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Income Taxes - Differences between the U.S. statutory rate and the aggregate income tax provision (Details) - USD ($) $ in Millions | 12 Months Ended
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Jan. 31, 2022 | Jan. 31, 2021 | Jan. 31, 2020
Income Tax Disclosure [Abstract] |  |  |
Income tax provision at U.S. Federal statutory rate | $ 118.6 | $ 114.8 | $ 61.9
State income tax benefit, net of the U.S. Federal benefit | 2.2 | (43.0) | 1.8
Foreign income taxed at rates different from the U.S. statutory rate | (25.4) | (11.5) | (81.0)
Valuation allowance adjustment | (0.2) | (637.4) | 93.9
Transition tax and revisions due to subsequent regulations | 0.0 | 0.0 | 9.6
Tax effect of non-deductible stock-based compensation | 32.3 | 24.8 | 29.2
Stock compensation (windfall) / shortfall | (43.2) | (35.1) | (22.5)
Research and development tax credit benefit | (18.5) | (15.5) | (19.8)
Closure of income tax audits and changes in uncertain tax positions | (0.4) | 0.1 | (2.1)
Tax effect of officer compensation in excess of $1.0 million | 7.0 | 4.6 | 3.4
Non-deductible expenses | 4.5 | 2.3 | 5.4
Global intangible low-taxed income, foreign derived intangible income | 24.1 | (65.0) | 0.0
India withholding tax refund | (43.8) | 0.0 | 0.0
Acquisition-related integrations | 9.0 | 0.0 | 0.0
Other | 1.5 | (0.6) | 0.5
Income tax provision (benefit) | 67.7 | $ (661.5) | $ 80.3
First $1M of officer compensation | $ 1.0 |  |

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- Definition Effective Income Tax Rate Reconciliation, Tax Cuts and Jobs Act, Transition Tax on Accumulated Foreign Earnings, Amount + References No definition available. + Details
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- Definition The portion of the difference between total income tax expense (benefit) as reported in the Income Statement and the expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income from continuing operations attributable to closure of income tax audits and changes in uncertain tax positions. + References No definition available. + Details
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- Definition The amount of income tax expense or benefit for the period computed by applying the domestic federal statutory tax rates to pretax income from continuing operations. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319 + Details
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- Definition Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to other nondeductible expenses. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 12 -URI http://asc.fasb.org/extlink&oid=121826272&loc=d3e32687-109319 + Details
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