Stock-based Compensation - Summary of Stock Option Activity under NSO Plan (Detail) - NSO Plan [Member] $ / shares in Units, $ in Millions	6 Months Ended	12 Months Ended
Jun. 30, 2019 USD ($) $ / shares shares	Dec. 31, 2018 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, Beginning Balance \| shares	4,337,856
Number of options, Exercised \| shares	(522,508)
Number of options, Forfeited \| shares	0
Number of options, Outstanding and exercisable, Ending Balance \| shares	3,815,348
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per share, Outstanding, Beginning Balance \| $ / shares	$ 0.000025
Weighted average exercise price per share, Exercised \| $ / shares	0.000025
Weighted average exercise price per share, Forfeited \| $ / shares	0
Weighted average exercise price per share, Outstanding and exercisable, Ending Balance \| $ / shares	$ 0.000025
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]
Weighted average remaining contractual term (years), Outstanding		18 years
Weighted average remaining contractual term (years), Outstanding and exercisable	17 years 6 months
Aggregate intrinsic value, Outstanding \| $		$ 119.6
Aggregate intrinsic value, Outstanding and exercisable \| $	$ 154.1

Share based compensation arrangement by share based payment award options outstanding and exercisable intrinsic value.

No definition available.

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableIntrinsicValue
Namespace Prefix:	altr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Share based compensation arrangement by share based payment award options outstanding and exercisable number.

+ References

No definition available.

+ Details

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableNumber
Namespace Prefix:	altr_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Share based compensation arrangement by share based payment award options outstanding and exercisable weighted average exercise price.

+ References

No definition available.

+ Details

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableWeightedAverageExercisePrice
Namespace Prefix:	altr_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Share based compensation arrangement by share based payment award options outstanding and exercisable weighted average remaining contractual term.

+ References

No definition available.

+ Details

Name:	altr_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingAndExercisableWeightedAverageRemainingContractualTerm
Namespace Prefix:	altr_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

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

- Definition

The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
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

Number of options outstanding, including both vested and non-vested options.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)-(ii)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

+ References

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Weighted average price at which option holders acquired shares when converting their stock options into shares.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price at which grantees could have acquired the underlying shares with respect to stock options that were terminated.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average remaining contractual term for option awards outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of share options (or share units) exercised during the current period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(2)
-URI http://asc.fasb.org/extlink&oid=109197908&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=27012166&loc=d3e187085-122770

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=109259400&loc=d3e21463-112644

+ Details

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

- Details

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