Segment information - Summary of Operations by Segment (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
Segment Reporting Information [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
Operating income (loss)									284.1	97.1	[1]	129.2	[1]
Depreciation and amortization									164.1	156.5		155.6
Total assets	2,457.6				2,542.4				2,457.6	2,542.4		2,021.6
Capital expenditures									189.3	176.5		147.1
Intersegment
Segment Reporting Information [Line Items]
Revenue									(24.7)	(25.9)		(22.6)
Operating Segments
Segment Reporting Information [Line Items]
Operating income (loss)									305.4	235.4		208.4
Total assets	1,436.6				1,364.5				1,436.6	1,364.5		1,339.0
Corporate
Segment Reporting Information [Line Items]
Revenue									(24.7)	(25.9)		(22.6)
Operating income (loss)									(21.3)	(138.3)		(79.2)
Total assets	1,021.0				1,177.9				1,021.0	1,177.9		682.6
Capital expenditures									8.0	4.3		3.0
Services
Segment Reporting Information [Line Items]
Revenue									2,386.3	2,328.2		2,406.3
Operating income (loss)									67.6	64.8		46.9
Depreciation and amortization									97.2	84.6		81.8
Total assets	1,013.1				985.9				1,013.1	985.9		963.3
Capital expenditures									92.9	102.7		74.8
Services | Intersegment
Segment Reporting Information [Line Items]
Revenue									0.0	0.0		0.0
Services | Operating Segments
Segment Reporting Information [Line Items]
Revenue									2,386.3	2,328.2		2,406.3
Technology
Segment Reporting Information [Line Items]
Revenue									438.7	413.6		414.4
Operating income (loss)									237.8	170.6		161.5
Depreciation and amortization									66.9	71.9		73.8
Total assets	$ 423.5				$ 378.6				423.5	378.6		375.7
Capital expenditures									88.4	69.5		69.3
Technology | Intersegment
Segment Reporting Information [Line Items]
Revenue									24.7	25.9		22.6
Technology | Operating Segments
Segment Reporting Information [Line Items]
Revenue									$ 463.4	$ 439.5		$ 437.0

[1] Amounts were changed to conform to the current-year presentation. See Note 2.