Goodwill and Other Intangible Assets - Narrative (Detail) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill	$ 1,116.5	$ 982.4	$ 913.8
Gross carrying value, finite-lived intangible assets	495.0	440.8
Non-amortized trademarks	$ 142.6	129.6
Weighted-average amortization period (in years)	12 years
Aggregate amortization expense	$ 29.2	23.4	22.3
Estimated annual amortization expense for fiscal period 2022	28.0
Estimated annual amortization expense for fiscal period 2023	24.5
Estimated annual amortization expense for fiscal period 2024	18.8
Estimated annual amortization expense for fiscal period 2025	14.0
Estimated annual amortization expense for fiscal period 2026	10.8
Repair Systems  & Information Group
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill	778.3	638.8	615.1
Dealer-FX
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill	150.8
Dealer-FX | Repair Systems  & Information Group
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill	150.8
Sigmavision Limited
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill		5.6
Cognitran Limited
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill		14.5
Increase in goodwill associated with acquisition, purchase accounting adjustment		3.1
AutoCrib
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill	18.3	18.3
Non-amortized trademarks	17.7	7.4
Power Hawk Technologies Inc
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Goodwill			$ 6.4
Patents
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	$ 45.7	43.2
Weighted-average amortization period (in years)	14 years
Patents | Sigmavision Limited
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets		0.3
Customer relationships
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	$ 217.8	191.5
Weighted-average amortization period (in years)	14 years
Customer relationship contractual term, minimum (in years)	3 years
Customer relationship contractual term, maximum (in years)	5 years
Customer relationships | AutoCrib
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	$ 28.4	4.6
Developed technology
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	$ 36.6	21.8
Weighted-average amortization period (in years)	5 years
Developed technology | AutoCrib
Acquired Finite And Indefinite Lived Intangible Assets [Line Items]
Gross carrying value, finite-lived intangible assets	$ 14.8	$ 1.7