{"abstract":"0.125 at two fractional bits quantizes to code 0 instead of 1 (half away from zero).","category":"Digital signal filters","checks":6,"contract":"Input [coeffs, f, B, mode]: quantize each decimal coefficient to a B-bit two's-complement code with f fractional bits; \"nearest\" rounds half away from zero, \"truncate\" floors. Codes saturate to [-2^(B-1), 2^(B-1)-1]. Return {\"codes\", \"saturated\": count of clipped codes, \"max_error\": max |code/2^f - c| after saturation as a fraction string}.","contract_signature":"x","evaluation_group":"w2-digital_signal_filters-coefficient-quantization","failed_approach":"The attempted repair uses floor(v + 1/2), which rounds negative ties toward positive infinity.","family":"w2-digital_signal_filters-coefficient-quantization-tie-rounding-rule","id":"FA-91596","implementations":{"attempt":{"sha256":"3b40465180b296fbdc0a2b854f35efff77e9e4510604d2ba6df88797850d461d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    coeffs, f, B, mode = x\n    scale = 2 ** f\n    hi, lo = 2 ** (B - 1) - 1, -2 ** (B - 1)\n    codes = []\n    sat = 0\n    err = Fraction(0)\n    for s in coeffs:\n        c = Fraction(s)\n        v = c * scale\n        if mode == 'nearest':\n            q = math.floor(v + Fraction(1, 2))\n        else:\n            q = math.floor(v)\n        if q > hi or q < lo:\n            sat += 1\n            q = max(lo, min(hi, q))\n        codes.append(q)\n        err = max(err, abs(Fraction(q, scale) - c))\n    return {'codes': codes, 'saturated': sat, 'max_error': str(err)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['control: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: integer multiple truncate', [['-0.5', '1.25'], 3, 6, 'truncate'], {'codes': [-4, 10], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: random quantize 1', [['-1.919', '-2.19', '0.764', '-2.046'], 4, 7, 'truncate'], {'codes': [-31, -36, 12, -33], 'saturated': 0, 'max_error': '3/50'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['control: random quantize 4', [['-1.49', '-1.91'], 2, 3, 'nearest'], {'codes': [-4, -4], 'saturated': 2, 'max_error': '91/100'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: random quantize 5', [['1.92'], 4, 6, 'truncate'], {'codes': [30], 'saturated': 0, 'max_error': '9/200'}], ['control: random quantize 6', [['2.04', '0.49'], 3, 6, 'nearest'], {'codes': [16, 4], 'saturated': 0, 'max_error': '1/25'}], ['control: random quantize 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}], ['control: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['control: random quantize 10', [['-1.232', '-0.29', '-0.82', '0.594'], 4, 5, 'truncate'], {'codes': [-16, -5, -14, 9], 'saturated': 1, 'max_error': '29/125'}], ['control: random quantize 11', [['-0.158', '1.311', '1.13', '-0.89'], 6, 8, 'truncate'], {'codes': [-11, 83, 72, -57], 'saturated': 0, 'max_error': '113/8000'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\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":"57d74ee6425f22c313546f1009b50947eaf08398d06d6190af04684421cd9d3a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    coeffs, f, B, mode = x\n    scale = 2 ** f\n    hi, lo = 2 ** (B - 1) - 1, -2 ** (B - 1)\n    codes = []\n    sat = 0\n    err = Fraction(0)\n    for s in coeffs:\n        c = Fraction(s)\n        v = c * scale\n        if mode == 'nearest':\n            q = round(v)\n        else:\n            q = math.floor(v)\n        if q > hi or q < lo:\n            sat += 1\n            q = max(lo, min(hi, q))\n        codes.append(q)\n        err = max(err, abs(Fraction(q, scale) - c))\n    return {'codes': codes, 'saturated': sat, 