FA-16911 / Floating-point arithmetic / Open access

Decimal quantization drops Rounded unless the value was inexact · case 01

Decimal quantization drops Rounded unless the value was inexact.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Decimal quantization drops Rounded unless the value was inexact. The faulty expression is flags=sorted(signal.name for signal,raised in ctx.flags.items() if raised and (signal is not decimal.Rounded or ctx.flags[decimal.Inexact])).

THE FAILURE

Decimal quantization drops Rounded unless the value was inexact. The faulty expression is flags=sorted(signal.__name__ for signal,raised in ctx.flags.items() if raised and (signal is not decimal.Rounded or ctx.flags[decimal.Inexact])).

Unsuccessful approach: The attempted local correction flags=sorted(signal.__name__ for signal,raised in ctx.flags.items() if raised and signal is not decimal.Rounded) still violates the explicit regression fixtures.

Case contract

Quantize a decimal text to 10**exponent using a fresh precision-limited decimal context, half-even rounding, Emin=-9 and Emax=9. All traps are disabled; return result string and raised flag names. The coefficient precision includes trailing zeros imposed by the target quantum.

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 decimal
from decimal import Decimal, Context, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_DOWN

N = 1
observations = []
def solve(text, exponent, precision):
    ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN,Emin=-9,Emax=9)
    for signal in ctx.traps: ctx.traps[signal]=False
    ctx.clear_flags()
    value=Decimal(text)
    quantum=Decimal((0,(1,),exponent))
    result=ctx.quantize(value,quantum)
    flags=sorted(signal.__name__ for signal,raised in ctx.flags.items() if raised and (signal is not decimal.Rounded or ctx.flags[decimal.Inexact]))
    return [str(result),flags]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('tie odd', solve(str(N)+".255",-2,6), [str(N)+".26",["Inexact","Rounded"]])
check('tie even', solve(str(N)+".245",-2,6), [str(N)+".24",["Inexact","Rounded"]])
check('rounded exact', solve(str(N)+".200",-2,6), [str(N)+".20",["Rounded"]])
check('already exact', solve(str(N)+".20",-2,6), [str(N)+".20",[]])
check('one excess digit', solve("123.45",-2,4), ["NaN",["InvalidOperation"]])
check('coefficient too large', solve("12345.67",-2,4), ["NaN",["InvalidOperation"]])
check('subnormal exact', solve("1e-10",-10,6), ["1E-10",["Subnormal"]])
check('negative zero', solve("-0.004",-2,6), ["-0.00",["Inexact","Rounded"]])
check('positive zero', solve("0.004",-2,6), ["0.00",["Inexact","Rounded"]])
check('integer quantum', solve("123.4",1,6), ["1.2E+2",["Inexact","Rounded"]])
check('overflow exponent', solve("1e10",0,6), ["NaN",["InvalidOperation"]])
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
tie odd	`['1.26', ['Inexact', 'Rounded']]`	`['1.26', ['Inexact', 'Rounded']]`	Passed
tie even	`['1.24', ['Inexact', 'Rounded']]`	`['1.24', ['Inexact', 'Rounded']]`	Passed
rounded exact	`['1.20', []]`	`['1.20', ['Rounded']]`	Failed
already exact	`['1.20', []]`	`['1.20', []]`	Passed
one excess digit	`['NaN', ['InvalidOperation']]`	`['NaN', ['InvalidOperation']]`	Passed
coefficient too large	`['NaN', ['InvalidOperation']]`	`['NaN', ['InvalidOperation']]`	Passed
subnormal exact	`['1E-10', ['Subnormal']]`	`['1E-10', ['Subnormal']]`	Passed
negative zero	`['-0.00', ['Inexact', 'Rounded']]`	`['-0.00', ['Inexact', 'Rounded']]`	Passed
positive zero	`['0.00', ['Inexact', 'Rounded']]`	`['0.00', ['Inexact', 'Rounded']]`	Passed
integer quantum	`['1.2E+2', ['Inexact', 'Rounded']]`	`['1.2E+2', ['Inexact', 'Rounded']]`	Passed
overflow exponent	`['NaN', ['InvalidOperation']]`	`['NaN', ['InvalidOperation']]`	Passed

SHA-256 / 1b135504d7b632c23d9b9b98a13a46b7c7e68154491f6e28307e2e65ce1a4da1

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import decimal
from decimal import Decimal, Context, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_DOWN

N = 1
observations = []
def solve(text, exponent, precision):
    ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN,Emin=-9,Emax=9)
    for signal in ctx.traps: ctx.traps[signal]=False
    ctx.clear_flags()
    value=Decimal(text)
    quantum=Decimal((0,(1,),exponent))
    result=ctx.quantize(value,quantum)
    flags=sorted(signal.__name__ for signal,raised in ctx.flags.items() if raised and signal is not decimal.Rounded)
    return [str(result),flags]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('tie odd', solve(str(N)+".255",-2,6), [str(N)+".26",["Inexact","Rounded"]])
check('tie even', solve(str(N)+".245",-2,6), [str(N)+".24",["Inexact","Rounded"]])
check('rounded exact', solve(str(N)+".200",-2,6), [str(N)+".20",["Rounded"]])
check('already exact', solve(str(N)+".20",-2,6), [str(N)+".20",[]])
check('one excess digit', solve("123.45",-2,4), ["NaN",["InvalidOperation"]])
check('coefficient too large', solve("12345.67",-2,4), ["NaN",["InvalidOperation"]])
check('subnormal exact', solve("1e-10",-10,6), ["1E-10",["Subnormal"]])
check('negative zero', solve("-0.004",-2,6), ["-0.00",["Inexact","Rounded"]])
check('positive zero', solve("0.004",-2,6), ["0.00",["Inexact","Rounded"]])
check('integer quantum', solve("123.4",1,6), ["1.2E+2",["Inexact","Rounded"]])
check('overflow exponent', solve("1e10",0,6), ["NaN",["InvalidOperation"]])
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
tie odd	`['1.26', ['Inexact']]`	`['1.26', ['Inexact', 'Rounded']]`	Failed
tie even	`['1.24', ['Inexact']]`	`['1.24', ['Inexact', 'Rounded']]`	Failed
rounded exact	`['1.20', []]`	`['1.20', ['Rounded']]`	Failed
already exact	`['1.20', []]`	`['1.20', []]`	Passed
one excess digit	`['NaN', ['InvalidOperation']]`	`['NaN', ['InvalidOperation']]`	Passed
coefficient too large	`['NaN', ['InvalidOperation']]`	`['NaN', ['InvalidOperation']]`	Passed
subnormal exact	`['1E-10', ['Subnormal']]`	`['1E-10', ['Subnormal']]`	Passed
negative zero	`['-0.00', ['Inexact']]`	`['-0.00', ['Inexact', 'Rounded']]`	Failed
positive zero	`['0.00', ['Inexact']]`	`['0.00', ['Inexact', 'Rounded']]`	Failed
integer quantum	`['1.2E+2', ['Inexact']]`	`['1.2E+2', ['Inexact', 'Rounded']]`	Failed
overflow exponent	`['NaN', ['InvalidOperation']]`	`['NaN', ['InvalidOperation']]`	Passed

SHA-256 / 11dddfbd2c94a9b64e999d16712eb2457611794a6a8cfe2659bf264a61c8b07f

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 11 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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:41.139976+00:00.

Case digest / 276b0f7ded59aab114fed724abb4c4de711eac827402efc859284face6b7ab32