FA-5331 / Integer arithmetic / Open access
Ceiling integer quotient · case 01
Floor division is substituted for ceiling division.
ROOT CAUSE
Floor division is substituted for ceiling division.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return -(-a // b)
Unsuccessful approach: The signed shortcut truncates negative nonmultiples incorrectly.
Case 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. Return the least integer greater than or equal to a/b, including negative a. Exact operational definition: -(-a // b)
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Integer mathematics results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(a, b):
return a // b
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (7, 3)', solve(*(7, 3)), 3)
check('fixture 2: (-7, 3)', solve(*(-7, 3)), -2)
check('fixture 3: (6, 3)', solve(*(6, 3)), 2)
check('fixture 4: (0, 3)', solve(*(0, 3)), 0)
check('fixture 5: (-1, 3)', solve(*(-1, 3)), 0)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: (7, 3) | 2 | 3 | Failed |
| fixture 2: (-7, 3) | -3 | -2 | Failed |
| fixture 3: (6, 3) | 2 | 2 | Passed |
| fixture 4: (0, 3) | 0 | 0 | Passed |
| fixture 5: (-1, 3) | -1 | 0 | Failed |
SHA-256 / 9242eafef1ec4662481a07c2111ca89fc404e8d2286027b2b52a29159cf85100
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(a, b):
return (a + b - 1) // b if a >= 0 else -((abs(a)+b-1) // b)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (7, 3)', solve(*(7, 3)), 3)
check('fixture 2: (-7, 3)', solve(*(-7, 3)), -2)
check('fixture 3: (6, 3)', solve(*(6, 3)), 2)
check('fixture 4: (0, 3)', solve(*(0, 3)), 0)
check('fixture 5: (-1, 3)', solve(*(-1, 3)), 0)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: (7, 3) | 3 | 3 | Passed |
| fixture 2: (-7, 3) | -3 | -2 | Failed |
| fixture 3: (6, 3) | 2 | 2 | Passed |
| fixture 4: (0, 3) | 0 | 0 | Passed |
| fixture 5: (-1, 3) | -1 | 0 | Failed |
SHA-256 / c0cb20fef18cbc41ad8d28b8dbba8333736fd7b8ba982d847da45af4596fa478
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(a, b):
return -(-a // b)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (7, 3)', solve(*(7, 3)), 3)
check('fixture 2: (-7, 3)', solve(*(-7, 3)), -2)
check('fixture 3: (6, 3)', solve(*(6, 3)), 2)
check('fixture 4: (0, 3)', solve(*(0, 3)), 0)
check('fixture 5: (-1, 3)', solve(*(-1, 3)), 0)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| fixture 1: (7, 3) | 3 | 3 | Passed |
| fixture 2: (-7, 3) | -2 | -2 | Passed |
| fixture 3: (6, 3) | 2 | 2 | Passed |
| fixture 4: (0, 3) | 0 | 0 | Passed |
| fixture 5: (-1, 3) | 0 | 0 | Passed |
SHA-256 / 8ee377a33e80a3863c14a0ada37c884283910eb472c74ecf1854ab0f22002ab3
Verification & scope
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.
Observations recorded using Python 3.12.14 at 2026-09-29T14:37:48.408919+00:00.
Case digest / 8edb856a688e537b0e3c2384cc23e0c4fc2086e8d65c30f325a0412d5acc4f42