Income Taxes - Additional Information (Details) - USD ($)	12 Months Ended
	Jan. 31, 2020	Jan. 31, 2019	Jan. 31, 2018	Jan. 31, 2017
Income Taxes [Line Items]
Foreign pretax income (loss)	$ 475,500,000	$ 181,400,000	$ (76,200,000)
Valuation allowance increase (decrease)	85,600,000	163,600,000	(113,800,000)
Valuation allowance release, non-cash benefit	42,000,000.0
Valuation allowance adjustment	65,300,000	18,800,000	(82,500,000)
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, transition tax, adjustment for foreign tax credits	45,500,000
Deferred Tax Asset, Foreign Tax Credit	43,200,000
Deferred income taxes, net	152,600,000	53,100,000
Foreign tax credit carryforwards	253,900,000	198,600,000
Gross unrecognized tax benefits	220,600,000	209,000,000.0	337,600,000	$ 261,400,000
Unrecognized tax benefits that would reduce the valuation allowance if recognized	203,700,000
Amount of gross unrecognized tax benefits that would impact the effective tax rate, if recognized	16,900,000
Unrecognized tax benefits	2,300,000	3,100,000	2,800,000
Income tax expense from penalties and interest	(800,000)	300,000	300,000
Foreign income tax expense (benefit)		$ 11,400,000	$ 0.0
Income tax benefits per share (in dollars per share)		$ 0.05	$ 0.00
Domestic Country
Income Taxes [Line Items]
Operating loss carryforwards	742,800,000
Domestic Country | Research Tax Credit Carryforward
Income Taxes [Line Items]
Tax credit carryforward	186,300,000
State and Local Jurisdiction
Income Taxes [Line Items]
Operating loss carryforwards	1,486,200,000
State and Local Jurisdiction | Research Tax Credit Carryforward
Income Taxes [Line Items]
Tax credit carryforward	98,000,000.0
Foreign Country
Income Taxes [Line Items]
Deferred tax assets, net	56,400,000
Tax credit carryforward	267,100,000
Foreign Country | Ireland, Netherlands, and Singapore
Income Taxes [Line Items]
Operating loss carryforwards	277,700,000
Foreign Country | Ireland
Income Taxes [Line Items]
Operating loss carryforwards	37,900,000
Foreign Country | SINGAPORE
Income Taxes [Line Items]
Operating loss carryforwards	195,600,000
Foreign Country | Canada
Income Taxes [Line Items]
Tax credit carryforward	$ 58,400,000