Stock-based Compensation - Schedule of Stock-Based Compensation Expense Recognized (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	$ 203.3	$ 159.4	$ 124.8
Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	84.3	100.6	129.3
RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	119.0	58.8	(4.5)
Total Cost of Revenues
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	78.9	63.8	51.6
Total Cost of Revenues | Software-enabled Services [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	70.9	57.0	46.1
Total Cost of Revenues | License, Maintenance and Other Related [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	8.0	6.8	5.5
Total Cost of Revenues | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	31.0	38.9	52.8
Total Cost of Revenues | Stock Options, (SARs) [Member] | Software-enabled Services [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	27.8	34.4	47.2
Total Cost of Revenues | Stock Options, (SARs) [Member] | License, Maintenance and Other Related [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	3.2	4.5	5.6
Total Cost of Revenues | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	47.9	24.9	(1.2)
Total Cost of Revenues | RSUs and PSUs [Member] | Software-enabled Services [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	43.1	22.6	(1.1)
Total Cost of Revenues | RSUs and PSUs [Member] | License, Maintenance and Other Related [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	4.8	2.3	(0.1)
Selling and Marketing
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	35.4	29.0	22.9
Selling and Marketing | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	17.1	19.7	24.2
Selling and Marketing | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	18.3	9.3	(1.3)
Research and Development
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	29.8	21.4	16.6
Research and Development | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	12.2	13.9	17.2
Research and Development | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	17.6	7.5	(0.6)
General and Administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	59.2	45.2	33.7
General and Administrative | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	24.0	28.1	35.1
General and Administrative | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	35.2	17.1	(1.4)
Total Operating Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	124.4	95.6	73.2
Total Operating Expenses | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	53.3	61.7	76.5
Total Operating Expenses | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	$ 71.1	$ 33.9	$ (3.3)