Intellij 2016 never finishes indexing

As of today, for any IntelliJ project I open, the "Indexing..." progress bar in the status bar gets around 25% done and never completes.  The EDT is blocked and the UI is unresponsive.  I've waited over 10 minutes and not the UI never wakes up.

One of my CPUs is pegged at 100% usage.  These are TypeScript/gulp projects.

I'm not sure if this is a bug; I've recently updated to IntelliJ 2016.2 from 2016.1, I've opened and worked on projects in 2016.2 before (2 days ago, judging from logs).  I know nothing has changed as far as the environment, hardware, etc.

The log file <home-dir>/.IntelliJIdea2016.2/system/log/idea.log has the following stack trace in it, but I'm not sure it's related (as there are lines in the log after the stack trace:

2016-07-21 22:27:59,592 [ 18241] INFO - il.indexing.FileBasedIndexImpl - Rebuild requested for index IdIndex
java.lang.RuntimeException: java.io.EOFException
at com.intellij.util.indexing.MapReduceIndex.update(MapReduceIndex.java:449)
at com.intellij.util.indexing.FileBasedIndexImpl.updateSingleIndex(FileBasedIndexImpl.java:1632)
at com.intellij.util.indexing.FileBasedIndexImpl.a(FileBasedIndexImpl.java:1558)
at com.intellij.openapi.fileTypes.impl.FileTypeManagerImpl.freezeFileTypeTemporarilyIn(FileTypeManagerImpl.java:505)
at com.intellij.util.indexing.FileBasedIndexImpl.a(FileBasedIndexImpl.java:1515)
at com.intellij.util.indexing.FileBasedIndexImpl.indexFileContent(FileBasedIndexImpl.java:1500)
at com.intellij.util.indexing.UnindexedFilesUpdater.a(UnindexedFilesUpdater.java:107)
at com.intellij.openapi.project.CacheUpdateRunner$MyRunnable.a(CacheUpdateRunner.java:219)
at com.intellij.openapi.application.impl.ApplicationImpl.tryRunReadAction(ApplicationImpl.java:1033)
at com.intellij.openapi.project.CacheUpdateRunner$MyRunnable.a(CacheUpdateRunner.java:236)
at com.intellij.openapi.progress.impl.CoreProgressManager$3.run(CoreProgressManager.java:170)
at com.intellij.openapi.progress.impl.CoreProgressManager.a(CoreProgressManager.java:494)
at com.intellij.openapi.progress.impl.CoreProgressManager.executeProcessUnderProgress(CoreProgressManager.java:443)
at com.intellij.openapi.progress.impl.ProgressManagerImpl.executeProcessUnderProgress(ProgressManagerImpl.java:54)
at com.intellij.openapi.progress.impl.CoreProgressManager.runProcess(CoreProgressManager.java:155)
at com.intellij.openapi.project.CacheUpdateRunner$MyRunnable.run(CacheUpdateRunner.java:232)
at com.intellij.openapi.application.impl.ApplicationImpl$2.run(ApplicationImpl.java:308)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)
at java.util.concurrent.FutureTask.run(FutureTask.java:266)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)
at java.lang.Thread.run(Thread.java:745)
Caused by: java.io.EOFException
at java.io.DataInputStream.readFully(DataInputStream.java:197)
at com.intellij.util.io.PersistentHashMapValueStorage.readBytes(PersistentHashMapValueStorage.java:377)
at com.intellij.util.io.PersistentHashMap.doGet(PersistentHashMap.java:518)
at com.intellij.util.io.PersistentHashMap.get(PersistentHashMap.java:472)
at com.intellij.util.indexing.MapReduceIndex.a(MapReduceIndex.java:612)
at com.intellij.util.indexing.MapReduceIndex.update(MapReduceIndex.java:420)
... 21 more
2016-07-21 22:28:00,393 [ 19042] INFO - il.indexing.FileBasedIndexImpl - scheduleIndexRebuild, reason: checkRebuild
2016-07-21 22:28:21,787 [ 40436] INFO - ols.gulp.GulpTaskListFetchUtil - D:/dev/htmlgames/zelda/zelda-main/gulpfile.js: 14 tasks listed in 24105 ms

There are many, many threadDumps-* files accumulating in .IntelliJIdea2016.2/system/log.  It looks like 12 per minute, for as long as I let the UI be frozen.  From a cursory look, the thread dump files all appear to have identical content.

Any clues as to where I can look to get IntelliJ happy again?