{"abstract":"Exact ratio conversion loses sign on integral outputs.","category":"Floating-point arithmetic","checks":11,"contract":"Decode a finite binary64 value into its exact reduced signed numerator and positive power-of-two denominator, using (0,1) for either zero. Infinity and NaN return null.","contract_signature":"bits","evaluation_group":"s3-float-float-ratio","failed_approach":"The attempted local correction if power>=0: return [sign*mantissa,1] still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-float-ratio-integer-sign","id":"FA-16641","implementations":{"attempt":{"sha256":"7cdc75f9b353100b6dfbbbdcd09f8305a2bfbe79f5c76ff5e82c87a2819f23e2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport struct\nN = 1\nobservations = []\ndef solve(bits):\n sign=-1 if bits>>63 else 1\n e=(bits>>52)&2047\n f=bits&((1<<52)-1)\n if e==2047: return None\n if e:\n mantissa=f|(1<<52)\n power=e-1023-52\n else:\n mantissa=f\n power=-1074\n if mantissa==0: return [0,1]\n while power<0 and mantissa%2==0:\n mantissa//=2\n power+=1\n if power>=0: return [sign*mantissa,1]\n return [sign*mantissa,1<<(-power)]\ndef check(label, actual, expected):\n observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('large integer', solve((1023+60+N)<<52), [1<<(60+N),1])\ncheck('positive integer', solve((1023+N)<<52), [1<>63 else 1\n e=(bits>>52)&2047\n f=bits&((1<<52)-1)\n if e==2047: return None\n if e:\n mantissa=f|(1<<52)\n power=e-1023-52\n else:\n mantissa=f\n power=-1074\n if mantissa==0: return [0,1]\n while power<0 and mantissa%2==0:\n mantissa//=2\n power+=1\n if power>=0: return [mantissa<=0: return [mantissa<