Goodwill and Intangible Assets, Net - Components and Reconciliation of Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Jan. 01, 2017	Jan. 03, 2016	Jan. 01, 2017	Oct. 02, 2016
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			$ 648.0	$ 693.6
Goodwill	$ 2,479.4		2,484.1	2,479.4
Goodwill [Roll Forward]
Balance as of October 2, 2016	2,479.4
Adjustments from prior acquisitions and divestitures	4.7
Balance as of January 1, 2017	2,484.1
Amortization of intangible assets	45.5	$ 25.4
Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			540.9	572.6
Goodwill [Roll Forward]
Amortization of intangible assets	31.7	14.2
Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			106.8	118.8
Goodwill [Roll Forward]
Amortization of intangible assets	12.0	10.9
Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			0.3	2.2
Goodwill [Roll Forward]
Amortization of intangible assets	$ 1.8	$ 0.3
In-process research and development
Goodwill and Intangible Assets Disclosure [Line Items]
Non-amortizable intangible assets			$ 241.0	$ 241.0