{ "protocol": { "name": "CVP", "version": "1.0.0-proposed" }, "document_status": "proposed", "calculator": { "id": "tan", "version": "1.0.4", "title": "Tangent Calculator", "formula_family": "tangent", "capability_id": "math.tan", "verification_revision": "2026-09-08.policy" }, "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": "tan", "version": "1.0.4", "uri": "https://www.calculatorx.com/evidence/math.tan/1.0.4.json", "verification_revision": "2026-09-08.policy" }, "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-DIM-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": "Elementary Functions", "url": "https://dlmf.nist.gov/4" }, { "label": "NIST DLMF §4.14", "kind": "other", "reference": "Trigonometric functions", "url": "https://dlmf.nist.gov/4.14" }, { "label": "CalculatorX mathematical conventions", "kind": "other", "reference": "Poles are UNDEFINED, not Infinity; inverse is Arctan" } ] }, "reference": { "items": [ { "class": "O1", "reference_scope": "model", "scope": "model", "label": "Tangent of angle θ" }, { "class": "O3", "reference_scope": "expected_values", "scope": "expected_values", "label": "Precomputed mpmath 1.4.1 tan (80 dps, python backend, round-to-nearest-binary64) — not Node Math.*", "engine": { "name": "tan-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": "tan-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 tangent oracle — independent Math.tan + documented snap/cleanup", "engine": { "name": "tan-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": "tan-reference", "precision_bits": 53, "independent_of_iut": true } } ], "notes": "Golden expected values prefer an O3 mpmath/MPFR table (independent of Node Math.tan). 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": "tan(θ); documented 1e-12° pole classification → UNDEFINED; principal inverse on (−90°, 90°)" }, "CVP-SCOPE-01": { "result": "PASS", "applicability": "required", "notes": "deg|rad; pole classification / snap / |y| cleanup are documented numerical policies" }, "CVP-UNIT-01": { "result": "PASS", "applicability": "required", "notes": "angle in; dimensionless out" }, "CVP-REF-01": { "result": "PASS", "applicability": "required", "notes": "O1 model + O3 expected_values/numerical_behavior (mpmath table) + O2 live identities" }, "CVP-GOLD-01": { "result": "PASS", "applicability": "required", "notes": "15/15 legacy golden; 4/4 oracle-backed numeric" }, "CVP-BND-01": { "result": "PASS", "applicability": "required", "notes": "10/10 boundary" }, "CVP-INV-01": { "result": "PASS", "applicability": "required", "notes": "8 invalid-domain cases" }, "CVP-NUM-01": { "result": "PASS", "applicability": "required", "notes": "≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros. Legacy Evidence `tol` is not this policy." }, "CVP-COV-01": { "result": "PASS", "applicability": "required", "notes": "3/3 declared partitions (tan, invalid-domain, xcal) · 15 golden / 10 boundary unique cases · 8 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 tan; 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 · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20" }, "CVP-DIM-01": { "result": "PASS", "applicability": "applicable", "notes": "angle in → dimensionless tangent (unitless core)" }, "CVP-PROP-01": { "result": "PASS", "applicability": "applicable", "notes": "5/5 property" }, "CVP-META-01": { "result": "PASS", "applicability": "applicable", "notes": "4/4 metamorphic" }, "CVP-ROUND-01": { "result": "PASS", "applicability": "applicable", "notes": "4/4 round-trips" }, "CVP-XCAL-01": { "result": "PASS", "applicability": "applicable", "notes": "11/11 cross-calculator · xcal-arctan-45 PASS vs math.arctan; xcal-arctan-0 PASS vs math.arctan; xcal-arctan-neg-30 PASS vs math.arctan; xcal-arctan-33 PASS vs math.arctan; xcal-cos-45 PASS vs math.cos; xcal-cos-0 PASS vs math.cos; xcal-cos-neg-30 PASS vs math.cos; xcal-cos-33 PASS vs math.cos; xcal-sin-45 PASS vs math.sin; xcal-sin-30 PASS vs math.sin; xcal-sin-33 PASS vs math.sin; xcal-arctan-huge-na N/A (arctan(tan θ)=θ is not claimed as a binary64 identity for huge angles (e.g. 1e16°) after degree→radian conversion loses phase bits, nor at poles. Those inputs are outside the O3 table and XCAL vectors.); xcal-arcsin-na N/A (Arcsin is listed as a related inverse-trig tool. It does not encode arctan(tan θ)=θ, 1+tan²θ=sec²θ, or 1+cot²θ=csc²θ.)" }, "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 vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros." }, "CVP-EXP-01": { "result": "SKIP", "applicability": "optional", "notes": "expert_reviewed=false" } }, "tests": { "golden": { "passed": 