FA-16896 / Floating-point arithmetic / Open access

Decimal quantization ignores the specified exponent range · case 01

Decimal quantization ignores the specified exponent range.

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

ROOT CAUSE

Decimal quantization ignores the specified exponent range. The faulty expression is ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN).

THE FAILURE

Decimal quantization ignores the specified exponent range. The faulty expression is ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN).

Unsuccessful approach: The attempted local correction ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN,Emin=-99,Emax=99) 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)
    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)
    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', ['Rounded']]`	`['1.20', ['Rounded']]`	Passed
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', []]`	`['1E-10', ['Subnormal']]`	Failed
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 / 789981ccf7bf1563c24f47b9726430b7a1aaf4e3df421f58b17b15f8dded3790

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=-99,Emax=99)
    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)
    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', ['Rounded']]`	`['1.20', ['Rounded']]`	Passed
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', []]`	`['1E-10', ['Subnormal']]`	Failed
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 / 732b76e67dd0f3f661e964e4643e755efbd07798ef4001bad2a887542b8d2726

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 / 8ad83a4ff6baa723a4d1f8af3813435995a45cdc1cf2a8643df4628dbc54abf1