Goodwill and Intangible Assets, Net - Components and Reconciliation of Goodwill (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Apr. 01, 2018	Apr. 02, 2017	Apr. 01, 2018	Apr. 02, 2017	Apr. 01, 2018	Oct. 01, 2017
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					$ 698.6	$ 745.3
Goodwill	$ 2,538.4		$ 2,497.3		2,538.4	2,497.3
Goodwill [Roll Forward]
Balance as of October 1, 2017			2,497.3
Additions from acquisitions			41.1
Balance as of April 1, 2018	2,538.4		2,538.4
Amortization of intangible assets	42.2	$ 46.5	92.4	$ 92.1
Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					627.2	670.9
Goodwill [Roll Forward]
Amortization of intangible assets	38.9	34.5	77.3	66.2
Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					69.5	73.8
Goodwill [Roll Forward]
Amortization of intangible assets	3.0	11.7	7.6	23.7
Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets					1.9	0.6
Goodwill [Roll Forward]
Amortization of intangible assets	$ 0.3	$ 0.3	$ 7.5	$ 2.2
In-process research and development
Goodwill and Intangible Assets Disclosure [Line Items]
Non-amortizable intangible assets					$ 0.0	$ 7.0