Restructuring charges and other facility exit costs, net (Details) $ in Millions	3 Months Ended	12 Months Ended
	Jan. 31, 2018 USD ($) Position	Jan. 31, 2018 USD ($)	Jan. 31, 2017 USD ($)	Jan. 31, 2018 USD ($)
Restructuring Cost and Reserve [Line Items]
Additions	$ 94.0	$ 94.1	$ 77.8
Restructuring Reserve [Roll Forward]
Total, beginning balance		7.5	0.0
Current portion, beginning balance		5.9	0.0
Non-current portion, beginning balance		1.6	0.0
Additions	94.0	94.1	77.8
Payments		(42.4)	(67.2)
Adjustments		(2.0)	(3.1)
Total, ending balance	57.2	57.2	7.5
Current portion, ending balance	57.2	57.2	5.9
Non-current portion, ending balance	0.0	0.0	1.6
Total	$ 57.2	7.5	7.5	$ 57.2
Fiscal 2018 Plan
Restructuring Cost and Reserve [Line Items]
Percentage of workforce eliminated	13.00%
Number of positions eliminated | Position	1,150
Facility Closing
Restructuring Cost and Reserve [Line Items]
Additions		0.3	7.4
Lease termination and other exit costs		0.4
Restructuring Reserve [Roll Forward]
Total, beginning balance		4.5	0.0
Additions		0.3	7.4
Payments		(3.0)	(1.8)
Adjustments		(0.3)	(1.1)
Total, ending balance	$ 1.5	1.5	4.5
Total	1.5	4.5	4.5	1.5
Facility Closing | Fiscal 2018 Plan
Restructuring Cost and Reserve [Line Items]
Additions		6.3
Restructuring Reserve [Roll Forward]
Total, beginning balance		0.0
Additions		6.3
Payments		(1.3)
Adjustments		(2.5)
Total, ending balance	2.5	2.5	0.0
Total	2.5	0.0	0.0	2.5
Facility Closing | Fiscal 2017 Plan
Restructuring Cost and Reserve [Line Items]
Additions		0.1	7.1
Restructuring Reserve [Roll Forward]
Total, beginning balance		1.9	0.0
Additions		0.1	7.1
Payments		(1.5)	(3.2)
Adjustments		(0.3)	(2.0)
Total, ending balance	0.2	0.2	1.9
Total	0.2	1.9	1.9	0.2
Employee Severance | Fiscal 2018 Plan
Restructuring Cost and Reserve [Line Items]
Additions		87.3
Restructuring Reserve [Roll Forward]
Total, beginning balance		0.0
Additions		87.3
Payments		(35.1)
Adjustments		0.8
Total, ending balance	53.0	53.0	0.0
Total	53.0	0.0	0.0	53.0
Employee Severance | Fiscal 2017 Plan
Restructuring Cost and Reserve [Line Items]
Additions		0.1	63.3
Restructuring Reserve [Roll Forward]
Total, beginning balance		1.1	0.0
Additions		0.1	63.3
Payments		(1.5)	(62.2)
Adjustments		0.3	0.0
Total, ending balance	0.0	0.0	1.1
Total	$ 0.0	$ 0.0	$ 0.0	0.0
Minimum
Restructuring Cost and Reserve [Line Items]
Expected restructuring cost				135.0
Minimum | One-time Termination Benefits
Restructuring Cost and Reserve [Line Items]
Expected restructuring cost				124.0
Minimum | Facility Closing
Restructuring Cost and Reserve [Line Items]
Expected restructuring cost				11.0
Maximum
Restructuring Cost and Reserve [Line Items]
Expected restructuring cost				149.0
Maximum | One-time Termination Benefits
Restructuring Cost and Reserve [Line Items]
Expected restructuring cost				137.0
Maximum | Facility Closing
Restructuring Cost and Reserve [Line Items]
Expected restructuring cost				$ 12.0