Cost-reduction actions - Additional Information (Detail) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2019 USD ($)	Sep. 30, 2019 USD ($)	Jun. 30, 2019 USD ($)	Mar. 31, 2019 USD ($)	Dec. 31, 2018 USD ($)	Sep. 30, 2018 USD ($)	Jun. 30, 2018 USD ($)	Mar. 31, 2018 USD ($)	Dec. 31, 2019 USD ($) employee	Dec. 31, 2018 USD ($) employee	Dec. 31, 2017 USD ($) employee
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs	$ 23.3	$ 0.2	$ 2.6	$ 2.6	$ 22.8	$ (0.9)	$ 0.7	$ (2.9)	$ 28.7	$ 19.7	$ 146.8
Charges related to work-force reductions									22.1	19.0	117.9
Other expenses related to the cost-reduction effort									6.6		28.9
Cost of revenue | Services
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									10.8	18.1	99.6
Cost of revenue | Technology
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									0.2		0.4
Selling, general and administrative expenses
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									15.5	1.6	33.6
Research and development expenses
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs									2.2		1.4
Other income (expense), net
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs											11.8
Lease abandonment costs
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort									4.6
Net asset sales and write-offs
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort											1.8
Asset write-offs
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort									1.1
Professional fees and other expenses related to the cost-reduction effort
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort											5.2
Other expenses related to the cost-reduction effort
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort									0.9
Idle leased facilities
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort										0.7	4.7
Contract amendment and termination
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort											5.4
Net foreign currency translation losses
Restructuring Cost and Reserve [Line Items]
Other expenses related to the cost-reduction effort											11.8
Net foreign currency translation losses | Other income (expense), net
Restructuring Cost and Reserve [Line Items]
Cost-reduction charges and other costs											(11.8)
U.S.
Restructuring Cost and Reserve [Line Items]
Charges related to work-force reductions									$ 4.6	$ 5.2	$ 9.4
Number of employees | employee									509	264	542
U.S. | Changes in estimates
Restructuring Cost and Reserve [Line Items]
Charges related to work-force reductions									$ (1.5)	$ 0.1	$ (1.3)
Non-U.S.
Restructuring Cost and Reserve [Line Items]
Charges related to work-force reductions									$ 21.1	$ 22.5	$ 109.4
Number of employees | employee									255	325	2,274
Non-U.S. | Changes in estimates
Restructuring Cost and Reserve [Line Items]
Charges related to work-force reductions									$ (2.1)	$ (8.8)	$ (7.8)
Non-U.S. | Additional benefits provided in 2017
Restructuring Cost and Reserve [Line Items]
Charges related to work-force reductions											$ 8.2