'max_error': str(err)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['control: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: integer multiple truncate', [['-0.5', '1.25'], 3, 6, 'truncate'], {'codes': [-4, 10], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: random quantize 1', [['-1.919', '-2.19', '0.764', '-2.046'], 4, 7, 'truncate'], {'codes': [-31, -36, 12, -33], 'saturated': 0, 'max_error': '3/50'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['control: random quantize 4', [['-1.49', '-1.91'], 2, 3, 'nearest'], {'codes': [-4, -4], 'saturated': 2, 'max_error': '91/100'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: random quantize 5', [['1.92'], 4, 6, 'truncate'], {'codes': [30], 'saturated': 0, 'max_error': '9/200'}], ['control: random quantize 6', [['2.04', '0.49'], 3, 6, 'nearest'], {'codes': [16, 4], 'saturated': 0, 'max_error': '1/25'}], ['control: random quantize 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}], ['control: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}]], [['regression: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['control: random quantize 10', [['-1.232', '-0.29', '-0.82', '0.594'], 4, 5, 'truncate'], {'codes': [-16, -5, -14, 9], 'saturated': 1, 'max_error': '29/125'}], ['control: random quantize 11', [['-0.158', '1.311', '1.13', '-0.89'], 6, 8, 'truncate'], {'codes': [-11, 83, 72, -57], 'saturated': 0, 'max_error': '113/8000'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(args), expected)\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":"A deterministic bounded teaching model with a stipulated toy contract; exact rational arithmetic or fixed-decimal rounding keeps outputs strict JSON. It is not a production DSP library and claims no standards conformance. 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":"w2-digital_signal_filters-coefficient-quantization-tie-rounding-rule","generated_at":"2026-09-29T14:51:37.528413+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Coefficient quantization decides whether a fixed-point filter still meets spec; rounding and saturation slips shift poles.","root_cause":"Python round() on the scaled value uses banker rounding.","sha256":"c9924116ead0d0f86709f8484d9ffcdfe9ae169a3aa8366ac5d567fbe0a95e1d","title":"Coefficient quantizer rounds ties to even · 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":40.468,"exit_code":1,"observations":[{"actual":{"codes":[1,2,0],"max_error":"1/8","saturated":0},"check":"regression: tie cases nearest","expected":{"codes":[1,2,-1],"max_error":"1/8","saturated":0},"passed":false},{"actual":{"codes":[-3,2],"max_error":"3/40","saturated":0},"check":"control: negative truncate","expected":{"codes":[-3,2],"max_error":"3/40","saturated":0},"passed":true},{"actual":{"codes":[127,127],"max_error":"1/128","saturated":1},"check":"control: positive overflow","expected":{"codes":[127,127],"max_error":"1/128","saturated":1},"passed":true},{"actual":{"codes":[-128],"max_error":"0","saturated":0},"check":"control: negative full scale","expected":{"codes":[-128],"max_error":"0","saturated":0},"passed":true},{"actual":{"codes":[-128],"max_error":"1/2","saturated":1},"check":"control: negative overflow","expected":{"codes":[-128],"max_error":"1/2","saturated":1},"passed":true},{"actual":{"codes":[2,-1,3],"max_error":"0","saturated":0},"check":"control: exact grid truncate","expected":{"codes":[2,-1,3],"max_error":"0","saturated":0},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: tie cases nearest\", \"actual\": {\"codes\": [1, 2, 0], \"saturated\": 0, \"max_error\": \"1/8\"}, \"expected\": {\"codes\": [1, 