Summary of significant accounting policies - Narrative (Details) $ in Millions	12 Months Ended
	Dec. 31, 2023 USD ($) financial_institution	Dec. 31, 2022 USD ($)	Dec. 31, 2021 USD ($)
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Gross amount of outsourcing assets	$ 563.4	$ 559.4
Outsourcing assets, accumulated amortization	531.8	493.0
Gross amount of marketable software	2,213.9	2,174.5
Marketable software, accumulated amortization	$ 2,047.7	2,009.4
Period of recognition in changes in fair value of plan assets	4 years
Advertising costs incurred	$ 10.7	$ 8.0	$ 3.6
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