Income taxes - Reconciliation of the Provision (Benefit) for Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Income Tax Disclosure [Abstract]
United States statutory income tax benefit	$ (13.2)	$ (96.9)	$ (57.1)
Income and losses for which no provision or benefit has been recognized	40.9	91.1	78.6
Foreign rate differential and other foreign tax expense	6.4	0.4	5.9
Income tax withholdings	19.7	13.5	16.8
Permanent items	(2.1)	(1.8)	0.8
Enacted rate changes	0.0	(17.1)	(4.0)
Change in uncertain tax positions	0.4	(0.3)	3.6
Change in valuation allowances	(9.8)	(0.8)	2.9
Income tax credits, U.S.	0.0	0.0	(2.1)
Total provision (benefit) for income taxes	$ 42.3	$ (11.9)	$ 45.4