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Income Taxes - Narrative (Details)
€ in Thousands, $ in Thousands
1 Months Ended 12 Months Ended 72 Months Ended
Dec. 31, 2021
EUR (€)
Jun. 30, 2021
EUR (€)
Dec. 31, 2021
USD ($)
Dec. 31, 2020
USD ($)
Dec. 31, 2019
USD ($)
Dec. 31, 2010
EUR (€)
Income Taxes [Line Items]            
Percentage of earnings from continuing operations before income taxes attributable to the United States (as a percent)     30.00%      
Valuation allowance against deferred tax asset     $ 236,357 $ 267,838    
Increase (decrease) in the valuation allowance     (31,481) 35,642    
Net operating loss carryforwards and tax credit     408,434 433,822    
Net operating loss carryforwards in the U.S.     6,173      
Net operating loss carryforwards in various foreign jurisdictions     1,596,351      
Gross unrecognized tax benefits     1,296,523 1,388,391 $ 1,260,970  
Unrecognized tax benefits that would impact effective tax rate     45,147      
Interest and penalties     14,494 11,485    
Accrued/(reversed) interest and penalties     3,236 $ (695) 5,368  
Expected decrease in unrecognized tax benefits within next twelve months     $ 19,510      
Luxembourg            
Income Taxes [Line Items]            
Net operating loss carryforwards in various foreign jurisdictions         $ 1,238,277  
Domestic tax authority            
Income Taxes [Line Items]            
Effective income tax rate (as a percent)     33.80% (12.00%) 36.60%  
Foreign tax authority            
Income Taxes [Line Items]            
Effective income tax rate (as a percent)     14.10% 16.30% (9.40%)  
Foreign tax authority | Tax Years 2005 to 2010 | Belgium            
Income Taxes [Line Items]            
Foreign tax assessment | €           € 223,321
Foreign tax authority | Tax Year 2018 | Luxembourg            
Income Taxes [Line Items]            
Foreign tax assessment | € € 182,594 € 371,696        
State            
Income Taxes [Line Items]            
Net operating loss carryforwards and tax credit     $ 44,186      
State deferred tax assets            
Income Taxes [Line Items]            
Valuation allowance against deferred tax asset     22,851      
Operating Loss Carryforward, Domestic            
Income Taxes [Line Items]            
Valuation allowance against deferred tax asset     5,882      
Operating Loss Carryforward, Foreign Jurisdiction            
Income Taxes [Line Items]            
Valuation allowance against deferred tax asset     $ 207,624