{"abstract":"Bit length advances exact powers unnecessarily.","category":"Integer arithmetic","checks":4,"contract":"Integer arguments; denominators, steps, moduli, and bit widths are positive. Unsigned word inputs fit the specified width except where masking is explicitly the operation. Sequence sizes are nonnegative. n is nonnegative; return the least positive power of two >=n. Exact operational definition: 1 if n <= 1 else 1 << (n-1).bit_length()","evaluation_group":"model-c7c32504fca7ebaa","failed_approach":"Rounding downward cannot enclose a nonpower.","family":"xn-next-power-of-two-inclusive","id":"FA-5411","implementations":{"attempt":{"sha256":"383375f620cce9a14e23f972469eab44ccb24d83fd52e4f20388acbabbbb8d0e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return 1 << max(0,n.bit_length()-1)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (8,)', solve(*(8,)), 8)\ncheck('fixture 4: (9,)', solve(*(9,)), 16)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"8129e432aa582ddccc36c5566e855b4b1dfb7f03b8740e670f263914b27c5dff","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return 1 << n.bit_length()\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (8,)', solve(*(8,)), 8)\ncheck('fixture 4: (9,)', solve(*(9,)), 16)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"a86c2f8ef42f1966c0fe3a91412a17c667b13a2a7d78f9205f1879e0ec8ed4cb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return 1 if n <= 1 else 1 << (n-1).bit_length()\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 1)\ncheck('fixture 3: (8,)', solve(*(8,)), 8)\ncheck('fixture 4: (9,)', solve(*(9,)), 16)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"xn-next-power-of-two-inclusive","generated_at":"2026-09-29T14:37:49.399135+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Integer mathematics results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return 1 if n <= 1 else 1 << (n-1).bit_length()","root_cause":"Bit length advances exact powers unnecessarily.","sha256":"684a79bea92595741feb25d3f6361ca5b656917c0a035f50bc4f582b7e7c8a31","title":"Next power of two inclusive · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":132.669,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":8,"check":"fixture 3: (8,)","expected":8,"passed":true},{"actual":8,"check":"fixture 4: (9,)","expected":16,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (8,)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 4: (9,)\", \"actual\": 8, \"expected\": 16, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.264,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":2,"check":"fixture 2: (1,)","expected":1,"passed":false},{"actual":16,"check":"fixture 3: (8,)","expected":8,"passed":false},{"actual":16,"check":"fixture 4: (9,)","expected":16,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (8,)\", \"actual\": 16, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 4: (9,)\", \"actual\": 16, \"expected\": 16, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.921,"exit_code":0,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":1,"passed":true},{"actual":8,"check":"fixture 3: (8,)","expected":8,"passed":true},{"actual":16,"check":"fixture 4: (9,)","expected":16,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (8,)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 4: (9,)\", \"actual\": 16, \"expected\": 16, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}