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Stock-based Compensation Expense Additional Information (Details) $ / shares in Units, $ in Millions | 3 Months Ended | 6 Months Ended
--- | --- | ---
Jul. 31, 2017 USD ($) | Jul. 31, 2016 USD ($) | Jul. 31, 2017 USD ($) period $ / shares shares | Jul. 31, 2016 USD ($) $ / shares shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Allocated share-based compensation expense | $ 67.6 | $ 54.3 | $ 134.4 | $ 105.9
Market capitalization |  |  | 2,000.0 |
Restricted Stock Units (RSUs) and Performance Shares |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards vested in period, fair value |  |  | $ 116.9 | 93.4
Awards granted in period (shares) | shares |  |  | 815,800 |
Restricted Stock Units (RSUs) |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 500,000 |
Allocated share-based compensation expense | 52.0 | 41.5 | $ 102.0 | 80.3
Acceleration of eligible stock awards | 5.9 |  | $ 9.1 |
Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 300,000 |
Allocated share-based compensation expense | 9.7 | $ 5.9 | $ 20.6 | $ 12.2
Acceleration of eligible stock awards | $ 2.8 |  | $ 7.5 |
Award vesting period |  |  | 3 years |
Employee Qualified Stock Purchase Plan 1998 ESP Plan |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Employee stock purchase plan maximum percentage of compensation to purchase shares by eligible participants |  |  | 15.00% |
Employee stock purchase plan minimum percentage of common stock fair value defined to purchase shares by eligible participants |  |  | 85.00% |
Employee stock purchase plan, number of exercise periods | period |  |  | 4 |
Employee stock purchase plan, term of exercise period |  |  | 6 months |
Employee stock purchase plan, term of offering period |  |  | 24 months |
Shares issued under employee stock purchase plans (shares) | shares |  |  | 1,100,000 | 1,200,000
Awards issued, share average price (in usd per share) | $ / shares |  |  | $ 38.34 | $ 36.67
Weighted average grant date fair value per share of stock options granted (in dollars per share) | $ / shares |  |  | $ 25.13 | $ 17.88
Share-based Compensation Award, Tranche One | Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
PSU Annual Vesting Percentage |  |  | 33.33% |
Share-based Compensation Award, Tranche Two | Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
PSU Annual Vesting Percentage |  |  | 33.33% |
Share-based Compensation Award, Tranche Three | Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
PSU Annual Vesting Percentage |  |  | 33.33% |

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- Definition Represents the expense recognized during the period arising from equity-based compensation arrangements (for example, shares of stock, unit, stock options or other equity instruments) with employees, directors and certain consultants qualifying for treatment as employees. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.F) -URI http://asc.fasb.org/extlink&oid=27013229&loc=d3e301413-122809 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5047-113901 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI http://asc.fasb.org/extlink&oid=96867065&loc=d3e5070-113901 + Details
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