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FA-16526 / Floating-point arithmetic / Open access

Floating exceptions select the lowest-priority simultaneous trap · case 01

Floating exceptions select the lowest-priority simultaneous trap.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Floating exceptions select the lowest-priority simultaneous trap. The faulty expression is trap=next((flag for flag in reversed(priority) if flag in pending),None).

THE FAILURE

Floating exceptions select the lowest-priority simultaneous trap. The faulty expression is trap=next((flag for flag in reversed(priority) if flag in pending),None).

Unsuccessful approach: The attempted local correction trap=sorted(pending)[-1] if pending else None still violates the explicit regression fixtures.

Case contract

Stipulated floating exception environment: apply an operation flag set, accrue sticky flags, select enabled trap by priority invalid/divzero/overflow/underflow/inexact, save prior state and clear only requested flags after reporting the trap. Inputs are valid flag names.

Why this case matters

An offline floating representation model isolates a reproducible arithmetic fault.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(sticky, enabled, raised, clear):
    priority=['invalid','divzero','overflow','underflow','inexact']
    prior=set(sticky)
    new=set(raised)
    if 'overflow' in new: new.add('inexact')
    if 'underflow' in new: new.add('inexact')
    accrued=prior|new
    pending=new & set(enabled)
    trap=next((flag for flag in reversed(priority) if flag in pending),None)
    remaining=accrued-set(clear)
    return [sorted(prior),sorted(accrued),trap,sorted(remaining)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('sticky survives', solve(["invalid"],[],["inexact"],[]), [["invalid"],["inexact","invalid"],None,["inexact","invalid"]])
check('overflow implies inexact', solve([],[],["overflow"],[]), [[],["inexact","overflow"],None,["inexact","overflow"]])
check('underflow implies inexact', solve([],[],["underflow"],[]), [[],["inexact","underflow"],None,["inexact","underflow"]])
check('priority', solve([],["overflow","invalid"],["overflow","invalid"],[]), [[],["inexact","invalid","overflow"],"invalid",["inexact","invalid","overflow"]])
check('old flag no retrap', solve(["invalid"],["invalid"],["inexact"],[]), [["invalid"],["inexact","invalid"],None,["inexact","invalid"]])
check('clear after trap', solve([],["divzero"],["divzero"],["divzero"]), [[],["divzero"],"divzero",[]])
check('selective clear', solve(["invalid","inexact"],[],[],["inexact"]), [["inexact","invalid"],["inexact","invalid"],None,["invalid"]])
check('masked flag still sticky', solve([],[],["divzero"],[]), [[],["divzero"],None,["divzero"]])
check('five distinct flag sets', solve([],[],["invalid","divzero","inexact","underflow","overflow"][:N],[]), [[],sorted(["invalid","divzero","inexact","underflow","overflow"][:N]),None,sorted(["invalid","divzero","inexact","underflow","overflow"][:N])])
check('empty operation', solve(["inexact"] if N%2 else ["invalid"],[],[],[]), [["inexact"] if N%2 else ["invalid"],["inexact"] if N%2 else ["invalid"],None,["inexact"] if N%2 else ["invalid"]])
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 fixtureActualExpectedOutcome
sticky survives[['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']][['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']]Passed
overflow implies inexact[[], ['inexact', 'overflow'], None, ['inexact', 'overflow']][[], ['inexact', 'overflow'], None, ['inexact', 'overflow']]Passed
underflow implies inexact[[], ['inexact', 'underflow'], None, ['inexact', 'underflow']][[], ['inexact', 'underflow'], None, ['inexact', 'underflow']]Passed
priority[[], ['inexact', 'invalid', 'overflow'], 'overflow', ['inexact', 'invalid', 'overflow']][[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']]Failed
old flag no retrap[['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']][['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']]Passed
clear after trap[[], ['divzero'], 'divzero', []][[], ['divzero'], 'divzero', []]Passed
selective clear[['inexact', 'invalid'], ['inexact', 'invalid'], None, ['invalid']][['inexact', 'invalid'], ['inexact', 'invalid'], None, ['invalid']]Passed
masked flag still sticky[[], ['divzero'], None, ['divzero']][[], ['divzero'], None, ['divzero']]Passed
five distinct flag sets[[], ['invalid'], None, ['invalid']][[], ['invalid'], None, ['invalid']]Passed
empty operation[['inexact'], ['inexact'], None, ['inexact']][['inexact'], ['inexact'], None, ['inexact']]Passed

