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Income Taxes - Changes in Uncertain Tax Positions (Detail) - USD ($) $ in Millions | 12 Months Ended
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Dec. 31, 2018 | Dec. 31, 2017 | Dec. 31, 2016
Unrecognized tax benefits: |  |  |
Amount beginning of year | $ 17.1 | $ 35.6 | $ 28.8
Net increase (decrease): |  |  |
Tax positions taken in prior periods | 1.3 | (13.3) | (0.6)
Tax positions taken in current period | 4.5 | 4.5 | 11.0
Lapse due to applicable statute of limitations | (1.8) | (8.1) | (1.6)
Settlement with taxing authorities |  | (2.3) | (2.3)
Changes in currency exchange rates | (0.1) | 0.7 | 0.3
Amount at end of year | $ 21.0 | $ 17.1 | $ 35.6

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- Definition Amount of unrecognized tax benefits. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 45 -Paragraph 10B -URI http://asc.fasb.org/extlink&oid=84176650&loc=SL37586934-109318 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=84230637&loc=SL6600010-109319 + Details
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