4, "total": 4, "failed": 0, "case_ids": [ "g-tan-45", "g-tan-0", "g-tan-30", "g-tan-33" ] }, "boundary": { "passed": 10, "total": 10, "failed": 0, "case_ids": [ "deg-90", "deg-270", "deg-neg-90", "rad-pi-2", "near-pole-89.99999995", "near-pole-90.00000005", "missing-theta", "theta-abc", "invalid-unit", "boundary-tan-pole" ] }, "invalid": { "passed": 8, "total": 8, "failed": 0, "case_ids": [ "deg-90", "deg-270", "deg-neg-90", "rad-pi-2", "missing-theta", "theta-abc", "invalid-unit", "boundary-tan-pole" ] }, "property": { "passed": 5, "total": 5, "failed": 0, "case_ids": [ "prop-no-snap-60", "prop-near-pole-finite", "prop-period-45", "prop-cleanup-tiny", "prop-pole-classified" ], "definition_ids": [ "snap-is-classification-window", "near-pole-not-undefined", "period-180-at-listed-snap", "documented-zero-cleanup", "pole-classification-threshold" ] }, "round_trip": { "passed": 4, "total": 4, "failed": 0, "case_ids": [ "rt-45", "rt-0", "rt-neg-30", "rt-33" ] }, "metamorphic": { "passed": 4, "total": 4, "failed": 0, "case_ids": [ "meta-odd-15", "meta-odd-33", "meta-period-45", "meta-period-33" ], "definition_ids": [ "tan-odd", "tan-period-180-listed-snap", "tan-period-180-iut-o2" ] }, "contract": { "passed": 1, "total": 1, "failed": 0 }, "cross_interface": { "passed": 1, "total": 1, "failed": 0, "case_ids": [ "iface-tan" ] }, "cross_calculator": { "passed": 11, "total": 11, "failed": 0, "case_ids": [ "xcal-arctan-45", "xcal-arctan-0", "xcal-arctan-neg-30", "xcal-arctan-33", "xcal-cos-45", "xcal-cos-0", "xcal-cos-neg-30", "xcal-cos-33", "xcal-sin-45", "xcal-sin-30", "xcal-sin-33" ] }, "ui_integration": { "passed": 4, "total": 4, "failed": 0, "case_ids": [ "ui-tan-45", "ui-tan-0", "ui-tan-30", "ui-tan-outside" ] }, "o3": { "passed": 16, "total": 16, "failed": 0, "case_ids": [ "o3-tan-0", "o3-tan-30", "o3-tan-45", "o3-tan-60", "o3-tan-33.3", "o3-tan-12.5", "o3-tan--30", "o3-tan-15", "o3-tan-rand-00", "o3-tan-rand-01", "o3-tan-rand-02", "o3-tan-rand-03", "o3-tan-rand-04", "o3-tan-rand-05", "o3-tan-rand-06", "o3-tan-rand-07" ], "generator_id": "math-mpmath-o3", "seed": "20260907", "table_sha256": "efdad939a92a67df1f3995db36c52bb87f428a59fc73568f789c02540f4372ee", "max_error_ulp": 1, "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 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros.", "reproduce_url": "https://www.calculatorx.com/evidence/math.tan/reproduce" } }, "coverage": { "partitions": [ { "id": "tan", "description": "tan(θ)", "exercised": true, "case_count": 61 }, { "id": "invalid-domain", "description": "Invalid / poles", "exercised": true, "case_count": 8 }, { "id": "xcal", "description": "Cross-calculator arctan(tan θ)≈θ vs Arctan, 1+tan²θ=sec²θ vs Cos, 1+cot²θ=csc²θ vs Sin; Arcsin N/A", "exercised": true, "case_count": 11 } ] }, "numerical": { "representation": "IEEE-754 binary64 Math.tan with documented snap/cleanup", "tolerance": { "type": "ulp", "value": 2, "rationale": "Independent tan with the same documented snap/pole/cleanup policy vs IUT; ≤2 ULP on tabulated O3 vectors, declared a priori. Not a whole-domain ULP guarantee.", "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 vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, huge angles, or unlisted neighborhoods of zeros.", "max_error_observed": 2, "records": [ { "id": "g-tan-45", "reference": 1, "actual": 1, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "g-tan-0", "reference": 0, "actual": 0, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "g-tan-30", "reference": 0.5773502691896257, "actual": 0.5773502691896258, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "g-tan-33", "reference": 0.6568772224012793, "actual": 0.6568772224012792, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "o3-tan-0", "reference": 0, "actual": 0, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-30", "reference": 0.5773502691896257, "actual": 0.5773502691896258, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "o3-tan-45", "reference": 1, "actual": 1, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-60", "reference": 1.7320508075688772, "actual": 1.7320508075688772, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-33.3", "reference": 0.6568772224012793, "actual": 0.6568772224012792, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "o3-tan-12.5", "reference": 0.2216946626429399, "actual": 0.2216946626429399, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan--30", "reference": -0.5773502691896257, "actual": -0.5773502691896258, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "o3-tan-15", "reference": 