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Intangible assets, net - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Jun. 30, 2018
Jun. 30, 2017
Jun. 30, 2018
Jun. 30, 2017
Finite-Lived Intangible Assets [Line Items]        
Amortization of intangible assets $ 9.0 $ 8.6 $ 17.4 $ 17.0
Capitalized Software Development Costs        
Finite-Lived Intangible Assets [Line Items]        
Software development costs capitalized 3.9 13.7 11.9 26.0
Amortization expense of capitalized software development costs 6.8 5.5 12.9 10.8
Costs related to stock based compensation $ 0.2 $ 0.5 $ 0.5 $ 1.0
Minimum | Capitalized Software Development Costs        
Finite-Lived Intangible Assets [Line Items]        
Intangible assets amortization period (in years)     3 years  
Minimum | Acquired Technology        
Finite-Lived Intangible Assets [Line Items]        
Intangible assets amortization period (in years)     3 years  
Minimum | Patents        
Finite-Lived Intangible Assets [Line Items]        
Intangible assets amortization period (in years)     10 years  
Maximum | Capitalized Software Development Costs        
Finite-Lived Intangible Assets [Line Items]        
Intangible assets amortization period (in years)     6 years  
Maximum | Acquired Technology        
Finite-Lived Intangible Assets [Line Items]        
Intangible assets amortization period (in years)     8 years  
Maximum | Patents        
Finite-Lived Intangible Assets [Line Items]        
Intangible assets amortization period (in years)     17 years