FA-62011 / Currency rounding and FX conversion / Open access
A 5-rappen tie on a cash refund rounds toward positive infinity · case 01
A cash refund of -2.075 pays out -2.05 while a 2.075 sale charges 2.10.
ROOT CAUSE
Rounding adds one half and floors, which is not symmetric for negative totals.
VERIFIED REPAIR
Round ties away from zero for both sales and refunds.
Unsuccessful approach: Switching to half-even rounding breaks ties toward even multiples instead of away from zero.
Case contract
solve(lines, tender): lines are CHF decimal strings with up to three decimals (weight- or volume-priced items; refund lines negative). The exact total is their sum. For tender 'cash' (compared after trimming and lower-casing) the total is rounded to the nearest 0.05 with ties away from zero; every other tender ('card', 'twint', 'voucher', ...) pays the total rounded half-up to 0.01. Return [payable as a 2-decimal string, adjustment as a 3-decimal string] where adjustment = payable - exact; zeros are unsigned.
Why this case matters
Currency amounts must be rounded at the right stage and in the right unit, or ledgers, quotes and settlements drift by minor units.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from decimal import Decimal, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_FLOOR, ROUND_CEILING, ROUND_DOWN, ROUND_UP, ROUND_HALF_DOWN
N = 1
observations = []
def solve(lines, tender):
def cash(v):
return (v / Decimal('0.05') + Decimal('0.5')).quantize(Decimal(1), rounding=ROUND_FLOOR) * Decimal('0.05')
def z(d, e):
d = d.quantize(Decimal(1).scaleb(-e), rounding=ROUND_HALF_UP)
return format(abs(d) if d == 0 else d, 'f')
exact = sum((Decimal(l) for l in lines), Decimal('0.000'))
if tender.strip().lower() == 'cash':
r = cash(exact)
else:
r = exact.quantize(Decimal('0.01'), rounding=ROUND_HALF_UP)
return [z(r, 2), z(r - exact, 3)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 2', (['3.00', '0.025'], 'cash'), ['3.05', '0.025']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020']),
('control: round to franc', (['0.99', '0.03'], 'cash'), ['1.00', '-0.020']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020'])],
[('regression refund-tie-direction 1', (['-0.075'], 'cash'), ['-0.10', '-0.025']),
('regression refund-tie-direction 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('partial repair guard 1', (['7.95', '16.09', '-3.325', '23.21'], 'cash'), ['43.95', '0.025']),
('partial repair guard 2', (['-0.46', '-0.885', '26.47'], 'CASH'), ['25.15', '0.025']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020']),
('control: card exact', (['1.02'], 'card'), ['1.02', '0.000']),
('control: twint exact', (['3.33', '4.44'], 'twint'), ['7.77', '0.000']),
('control: positive tie', (['3.00', '0.025'], 'cash'), ['3.05', '0.025'])],
[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 1', (['1.825'], 'CASH'), ['1.85', '0.025']),
('partial repair guard 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('control: positive tie', (['3.00', '0.025'], 'cash'), ['3.05', '0.025']),
('control: voucher exact', (['7.07'], 'voucher'), ['7.07', '0.000']),
('control: mixed basket', (['12.40', '-3.12', '0.99'], ' CASH'), ['10.25', '-0.020']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020'])],
[('regression refund-tie-direction 1', (['-0.075'], 'cash'), ['-0.10', '-0.025']),
('regression refund-tie-direction 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('partial repair guard 1', (['22.51', '1.915'], 'Cash'), ['24.45', '0.025']),
('partial repair guard 2', (['8.51', '22.58', '28.67', '0.565'], 'Cash'), ['60.35', '0.025']),
('control: mixed basket', (['12.40', '-3.12', '0.99'], ' CASH'), ['10.25', '-0.020']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020']),
('control: round to franc', (['0.99', '0.03'], 'cash'), ['1.00', '-0.020']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020'])],
[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 1', (['3.51', '-0.375', '11.09'], 'Cash'), ['14.25', '0.025']),
('partial repair guard 2', (['15.83', '18.48', '1.715'], 'Cash'), ['36.05', '0.025']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020']),
('control: card exact', (['1.02'], 'card'), ['1.02', '0.000']),
('control: twint exact', (['3.33', '4.44'], 'twint'), ['7.77', '0.000'])]]
for label, args, expected in cases[N - 1]:
check(label, solve(*args), expected)
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 |
|---|---|---|---|
