Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions	Dec. 31, 2021	Dec. 31, 2020
Deferred tax assets
Tax loss carryforwards	$ 840.4	$ 795.2
Postretirement benefits	211.8	253.0
Foreign tax credit carryforwards	145.9	201.3
Other tax credit carryforwards	31.9	29.2
Deferred revenue	35.8	31.1
Employee benefits and compensation	25.8	25.3
Purchased capitalized software	24.2	24.1
Depreciation	31.6	28.2
Warranty, bad debts and other reserves	7.5	10.5
Capitalized costs	3.9	8.1
Other	46.1	52.0
Total deferred tax assets, gross	1,404.9	1,458.0
Valuation allowance	(1,226.2)	(1,271.5)
Total deferred tax assets	178.7	186.5
Deferred tax liabilities
Capitalized research and development	43.1	47.4
Other	29.5	29.8
Total deferred tax liabilities	72.6	77.2
Net deferred tax assets	$ 106.1	$ 109.3