Restructuring and other exit costs, net (Details) $ in Millions	3 Months Ended	12 Months Ended
	Jan. 31, 2018 USD ($) Position	Jan. 31, 2019 USD ($)	Jan. 31, 2018 USD ($)
Restructuring Cost and Reserve [Line Items]
Additions			$ 94.1
Restructuring Reserve [Roll Forward]
Total, beginning balance		$ 57.2	7.5
Current portion, beginning balance		57.2	5.9
Non-current portion, beginning balance		0.0	1.6
Additions			94.1
Payments			(42.4)
Adjustments			(2.0)
Total, ending balance	$ 57.2		57.2
Current portion, ending balance	57.2		57.2
Non-current portion, ending balance	0.0		0.0
Total	$ 57.2	57.2	7.5
Fiscal 2018 Plan
Restructuring Cost and Reserve [Line Items]
Percentage of workforce eliminated	11.00%
Number of positions eliminated | Position	1,027
Additions		42.4
Restructuring Reserve [Roll Forward]
Total, beginning balance		55.5
Current portion, beginning balance		55.5
Additions		42.4
Payments		(95.4)
Adjustments		(0.4)
Total, ending balance	$ 55.5	2.1	55.5
Current portion, ending balance	55.5	2.1	55.5
Total	55.5	55.5	55.5
Facility Closing | Fiscal 2018 Plan
Restructuring Cost and Reserve [Line Items]
Additions		3.2	6.3
Restructuring Reserve [Roll Forward]
Total, beginning balance		2.5	0.0
Additions		3.2	6.3
Payments		(5.7)	(1.3)
Adjustments		0.1	(2.5)
Total, ending balance	2.5	0.1	2.5
Total	2.5	2.5	2.5
Facility Closing | Fiscal 2017 Plan
Restructuring Cost and Reserve [Line Items]
Additions			0.1
Restructuring Reserve [Roll Forward]
Total, beginning balance		0.2	1.9
Additions			0.1
Payments			(1.5)
Adjustments			(0.3)
Total, ending balance	0.2		0.2
Total	0.2	0.2	1.9
Facility Closing | Other facility termination costs
Restructuring Cost and Reserve [Line Items]
Additions			0.3
Restructuring Reserve [Roll Forward]
Total, beginning balance		1.5	4.5
Additions			0.3
Payments			(3.0)
Adjustments			(0.3)
Total, ending balance	1.5		1.5
Total	1.5	1.5	4.5
Employee Severance | Fiscal 2018 Plan
Restructuring Cost and Reserve [Line Items]
Additions		39.2	87.3
Restructuring Reserve [Roll Forward]
Total, beginning balance		53.0	0.0
Additions		39.2	87.3
Payments		(89.7)	(35.1)
Adjustments		(0.5)	0.8
Total, ending balance	53.0	2.0	53.0
Total	53.0	2.0	0.0
Employee Severance | Fiscal 2017 Plan
Restructuring Cost and Reserve [Line Items]
Additions			0.1
Restructuring Reserve [Roll Forward]
Total, beginning balance		0.0	1.1
Additions			0.1
Payments			(1.5)
Adjustments			0.3
Total, ending balance	0.0		0.0
Total	$ 0.0	$ 0.0	$ 1.1