diff --git a/llvm/include/llvm/ADT/APFloat.h b/llvm/include/llvm/ADT/APFloat.h
index acb3b2e2103009..40131c83a8ef45 100644
--- a/llvm/include/llvm/ADT/APFloat.h
+++ b/llvm/include/llvm/ADT/APFloat.h
@@ -195,6 +195,13 @@ struct APFloatBase {
     // improved range compared to half (16-bit) formats, at (potentially)
     // greater throughput than single precision (32-bit) formats.
     S_FloatTF32,
+    // 8-bit floating point number with (all the) 8 bits for the exponent
+    // like in FP32. There are no zeroes, no infinities, and no denormal values.
+    // This format has unsigned representation only. (U -> Unsigned only).
+    // NaN is represented with all bits set to 1. Bias is 127.
+    // This format represents the scale data type in the MX specification from:
+    // https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf
+    S_Float8E8M0FNU,
     // 6-bit floating point number with bit layout S1E3M2. Unlike IEEE-754
     // types, there are no infinity or NaN values. The format is detailed in
     // https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf
@@ -229,6 +236,7 @@ struct APFloatBase {
   static const fltSemantics &Float8E4M3B11FNUZ() LLVM_READNONE;
   static const fltSemantics &Float8E3M4() LLVM_READNONE;
   static const fltSemantics &FloatTF32() LLVM_READNONE;
+  static const fltSemantics &Float8E8M0FNU() LLVM_READNONE;
   static const fltSemantics &Float6E3M2FN() LLVM_READNONE;
   static const fltSemantics &Float6E2M3FN() LLVM_READNONE;
   static const fltSemantics &Float4E2M1FN() LLVM_READNONE;
@@ -581,7 +589,8 @@ class IEEEFloat final : public APFloatBase {
   integerPart addSignificand(const IEEEFloat &);
   integerPart subtractSignificand(const IEEEFloat &, integerPart);
   lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
-  lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat);
+  lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat,
+                                   bool ignoreAddend = false);
   lostFraction multiplySignificand(const IEEEFloat&);
   lostFraction divideSignificand(const IEEEFloat &);
   void incrementSignificand();
@@ -591,6 +600,7 @@ class IEEEFloat final : public APFloatBase {
   unsigned int significandLSB() const;
   unsigned int significandMSB() const;
   void zeroSignificand();
+  unsigned int getNumHighBits() const;
   /// Return true if the significand excluding the integral bit is all ones.
   bool isSignificandAllOnes() const;
   bool isSignificandAllOnesExceptLSB() const;
@@ -652,6 +662,7 @@ class IEEEFloat final : public APFloatBase {
   APInt convertFloat8E4M3B11FNUZAPFloatToAPInt() const;
   APInt convertFloat8E3M4APFloatToAPInt() const;
   APInt convertFloatTF32APFloatToAPInt() const;
+  APInt convertFloat8E8M0FNUAPFloatToAPInt() const;
   APInt convertFloat6E3M2FNAPFloatToAPInt() const;
   APInt convertFloat6E2M3FNAPFloatToAPInt() const;
   APInt convertFloat4E2M1FNAPFloatToAPInt() const;
@@ -672,6 +683,7 @@ class IEEEFloat final : public APFloatBase {
   void initFromFloat8E4M3B11FNUZAPInt(const APInt &api);
   void initFromFloat8E3M4APInt(const APInt &api);
   void initFromFloatTF32APInt(const APInt &api);
+  void initFromFloat8E8M0FNUAPInt(const APInt &api);
   void initFromFloat6E3M2FNAPInt(const APInt &api);
   void initFromFloat6E2M3FNAPInt(const APInt &api);
   void initFromFloat4E2M1FNAPInt(const APInt &api);
@@ -1079,6 +1091,9 @@ class APFloat : public APFloatBase {
   /// \param Semantics - type float semantics
   static APFloat getAllOnesValue(const fltSemantics &Semantics);
 
+  /// Returns true if the given semantics supports either NaN or Infinity.
+  ///
+  /// \param Sem - type float semantics
   static bool hasNanOrInf(const fltSemantics &Sem) {
     switch (SemanticsToEnum(Sem)) {
     default:
@@ -1091,6 +1106,13 @@ class APFloat : public APFloatBase {
     }
   }
 
