Goodwill and Intangible Assets, Net - Components and Reconciliation of Goodwill (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Apr. 02, 2017	Apr. 03, 2016	Apr. 02, 2017	Apr. 03, 2016	Apr. 02, 2017	Oct. 02, 2016
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					$ 801.5	$ 693.6
Goodwill	$ 2,483.6		$ 2,479.4		2,483.6	2,479.4
Goodwill [Roll Forward]
Balance as of October 2, 2016			2,479.4
Adjustments from prior acquisitions and divestitures			4.2
Balance as of April 2, 2017	2,483.6		2,483.6
Amortization of intangible assets	46.5	$ 45.3	92.1	$ 70.7
Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					706.5	572.6
Goodwill [Roll Forward]
Amortization of intangible assets	34.5	30.3	66.2	44.6
Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					95.0	118.8
Goodwill [Roll Forward]
Amortization of intangible assets	11.7	12.0	23.7	23.0
Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					0.0	2.2
Goodwill [Roll Forward]
Amortization of intangible assets	$ 0.3	$ 3.0	$ 2.2	$ 3.1
In-process research and development
Goodwill and Intangible Assets Disclosure [Line Items]
Non-amortizable intangible assets					$ 41.0	$ 241.0