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Segment information - Customer Revenue by Classes of Similar Products or Services (Details) - USD ($)
$ in Millions
3 Months Ended 12 Months Ended
Dec. 31, 2019
Sep. 30, 2019
Jun. 30, 2019
Mar. 31, 2019
Dec. 31, 2018
Sep. 30, 2018
Jun. 30, 2018
Mar. 31, 2018
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2017
Revenue from External Customer [Line Items]                      
Revenue $ 741.5 $ 757.6 $ 753.8 $ 695.8 $ 760.9 $ 688.3 $ 667.4 $ 708.4 $ 2,948.7 $ 2,825.0 $ 2,741.8
Services                      
Revenue from External Customer [Line Items]                      
Revenue                 2,552.7 2,386.3 2,328.2
Technology                      
Revenue from External Customer [Line Items]                      
Revenue                 396.0 438.7 413.6
Cloud & infrastructure services | Services                      
Revenue from External Customer [Line Items]                      
Revenue                 1,567.7 1,363.4 1,334.3
Application services | Services                      
Revenue from External Customer [Line Items]                      
Revenue                 750.4 772.4 791.0
BPO services | Services                      
Revenue from External Customer [Line Items]                      
Revenue                 $ 234.6 $ 250.5 $ 202.9