Income Taxes - Unrecognized Tax Benefits Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 31, 2022	Jan. 31, 2021	Jan. 31, 2020
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Gross unrecognized tax benefits at the beginning of the fiscal year	$ 198.0	$ 220.6	$ 209.0
Increases for tax positions of prior years	9.0	12.7	2.8
Decreases for tax positions of prior years	(6.6)	(41.1)	(0.4)
Increases for tax positions related to the current year	6.7	6.4	11.1
Decreases relating to settlements with taxing authorities	0.0	0.0	0.0
Reductions as a result of lapse of the statute of limitations	(0.4)	(0.6)	(1.9)
Gross unrecognized tax benefits at the end of the fiscal year	$ 206.7	$ 198.0	$ 220.6