Goodwill and Intangible Assets, Net - Components and Reconciliation of Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2017	Jan. 01, 2017	Dec. 31, 2017	Oct. 01, 2017
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			$ 737.8	$ 745.3
Goodwill	$ 2,497.3		2,542.9	2,497.3
Goodwill [Roll Forward]
Balance as of October 1, 2017	2,497.3
Additions from acquisitions	45.6
Balance as of December 31, 2017	2,542.9
Amortization of intangible assets	50.3	$ 45.5
Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			660.0	670.9
Goodwill [Roll Forward]
Amortization of intangible assets	38.5	31.7
Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			75.4	73.8
Goodwill [Roll Forward]
Amortization of intangible assets	4.6	12.0
Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Amortizable intangible assets			2.4	0.6
Goodwill [Roll Forward]
Amortization of intangible assets	$ 7.2	$ 1.8
In-process research and development
Goodwill and Intangible Assets Disclosure [Line Items]
Non-amortizable intangible assets			$ 0.0	$ 7.0