Business Acquisitions, Goodwill and Acquired Intangible Assets (Other Acquired Intangible Assets) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 03, 2016	Dec. 28, 2014
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	$ 330.4	$ 338.6
Accumulated amortization	189.1	166.8
Net carrying amount	141.3	171.8
Total other acquired intangible assets, gross carrying amount	432.4	444.4
Total other acquired intangible assets, accumulated amortization	189.1	166.8
Total other acquired intangible assets, net carrying amount	243.3	277.6
Proprietary technology
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	198.6	202.8
Accumulated amortization	114.2	99.7
Net carrying amount	84.4	103.1
Customer list/relationships
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	114.3	117.6
Accumulated amortization	58.8	51.0
Net carrying amount	55.5	66.6
Patents
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	0.7	0.7
Accumulated amortization	0.6	0.6
Net carrying amount	0.1	0.1
Non-compete agreements
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	0.9	0.9
Accumulated amortization	0.9	0.9
Net carrying amount	0.0	0.0
Trademarks
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	3.4	3.4
Accumulated amortization	2.1	1.9
Net carrying amount	1.3	1.5
Backlog
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	12.5	13.2
Accumulated amortization	12.5	12.7
Net carrying amount	0.0	0.5
Trademarks
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Other acquired intangible assets not subject to amortization	$ 102.0	$ 105.8