Operating Segments and Geographic Information - Reconciliation of Total Reportable Segments' Revenues and EBITDA to Consolidated Revenues and Consolidated Income Before Taxes (Details) - USD ($)			3 Months Ended								12 Months Ended
	Dec. 31, 2016	Jan. 07, 2016	Dec. 31, 2018	Sep. 30, 2018	Jul. 01, 2018	Apr. 01, 2018	Dec. 31, 2017	Oct. 01, 2017	Jul. 02, 2017	Apr. 02, 2017	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues			$ 655,390,000	$ 655,774,000	$ 668,639,000	$ 605,565,000	$ 604,884,000	$ 621,745,000	$ 610,633,000	$ 551,381,000	$ 2,585,368,000	$ 2,388,643,000	$ 2,356,672,000
Amortization of intangibles											(98,829,000)	(103,997,000)	(98,385,000)
Severance, restructuring, and acquisition integration costs (3)			(11,600,000)	(11,700,000)	(24,900,000)	(20,400,000)	(9,900,000)	(16,700,000)	(9,600,000)	(6,600,000)	(68,613,000)	(42,790,000)	(31,140,000)
Depreciation expense											(47,600,000)	(45,600,000)	(47,200,000)
Impairment of assets held for sale											0	0	(23,931,000)
Gain from patent litigation											(62,141,000)	0	0
Operating income			$ 73,234,000	$ 131,278,000	$ 56,506,000	$ 44,203,000	$ 59,915,000	$ 61,116,000	$ 62,776,000	$ 51,597,000	305,221,000	235,404,000	232,083,000
Interest expense, net											(61,559,000)	(82,901,000)	(95,050,000)
Non-operating pension cost											(342,000)	(714,000)	(8,230,000)
Loss on debt extinguishment											(22,990,000)	(52,441,000)	(2,342,000)
Consolidated income before taxes											220,330,000	99,348,000	126,461,000
Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues											2,585,368,000	2,388,643,000	2,356,672,000
Deferred revenue adjustments (1)											(6,612,000)	0	(6,687,000)
Total Segment EBITDA											475,380,000	430,748,000	433,789,000
Amortization of intangibles											(98,829,000)	(103,997,000)	(98,385,000)
Severance, restructuring, and acquisition integration costs (3)											(68,613,000)	(42,790,000)	(31,140,000)
Depreciation expense											(47,615,000)	(45,597,000)	(47,208,000)
Purchase accounting effects related to acquisitions (4)											(3,497,000)	(6,133,000)	2,079,000
Costs related to patent litigation											(2,634,000)	0	0
Amortization of software development intangible assets											(2,188,000)	(56,000)	0
Loss on sale of assets (5)											(94,000)	(1,013,000)	0
Impairment of assets held for sale											0	0	(23,931,000)
Income from equity method investment											0	7,502,000	1,793,000
Gain from patent litigation											62,141,000	0	0
Eliminations
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income											(2,218,000)	(3,260,000)	(3,781,000)
M2 FX Limited
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Adjustment to reduce earn-out liability	$ 0	$ 3,200,000											3,200,000
Inventory adjustment													200,000
Enterprise Solutions
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Severance, restructuring, and acquisition integration costs (3)											(57,563,000)	(29,043,000)	(18,561,000)
Inventory adjustment													800,000
Enterprise Solutions | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Deferred revenue adjustments (1)											(6,612,000)	0	(1,774,000)
Total Segment EBITDA											267,656,000	216,558,000	239,978,000
Amortization of intangibles											(45,944,000)	(51,054,000)	(48,966,000)
Severance, restructuring, and acquisition integration costs (3)											(57,563,000)	(29,043,000)	(18,561,000)
Depreciation expense											(28,861,000)	(26,272,000)	(29,455,000)
Purchase accounting effects related to acquisitions (4)											(3,497,000)	(6,133,000)	2,079,000
Amortization of software development intangible assets											(2,180,000)	(56,000)	0
Segment revenues | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues											2,591,980,000	2,388,643,000	2,357,805,000
Segment revenues | Enterprise Solutions | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues											1,522,178,000	1,356,305,000	1,372,941,000
Patent settlement | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues											0	0	5,554,000
Patent settlement | Enterprise Solutions | Reportable Segment
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Total Segment Revenues											$ 0	$ 0	$ 5,554,000