Share-Based Compensation - Shares Purchased, Weighted Average Purchase Price, Cash Received, and Aggregate Intrinsic Value for ESPP (Detail) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
Jun. 24, 2017	Jun. 25, 2016	Jun. 27, 2015
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Shares purchased	302,085
Aggregate intrinsic value	$ 41.1
Employee Stock Purchase Plan [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Shares purchased	302,085	302,781	367,646
Weighted average purchase price	$ 46.74	$ 52.42	$ 35.11
Cash received	$ 14.1	$ 15.8	$ 12.9
Aggregate intrinsic value	$ 2.7	$ 7.0	$ 13.7

The cash inflow associated with the amount received from the stock plan during the period.

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=98514028&loc=d3e3255-108585

+ Details

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

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

- Definition

Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding.

+ References

+ Details

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

- Definition

The weighted average of per share prices paid for shares purchased on the open market for issuance to employees under the plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5070-113901

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5047-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

The number of shares purchased on the open market during the period for issuance to employees under the plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5047-113901

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_PlanNameAxis=syna_EmployeeStockPurchasePlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: