Business Acquisitions, Goodwill and Acquired Intangible Assets (Other Acquired Intangible Assets) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2017	Jan. 03, 2016
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	$ 347.2	$ 330.4
Accumulated amortization	214.9	189.1
Net carrying amount	132.3	141.3
Total other acquired intangible assets, gross carrying amount	449.5	432.4
Total other acquired intangible assets, net carrying amount	234.6	243.3
Proprietary technology
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	207.2	198.6
Accumulated amortization	130.1	114.2
Net carrying amount	77.1	84.4
Customer list/relationships
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	121.9	114.3
Accumulated amortization	68.3	58.8
Net carrying amount	53.6	55.5
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	3.8	3.4
Accumulated amortization	2.4	2.1
Net carrying amount	1.4	1.3
Backlog
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Gross carrying amount	12.7	12.5
Accumulated amortization	12.6	12.5
Net carrying amount	0.1	0.0
Trademarks
Schedule of Acquired Intangible Assets by Major Class [Line Items]
Other acquired intangible assets not subject to amortization	$ 102.3	$ 102.0