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Cost-reduction actions - Statement of Income Classifications (Details) - USD ($)
$ in Millions
 12 Months Ended
Dec. 31, 2021
Dec. 31, 2020
Dec. 31, 2019
Restructuring Cost and Reserve [Line Items]      
Cost-reduction charges and other costs $ 23.2 $ 95.5 $ 28.7
Cost of revenue | Services      
Restructuring Cost and Reserve [Line Items]      
Cost-reduction charges and other costs (2.5) 22.2 10.8
Cost of revenue | Technology      
Restructuring Cost and Reserve [Line Items]      
Cost-reduction charges and other costs 7.6 0.0 0.2
Selling, general and administrative      
Restructuring Cost and Reserve [Line Items]      
Cost-reduction charges and other costs 11.1 38.5 15.5
Research and development      
Restructuring Cost and Reserve [Line Items]      
Cost-reduction charges and other costs 3.0 2.5 2.2
Other (expenses), net      
Restructuring Cost and Reserve [Line Items]      
Cost-reduction charges and other costs $ 4.0 $ 32.3 $ 0.0