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diff -ru icu/source/common/unistr.cpp icu.new/source/common/unistr.cpp
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--- icu/source/common/unistr.cpp	2019-04-12 00:26:16.000000000 +0200
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+++ icu.new/source/common/unistr.cpp	2020-03-03 15:39:37.069874709 +0100
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@@ -1544,7 +1544,11 @@
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   }
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   int32_t oldLength = length();
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-  int32_t newLength = oldLength + srcLength;
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+  int32_t newLength;
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+  if (uprv_add32_overflow(oldLength, srcLength, &newLength)) {
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+    setToBogus();
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+    return *this;
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+  }
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   // optimize append() onto a large-enough, owned string
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   if((newLength <= getCapacity() && isBufferWritable()) ||
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       cloneArrayIfNeeded(newLength, getGrowCapacity(newLength))) {
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diff -ru icu/source/test/intltest/ustrtest.cpp icu.new/source/test/intltest/ustrtest.cpp
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--- icu/source/test/intltest/ustrtest.cpp	2019-04-12 00:26:16.000000000 +0200
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+++ icu.new/source/test/intltest/ustrtest.cpp	2020-03-03 15:44:59.059239188 +0100
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@@ -64,6 +64,7 @@
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     TESTCASE_AUTO(TestUInt16Pointers);
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     TESTCASE_AUTO(TestWCharPointers);
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     TESTCASE_AUTO(TestNullPointers);
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+    TESTCASE_AUTO(TestLargeAppend);
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     TESTCASE_AUTO_END;
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 }
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@@ -2248,3 +2249,64 @@
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     UnicodeString(u"def").extract(nullptr, 0, errorCode);
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     assertEquals("buffer overflow extracting to nullptr", U_BUFFER_OVERFLOW_ERROR, errorCode);
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 }
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+
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+void UnicodeStringTest::TestLargeAppend() {
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+    if(quick) return;
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+
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+    IcuTestErrorCode status(*this, "TestLargeAppend");
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+    // Make a large UnicodeString
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+    int32_t len = 0xAFFFFFF;
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+    UnicodeString str;
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+    char16_t *buf = str.getBuffer(len);
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+    // A fast way to set buffer to valid Unicode.
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+    // 4E4E is a valid unicode character
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+    uprv_memset(buf, 0x4e, len * 2);
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+    str.releaseBuffer(len);
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+    UnicodeString dest;
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+    // Append it 16 times
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+    // 0xAFFFFFF times 16 is 0xA4FFFFF1,
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+    // which is greater than INT32_MAX, which is 0x7FFFFFFF.
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+    int64_t total = 0;
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+    for (int32_t i = 0; i < 16; i++) {
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+        dest.append(str);
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+        total += len;
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+        if (total <= INT32_MAX) {
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+            assertFalse("dest is not bogus", dest.isBogus());
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+        } else {
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+            assertTrue("dest should be bogus", dest.isBogus());
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+        }
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+    }
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+    dest.remove();
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+    total = 0;
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+    for (int32_t i = 0; i < 16; i++) {
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+        dest.append(str);
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+        total += len;
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+        if (total + len <= INT32_MAX) {
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+            assertFalse("dest is not bogus", dest.isBogus());
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+        } else if (total <= INT32_MAX) {
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+            // Check that a string of exactly the maximum size works
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+            UnicodeString str2;
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+            int32_t remain = INT32_MAX - total;
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+            char16_t *buf2 = str2.getBuffer(remain);
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+            if (buf2 == nullptr) {
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+                // if somehow memory allocation fail, return the test
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+                return;
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+            }
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+            uprv_memset(buf2, 0x4e, remain * 2);
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+            str2.releaseBuffer(remain);
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+            dest.append(str2);
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+            total += remain;
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+            assertEquals("When a string of exactly the maximum size works", (int64_t)INT32_MAX, total);
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+            assertEquals("When a string of exactly the maximum size works", INT32_MAX, dest.length());
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+            assertFalse("dest is not bogus", dest.isBogus());
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+
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+            // Check that a string size+1 goes bogus
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+            str2.truncate(1);
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+            dest.append(str2);
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+            total++;
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+            assertTrue("dest should be bogus", dest.isBogus());
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+        } else {
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+            assertTrue("dest should be bogus", dest.isBogus());
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+        }
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+    }
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+}
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diff -ru icu/source/test/intltest/ustrtest.h icu.new/source/test/intltest/ustrtest.h
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--- icu/source/test/intltest/ustrtest.h	2019-04-12 00:26:16.000000000 +0200
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+++ icu.new/source/test/intltest/ustrtest.h	2020-03-03 15:45:36.147935611 +0100
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@@ -96,6 +96,7 @@
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     void TestUInt16Pointers();
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     void TestWCharPointers();
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     void TestNullPointers();
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+    void TestLargeAppend();
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 };
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 #endif