FA-16921 / Floating-point arithmetic / Open access

Decimal quantization creates a context but uses the ambient one · case 01

Decimal quantization creates a context but uses the ambient one.

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

ROOT CAUSE

Decimal quantization creates a context but uses the ambient one. The faulty expression is result=value.quantize(quantum).

THE FAILURE

Decimal quantization creates a context but uses the ambient one. The faulty expression is result=value.quantize(quantum).

Unsuccessful approach: The attempted local correction result=value.quantize(quantum,rounding=ROUND_HALF_EVEN) 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=value.quantize(quantum)
    flags=sorted(signal.__name__ for signal,raised in ctx.flags.items() if raised)
    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', []]`	`['1.26', ['Inexact', 'Rounded']]`	Failed
tie even	`['1.24', []]`	`['1.24', ['Inexact', 'Rounded']]`	Failed
rounded exact	`['1.20', []]`	`['1.20', ['Rounded']]`	Failed
already exact	`['1.20', []]`	`['1.20', []]`	Passed
one excess digit	`['123.45', []]`	`['NaN', ['InvalidOperation']]`	Failed
coefficient too large	`['12345.67', []]`	`['NaN', ['InvalidOperation']]`	Failed
subnormal exact	`['1E-10', []]`	`['1E-10', ['Subnormal']]`	Failed
negative zero	`['-0.00', []]`	`['-0.00', ['Inexact', 'Rounded']]`	Failed
positive zero	`['0.00', []]`	`['0.00', ['Inexact', 'Rounded']]`	Failed
integer quantum	`['1.2E+2', []]`	`['1.2E+2', ['Inexact', 'Rounded']]`	Failed
overflow exponent	`['10000000000', []]`	`['NaN', ['InvalidOperation']]`	Failed

SHA-256 / de3a21b50baa784365b3bfaacb590509b09e0c690c02d7fa648c019d352c2e62

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=value.quantize(quantum,rounding=ROUND_HALF_EVEN)
    flags=sorted(signal.__name__ for signal,raised in ctx.flags.items() if raised)
    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', []]`	`['1.26', ['Inexact', 'Rounded']]`	Failed
tie even	`['1.24', []]`	`['1.24', ['Inexact', 'Rounded']]`	Failed
rounded exact	`['1.20', []]`	`['1.20', ['Rounded']]`	Failed
already exact	`['1.20', []]`	`['1.20', []]`	Passed
one excess digit	`['123.45', []]`	`['NaN', ['InvalidOperation']]`	Failed
coefficient too large	`['12345.67', []]`	`['NaN', ['InvalidOperation']]`	Failed
subnormal exact	`['1E-10', []]`	`['1E-10', ['Subnormal']]`	Failed
negative zero	`['-0.00', []]`	`['-0.00', ['Inexact', 'Rounded']]`	Failed
positive zero	`['0.00', []]`	`['0.00', ['Inexact', 'Rounded']]`	Failed
integer quantum	`['1.2E+2', []]`	`['1.2E+2', ['Inexact', 'Rounded']]`	Failed
overflow exponent	`['10000000000', []]`	`['NaN', ['InvalidOperation']]`	Failed

SHA-256 / a1cff283b0168ade27d68cce42ed8fdbf859a7270261eb39b17807769843668b

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 / 32abee37ce53e1a2b3623fee1d4942db2b82211c1a95c1cec6dd154e63d27154