diff --git a/include/llvm/MC/MCParser/AsmLexer.h b/include/llvm/MC/MCParser/AsmLexer.h
index 0dab31489fb..1b3ab577519 100644
--- a/include/llvm/MC/MCParser/AsmLexer.h
+++ b/include/llvm/MC/MCParser/AsmLexer.h
@@ -63,6 +63,7 @@ private:
   AsmToken LexSingleQuote();
   AsmToken LexQuote();
   AsmToken LexFloatLiteral();
+  AsmToken LexHexFloatLiteral(bool NoIntDigits);
 };
 
 } // end namespace llvm
diff --git a/lib/MC/MCParser/AsmLexer.cpp b/lib/MC/MCParser/AsmLexer.cpp
index c1c594a7469..1ce0cc2a1d7 100644
--- a/lib/MC/MCParser/AsmLexer.cpp
+++ b/lib/MC/MCParser/AsmLexer.cpp
@@ -91,6 +91,53 @@ AsmToken AsmLexer::LexFloatLiteral() {
                   StringRef(TokStart, CurPtr - TokStart));
 }
 
+/// LexHexFloatLiteral matches essentially (.[0-9a-fA-F]*)?[pP][+-]?[0-9a-fA-F]+
+/// while making sure there are enough actual digits around for the constant to
+/// be valid.
+///
+/// The leading "0x[0-9a-fA-F]*" (i.e. integer part) has already been consumed
+/// before we get here.
+AsmToken AsmLexer::LexHexFloatLiteral(bool NoIntDigits) {
+  assert((*CurPtr == 'p' || *CurPtr == 'P' || *CurPtr == '.') &&
+         "unexpected parse state in floating hex");
+  bool NoFracDigits = true;
+
+  // Skip the fractional part if there is one
+  if (*CurPtr == '.') {
+    ++CurPtr;
+
+    const char *FracStart = CurPtr;
+    while (isxdigit(*CurPtr))
+      ++CurPtr;
+
+    NoFracDigits = CurPtr == FracStart;
+  }
+
+  if (NoIntDigits && NoFracDigits)
+    return ReturnError(TokStart, "invalid hexadecimal floating-point constant: "
+                                 "expected at least one significand digit");
+
+  // Make sure we do have some kind of proper exponent part
+  if (*CurPtr != 'p' && *CurPtr != 'P')
+    return ReturnError(TokStart, "invalid hexadecimal floating-point constant: "
+                                 "expected exponent part 'p'");
+  ++CurPtr;
+
+  if (*CurPtr == '+' || *CurPtr == '-')
+    ++CurPtr;
+
+  // N.b. exponent digits are *not* hex
+  const char *ExpStart = CurPtr;
+  while (isdigit(*CurPtr))
+    ++CurPtr;
+
+  if (CurPtr == ExpStart)
+    return ReturnError(TokStart, "invalid hexadecimal floating-point constant: "
+                                 "expected at least one exponent digit");
+
+  return AsmToken(AsmToken::Real, StringRef(TokStart, CurPtr - TokStart));
+}
+
 /// LexIdentifier: [a-zA-Z_.][a-zA-Z0-9_$.@]*
 static bool IsIdentifierChar(char c) {
   return isalnum(c) || c == '_' || c == '$' || c == '.' || c == '@';
@@ -265,7 +312,12 @@ AsmToken AsmLexer::LexDigit() {
     while (isxdigit(CurPtr[0]))
       ++CurPtr;
 
-    // Requires at least one hex digit.
+    // "0x.0p0" is valid, and "0x0p0" (but not "0xp0" for example, which will be
+    // diagnosed by LexHexFloatLiteral).
+    if (CurPtr[0] == '.' || CurPtr[0] == 'p' || CurPtr[0] == 'P')
+      return LexHexFloatLiteral(NumStart == CurPtr);
+
+    // Otherwise requires at least one hex digit.
     if (CurPtr == NumStart)
       return ReturnError(CurPtr-2, "invalid hexadecimal number");
 
diff --git a/test/MC/AsmParser/floating-literals.s b/test/MC/AsmParser/floating-literals.s
index d44bb9830c0..512b7b36207 100644
--- a/test/MC/AsmParser/floating-literals.s
+++ b/test/MC/AsmParser/floating-literals.s
@@ -1,4 +1,5 @@
-# RUN: llvm-mc -triple i386-unknown-unknown %s | FileCheck %s
+# RUN: not llvm-mc -triple i386-unknown-unknown %s 2> /dev/null | FileCheck %s
+# RUN: not llvm-mc -triple i386-unknown-unknown %s 2>&1 > /dev/null| FileCheck %s --check-prefix=CHECK-ERROR
 
 # CHECK: .long	1067412619
 # CHECK: .long	1075000115
@@ -42,3 +43,37 @@
 // APFloat should reject these with an error, not crash:
 //.double -1.2e+
 //.double -1.2e
+
+# CHECK: .long 1310177520
+.float 0x12f7.1ep+17
+# CHECK: .long 1084227584
+.float 0x.ap+3
+# CHECK: .quad 4602678819172646912
+.double 0x2.p-2
+# CHECK: .long 1094713344
+.float 0x3p2
+# CHECK: .long 872284160
+.float 0x7fp-30
+# CHECK: .long 3212836864
+.float -0x1.0p0
+
+# CHECK-ERROR: invalid hexadecimal floating-point constant: expected at least one exponent digit
+# CHECK-ERROR: unexpected token in directive
+.float 0xa.apa
+
+# CHECK-ERROR: invalid hexadecimal floating-point constant: expected at least one exponent digit
+# CHECK-ERROR: unexpected token in directive
+.double -0x1.2p+
+
+# CHECK-ERROR: invalid hexadecimal floating-point constant: expected at least one exponent digit
+# CHECK-ERROR: unexpected token in directive
+.double -0x1.2p
+
+# CHECK-ERROR: invalid hexadecimal floating-point constant: expected at least one significand digit
+# CHECK-ERROR: unexpected token in directive
+.float 0xp2
+
+# CHECK-ERROR: invalid hexadecimal floating-point constant: expected at least one significand digit
+# CHECK-ERROR: unexpected token in directive
+.float 0x.p5
+