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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions | Dec. 31, 2023 | Dec. 31, 2022 | Dec. 31, 2021 | Dec. 31, 2020
--- | --- | --- | --- | ---
Deferred tax assets |  |  |  |
Tax loss carryforwards | $ 813.0 | $ 825.5 |  |
Postretirement benefits | 183.0 | 149.6 |  |
Foreign tax credit carryforwards | 83.6 | 109.2 |  |
Other tax credit carryforwards | 29.1 | 32.7 |  |
Deferred revenue | 31.9 | 28.2 |  |
Employee benefits and compensation | 31.5 | 21.2 |  |
Purchased capitalized software | 19.4 | 16.9 |  |
Depreciation | 33.0 | 32.6 |  |
Warranty, bad debts and other reserves | 7.6 | 7.1 |  |
Capitalized costs | 9.0 | 6.2 |  |
Other | 57.6 | 49.9 |  |
Total deferred tax assets, gross | 1,298.7 | 1,279.1 |  |
Valuation allowance | (1,150.1) | (1,110.5) | $ (1,226.2) | $ (1,271.5)
Total deferred tax assets | 148.6 | 168.6 |  |
Deferred tax liabilities |  |  |  |
Capitalized research and development | 10.4 | 31.0 |  |
Other | 25.1 | 29.2 |  |
Total deferred tax liabilities | 35.5 | 60.2 |  |
Net deferred tax assets | $ 113.1 | $ 108.4 |  |

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