Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Deferred tax assets
Tax loss carryforwards	$ 825.5	$ 840.4
Postretirement benefits	149.6	211.8
Foreign tax credit carryforwards	109.2	145.9
Other tax credit carryforwards	32.7	31.9
Deferred revenue	28.2	35.8
Employee benefits and compensation	21.2	25.8
Purchased capitalized software	16.9	24.2
Depreciation	32.6	31.6
Warranty, bad debts and other reserves	7.1	7.5
Capitalized costs	6.2	3.9
Other	49.9	46.1
Total deferred tax assets, gross	1,279.1	1,404.9
Valuation allowance	(1,110.5)	(1,226.2)	$ (1,271.5)	$ (1,524.7)
Total deferred tax assets	168.6	178.7
Deferred tax liabilities
Capitalized research and development	31.0	43.1
Other	29.2	29.5
Total deferred tax liabilities	60.2	72.6
Net deferred tax assets	$ 108.4	$ 106.1