0.2679491924311227, "actual": 0.2679491924311227, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-rand-00", "reference": -0.16771974138327453, "actual": -0.16771974138327453, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-rand-01", "reference": -1.1575417700993667, "actual": -1.1575417700993667, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-rand-02", "reference": -0.27029227487610746, "actual": -0.27029227487610746, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-rand-03", "reference": -0.371381992439033, "actual": -0.37138199243903297, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "o3-tan-rand-04", "reference": 0.8859991849240253, "actual": 0.8859991849240252, "error_ulp": 1, "threshold_ulp": 2 }, { "id": "o3-tan-rand-05", "reference": 0.3306722711014023, "actual": 0.3306722711014023, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-rand-06", "reference": -0.6450661727384714, "actual": -0.6450661727384714, "error_ulp": 0, "threshold_ulp": 2 }, { "id": "o3-tan-rand-07", "reference": 0.011387053231385207, "actual": 0.011387053231385206, "error_ulp": 1, "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). Hydration/slider/history are URL-canonical contracts, not a live browser session." }, "artifacts": { "evidence_bundle_sha256": "ab920a88aaf27f5e32cc431e7f5f3f327276e0a33a024fd1507fdea295404ca6", "evidence_digest": "494caf2c4f61ecefebf48bb718c54af5c4bd5e6f5cf0dff15a07b2d4fbe00926", "production_sha256": "9424f31d3ca937ec4a453e41479201945df6495214f0a220ebb742e7fd1c3f20", "attested_catalog_sha256": "e03ef81b30568018b171fd1fc4757c2abe9df7220d9ff35bbaf08038d7630cdb", "production_checks": [ { "id": "math.tan:output-const", "status": "pass", "detail": "output const 1.0.4 vs capability 1.0.4", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-10T02:52:51.379Z" }, { "id": "math.tan:evidence-sha256", "status": "pass", "detail": "1f4a555a1b14", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-10T02:52:51.379Z" }, { "id": "math.tan:semantic-contract", "status": "pass", "detail": "25/25", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-10T02:52:51.379Z" }, { "id": "math.tan:capability-html-public-origin-agree", "status": "pass", "detail": "public 1.0.4 vs origin 1.0.4", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-10T02:52:51.379Z" }, { "id": "math.tan:cvp-manifest-public-origin-agree", "status": "pass", "detail": "math.tan/1.0.4/2026-09-08.policy/core/494caf2c4f61", "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.tan:cvp-reproduce-manifest-agree", "status": "pass", "detail": "2026-09-08.policy · efdad939a92a", "scope": "last_attestation_snapshot", "current": true, "attestation_binding_current": true, "attested_at": "2026-09-10T02:52:51.379Z" }, { "id": "math.tan: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.tan: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": "tan-engine", "version": "1.0.4" }, { "name": "tan-reference-oracle", "version": "1.0.0" }, { "name": "tan-o3-mpmath-table", "version": "math-mpmath-o3" }, { "name": "math.arctan", "version": "1.0.7", "role": "cross_calculator_peer", "capability_id": "math.arctan", "evidence_digest": "cf317536e8dd9dfcbd1d400e305b97fd335d742afd545e16f3141b246b79466a", "evidence": "https://www.calculatorx.com/evidence/math.arctan/1.0.7.cvp.json" }, { "name": "math.cos", "version": "1.0.5", "role": "cross_calculator_peer", "capability_id": "math.cos", "evidence_digest": "ece0bdda8ca9515cd122d2544c9f69ccbc9c211a3294389127b1204dd18fcdae", "evidence": "https://www.calculatorx.com/evidence/math.cos/1.0.5.cvp.json" }, { "name": "math.sin", "version": "1.0.5", "role": "cross_calculator_peer", "capability_id": "math.sin", "evidence_digest": "f6d93820711850b8f88be0ab287f36990a6f663d1e1ed3c2cd2c88c69409c43e", "evidence": "https://www.calculatorx.com/evidence/math.sin/1.0.5.cvp.json" }, { "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": "1.0.4" }, "timestamps": { "verified_at": "2026-09-10T03:41:49.888Z", "generated_at": "2026-09-10T03:41:49.888Z" }, "links": { "legacy_evidence": "https://www.calculatorx.com/evidence/math.tan/1.0.4.json", "evidence_page": "https://www.calculatorx.com/evidence/math.tan/1.0.4", "calculator": "https://www.calculatorx.com/calc/math/tan", "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.tan/1.0.4.cvp.json", "manifest_immutable": "https://www.calculatorx.com/evidence/math.tan/1.0.4/2026-09-08.policy.cvp.json", "reproduce": "https://www.calculatorx.com/evidence/math.tan/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" } }