Accounts receivable, net - Credit Quality Indicator and Age Analysis (Details) - USD ($) $ in Millions	Oct. 28, 2017	Jan. 28, 2017	Oct. 29, 2016
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 706.5	$ 1,952.0	$ 1,679.3
Valuation allowance	$ (108.8)	$ (138.7)	$ (133.0)
Gross	100.00%	100.00%	100.00%
Valuation allowance	15.40%	7.10%	7.90%
Current, aged 0 – 30 days | Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 586.5	$ 1,538.2	$ 1,294.9
Valuation allowance	$ (50.3)	$ (47.2)	$ (39.3)
Gross	83.00%	78.80%	77.20%
Valuation allowance	8.60%	3.10%	3.00%
Past due, aged 31 – 60 days | Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 40.3	$ 282.0	$ 250.6
Valuation allowance	$ (3.5)	$ (9.0)	$ (8.1)
Gross	5.70%	14.50%	14.90%
Valuation allowance	8.70%	3.20%	3.20%
Past due, aged 61 – 90 days | Performing Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 27.1	$ 51.6	$ 50.7
Valuation allowance	$ (2.4)	$ (2.3)	$ (2.5)
Gross	3.80%	2.60%	3.00%
Valuation allowance	8.90%	4.50%	4.90%
Past due, aged more than 90 days | Nonperforming Financing Receivable
Accounts, Notes, Loans and Financing Receivable [Line Items]
Gross	$ 52.6	$ 80.2	$ 83.1
Valuation allowance	$ (52.6)	$ (80.2)	$ (83.1)
Gross	7.50%	4.10%	4.90%
Valuation allowance	100.00%	100.00%	100.00%