Goodwill and Intangible Assets, Net - Goodwill and Intangible Assets (Detail) - USD ($) $ in Millions	12 Months Ended
	Oct. 01, 2017	Oct. 02, 2016	Sep. 27, 2015
Goodwill and Intangible Assets Disclosure [Line Items]
Gross Carrying Value	$ 1,408.4	$ 1,270.6
Accumulated Amortization	(663.1)	(577.0)
Goodwill	2,497.3	2,479.4	$ 1,139.3
Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Gross Carrying Value	1,076.8	907.7
Accumulated Amortization	(405.9)	(335.1)
Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Gross Carrying Value	323.4	338.0
Accumulated Amortization	(249.6)	(219.2)
Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Gross Carrying Value	8.2	24.9
Accumulated Amortization	$ (7.6)	(22.7)
Minimum | Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Life (years)	2 years
Minimum | Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Life (years)	4 years
Minimum | Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Life (years)	1 year
Maximum | Completed technology
Goodwill and Intangible Assets Disclosure [Line Items]
Life (years)	15 years
Maximum | Customer relationships
Goodwill and Intangible Assets Disclosure [Line Items]
Life (years)	15 years
Maximum | Backlog, trade name and other
Goodwill and Intangible Assets Disclosure [Line Items]
Life (years)	5 years
In Process Research and Development [Member]
Goodwill and Intangible Assets Disclosure [Line Items]
Indefinite-Lived Intangible Assets (Excluding Goodwill)	$ 7.0	$ 241.0