| regression refund-tie-direction 1 | ['-2.05', '0.025'] | ['-2.10', '-0.025'] | Failed |
| regression refund-tie-direction 2 | ['-1.00', '0.025'] | ['-1.05', '-0.025'] | Failed |
| partial repair guard 2 | ['3.05', '0.025'] | ['3.05', '0.025'] | Passed |
| control: round down | ['2.00', '-0.020'] | ['2.00', '-0.020'] | Passed |
| control: round to franc | ['1.00', '-0.020'] | ['1.00', '-0.020'] | Passed |
| control: refund | ['-2.00', '0.020'] | ['-2.00', '0.020'] | Passed |
| control: refund to zero | ['0.00', '0.020'] | ['0.00', '0.020'] | Passed |
SHA-256 / 56a58067d5a87d090fd7ebd999f2e9fbff70cda9e77b89189ec52e5dd4bbdb98
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from decimal import Decimal, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_FLOOR, ROUND_CEILING, ROUND_DOWN, ROUND_UP, ROUND_HALF_DOWN
N = 1
observations = []
def solve(lines, tender):
def cash(v):
return (v / Decimal('0.05')).quantize(Decimal(1), rounding=ROUND_HALF_EVEN) * Decimal('0.05')
def z(d, e):
d = d.quantize(Decimal(1).scaleb(-e), rounding=ROUND_HALF_UP)
return format(abs(d) if d == 0 else d, 'f')
exact = sum((Decimal(l) for l in lines), Decimal('0.000'))
if tender.strip().lower() == 'cash':
r = cash(exact)
else:
r = exact.quantize(Decimal('0.01'), rounding=ROUND_HALF_UP)
return [z(r, 2), z(r - exact, 3)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 2', (['3.00', '0.025'], 'cash'), ['3.05', '0.025']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020']),
('control: round to franc', (['0.99', '0.03'], 'cash'), ['1.00', '-0.020']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020'])],
[('regression refund-tie-direction 1', (['-0.075'], 'cash'), ['-0.10', '-0.025']),
('regression refund-tie-direction 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('partial repair guard 1', (['7.95', '16.09', '-3.325', '23.21'], 'cash'), ['43.95', '0.025']),
('partial repair guard 2', (['-0.46', '-0.885', '26.47'], 'CASH'), ['25.15', '0.025']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020']),
('control: card exact', (['1.02'], 'card'), ['1.02', '0.000']),
('control: twint exact', (['3.33', '4.44'], 'twint'), ['7.77', '0.000']),
('control: positive tie', (['3.00', '0.025'], 'cash'), ['3.05', '0.025'])],
[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 1', (['1.825'], 'CASH'), ['1.85', '0.025']),
('partial repair guard 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('control: positive tie', (['3.00', '0.025'], 'cash'), ['3.05', '0.025']),
('control: voucher exact', (['7.07'], 'voucher'), ['7.07', '0.000']),
('control: mixed basket', (['12.40', '-3.12', '0.99'], ' CASH'), ['10.25', '-0.020']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020'])],
[('regression refund-tie-direction 1', (['-0.075'], 'cash'), ['-0.10', '-0.025']),
('regression refund-tie-direction 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('partial repair guard 1', (['22.51', '1.915'], 'Cash'), ['24.45', '0.025']),
('partial repair guard 2', (['8.51', '22.58', '28.67', '0.565'], 'Cash'), ['60.35', '0.025']),
('control: mixed basket', (['12.40', '-3.12', '0.99'], ' CASH'), ['10.25', '-0.020']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020']),
('control: round to franc', (['0.99', '0.03'], 'cash'), ['1.00', '-0.020']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020'])],
[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 1', (['3.51', '-0.375', '11.09'], 'Cash'), ['14.25', '0.025']),
('partial repair guard 2', (['15.83', '18.48', '1.715'], 'Cash'), ['36.05', '0.025']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020']),
('control: card exact', (['1.02'], 'card'), ['1.02', '0.000']),
('control: twint exact', (['3.33', '4.44'], 'twint'), ['7.77', '0.000'])]]
for label, args, expected in cases[N - 1]:
check(label, solve(*args), expected)
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 |
|---|---|---|---|
| regression refund-tie-direction 1 | ['-2.10', '-0.025'] | ['-2.10', '-0.025'] | Passed |
| regression refund-tie-direction 2 | ['-1.00', '0.025'] | ['-1.05', '-0.025'] | Failed |
| partial repair guard 2 | ['3.00', '-0.025'] | ['3.05', '0.025'] | Failed |
| control: round down | ['2.00', '-0.020'] | ['2.00', '-0.020'] | Passed |
| control: round to franc | ['1.00', '-0.020'] | ['1.00', '-0.020'] | Passed |
| control: refund | ['-2.00', '0.020'] | ['-2.00', '0.020'] | Passed |
| control: refund to zero | ['0.00', '0.020'] | ['0.00', '0.020'] | Passed |
SHA-256 / 3d18bda14f37d1b37ec527de78fb58b0f38fb15568af58f46c5f518bc882c1aa
