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Cost reduction actions - Additional Information (Detail)
$ in Millions
3 Months Ended 12 Months Ended 36 Months Ended
Dec. 31, 2017
USD ($)
Sep. 30, 2017
USD ($)
Jun. 30, 2017
USD ($)
Mar. 31, 2017
USD ($)
Dec. 31, 2016
USD ($)
Sep. 30, 2016
USD ($)
Jun. 30, 2016
USD ($)
Mar. 31, 2016
USD ($)
Dec. 31, 2017
USD ($)
employee
Dec. 31, 2016
USD ($)
employee
Dec. 31, 2015
USD ($)
employee
Dec. 31, 2017
USD ($)
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges $ 47.8 $ 46.1 $ 27.5 $ 25.4 $ 13.1 $ 31.9 $ 10.2 $ 26.9 $ 146.8 $ 82.1 $ 118.5 $ 347.4
Severance costs                 117.9 62.6 78.8  
Other expenses related to the cost reduction effort                 28.9 19.5 39.7  
Asset impairment charges                     20.2  
Cost of revenue | Services                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 99.6 42.4 52.3  
Cost of revenue | Technology                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 0.4   0.3  
Selling, general and administrative expenses                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 33.6 38.0 53.5  
Research and development expenses                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 1.4 1.7 12.4  
Other income (expense), net                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 11.8      
Idle leased facilities                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 4.2 1.4 0.0  
Other expenses related to the cost reduction effort                 4.7 1.4    
Contract amendment and termination                        
Restructuring Cost and Reserve [Line Items]                        
Other expenses related to the cost reduction effort                 5.4 4.1    
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 13.3 19.5  
Net asset sales and write-offs                        
Restructuring Cost and Reserve [Line Items]                        
Other expenses related to the cost reduction effort                 1.8 0.7    
Net foreign currency translation adjustment                        
Restructuring Cost and Reserve [Line Items]                        
Other expenses related to the cost reduction effort                 11.8      
Net foreign currency translation adjustment | Other income (expense), net                        
Restructuring Cost and Reserve [Line Items]                        
Restructuring charges                 11.8      
United States                        
Restructuring Cost and Reserve [Line Items]                        
Severance costs                 $ 9.4 $ 8.3 $ 27.9  
Number of employees | employee                 542 351 700  
United States | Changes in estimates                        
Restructuring Cost and Reserve [Line Items]                        
Severance costs                 $ (1.3) $ (1.3)    
Non-US                        
Restructuring Cost and Reserve [Line Items]                        
Severance costs                 $ 109.4 $ 58.6 $ 50.9  
Number of employees | employee                 2,274 1,048 782  
Non-US | Changes in estimates                        
Restructuring Cost and Reserve [Line Items]                        
Severance costs                 $ (7.8) $ (3.0)    
Non-US | Additional benefits provided in 2017                        
Restructuring Cost and Reserve [Line Items]                        
Severance costs                 $ 8.2