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Goodwill and intangible assets - Carrying Value of Goodwill (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021
Goodwill [Roll Forward]
Beginning balance	$ 315.0	$ 108.6
Acquisitions		206.3
Translation adjustments	(0.4)	0.1
Measurement period adjustments, increase in goodwill	(27.5)
Ending balance	287.1	315.0
Unify Square, Inc.
Goodwill [Roll Forward]
Measurement period adjustments, increase in goodwill		16.7
CompuGain
Goodwill [Roll Forward]
Measurement period adjustments, increase in goodwill	(27.5)
DWS
Goodwill [Roll Forward]
Beginning balance	140.9	0.0
Acquisitions		140.8
Translation adjustments	(0.4)	0.1
Measurement period adjustments, increase in goodwill	0.0
Ending balance	140.5	140.9
DWS | Unify Square, Inc.
Goodwill [Roll Forward]
Ending balance	132.9
DWS | Mobinergy
Goodwill [Roll Forward]
Ending balance	7.9
CA&I
Goodwill [Roll Forward]
Beginning balance	65.5	0.0
Acquisitions		65.5
Translation adjustments	0.0	0.0
Measurement period adjustments, increase in goodwill	(27.5)
Ending balance	38.0	65.5
CA&I | CompuGain
Goodwill [Roll Forward]
Beginning balance	65.5
Ending balance		65.5
ECS
Goodwill [Roll Forward]
Beginning balance	98.3	98.3
Acquisitions		0.0
Translation adjustments	0.0	0.0
Measurement period adjustments, increase in goodwill	0.0
Ending balance	98.3	98.3
Other
Goodwill [Roll Forward]
Beginning balance	10.3	10.3
Acquisitions		0.0
Translation adjustments	0.0	0.0
Measurement period adjustments, increase in goodwill	0.0
Ending balance	$ 10.3	$ 10.3

X

- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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