SHA-256 / e91744587c85e4713dd0d8b96766ac81c9c35859735315d9127eb246ca3ac64e

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(sticky, enabled, raised, clear):
    priority=['invalid','divzero','overflow','underflow','inexact']
    prior=set(sticky)
    new=set(raised)
    if 'overflow' in new: new.add('inexact')
    if 'underflow' in new: new.add('inexact')
    accrued=prior|new
    pending=new & set(enabled)
    trap=sorted(pending)[-1] if pending else None
    remaining=accrued-set(clear)
    return [sorted(prior),sorted(accrued),trap,sorted(remaining)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('sticky survives', solve(["invalid"],[],["inexact"],[]), [["invalid"],["inexact","invalid"],None,["inexact","invalid"]])
check('overflow implies inexact', solve([],[],["overflow"],[]), [[],["inexact","overflow"],None,["inexact","overflow"]])
check('underflow implies inexact', solve([],[],["underflow"],[]), [[],["inexact","underflow"],None,["inexact","underflow"]])
check('priority', solve([],["overflow","invalid"],["overflow","invalid"],[]), [[],["inexact","invalid","overflow"],"invalid",["inexact","invalid","overflow"]])
check('old flag no retrap', solve(["invalid"],["invalid"],["inexact"],[]), [["invalid"],["inexact","invalid"],None,["inexact","invalid"]])
check('clear after trap', solve([],["divzero"],["divzero"],["divzero"]), [[],["divzero"],"divzero",[]])
check('selective clear', solve(["invalid","inexact"],[],[],["inexact"]), [["inexact","invalid"],["inexact","invalid"],None,["invalid"]])
check('masked flag still sticky', solve([],[],["divzero"],[]), [[],["divzero"],None,["divzero"]])
check('five distinct flag sets', solve([],[],["invalid","divzero","inexact","underflow","overflow"][:N],[]), [[],sorted(["invalid","divzero","inexact","underflow","overflow"][:N]),None,sorted(["invalid","divzero","inexact","underflow","overflow"][:N])])
check('empty operation', solve(["inexact"] if N%2 else ["invalid"],[],[],[]), [["inexact"] if N%2 else ["invalid"],["inexact"] if N%2 else ["invalid"],None,["inexact"] if N%2 else ["invalid"]])
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 fixtureActualExpectedOutcome
sticky survives[['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']][['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']]Passed
overflow implies inexact[[], ['inexact', 'overflow'], None, ['inexact', 'overflow']][[], ['inexact', 'overflow'], None, ['inexact', 'overflow']]Passed
underflow implies inexact[[], ['inexact', 'underflow'], None, ['inexact', 'underflow']][[], ['inexact', 'underflow'], None, ['inexact', 'underflow']]Passed
priority[[], ['inexact', 'invalid', 'overflow'], 'overflow', ['inexact', 'invalid', 'overflow']][[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']]Failed
old flag no retrap[['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']][['invalid'], ['inexact', 'invalid'], None, ['inexact', 'invalid']]Passed
clear after trap[[], ['divzero'], 'divzero', []][[], ['divzero'], 'divzero', []]Passed
selective clear[['inexact', 'invalid'], ['inexact', 'invalid'], None, ['invalid']][['inexact', 'invalid'], ['inexact', 'invalid'], None, ['invalid']]Passed
masked flag still sticky[[], ['divzero'], None, ['divzero']][[], ['divzero'], None, ['divzero']]Passed
five distinct flag sets[[], ['invalid'], None, ['invalid']][[], ['invalid'], None, ['invalid']]Passed
empty operation[['inexact'], ['inexact'], None, ['inexact']][['inexact'], ['inexact'], None, ['inexact']]Passed

SHA-256 / 7d2da5ba11c848836cdebc5853a445935f770f14eee0f1b3244abe959822af01

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 10 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:39:37.358853+00:00.

Case digest / d7c70553b47dfece02a83f0666ce9323c5dafe96c23a51508733aeb2b2d1af0b