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Income taxes - Difference in Provision for Income Taxes from Amount Obtained by Applying U.S. Federal Statutory Rate (Details) - USD ($)
$ in Thousands
12 Months Ended
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2017
Income Tax Disclosure [Abstract]      
Federal statutory rate 21.00% 21.00% 35.00%
Tax at federal statutory rate $ 3,255 $ 8,869 $ 18,354
State taxes, net of federal benefit (3) 36 2
Mandatory repatriation/Section 956 0 0 (5,718)
Permanent differences 1,514 (371) (67)
Stock-based compensation (1,014) (1,079) (314)
Change in valuation allowance (5,186) (10,094) 16,273
Research and development 932 914 851
Foreign rate differences (531) (697) (2,819)
Foreign tax credit (405) 49 144
Change in prior year deferred balances 0 1,653 (28,262)
Other (195) (609) 647
Total provision $ (1,633) $ (1,329) $ (909)