Defined contribution and defined benefit retirement plans - Funded Status of Defined Benefit Pension Plans (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Amounts recognized in the balance sheet:
Accrued pension costs, noncurrent	$ (150.0)	$ (128.6)
Defined benefit pension plans
Change in plan assets:
Fair value of plan assets at beginning of the year	395.6
Fair value of plan assets at end of year	435.1	395.6
U S | Defined benefit pension plans
Change in projected benefit obligations (PBO):
Benefit obligations at beginning of the year	13.2	17.7
Interest cost	0.7	0.4	$ 0.5
Actuarial (gains) losses	0.5	(3.9)
Benefits paid	(1.1)	(1.0)
Benefit obligations at end of the year	13.3	13.2	17.7
Change in plan assets:
Fair value of plan assets at beginning of the year	12.0	15.9
Actual return on plan assets	1.1	(3.2)
Employer contributions	0.5	0.3
Benefits paid	(1.1)	(1.0)
Fair value of plan assets at end of year	12.5	12.0	15.9
Funded status	(0.8)	(1.2)
Amounts recognized in the balance sheet:
Accrued pension costs, noncurrent	(0.8)	(1.2)
Total	(0.8)	(1.2)
Amount recognized in accumulated other comprehensive loss, Actuarial losses	8.5	9.2
Accumulated benefit obligations (ABO)	13.3	13.2
Foreign Pension Plans Defined Benefit | Defined benefit pension plans
Change in projected benefit obligations (PBO):
Benefit obligations at beginning of the year	502.8	748.1
Service cost	6.3	11.3	14.7
Interest cost	19.7	10.5	8.2
Participant contributions	1.8	1.7
Actuarial (gains) losses	44.7	(195.8)
Settlements	(3.1)	(1.2)
Change in currency exchange rates	14.0	(50.3)
Benefits paid	(22.5)	(21.5)
Benefit obligations at end of the year	563.7	502.8	748.1
Change in plan assets:
Fair value of plan assets at beginning of the year	383.6	470.1
Actual return on plan assets	37.9	(49.5)
Employer contributions	15.6	15.0
Participant contributions	1.8	1.7
Settlements	(3.1)	(1.2)
Change in currency exchange rates	9.3	(31.0)
Benefits paid	(22.5)	(21.5)
Fair value of plan assets at end of year	422.6	383.6	$ 470.1
Funded status	(141.1)	(119.2)
Amounts recognized in the balance sheet:
Noncurrent pension asset	8.1	8.2
Accrued pension costs, noncurrent	(149.2)	(127.4)
Total	(141.1)	(119.2)
Amount recognized in accumulated other comprehensive loss, Actuarial losses	106.8	85.4
Amount recognized in accumulated other comprehensive loss, Prior service cost	0.3	0.4
Amount recognized in accumulated other comprehensive loss, Total	107.1	85.8
Accumulated benefit obligations (ABO)	$ 549.8	$ 488.0