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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions | Dec. 31, 2024 | Dec. 31, 2023 | Dec. 31, 2022 | Dec. 31, 2021
--- | --- | --- | --- | ---
Deferred tax assets |  |  |  |
Tax loss carryforwards | $ 787.6 | $ 813.0 |  |
Pension and postretirement benefits | 196.5 | 183.0 |  |
Foreign tax credit carryforwards | 61.9 | 83.6 |  |
Other tax credit carryforwards | 29.5 | 29.1 |  |
Deferred revenue | 48.2 | 31.9 |  |
Employee benefits and compensation | 31.2 | 31.5 |  |
Purchased capitalized software | 18.4 | 19.4 |  |
Depreciation | 28.6 | 33.0 |  |
Warranty, bad debts and other reserves | 2.9 | 7.6 |  |
Capitalized costs | 9.3 | 9.0 |  |
Capitalized research and development | 6.7 | 0.0 |  |
Other | 76.0 | 57.6 |  |
Total deferred tax assets, gross | 1,296.8 | 1,298.7 |  |
Valuation allowance | (1,168.6) | (1,150.1) | $ (1,110.5) | $ (1,226.2)
Total deferred tax assets | 128.2 | 148.6 |  |
Deferred tax liabilities |  |  |  |
Undistributed earnings of certain foreign subsidiaries | 27.7 | 0.0 |  |
Capitalized research and development | 0.0 | 10.4 |  |
Other | 32.6 | 25.1 |  |
Total deferred tax liabilities | 60.3 | 35.5 |  |
Net deferred tax assets | $ 67.9 | $ 113.1 |  |

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