Cost-reduction actions - Statement of Income Classifications (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	$ 46.9	$ 13.2	$ 7.9	$ 27.5	$ 23.3	$ 0.2	$ 2.6	$ 2.6	$ 95.5	$ 28.7	$ 19.7
Cost of revenue | Services
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									22.2	10.8	18.1
Cost of revenue | Technology
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									0.0	0.2	0.0
Selling, general and administrative
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									38.5	15.5	1.6
Research and development
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									2.5	2.2	0.0
Other (expenses), net
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									$ 32.3	$ 0.0	$ 0.0