+  /// Returns true if the given semantics has actual significand.
+  ///
+  /// \param Sem - type float semantics
+  static bool hasSignificand(const fltSemantics &Sem) {
+    return &Sem != &Float8E8M0FNU();
+  }
+
   /// Used to insert APFloat objects, or objects that contain APFloat objects,
   /// into FoldingSets.
   void Profile(FoldingSetNodeID &NID) const;
diff --git a/llvm/lib/Support/APFloat.cpp b/llvm/lib/Support/APFloat.cpp
index dee917fd56104c..03413f6eb6fe71 100644
--- a/llvm/lib/Support/APFloat.cpp
+++ b/llvm/lib/Support/APFloat.cpp
@@ -119,6 +119,13 @@ struct fltSemantics {
   fltNonfiniteBehavior nonFiniteBehavior = fltNonfiniteBehavior::IEEE754;
 
   fltNanEncoding nanEncoding = fltNanEncoding::IEEE;
+
+  /* Whether this semantics has an encoding for Zero */
+  bool hasZero = true;
+
+  /* Whether this semantics can represent signed values */
+  bool hasSignedRepr = true;
+
   // Returns true if any number described by this semantics can be precisely
   // represented by the specified semantics. Does not take into account
   // the value of fltNonfiniteBehavior.
@@ -145,6 +152,10 @@ static constexpr fltSemantics semFloat8E4M3B11FNUZ = {
     4, -10, 4, 8, fltNonfiniteBehavior::NanOnly, fltNanEncoding::NegativeZero};
 static constexpr fltSemantics semFloat8E3M4 = {3, -2, 5, 8};
 static constexpr fltSemantics semFloatTF32 = {127, -126, 11, 19};
+static constexpr fltSemantics semFloat8E8M0FNU = {
+    127,   -127, 1, 8, fltNonfiniteBehavior::NanOnly, fltNanEncoding::AllOnes,
+    false, false};
+
 static constexpr fltSemantics semFloat6E3M2FN = {
     4, -2, 3, 6, fltNonfiniteBehavior::FiniteOnly};
 static constexpr fltSemantics semFloat6E2M3FN = {
@@ -222,6 +233,8 @@ const llvm::fltSemantics &APFloatBase::EnumToSemantics(Semantics S) {
     return Float8E3M4();
   case S_FloatTF32:
     return FloatTF32();
+  case S_Float8E8M0FNU:
+    return Float8E8M0FNU();
   case S_Float6E3M2FN:
     return Float6E3M2FN();
   case S_Float6E2M3FN:
@@ -264,6 +277,8 @@ APFloatBase::SemanticsToEnum(const llvm::fltSemantics &Sem) {
     return S_Float8E3M4;
   else if (&Sem == &llvm::APFloat::FloatTF32())
     return S_FloatTF32;
+  else if (&Sem == &llvm::APFloat::Float8E8M0FNU())
+    return S_Float8E8M0FNU;
   else if (&Sem == &llvm::APFloat::Float6E3M2FN())
     return S_Float6E3M2FN;
   else if (&Sem == &llvm::APFloat::Float6E2M3FN())
@@ -294,6 +309,7 @@ const fltSemantics &APFloatBase::Float8E4M3B11FNUZ() {
 }
 const fltSemantics &APFloatBase::Float8E3M4() { return semFloat8E3M4; }
 const fltSemantics &APFloatBase::FloatTF32() { return semFloatTF32; }
+const fltSemantics &APFloatBase::Float8E8M0FNU() { return semFloat8E8M0FNU; }
 const fltSemantics &APFloatBase::Float6E3M2FN() { return semFloat6E3M2FN; }
 const fltSemantics &APFloatBase::Float6E2M3FN() { return semFloat6E2M3FN; }
 const fltSemantics &APFloatBase::Float4E2M1FN() { return semFloat4E2M1FN; }
@@ -396,7 +412,8 @@ static inline Error createError(const Twine &Err) {
 }
 
 static constexpr inline unsigned int partCountForBits(unsigned int bits) {
-  return ((bits) + APFloatBase::integerPartWidth - 1) / APFloatBase::integerPartWidth;
+  return std::max(1u, (bits + APFloatBase::integerPartWidth - 1) /
+                          APFloatBase::integerPartWidth);
 }
 
 /* Returns 0U-9U.  Return values >= 10U are not digits.  */
@@ -918,6 +935,10 @@ void IEEEFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill) {
   if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::FiniteOnly)
     llvm_unreachable("This floating point format does not support NaN");
 
+  if (Negative && !semantics->hasSignedRepr)
+    llvm_unreachable(
+        "This floating point format does not support signed values");
+
   category = fcNaN;
   sign = Negative;
   exponent = exponentNaN();
@@ -955,7 +976,8 @@ void IEEEFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill) {
       significand[part] = 0;
   }
 
-  unsigned QNaNBit = semantics->precision - 2;
+  unsigned QNaNBit =
+      (semantics->precision >= 2) ? (semantics->precision - 2) : 0;
 
   if (SNaN) {
     // We always have to clear the QNaN bit to make it an SNaN.
@@ -1025,6 +1047,19 @@ bool IEEEFloat::isSmallestNormalized() const {
          isSignificandAllZerosExceptMSB();
 }
 
