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Cost-reduction actions - Statement of Income Classifications (Details) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2021 | Dec. 31, 2020 | Dec. 31, 2019
Restructuring Cost and Reserve [Line Items] |  |  |
Cost-reduction charges and other costs | $ 23.2 | $ 95.5 | $ 28.7
Cost of revenue | Services |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Cost-reduction charges and other costs | (2.5) | 22.2 | 10.8
Cost of revenue | Technology |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Cost-reduction charges and other costs | 7.6 | 0.0 | 0.2
Selling, general and administrative |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Cost-reduction charges and other costs | 11.1 | 38.5 | 15.5
Research and development |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Cost-reduction charges and other costs | 3.0 | 2.5 | 2.2
Other (expenses), net |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |
Cost-reduction charges and other costs | $ 4.0 | $ 32.3 | $ 0.0

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