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Divestiture - Additional Information (Detail) - USD ($) $ in Millions	1 Months Ended	12 Months Ended
	Apr. 30, 2020	Jun. 27, 2020
Business Acquisition [Line Items]
Gain on sale of assets		$ 105.1
Asset Purchase Agreement [Member]
Business Acquisition [Line Items]
Assets held for sale	$ 33.6
Cash consideration receivable on divestiture of business	138.7
Gain on sale of assets	$ 105.1

X

- Definition

Amount of assets held-for-sale that are not part of a disposal group.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 15
-Paragraph 4
-Subparagraph (b)(2)
-URI http://asc.fasb.org/extlink&oid=77912953&loc=d3e400-110220

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

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.

+ References

No definition available.

+ Details

Name:	us-gaap_BusinessAcquisitionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of gain (loss) on sale or disposal of assets utilized in financial service operations.

+ References

No definition available.

+ Details

Name:	us-gaap_GainsLossesOnSalesOfAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

This element represents the cash inflow during the period from the sale of a component of the entity.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 12
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=118932676&loc=d3e3179-108585

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Details

Name:	us-gaap_TypeOfArrangementAxis=syna_AssetPurchaseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: