Income Taxes, Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 02, 2026	Oct. 03, 2025	Sep. 27, 2024
Effective Income Tax Rate Reconciliation [Line Items]
Tax jurisdiction	United States	United States	United States
Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]
Tax expense at United States statutory rate	$ 44.9	$ 110.6	$ 133.6
State and local income tax, net of federal	(0.1)
Foreign tax rate difference		(22.0)	(84.7)
Other adjustments		2.6	18.4
Global intangible low-taxed income	12.8	4.0	18.1
Foreign-derived intangible income	(19.4)	(44.7)	(49.3)
Other cross-border tax effects	0.7
R&D tax credits	(34.5)	(44.5)	(28.7)
Foreign tax credit	(12.5)
Changes in valuation allowances	0.5
Stock-based compensation	18.4	10.2	11.3
162(m) compensation	6.7	15.8	10.6
Transaction cost	15.7
Other non-deductible items	0.6
Changes in unrecognized tax benefits	21.9	(1.4)	11.1
Other reconciling items	(15.0)
Remeasurement of concessionary tax rate		19.0	0.0
Provision for income taxes	$ 41.6	$ 49.6	$ 40.4
Effective Income Tax Rate Reconciliation, Percent [Abstract]
US federal statutory income tax rate	21.00%
State and local income tax, net of federal	(0.10%)
Global intangible low-taxed income	6.00%
Foreign-derived intangible income	(9.10%)
Other cross-border tax effects	0.30%
R&D tax credits	(16.10%)
Foreign tax credit	(5.80%)
Changes in valuation allowances	0.20%
Stock-based compensation	8.60%
162(m) compensation	3.10%
Transaction cost	7.30%
Other non-deductible items	0.30%
Changes in unrecognized tax benefits	10.20%
Other reconciling items	(7.00%)
Effective income tax rate	19.50%
Singapore
Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]
Foreign tax rate difference	$ (19.7)
Withholding tax	$ 12.4
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Foreign tax rate difference	(9.20%)
Withholding tax	5.80%
Mexico
Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]
Foreign tax rate difference	$ 7.2
Prior adjustment / Return to provision	(5.5)
Other adjustments	$ 1.4
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Foreign tax rate difference	3.40%
Prior adjustment / Return to provision	(2.60%)
Other adjustments	0.70%
Japan
Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]
Local and other taxes	$ 9.7
Prior adjustment / Return to provision	2.8
Other adjustments	$ (6.1)
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Local and other taxes	4.60%
Prior adjustment / Return to provision	1.30%
Other adjustments	(2.80%)
Other foreign jurisdictions
Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]
Other adjustments	$ (1.3)
Effective Income Tax Rate Reconciliation, Percent [Abstract]
Other adjustments	(0.60%)