Business Acquisitions, Goodwill and Acquired Intangible Assets (Purchase Price) (Details) - USD ($) $ in Millions									12 Months Ended
	Dec. 06, 2016	Nov. 02, 2016	May 03, 2016	Apr. 15, 2016	Apr. 06, 2016	Jun. 05, 2015	Apr. 29, 2015	Feb. 02, 2015	Jan. 01, 2017	Jan. 03, 2016	Dec. 28, 2014
Business Acquisition [Line Items]
Goodwill									$ 1,193.5	$ 1,140.2	$ 1,150.6
Frontline
Business Acquisition [Line Items]
Cash paid					$ 13.7
Goodwill					11.3
Acquired Intangible Assets					$ 2.3
Quantum Data
Business Acquisition [Line Items]
Cash paid				$ 17.3
Goodwill				10.7
Acquired Intangible Assets				$ 5.4
CARIS
Business Acquisition [Line Items]
Cash paid			$ 26.2
Goodwill			22.2
Acquired Intangible Assets			$ 3.6
IN USA
Business Acquisition [Line Items]
Cash paid		$ 10.2
Goodwill		6.3
Acquired Intangible Assets		$ 3.0
Hanson Research
Business Acquisition [Line Items]
Cash paid	$ 25.0
Goodwill	13.5
Acquired Intangible Assets	$ 8.4
Bowtech
Business Acquisition [Line Items]
Cash paid								$ 18.9
Goodwill								7.0
Acquired Intangible Assets								$ 4.3
ICM
Business Acquisition [Line Items]
Cash paid						$ 21.8
Goodwill						19.2
Acquired Intangible Assets						$ 5.8
Purchase of remaining interest of Optech
Business Acquisition [Line Items]
Cash paid							$ 22.0
Goodwill							0.0
Acquired Intangible Assets							$ 0.0
Other investments
Business Acquisition [Line Items]
Cash paid									1.0	4.0
Goodwill									0.0	1.4
Acquired Intangible Assets									0.0	0.9
Acquisitions in 2015
Business Acquisition [Line Items]
Cash paid										66.7
Goodwill										27.6
Acquired Intangible Assets										$ 11.0
Acquisitions in 2016
Business Acquisition [Line Items]
Cash paid									93.4
Goodwill									64.0
Acquired Intangible Assets									$ 22.7