{"abstract":"Sinc divides the sine by unsigned magnitude.","category":"Floating-point arithmetic","checks":7,"contract":"Evaluate sin(x)/x on finite x with continuous value one at zero. Tiny values use the fourth-degree even series. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.","contract_signature":"x","evaluation_group":"s3-float-sinc","failed_approach":"The attempted local correction result=abs(math.sin(x))/abs(x) still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-sinc-denominator-sign","id":"FA-16346","implementations":{"attempt":{"sha256":"f69157289bc223e02d351d6d015fe5f1772c1be30d882ad28b444f6393f4ad4e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x==0: return '1'\n        if abs(x)<1e-3:\n            t=x*x\n            result=1-t/6+t*t/120\n        else:\n            result=abs(math.sin(x))/abs(x)\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('zero', solve(0.0), \"1\")\ncheck('negative zero', solve(-0.0), \"1\")\ncheck('small', solve(N*1e-4), render(math.sin(N*1e-4)/(N*1e-4)))\ncheck('negative small', solve(-N*1e-4), render(math.sin(-N*1e-4)/(-N*1e-4)))\ncheck('normal', solve(float(N)), render(math.sin(N)/N))\ncheck('negative normal', solve(-float(N)), render(math.sin(-N)/(-N)))\ncheck('phase crossing', solve(math.pi+0.125*N), render(math.sin(math.pi+0.125*N)/(math.pi+0.125*N)))\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":"08c0c3adf0c4888ca4e876142ab7475bfc45f5261f3da8d609ad0f63e09e623f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\ndef render(x):\n    if math.isnan(x): return 'nan'\n    if math.isinf(x): return '-infinity' if x<0 else '+infinity'\n    return format(x,'.11g')\n\nN = 1\nobservations = []\ndef solve(x):\n    try:\n        if x==0: return '1'\n        if abs(x)<1e-3:\n            t=x*x\n            result=1-t/6+t*t/120\n        else:\n            result=math.sin(x)/abs(x)\n        return render(result)\n    except (ValueError, OverflowError, ZeroDivisionError, TypeError):\n        return \"arithmetic-error\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('zero', solve(0.0), \"1\")\ncheck('negative zero', solve(-0.0), \"1\")\ncheck('small', solve(N*1e-4), render(math.sin(N*1e-4)/(N*1e-4)))\ncheck('negative small', solve(-N*1e-4), render(math.sin(-N*1e-4)/(-N*1e-4)))\ncheck('normal', solve(float(N)), render(math.sin(N)/N))\ncheck('negative normal', solve(-float(N)), render(math.sin(-N)/(-N)))\ncheck('phase crossing', solve(math.pi+0.125*N), render(math.sin(math.pi+0.125*N)/(math.pi+0.125*N)))\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":"Controlled binary64 or explicitly stipulated miniature format; no hardware exception flags or platform floating environment are modeled. 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":"s3-floating_point_arithmetic-sinc-denominator-sign","generated_at":"2026-09-29T14:39:35.400742+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"An offline floating representation model isolates a reproducible arithmetic fault.","root_cause":"Sinc divides the sine by unsigned magnitude. The faulty expression is result=math.sin(x)/abs(x).","sha256":"45885ca41a6b9730e1218af50dcbd7aa2b278c2f27c7c5a369f03ea62c3a3624","title":"Sinc divides the sine by unsigned magnitude · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":42.883,"exit_code":1,"observations":[{"actual":"1","check":"zero","expected":"1","passed":true},{"actual":"1","check":"negative zero","expected":"1","passed":true},{"actual":"0.99999999833","check":"small","expected":"0.99999999833","passed":true},{"actual":"0.99999999833","check":"negative small","expected":"0.99999999833","passed":true},{"actual":"0.84147098481","check":"normal","expected":"0.84147098481","passed":true},{"actual":"0.84147098481","check":"negative normal","expected":"0.84147098481","passed":true},{"actual":"0.038166599453","check":"phase crossing","expected":"-0.038166599453","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"negative zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"negative small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"negative normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"phase crossing\", \"actual\": \"0.038166599453\", \"expected\": \"-0.038166599453\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.071,"exit_code":1,"observations":[{"actual":"1","check":"zero","expected":"1","passed":true},{"actual":"1","check":"negative zero","expected":"1","passed":true},{"actual":"0.99999999833","check":"small","expected":"0.99999999833","passed":true},{"actual":"0.99999999833","check":"negative small","expected":"0.99999999833","passed":true},{"actual":"0.84147098481","check":"normal","expected":"0.84147098481","passed":true},{"actual":"-0.84147098481","check":"negative normal","expected":"0.84147098481","passed":false},{"actual":"-0.038166599453","check":"phase crossing","expected":"-0.038166599453","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"negative zero\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"negative small\", \"actual\": \"0.99999999833\", \"expected\": \"0.99999999833\", \"passed\": true}, {\"check\": \"normal\", \"actual\": \"0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": true}, {\"check\": \"negative normal\", \"actual\": \"-0.84147098481\", \"expected\": \"0.84147098481\", \"passed\": false}, {\"check\": \"phase crossing\", \"actual\": \"-0.038166599453\", \"expected\": \"-0.038166599453\", \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}