Income Taxes - Income Taxes Additional Information (Detail) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Jan. 31, 2018	Jan. 31, 2017	Jan. 31, 2016	Jan. 31, 2015
Income Taxes [Line Items]
Foreign pretax income (loss)	$ (76.2)	$ (27.6)	$ 218.2
Valuation allowance	$ (113.8)	352.4	327.2
Blended income tax rate	33.81%
Tax Cuts and Jobs Act of 2017, provisional income tax benefit	$ 32.3
Gross unrecognized tax benefits	337.6	261.4	254.3	$ 245.8
Unrecognized tax benefits that would reduce the valuation allowance if recognized	304.8
Amount of gross unrecognized tax benefits that would impact the effective tax rate, if recognized	32.8
Unrecognized tax benefits	2.8	2.5	3.3
Income tax expense from penalties and interest	0.3	1.5	1.3
Foreign income tax expense (benefit)	0.0	$ 27.1	$ 0.0
Income tax benefits per share		$ 0.12
Domestic Country
Income Taxes [Line Items]
Operating loss carryforwards	179.4
Domestic Country | Research Tax Credit Carryforward
Income Taxes [Line Items]
Tax credit carryforward	138.4
State and Local Jurisdiction
Income Taxes [Line Items]
Operating loss carryforwards	939.1
State and Local Jurisdiction | Research Tax Credit Carryforward
Income Taxes [Line Items]
Tax credit carryforward	72.6
Foreign Country
Income Taxes [Line Items]
Deferred income taxes, net	68.0
Tax credit carryforward	336.9
Foreign Country | Canada
Income Taxes [Line Items]
Tax credit carryforward	$ 58.1