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from decimal import Decimal, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_FLOOR, ROUND_CEILING, ROUND_DOWN, ROUND_UP, ROUND_HALF_DOWN
N = 1
observations = []
def solve(lines, tender):
def cash(v):
return (v / Decimal('0.05')).quantize(Decimal(1), rounding=ROUND_HALF_UP) * Decimal('0.05')
def z(d, e):
d = d.quantize(Decimal(1).scaleb(-e), rounding=ROUND_HALF_UP)
return format(abs(d) if d == 0 else d, 'f')
exact = sum((Decimal(l) for l in lines), Decimal('0.000'))
if tender.strip().lower() == 'cash':
r = cash(exact)
else:
r = exact.quantize(Decimal('0.01'), rounding=ROUND_HALF_UP)
return [z(r, 2), z(r - exact, 3)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 2', (['3.00', '0.025'], 'cash'), ['3.05', '0.025']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020']),
('control: round to franc', (['0.99', '0.03'], 'cash'), ['1.00', '-0.020']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020'])],
[('regression refund-tie-direction 1', (['-0.075'], 'cash'), ['-0.10', '-0.025']),
('regression refund-tie-direction 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('partial repair guard 1', (['7.95', '16.09', '-3.325', '23.21'], 'cash'), ['43.95', '0.025']),
('partial repair guard 2', (['-0.46', '-0.885', '26.47'], 'CASH'), ['25.15', '0.025']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020']),
('control: card exact', (['1.02'], 'card'), ['1.02', '0.000']),
('control: twint exact', (['3.33', '4.44'], 'twint'), ['7.77', '0.000']),
('control: positive tie', (['3.00', '0.025'], 'cash'), ['3.05', '0.025'])],
[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 1', (['1.825'], 'CASH'), ['1.85', '0.025']),
('partial repair guard 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('control: positive tie', (['3.00', '0.025'], 'cash'), ['3.05', '0.025']),
('control: voucher exact', (['7.07'], 'voucher'), ['7.07', '0.000']),
('control: mixed basket', (['12.40', '-3.12', '0.99'], ' CASH'), ['10.25', '-0.020']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020'])],
[('regression refund-tie-direction 1', (['-0.075'], 'cash'), ['-0.10', '-0.025']),
('regression refund-tie-direction 2', (['-0.625'], 'cash'), ['-0.65', '-0.025']),
('partial repair guard 1', (['22.51', '1.915'], 'Cash'), ['24.45', '0.025']),
('partial repair guard 2', (['8.51', '22.58', '28.67', '0.565'], 'Cash'), ['60.35', '0.025']),
('control: mixed basket', (['12.40', '-3.12', '0.99'], ' CASH'), ['10.25', '-0.020']),
('control: round down', (['1.02', '1.00'], 'cash'), ['2.00', '-0.020']),
('control: round to franc', (['0.99', '0.03'], 'cash'), ['1.00', '-0.020']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020'])],
[('regression refund-tie-direction 1', (['-2.075'], 'cash'), ['-2.10', '-0.025']),
('regression refund-tie-direction 2', (['-1.025'], 'cash'), ['-1.05', '-0.025']),
('partial repair guard 1', (['3.51', '-0.375', '11.09'], 'Cash'), ['14.25', '0.025']),
('partial repair guard 2', (['15.83', '18.48', '1.715'], 'Cash'), ['36.05', '0.025']),
('control: refund', (['-1.03', '-0.99'], 'cash'), ['-2.00', '0.020']),
('control: refund to zero', (['-0.02'], 'Cash '), ['0.00', '0.020']),
('control: card exact', (['1.02'], 'card'), ['1.02', '0.000']),
('control: twint exact', (['3.33', '4.44'], 'twint'), ['7.77', '0.000'])]]
for label, args, expected in cases[N - 1]:
check(label, solve(*args), expected)
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 |
|---|---|---|---|
| regression refund-tie-direction 1 | ['-2.10', '-0.025'] | ['-2.10', '-0.025'] | Passed |
| regression refund-tie-direction 2 | ['-1.05', '-0.025'] | ['-1.05', '-0.025'] | Passed |
| partial repair guard 2 | ['3.05', '0.025'] | ['3.05', '0.025'] | Passed |
| control: round down | ['2.00', '-0.020'] | ['2.00', '-0.020'] | Passed |
| control: round to franc | ['1.00', '-0.020'] | ['1.00', '-0.020'] | Passed |
| control: refund | ['-2.00', '0.020'] | ['-2.00', '0.020'] | Passed |
| control: refund to zero | ['0.00', '0.020'] | ['0.00', '0.020'] | Passed |
SHA-256 / b62b35ddd422334e28b3e8ef6add6536bbd45e280d3257161cf1a830820fef6f
Verification & scope
A deterministic, bounded teaching model with a stipulated toy contract; it makes no claim of conformance to any real regulation, standard, or institution's rules. 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 2026-09-29T14:47:00.699446+00:00.
Case digest / 7fcbb56d04f1acc058034d7f32b7a9fbb5d179cb11edeb5da96eef658f72d6f3