Segment information - Customer Revenue by Classes of Similar Products or Services (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2017	Jun. 30, 2017	Mar. 31, 2017	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Revenue from External Customer [Line Items]
Revenue	$ 760.9	$ 688.3	$ 667.4	$ 708.4	$ 744.8	$ 666.3	$ 666.2	$ 664.5	$ 2,825.0	$ 2,741.8	$ 2,820.7
Services
Revenue from External Customer [Line Items]
Revenue									2,386.3	2,328.2	2,406.3
Technology
Revenue from External Customer [Line Items]
Revenue									438.7	413.6	414.4
Cloud & infrastructure services | Services
Revenue from External Customer [Line Items]
Revenue									1,363.4	1,334.3	1,356.4
Application services | Services
Revenue from External Customer [Line Items]
Revenue									772.4	791.0	855.5
BPO services | Services
Revenue from External Customer [Line Items]
Revenue									$ 250.5	$ 202.9	$ 194.4