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Income Taxes - Additional Information (Details) - USD ($)
12 Months Ended
Jan. 31, 2019
Jan. 31, 2018
Jan. 31, 2017
Jan. 31, 2016
Income Taxes [Line Items]        
Foreign pretax income (loss) $ 181,400,000 $ (76,200,000) $ (27,600,000)  
Valuation allowance increase (decrease) 163,600,000 $ (113,800,000) 352,400,000  
Blended income tax rate   33.81%    
Tax Cuts and Jobs Act, provisional income tax benefit   $ 32,300,000    
Tax Cuts and Jobs Act, provisional transition tax for accumulated foreign earnings   831,500,000    
Tax Cuts and Jobs Act, transition tax for accumulated foreign earnings 819,600,000      
Tax Cuts and Jobs Act, foreign tax credits as a result of transition tax 45,100,000      
Deferred income taxes, net 53,100,000 72,100,000    
Gross unrecognized tax benefits 209,000,000.0 337,600,000 261,400,000 $ 254,300,000
Unrecognized tax benefits that would reduce the valuation allowance if recognized 190,600,000      
Amount of gross unrecognized tax benefits that would impact the effective tax rate, if recognized 18,400,000      
Unrecognized tax benefits 3,100,000 2,800,000 2,500,000  
Income tax expense from penalties and interest 300,000 300,000 1,500,000  
Foreign income tax expense (benefit) $ (11,400,000) $ 0 $ (27,100,000)  
Income tax benefits per share (in dollars per share) $ 0.05   $ 0.12  
Domestic Country        
Income Taxes [Line Items]        
Operating loss carryforwards $ 531,400,000      
Domestic Country | Research Tax Credit Carryforward        
Income Taxes [Line Items]        
Tax credit carryforward 164,900,000      
State and Local Jurisdiction        
Income Taxes [Line Items]        
Operating loss carryforwards 1,465,700,000      
State and Local Jurisdiction | Research Tax Credit Carryforward        
Income Taxes [Line Items]        
Tax credit carryforward 68,800,000      
Foreign Country        
Income Taxes [Line Items]        
Deferred income taxes, net 54,300,000      
Tax credit carryforward 242,400,000      
Foreign Country | Ireland, Netherlands, and Singapore        
Income Taxes [Line Items]        
Operating loss carryforwards 521,800,000      
Foreign Country | Ireland        
Income Taxes [Line Items]        
Operating loss carryforwards 238,800,000      
Foreign Country | Canada        
Income Taxes [Line Items]        
Tax credit carryforward $ 59,000,000.0