Stock-based Compensation - Schedule of Stock-Based Compensation Expense Recognized (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	$ 159.4	$ 124.8	$ 114.0
Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	100.6	129.3	106.0
RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	58.8	(4.5)	8.0
Total Cost of Revenues
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	63.8	51.6	48.1
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	57.0	46.1	42.8
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	6.8	5.5	5.3
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	38.9	52.8	44.3
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	34.4	47.2	39.1
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	4.5	5.6	5.2
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	24.9	(1.2)	3.8
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	22.6	(1.1)	3.7
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	2.3	(0.1)	0.1
Selling and Marketing
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	29.0	22.9	20.6
Selling and Marketing | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	19.7	24.2	19.1
Selling and Marketing | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	9.3	(1.3)	1.5
Research and Development
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	21.4	16.6	15.0
Research and Development | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	13.9	17.2	14.2
Research and Development | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	7.5	(0.6)	0.8
General and Administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	45.2	33.7	30.3
General and Administrative | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	28.1	35.1	28.4
General and Administrative | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	17.1	(1.4)	1.9
Total Operating Expenses
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	95.6	73.2	65.9
Total Operating Expenses | Stock Options, (SARs) [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	61.7	76.5	61.7
Total Operating Expenses | RSUs and PSUs [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total stock-based compensation expense	$ 33.9	$ (3.3)	$ 4.2