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FA-16506 / Floating-point arithmetic / Open access

Underflow does not accrue its implied inexact flag · case 01

Underflow does not accrue its implied inexact flag.

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

ROOT CAUSE

Underflow does not accrue its implied inexact flag. The faulty expression is if 'underflow' in new: new.discard('inexact').

VERIFIED REPAIR

Apply the contract at this fault site using if 'underflow' in new: new.add('inexact').

Unsuccessful approach: The attempted local correction if 'underflow' in new: new.add('overflow') 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.discard('inexact')
    accrued=prior|new
    pending=new & set(enabled)
    trap=next((flag for flag in 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[[], ['underflow'], None, ['underflow']][[], ['inexact', 'underflow'], None, ['inexact', 'underflow']]Failed
priority[[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']][[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']]Passed
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 / 40f282095a60f4cc2e37c6c11863f9b3965b7c1c83826f29bf6ec8bd72786af4

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('overflow')
    accrued=prior|new
    pending=new & set(enabled)
    trap=next((flag for flag in 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[[], ['overflow', 'underflow'], None, ['overflow', 'underflow']][[], ['inexact', 'underflow'], None, ['inexact', 'underflow']]Failed
priority[[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']][[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']]Passed
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 / 55f0b47a4fb92ee9361c1a24f4fef99f9a97e73ce5ba2f53f677224b5681502f

3 / The verified repair

Exit 0
"""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 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'], 'invalid', ['inexact', 'invalid', 'overflow']][[], ['inexact', 'invalid', 'overflow'], 'invalid', ['inexact', 'invalid', 'overflow']]Passed
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 / 8c5448c45e7db988fee6d1d3a4465b7ef7ea27f47429fd410fe793b4f9f41077

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 2026-09-29T14:39:37.000641+00:00.

Case digest / 6cbed5e18c25819211d3931dbe87384e2281b557019732ab605d9966f321eef2