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Summary of significant accounting policies - Narrative (Details)
$ in Millions
 3 Months Ended 12 Months Ended
Sep. 30, 2024
USD ($)
Dec. 31, 2024
USD ($)
financial_institution
Dec. 31, 2023
USD ($)
Dec. 31, 2022
USD ($)
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Gross amount of outsourcing assets   $ 553.0 $ 563.4  
Outsourcing assets, accumulated amortization   529.0 531.8  
Gross amount of marketable software   2,256.2 2,213.9  
Marketable software, accumulated amortization   2,091.2 2,047.7  
Goodwill impairment   $ 39.1 0.0 $ 0.0
Period of recognition in changes in fair value of plan assets   4 years    
Advertising costs incurred   $ 10.8 10.7 $ 8.0
Digital Workspace Services Segment        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Goodwill impairment $ 39.1      
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    
Cloud Computing Arrangement        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Gross amount of marketable software   $ 24.1 23.0  
Cloud Computing Arrangement | Prepaid Expenses and Other Current Assets        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Gross amount of marketable software   7.6 5.5  
Cloud Computing Arrangement | Other Long Term Assets        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Gross amount of marketable software   $ 16.5 $ 17.5  
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