diff --git a/llvm/include/llvm/Support/Alignment.h b/llvm/include/llvm/Support/Alignment.h
--- a/llvm/include/llvm/Support/Alignment.h
+++ b/llvm/include/llvm/Support/Alignment.h
@@ -164,17 +164,34 @@
 
 /// Returns a multiple of A needed to store `Size` bytes.
 inline uint64_t alignTo(uint64_t Size, Align A) {
-  const uint64_t value = A.value();
-  // The following line is equivalent to `(Size + value - 1) / value * value`.
+  const uint64_t Value = A.value();
+  // The following line is equivalent to `(Size + Value - 1) / Value * Value`.
 
   // The division followed by a multiplication can be thought of as a right
   // shift followed by a left shift which zeros out the extra bits produced in
-  // the bump; `~(value - 1)` is a mask where all those bits being zeroed out
+  // the bump; `~(Value - 1)` is a mask where all those bits being zeroed out
   // are just zero.
 
   // Most compilers can generate this code but the pattern may be missed when
   // multiple functions gets inlined.
-  return (Size + value - 1) & ~(value - 1);
+  return (Size + Value - 1) & ~(Value - 1U);
+}
+
+/// If non-zero \p Skew is specified, the return value will be a minimal integer
+/// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for
+/// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p
+/// Skew mod \p A'.
+///
+/// Examples:
+/// \code
+///   alignTo(5, Align(8), 7) = 7
+///   alignTo(17, Align(8), 1) = 17
+///   alignTo(~0LL, Align(8), 3) = 3
+/// \endcode
+inline uint64_t alignTo(uint64_t Size, Align A, uint64_t Skew) {
+  const uint64_t Value = A.value();
+  Skew %= Value;
+  return ((Size + Value - 1 - Skew) & ~(Value - 1U)) + Skew;
 }
 
 /// Returns a multiple of A needed to store `Size` bytes.
diff --git a/llvm/unittests/Support/AlignmentTest.cpp b/llvm/unittests/Support/AlignmentTest.cpp
--- a/llvm/unittests/Support/AlignmentTest.cpp
+++ b/llvm/unittests/Support/AlignmentTest.cpp
@@ -125,6 +125,13 @@
   }
 }
 
+TEST(AlignmentTest, AlignToWithSkew) {
+  EXPECT_EQ(alignTo(5, Align(8), 0), alignTo(5, Align(8)));
+  EXPECT_EQ(alignTo(5, Align(8), 7), 7U);
+  EXPECT_EQ(alignTo(17, Align(8), 1), 17U);
+  EXPECT_EQ(alignTo(~0LL, Align(8), 3), 3U);
+}
+
 TEST(AlignmentTest, Log2) {
   for (uint64_t Value : getValidAlignments()) {
     EXPECT_EQ(Log2(Align(Value)), Log2_64(Value));