Business Acquisitions, Goodwill and Acquired Intangible Assets (Acquired Intangible Assets) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 03, 2016	Dec. 28, 2014	Dec. 29, 2013
Schedule of Intangible Assets, Including Goodwill [Line Items]
Weighted average useful life in years	5 years 1 month 6 days
Goodwill	$ 1,140.2	$ 1,150.6	$ 1,037.8
Proprietary technology
Schedule of Intangible Assets, Including Goodwill [Line Items]
Weighted average useful life in years	4 years 10 months 25 days
Customer list/relationships
Schedule of Intangible Assets, Including Goodwill [Line Items]
Weighted average useful life in years	5 years 4 months 25 days
Trademarks
Schedule of Intangible Assets, Including Goodwill [Line Items]
Weighted average useful life in years	8 years
Trademarks
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles not subject to amortization	$ 102.0	105.8
Acquisitions in 2015
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization	8.7
Intangibles not subject to amortization	2.3
Total acquired intangible assets	$ 11.0
Weighted average useful life in years	9 years 4 months 8 days
Goodwill	$ 27.6
Acquisitions in 2015 | Proprietary technology
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization	$ 5.7
Weighted average useful life in years	9 years 11 months 8 days
Acquisitions in 2015 | Customer list/relationships
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization	$ 3.0
Weighted average useful life in years	8 years 3 months 8 days
Acquisitions in 2015 | Backlog
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization	$ 0.0
Acquisitions in 2015 | Trademarks
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles not subject to amortization	$ 2.3
Acquisitions in 2014
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization		40.6
Intangibles not subject to amortization		7.6
Total acquired intangible assets		$ 48.2
Weighted average useful life in years		11 years 8 days
Goodwill		$ 142.8
Acquisitions in 2014 | Proprietary technology
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization		$ 18.4
Weighted average useful life in years		11 years 8 days
Acquisitions in 2014 | Customer list/relationships
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization		$ 21.4
Weighted average useful life in years		11 years 3 months 8 days
Acquisitions in 2014 | Backlog
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles subject to amortization		$ 0.8
Weighted average useful life in years		4 months 6 days
Acquisitions in 2014 | Trademarks
Schedule of Intangible Assets, Including Goodwill [Line Items]
Intangibles not subject to amortization		$ 7.6