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Summary of significant accounting policies - Narrative (Details) $ in Millions | 12 Months Ended
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Dec. 31, 2022 USD ($) financial_institution | Dec. 31, 2021 USD ($) | Dec. 31, 2020 USD ($)
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Gross amount of outsourcing assets | $ 559.4 | $ 568.3 |
Outsourcing assets, accumulated amortization | 493.0 | 443.7 |
Gross amount of marketable software | 2,174.5 | 2,266.1 |
Marketable software, accumulated amortization | $ 2,009.4 | 2,089.9 |
Goodwill (in percent) | 6.00% |  |
Period of recognition in changes in fair value of plan assets | 4 years |  |
Advertising costs incurred | $ 8.0 | $ 3.6 | $ 2.5
Intelligent Processing Solutions Ltd. |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Ownership interest (as a percent) | 51.00% |  |
Number of financial institutions that own remaining interests for which iPSL performs services | financial_institution | 3 |  |
Enterprise Software |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated revenue-producing lives of computer software products from the date of release | 5 years |  |
Remaining Products |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated revenue-producing lives of computer software products from the date of release | 3 years |  |
Minimum | Technology |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Period over which payment is generally received for contracts | 30 days |  |
Maximum | Technology |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Period over which payment is generally received for contracts | 60 days |  |
Buildings | Minimum |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 20 years |  |
Buildings | Maximum |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 50 years |  |
Machinery and office equipment | Minimum |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 4 years |  |
Machinery and office equipment | Maximum |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 7 years |  |
Rental equipment |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 4 years |  |
Internal-use software | Minimum |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 3 years |  |
Internal-use software | Maximum |  |  |
New Accounting Pronouncements or Change in Accounting Principle [Line Items] |  |  |
Estimated useful lives | 10 years |  |

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