Significant Accounting Policies - Narrative (Details)	12 Months Ended
	Mar. 31, 2019 USD ($)	Mar. 31, 2019 USD ($) segment	Mar. 31, 2019 USD ($)	Mar. 31, 2019 USD ($) day	Mar. 31, 2019 USD ($) reporting_unit	Mar. 31, 2019 USD ($) unit	Jun. 30, 2018 USD ($)	Apr. 01, 2018 USD ($)	Mar. 31, 2018 USD ($)
Accounting Policies [Abstract]
Deferred revenue on shipments to distributors									$ 479,600,000
Deferred cost of sales on shipments to distributors									145,800,000
Deferred income on shipments to distributors	$ 0	$ 0	$ 0	$ 0	$ 0	$ 0		$ 0	333,800,000
Property, Plant and Equipment [Line Items]
Number of reporting units (in units)					2	2
Impairment of goodwill			0
Amount of distributor advances, included in deferred income on shipments to distributors in consolidated balance sheets	170,700,000	$ 170,700,000	170,700,000	$ 170,700,000	$ 170,700,000	$ 170,700,000			203,900,000
Number of days requiring distributor to settle receivable balances (in days) | day				30
Number of operating segments (in segments) | segment		2
Long-term deferred tax liability	706,100,000	$ 706,100,000	706,100,000	$ 706,100,000	706,100,000	706,100,000		221,500,000	205,800,000
Other assets	111,800,000	111,800,000	111,800,000	111,800,000	111,800,000	111,800,000		47,700,000	71,800,000
Other long-term liabilities	279,500,000	279,500,000	279,500,000	279,500,000	279,500,000	279,500,000		239,200,000	240,900,000
Long-term deferred tax assets	$ 1,677,200,000	$ 1,677,200,000	$ 1,677,200,000	$ 1,677,200,000	$ 1,677,200,000	$ 1,677,200,000		$ 1,656,500,000	100,200,000
Minimum
Property, Plant and Equipment [Line Items]
Upgrade period	1 year
Product warranty	12 months
Useful life (in years)	1 year
Minimum | Building and building improvements
Property, Plant and Equipment [Line Items]
Property, plant and equipment, useful life (in years)	10 years
Minimum | Machinery and equipment
Property, Plant and Equipment [Line Items]
Property, plant and equipment, useful life (in years)	3 years
Maximum
Property, Plant and Equipment [Line Items]
Upgrade period	3 years
Product warranty	24 months
Useful life (in years)	15 years
Maximum | Building and building improvements
Property, Plant and Equipment [Line Items]
Property, plant and equipment, useful life (in years)	40 years
Maximum | Machinery and equipment
Property, Plant and Equipment [Line Items]
Property, plant and equipment, useful life (in years)	7 years
Accounting Standards Update 2016-16
Accounting Policies [Abstract]
Deferred income on shipments to distributors									0
Property, Plant and Equipment [Line Items]
Long-term deferred tax liability							$ (1,100,000)		(1,100,000)
Other assets							(24,100,000)		(24,100,000)
Other long-term liabilities							(1,700,000)		(1,700,000)
Cumulative adjustment									1,558,100,000
Long-term deferred tax assets							$ 1,580,000,000		$ 1,579,400,000