Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions	Dec. 31, 2018	Dec. 31, 2017
Deferred tax assets
Tax loss carryforwards	$ 860.0	$ 837.6
Postretirement benefits	440.3	437.7
Foreign tax credit carryforwards	221.6	127.0
Other tax credit carryforwards	29.8	29.1
Deferred revenue	37.1	40.9
Employee benefits and compensation	31.1	35.2
Purchased capitalized software	22.9	22.2
Depreciation	20.1	24.5
Warranty, bad debts and other reserves	4.8	5.3
Capitalized costs	5.1	3.1
Other	30.4	39.3
Total deferred tax assets, gross	1,703.2	1,601.9
Valuation allowance	(1,547.5)	(1,441.1)
Total deferred tax assets	155.7	160.8
Deferred tax liabilities
Capitalized research and development	36.1	24.3
Other	30.2	25.8
Total deferred tax liabilities	66.3	50.1
Net deferred tax assets	$ 89.4	$ 110.7