Goodwill and Other Intangible Assets - Other Intangible Assets by Major class (Detail) - USD ($) $ in Millions	Jan. 01, 2022	Jan. 02, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	$ 495.0	$ 440.8
Non-amortized trademarks	142.6	129.6
Total gross carrying value, other intangible assets	637.6	570.4
Accumulated Amortization, Total	(335.9)	(309.6)
Total accumulated amortization, other intangible assets	(335.9)	(309.6)
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	217.8	191.5
Accumulated Amortization, Total	(142.1)	(130.1)
Developed technology
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	36.6	21.8
Accumulated Amortization, Total	(23.2)	(19.9)
Internally developed software
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	182.7	172.2
Accumulated Amortization, Total	(139.1)	(128.0)
Patents
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	45.7	43.2
Accumulated Amortization, Total	(25.1)	(25.3)
Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	3.9	3.9
Accumulated Amortization, Total	(2.3)	(2.4)
Other
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	8.3	8.2
Accumulated Amortization, Total	$ (4.1)	$ (3.9)