Accounting Policies (Narrative) (Details) $ in Millions	3 Months Ended	12 Months Ended
	Mar. 31, 2017 segment	Dec. 29, 2017 USD ($) segment	Dec. 30, 2016 USD ($) segment	Jan. 01, 2016 USD ($)	Oct. 01, 2016	Jan. 02, 2015 USD ($)
Accounting Policies [Line Items]
Other than Temporary Impairment Losses, Investments, Portion Recognized in Earnings, Net, Available-for-sale Securities		$ 0.0
Number of Reportable Segments | segment	4	4	4
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest		$ 2,366.0	$ 2,305.7	$ 2,220.6		$ 2,353.4
Allowance for Doubtful Accounts Receivable, Current		3.6	5.0
Additional paid-in-capital		1,461.1	1,348.3
Other than Temporary Impairment Losses, Investments, Available-for-sale Securities		0.0
Depreciation expense		34.6	37.0	36.7
Net Cash Provided by (Used in) Operating Activities		411.9	413.6	357.0
Net Cash Provided by (Used in) Financing Activities, Continuing Operations		79.1	(162.3)	(204.9)
Advertising expense		37.2	37.2	32.3
Research and Development expense with third party funding earned		18.1	13.0	12.5
Unamortized Debt Issuance Expense		2.1	2.4
Revenue Recognition, Sales Returns, Reserve for Sales Returns		$ 4.2	3.6
Building [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		39 years
Leasehold Improvements [Member]
Accounting Policies [Line Items]
Property, Plant and Equipment, Estimated Useful Lives		the life of the lease
Minimum [Member]
Accounting Policies [Line Items]
Maturity period of derivative financial instrument, minimum, in months		1 month
Estimated useful lives goodwill and purchased intangible assets, in years		4 years
Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount					311.00%
Warranty periods for products sold		1 year
Minimum [Member] | Machinery And Equipment [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		4 years
Minimum [Member] | Furniture And Fixtures [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		5 years
Minimum [Member] | Computer Equipment And Software [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		2 years
Minimum [Member] | Internal-Use Of Software [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		2 years
Maximum [Member]
Accounting Policies [Line Items]
Investments, Weighted Average Maturity Term		6 months
Maturity period of derivative financial instrument, minimum, in months		2 months
Estimated useful lives goodwill and purchased intangible assets, in years		8 years
Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount					903.00%
Warranty periods for products sold		2 years
Maximum [Member] | Machinery And Equipment [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		6 years
Maximum [Member] | Furniture And Fixtures [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		7 years
Maximum [Member] | Computer Equipment And Software [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		5 years
Maximum [Member] | Internal-Use Of Software [Member]
Accounting Policies [Line Items]
Useful life of asset, in years		5 years
Weighted Average [Member]
Accounting Policies [Line Items]
Estimated useful lives goodwill and purchased intangible assets, in years		6 years 1 month
Forward Contracts [Member]
Accounting Policies [Line Items]
Foreign Currency Derivative Instruments Not Designated as Hedging Instruments at Fair Value, Net		$ 0.0	0.0
Indemnification Agreement [Member]
Accounting Policies [Line Items]
Loss Contingency Accrual		0.0	0.0
Additional Paid-in Capital [Member]
Accounting Policies [Line Items]
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest		1,461.1	1,348.3	1,238.0		$ 1,207.0
Accounting Standards Update 2016-09 [Member]
Accounting Policies [Line Items]
Net Cash Provided by (Used in) Operating Activities			$ 6.5	$ 2.1
income expense benefit [Member] | Accounting Standards Update 2016-09 [Member]
Accounting Policies [Line Items]
New Accounting Pronouncement or Change in Accounting Principle, Effect of Adoption, Quantification		8.9
Deferred Revenue [Member] | Accounting Standards Update 2014-09 [Member] | Minimum [Member]
Accounting Policies [Line Items]
New Accounting Pronouncement or Change in Accounting Principle, Effect of Adoption, Quantification		40.0
Deferred Revenue [Member] | Accounting Standards Update 2014-09 [Member] | Maximum [Member]
Accounting Policies [Line Items]
New Accounting Pronouncement or Change in Accounting Principle, Effect of Adoption, Quantification		55.0
Prepaid Expenses and Other Current Assets [Member] | Accounting Standards Update 2014-09 [Member] | Minimum [Member]
Accounting Policies [Line Items]
New Accounting Pronouncement or Change in Accounting Principle, Effect of Adoption, Quantification		30.0
Prepaid Expenses and Other Current Assets [Member] | Accounting Standards Update 2014-09 [Member] | Maximum [Member]
Accounting Policies [Line Items]
New Accounting Pronouncement or Change in Accounting Principle, Effect of Adoption, Quantification		$ 40.0