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Stockholders' equity - Changes in Common Stock and Treasury Stock (Details) - shares shares in Millions	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning Balance (in shares)	54.2	53.4	52.8
Stock-based compensation (in shares)	1.1	0.8	0.6
Debt exchange (in shares)	10.6
Ending Balance (in shares)	65.9	54.2	53.4
Treasury Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning Balance (in shares)	3.1	2.9	2.7
Stock-based compensation (in shares)	0.4	0.2	0.2
Debt exchange (in shares)	0.0
Ending Balance (in shares)	3.5	3.1	2.9

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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Number of shares of stock issued as of the balance sheet date, including shares that had been issued and were previously outstanding but which are now held in the treasury.

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Number of shares issued during the period as a result of the conversion of convertible securities.

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