Derivative Instruments - Effect of Derivative Instruments on Statements of Income (Detail) - Cash Flow Hedging - USD ($) $ in Millions	3 Months Ended
Nov. 30, 2023	Nov. 30, 2022
Derivative Instruments, Gain (Loss) [Line Items]
Gain (loss) recognized in OCI on derivatives	$ 5.3	$ 12.2
Gain (loss) reclassified from accumulated OCI into income	4.4	0.8
Gain (loss) recognized on derivative (amount excluded from effectiveness testing)	0.9	0.4
Foreign Exchange Forward
Derivative Instruments, Gain (Loss) [Line Items]
Gain (loss) recognized in income on derivatives	$ 0.2
Derivative, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]	Interest And Foreign Exchange Net
Foreign Exchange Forward \| Sales
Derivative Instruments, Gain (Loss) [Line Items]
Gain (loss) recognized in OCI on derivatives	$ 2.4	1.5
Gain (loss) reclassified from accumulated OCI into income	0.2	(0.4)
Gain (loss) recognized on derivative (amount excluded from effectiveness testing)	$ 0.6	$ 0.3
Derivative Instrument, Gain (Loss) Reclassified from AOCI into Income, Effective Portion, Statement of Income or Comprehensive Income [Extensible Enumeration]	Revenue from Contract with Customer, Excluding Assessed Tax	Revenue from Contract with Customer, Excluding Assessed Tax
Foreign Exchange Forward \| Cost Of Revenue
Derivative Instruments, Gain (Loss) [Line Items]
Gain (loss) recognized in OCI on derivatives	$ (0.2)	$ 0.3
Gain (loss) reclassified from accumulated OCI into income	(0.1)	0.2
Gain (loss) recognized on derivative (amount excluded from effectiveness testing)	$ 0.3	$ 0.1
Derivative Instrument, Gain (Loss) Reclassified from AOCI into Income, Effective Portion, Statement of Income or Comprehensive Income [Extensible Enumeration]	Cost of Revenue	Cost of Revenue
Interest rate swap contracts
Derivative Instruments, Gain (Loss) [Line Items]
Gain (loss) recognized in OCI on derivatives	$ 3.1	$ 10.4
Gain (loss) reclassified from accumulated OCI into income	$ 4.3	$ 1.0
Derivative Instrument, Gain (Loss) Reclassified from AOCI into Income, Effective Portion, Statement of Income or Comprehensive Income [Extensible Enumeration]	Interest And Foreign Exchange Net	Interest And Foreign Exchange Net

Amount of increase (decrease) in the fair value of derivatives recognized in the income statement.

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Indicates line item in statement of income or comprehensive income that includes gain (loss) from effective portion of derivative instrument reclassified from accumulated other comprehensive income (AOCI) into income.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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The effective portion of net gain (loss) reclassified from accumulated other comprehensive income into income on derivative instruments designated and qualifying as hedging instruments.

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The portion of gains and losses (net) on derivative instruments designated and qualifying as hedging instruments representing (a) the amount of the hedge ineffectiveness and (b) the amount, if any, excluded from the assessment of hedge effectiveness.

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Amount, before tax and reclassification, of gain (loss) from derivative instrument designated and qualifying cash flow hedge included in assessment of hedge effectiveness.

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