Cost-reduction actions - Statement of Income Classifications (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	$ 54.9	$ 23.2	$ 95.5
Cost of revenue | Services
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	19.1	(2.5)	22.2
Cost of revenue | Technology
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	7.6	7.6	0.0
Selling, general and administrative
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	24.7	11.1	38.5
Research and development
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	0.6	3.0	2.5
Other (expenses), net
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	$ 2.9	$ 4.0	$ 32.3