Accounting Policies (Narrative) (Details) $ in Millions	12 Months Ended
	Jan. 03, 2020 USD ($) segment	Dec. 28, 2018 USD ($)	Dec. 29, 2017 USD ($)	Dec. 31, 2018 USD ($)
Accounting Policies [Line Items]
Number of Reportable Segments | segment	4
Subscription revenue term	5 years
Unbilled Receivables, Current	$ 129.5	$ 22.3
Accounts Receivable, Allowance for Doubtful Accounts	5.9	4.6
Depreciation	$ 39.4	35.6	$ 34.6
Business Combination Valuation Remeasurement Window	1 year
Revenue, Practical Expedient, Incremental Cost of Obtaining Contract [true false]	true
Accrued Warranty Expenses	$ 16.3	15.3
Advertising expense	42.7	42.7	37.2
Research and Development expense with third party funding earned	16.5	19.5	$ 18.1
Operating Lease, Right-of-Use Asset	140.3
Operating Lease, Liability	$ 143.0
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]
Post Contract Support Term	1 year
Capitalized Contract Cost, Amortization Period	3 years
Maturity period of derivative financial instrument, minimum, in months	1 month
Estimated useful lives goodwill and purchased intangible assets, in years	3 years
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]
Post Contract Support Term	3 years
Capitalized Contract Cost, Amortization Period	7 years
Maturity period of derivative financial instrument, minimum, in months	2 months
Estimated useful lives goodwill and purchased intangible assets, in years	10 years
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	10 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 7 months 6 days
Forward Contracts [Member]
Accounting Policies [Line Items]
Derivative Financial Instruments Accounted for as Hedges	$ 0.0	0.0
Accounting Standards Update 2016-02 [Member]
Accounting Policies [Line Items]
Operating Lease, Right-of-Use Asset				$ 123.5
Operating Lease, Liability				$ 126.1
Not Designated as Hedging Instrument, Trading [Member] | Forward Contracts [Member]
Accounting Policies [Line Items]
Derivative Financial Instruments Accounted for as Hedges	$ 0.0	$ 0.0
Not a Lease At Inception [Member] | Maximum [Member]
Accounting Policies [Line Items]
Lease term to determine if arrangement is a lease at inception	1 year