Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
Mar. 31, 2023	Mar. 31, 2022	Dec. 31, 2022
Intangible assets
Total intangible assets, gross	$ 7,492.7		$ 7,479.3
Accumulated Amortization	(5,679.4)		(5,629.2)
Intangible assets, net	1,813.3		1,850.1
Amortization and impairment of acquired intangible assets	50.2	$ 66.9
Expected future amortization expense, 2023 (remaining three months)	165.0
Expected future amortization expense, 2024	195.0
Expected future amortization expense, 2025	190.0
Expected future amortization expense, 2026	175.0
Expected future amortization expense, 2027	170.0
Expected future amortization expense, 2028	165.0
Completed technology
Intangible assets
Cost	7,428.7		7,415.3
Net	1,749.3		1,786.1
Accumulated Amortization	$ (5,679.4)		(5,629.2)
Completed technology \| Minimum
Intangible assets
Useful life	4 years
Completed technology \| Maximum
Intangible assets
Useful life	28 years
Trademarks and Trade Names
Intangible assets
Cost and Net	$ 64.0		64.0
Accumulated Amortization	0.0		0.0
Indefinite-lived Intangible Assets (Excluding Goodwill)	$ 64.0		$ 64.0

Amortization and Impairment of Acquired Intangible Assets

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Useful life of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount before amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount of assets, excluding financial assets and goodwill, lacking physical substance and having a projected indefinite period of benefit.

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Amount before accumulated amortization of intangible assets, excluding goodwill.

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Sum of the carrying amounts of all intangible assets, excluding goodwill, as of the balance sheet date, net of accumulated amortization and impairment charges.

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