2, -1], \"saturated\": 0, \"max_error\": \"1/8\"}, \"passed\": false}, {\"check\": \"control: negative truncate\", \"actual\": {\"codes\": [-3, 2], \"saturated\": 0, \"max_error\": \"3/40\"}, \"expected\": {\"codes\": [-3, 2], \"saturated\": 0, \"max_error\": \"3/40\"}, \"passed\": true}, {\"check\": \"control: positive overflow\", \"actual\": {\"codes\": [127, 127], \"saturated\": 1, \"max_error\": \"1/128\"}, \"expected\": {\"codes\": [127, 127], \"saturated\": 1, \"max_error\": \"1/128\"}, \"passed\": true}, {\"check\": \"control: negative full scale\", \"actual\": {\"codes\": [-128], \"saturated\": 0, \"max_error\": \"0\"}, \"expected\": {\"codes\": [-128], \"saturated\": 0, \"max_error\": \"0\"}, \"passed\": true}, {\"check\": \"control: negative overflow\", \"actual\": {\"codes\": [-128], \"saturated\": 1, \"max_error\": \"1/2\"}, \"expected\": {\"codes\": [-128], \"saturated\": 1, \"max_error\": \"1/2\"}, \"passed\": true}, {\"check\": \"control: exact grid truncate\", \"actual\": {\"codes\": [2, -1, 3], \"saturated\": 0, \"max_error\": \"0\"}, \"expected\": {\"codes\": [2, -1, 3], \"saturated\": 0, \"max_error\": \"0\"}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.065,"exit_code":1,"observations":[{"actual":{"codes":[0,2,0],"max_error":"1/8","saturated":0},"check":"regression: tie cases nearest","expected":{"codes":[1,2,-1],"max_error":"1/8","saturated":0},"passed":false},{"actual":{"codes":[-3,2],"max_error":"3/40","saturated":0},"check":"control: negative truncate","expected":{"codes":[-3,2],"max_error":"3/40","saturated":0},"passed":true},{"actual":{"codes":[127,127],"max_error":"1/128","saturated":1},"check":"control: positive overflow","expected":{"codes":[127,127],"max_error":"1/128","saturated":1},"passed":true},{"actual":{"codes":[-128],"max_error":"0","saturated":0},"check":"control: negative full scale","expected":{"codes":[-128],"max_error":"0","saturated":0},"passed":true},{"actual":{"codes":[-128],"max_error":"1/2","saturated":1},"check":"control: negative overflow","expected":{"codes":[-128],"max_error":"1/2","saturated":1},"passed":true},{"actual":{"codes":[2,-1,3],"max_error":"0","saturated":0},"check":"control: exact grid truncate","expected":{"codes":[2,-1,3],"max_error":"0","saturated":0},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: tie cases nearest\", \"actual\": {\"codes\": [0, 2, 0], \"saturated\": 0, \"max_error\": \"1/8\"}, \"expected\": {\"codes\": [1, 2, -1], \"saturated\": 0, \"max_error\": \"1/8\"}, \"passed\": false}, {\"check\": \"control: negative truncate\", \"actual\": {\"codes\": [-3, 2], \"saturated\": 0, \"max_error\": \"3/40\"}, \"expected\": {\"codes\": [-3, 2], \"saturated\": 0, \"max_error\": \"3/40\"}, \"passed\": true}, {\"check\": \"control: positive overflow\", \"actual\": {\"codes\": [127, 127], \"saturated\": 1, \"max_error\": \"1/128\"}, \"expected\": {\"codes\": [127, 127], \"saturated\": 1, \"max_error\": \"1/128\"}, \"passed\": true}, {\"check\": \"control: negative full scale\", \"actual\": {\"codes\": [-128], \"saturated\": 0, \"max_error\": \"0\"}, \"expected\": {\"codes\": [-128], \"saturated\": 0, \"max_error\": \"0\"}, \"passed\": true}, {\"check\": \"control: negative overflow\", \"actual\": {\"codes\": [-128], \"saturated\": 1, \"max_error\": \"1/2\"}, \"expected\": {\"codes\": [-128], \"saturated\": 1, \"max_error\": \"1/2\"}, \"passed\": true}, {\"check\": \"control: exact grid truncate\", \"actual\": {\"codes\": [2, -1, 3], \"saturated\": 0, \"max_error\": \"0\"}, \"expected\": {\"codes\": [2, -1, 3], \"saturated\": 0, \"max_error\": \"0\"}, \"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."}}