Employee Stock Benefit Plans (Components of Stock-based Compensation Expense) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2021	Jan. 03, 2020	Dec. 28, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 83.0	$ 75.0	$ 76.9
Cost of sales
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	6.7	5.6	4.5
Research and development
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	22.1	16.7	15.0
Sales and marketing
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	16.2	13.0	10.0
General and administrative
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	38.0	39.7	47.4
Restricted stock units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	73.2	67.3	68.9
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	1.5	0.6	1.5
ESPP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 8.3	$ 7.1	$ 6.5