ln" ] }, "cross_calculator": { "passed": 12, "total": 12, "failed": 0, "case_ids": [ "xcal-antilog-10", "xcal-antilog-2", "xcal-antilog-e", "xcal-antilog-half", "xcal-log-10", "xcal-log-2", "xcal-log-e", "xcal-log-half", "xcal-exponent-0", "xcal-exponent-1", "xcal-exponent-2", "xcal-exponent-neg1" ] }, "ui_integration": { "passed": 4, "total": 4, "failed": 0, "case_ids": [ "ui-ln-10", "ui-ln-1", "ui-ln-2", "ui-ln-outside-overview" ] }, "o3": { "passed": 16, "total": 16, "failed": 0, "case_ids": [ "o3-ln-1p0", "o3-ln-2p718281828459045", "o3-ln-10p0", "o3-ln-0p5", "o3-ln-2p0", "o3-ln-100p0", "o3-ln-1em06", "o3-ln-1000000p0", "o3-ln-rand-00", "o3-ln-rand-01", "o3-ln-rand-02", "o3-ln-rand-03", "o3-ln-rand-04", "o3-ln-rand-05", "o3-ln-rand-06", "o3-ln-rand-07" ], "generator_id": "math-mpmath-o3", "seed": "20260907", "max_error_ulp": 0, "claim_scope": "≤2 ULP vs O3 applies to the 16 published tabulated natural-log vectors. It is not a guarantee over the whole positive reals or unlisted neighborhoods of 0 and 1." } }, "coverage": { "partitions": [ { "id": "ln", "description": "Natural logarithm", "exercised": true, "case_count": 49 }, { "id": "invalid-domain", "description": "Invalid inputs", "exercised": true, "case_count": 12 }, { "id": "xcal", "description": "Cross-calculator antilog(ln x, e)=x vs Antilog, log_e(x)=ln(x) vs Log, ln(e^n)=n vs Exponent; exponential growth N/A", "exercised": true, "case_count": 12 } ] }, "numerical": { "representation": "IEEE-754 binary64 Math.log", "tolerance": { "type": "ulp", "value": 2, "rationale": "Independent Math.log vs IUT ln; ≤2 ULP on value. 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 16 published tabulated natural-log vectors. It is not a guarantee over the whole positive reals or unlisted neighborhoods of 0 and 1.", "max_error_observed": 1, "records": [ { "id": "g-ln-e", "reference": { "value": 1, "y": 1 }, "actual": { "y": 1, "value": 1, "verification": { "expression": "exp(result)", "value": 2.718281828459045, "passed": true }, "exact": true }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "g-ln-1", "reference": { "value": 0, "y": 0 }, "actual": { "y": 0, "value": 0, "verification": { "expression": "exp(result)", "value": 1, "passed": true }, "exact": true }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "g-ln-10", "reference": { "value": 2.302585092994046, "y": 2.302585092994046 }, "actual": { "y": 2.302585092994046, "value": 2.302585092994046, "verification": { "expression": "exp(result)", "value": 10.000000000000002, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-1p0", "reference": { "value": 0, "y": 0 }, "actual": { "y": 0, "value": 0, "verification": { "expression": "exp(result)", "value": 1, "passed": true }, "exact": true }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-2p718281828459045", "reference": { "value": 1, "y": 1 }, "actual": { "y": 1, "value": 1, "verification": { "expression": "exp(result)", "value": 2.718281828459045, "passed": true }, "exact": true }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-10p0", "reference": { "value": 2.302585092994046, "y": 2.302585092994046 }, "actual": { "y": 2.302585092994046, "value": 2.302585092994046, "verification": { "expression": "exp(result)", "value": 10.000000000000002, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-0p5", "reference": { "value": -0.6931471805599453, "y": -0.6931471805599453 }, "actual": { "y": -0.6931471805599453, "value": -0.6931471805599453, "verification": { "expression": "exp(result)", "value": 0.5, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-2p0", "reference": { "value": 0.6931471805599453, "y": 0.6931471805599453 }, "actual": { "y": 0.6931471805599453, "value": 0.6931471805599453, "verification": { "expression": "exp(result)", "value": 2, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-100p0", "reference": { "value": 4.605170185988092, "y": 4.605170185988092 }, "actual": { "y": 4.605170185988092, "value": 4.605170185988092, "verification": { "expression": "exp(result)", "value": 100.00000000000004, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-1em06", "reference": { "value": -13.815510557964274, "y": -13.815510557964274 }, "actual": { "y": -13.815510557964274, "value": -13.815510557964274, "verification": { "expression": "exp(result)", "value": 0.0000010000000000000004, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-1000000p0", "reference": { "value": 13.815510557964274, "y": 13.815510557964274 }, "actual": { "y": 13.815510557964274, "value": 13.815510557964274, "verification": { "expression": "exp(result)", "value": 999999.9999999995, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-00", "reference": { "value": -1.2778976290939674, "y": -1.2778976290939674 }, "actual": { "y": -1.2778976290939674, "value": -1.2778976290939674, "verification": { "expression": "exp(result)", "value": 0.27862245287264054, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-01", "reference": { "value": 1.9778783464050913, "y": 1.9778783464050913 }, "actual": { "y": 1.9778783464050913, "value": 1.9778783464050913, "verification": { "expression": "exp(result)", "value": 7.227392683239344, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-02", "reference": { "value": -4.950013380716971, "y": -4.950013380716971 }, "actual": { "y": -4.950013380716971, "value": -4.950013380716971, "verification": { "expression": "exp(result)", "value": 0.007083314148596167, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-03", "reference": { "value": 0.7650154108690876, "y": 0.7650154108690876 }, "actual": { "y": 0.7650154108690876, "value": 0.7650154108690876, "verification": { "expression": "exp(result)", "value": 2.149027492781387, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-04", "reference": { "value": 1.1145383143859506, "y": 1.1145383143859506 }, "actual": { "y": 1.1145383143859506, "value": 1.1145383143859506, "verification": { "expression": "exp(result)", "value": 3.048160562388507, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-05", "reference": { "value": 5.76040828685017, "y": 5.76040828685017 }, "actual": { "y": 5.76040828685017, "value": 5.76040828685017, "verification": { "expression": "exp(result)", "value": 317.47792452176134, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-06", "reference": { "value": -4.296453978331587, "y": -4.296453978331587 }, "actual": { "y": -4.296453978331587, "value": -4.296453978331587, "verification": { "expression": "exp(result)", "value": 0.013616758824750753, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-ln-rand-07", "reference": { "value": 5.796915718559824, "y": 5.796915718559824 }, "actual": { "y": 5.796915718559824, "value": 5.796915718559824, "verification": { "expression": "exp(result)", "value": 329.28239252889983, "passed": true } }, "error_ulp": 0, "threshold_ulp": 2 } ] }, "interfaces": { "compared": [ "ui-ssr", "rest", "mcp", "ui-url-result-graph" ], "result": "PASS", "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). 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