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Fair Value - Additional Information (Detail) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 26, 2020	Jun. 30, 2020	Jun. 27, 2020
Fair Value Disclosures [Abstract]
Convertible notes, net	$ 496.1	$ 496.1	$ 486.6	$ 486.6
Convertible notes		$ 676.1		$ 542.5

X

- Definition

Convertible notes payable, net.

+ References

No definition available.

+ Details

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Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Fair value portion of borrowing which can be exchanged for a specified number of another security at the option of the issuer or the holder, for example, but not limited to, the entity's common stock.

+ References

No definition available.

+ Details

Name:	us-gaap_ConvertibleDebtFairValueDisclosures
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- References

No definition available.

+ Details

Name:	us-gaap_FairValueDisclosuresAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
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