{"abstract":"Exact ratio conversion returns a zero denominator for zero.","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.","evaluation_group":"s3-float-float-ratio","failed_approach":"The attempted local correction if mantissa==0: return [sign,1] still violates the explicit regression fixtures.","family":"s3-floating_point_arithmetic-float-ratio-zero-ratio","id":"FA-16626","implementations":{"attempt":{"sha256":"90ee0b5f5905d32422b9b4e87b7e8a8bb045ec5f454b953fd913a546094c446b","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 [sign,1]\n while power<0 and mantissa%2==0:\n mantissa//=2\n power+=1\n if power>=0: return [sign*(mantissa<>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 [0,0]\n while power<0 and mantissa%2==0:\n mantissa//=2\n power+=1\n if power>=0: return [sign*(mantissa<>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<