Income Taxes - Income Taxes Additional Information (Detail) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Jan. 31, 2017	Jan. 31, 2016	Jan. 31, 2015	Jan. 31, 2014
Income Taxes [Line Items]
Foreign pretax income (loss)	$ (27.6)	$ 218.2	$ 302.5
Valuation allowance	352.4	327.2	3.6
Deferred income taxes, net	63.9	9.2
Gross unrecognized tax benefits	261.4	254.3	245.8	$ 222.1
Amount of gross unrecognized tax benefits that would impact the effective tax rate, if recognized	247.3
Unrecognized tax benefits	2.5	3.3	2.0
Income tax expense from penalties and interest	1.5	1.3
Income benefit from penalties and interest			(0.8)
Cumulative earnings from Foreign subsidiaries for which income taxes have not been provided	1,738.9
Unrecognized deferred tax liability for earnings of foreign subsidiaries	435.1
Foreign income tax expense (benefit)	$ (27.1)	$ 0.0	$ (1.2)
Income tax benefits per share	$ 0.12		$ 0.01
Domestic Country
Income Taxes [Line Items]
Operating loss carryforwards	$ 575.0
Domestic Country | Research Tax Credit Carryforward
Income Taxes [Line Items]
Tax credit carryforward	127.1
State and Local Jurisdiction
Income Taxes [Line Items]
Operating loss carryforwards	526.8
State and Local Jurisdiction | Research Tax Credit Carryforward
Income Taxes [Line Items]
Tax credit carryforward	66.8
Foreign Country
Income Taxes [Line Items]
Deferred income taxes, net	49.7
Tax credit carryforward	211.5
Foreign Country | Canada
Income Taxes [Line Items]
Tax credit carryforward	$ 54.6