+unsigned int IEEEFloat::getNumHighBits() const {
+  const unsigned int PartCount = partCountForBits(semantics->precision);
+  const unsigned int Bits = PartCount * integerPartWidth;
+
+  // Compute how many bits are used in the final word.
+  // When precision is just 1, it represents the 'Pth'
+  // Precision bit and not the actual significand bit.
+  const unsigned int NumHighBits = (semantics->precision > 1)
+                                       ? (Bits - semantics->precision + 1)
+                                       : (Bits - semantics->precision);
+  return NumHighBits;
+}
+
 bool IEEEFloat::isSignificandAllOnes() const {
   // Test if the significand excluding the integral bit is all ones. This allows
   // us to test for binade boundaries.
@@ -1035,13 +1070,12 @@ bool IEEEFloat::isSignificandAllOnes() const {
       return false;
 
   // Set the unused high bits to all ones when we compare.
-  const unsigned NumHighBits =
-    PartCount*integerPartWidth - semantics->precision + 1;
+  const unsigned NumHighBits = getNumHighBits();
   assert(NumHighBits <= integerPartWidth && NumHighBits > 0 &&
          "Can not have more high bits to fill than integerPartWidth");
   const integerPart HighBitFill =
     ~integerPart(0) << (integerPartWidth - NumHighBits);
-  if (~(Parts[PartCount - 1] | HighBitFill))
+  if ((semantics->precision <= 1) || (~(Parts[PartCount - 1] | HighBitFill)))
     return false;
 
   return true;
@@ -1062,8 +1096,7 @@ bool IEEEFloat::isSignificandAllOnesExceptLSB() const {
   }
 
   // Set the unused high bits to all ones when we compare.
-  const unsigned NumHighBits =
-      PartCount * integerPartWidth - semantics->precision + 1;
+  const unsigned NumHighBits = getNumHighBits();
   assert(NumHighBits <= integerPartWidth && NumHighBits > 0 &&
          "Can not have more high bits to fill than integerPartWidth");
   const integerPart HighBitFill = ~integerPart(0)
@@ -1085,13 +1118,12 @@ bool IEEEFloat::isSignificandAllZeros() const {
       return false;
 
   // Compute how many bits are used in the final word.
-  const unsigned NumHighBits =
-    PartCount*integerPartWidth - semantics->precision + 1;
+  const unsigned NumHighBits = getNumHighBits();
   assert(NumHighBits < integerPartWidth && "Can not have more high bits to "
          "clear than integerPartWidth");
   const integerPart HighBitMask = ~integerPart(0) >> NumHighBits;
 
-  if (Parts[PartCount - 1] & HighBitMask)
+  if ((semantics->precision > 1) && (Parts[PartCount - 1] & HighBitMask))
     return false;
 
   return true;
@@ -1106,25 +1138,26 @@ bool IEEEFloat::isSignificandAllZerosExceptMSB() const {
       return false;
   }
 
-  const unsigned NumHighBits =
-      PartCount * integerPartWidth - semantics->precision + 1;
-  return Parts[PartCount - 1] == integerPart(1)
-                                     << (integerPartWidth - NumHighBits);
+  const unsigned NumHighBits = getNumHighBits();
+  const integerPart MSBMask = integerPart(1)
+                              << (integerPartWidth - NumHighBits);
+  return ((semantics->precision <= 1) || (Parts[PartCount - 1] == MSBMask));
 }
 
 bool IEEEFloat::isLargest() const {
+  bool IsMaxExp = isFiniteNonZero() && exponent == semantics->maxExponent;
   if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly &&
       semantics->nanEncoding == fltNanEncoding::AllOnes) {
     // The largest number by magnitude in our format will be the floating point
     // number with maximum exponent and with significand that is all ones except
     // the LSB.
-    return isFiniteNonZero() && exponent == semantics->maxExponent &&
-           isSignificandAllOnesExceptLSB();
+    return (IsMaxExp && APFloat::hasSignificand(*semantics))
+               ? isSignificandAllOnesExceptLSB()
+               : IsMaxExp;
   } else {
     // The largest number by magnitude in our format will be the floating point
     // number with maximum exponent and with significand that is all ones.
-    return isFiniteNonZero() && exponent == semantics->maxExponent &&
-           isSignificandAllOnes();
+    return IsMaxExp && isSignificandAllOnes();
   }
 }
 
@@ -1165,7 +1198,13 @@ IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, integerPart value) {
 
 IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics) {
   initialize(&ourSemantics);
-  makeZero(false);
+  // The Float8E8MOFNU format does not have a representation
+  // for zero. So, use the closest representation instead.
+  // Moreover, the all-zero encoding represents a valid
+  // normal value (which is the smallestNormalized here).
+  // Hence, we call makeSmallestNormalized (where category is
+  // 'fcNormal') instead of makeZero (where category is 'fcZero').
+  ourSemantics.hasZero ? makeZero(false) : makeSmallestNormalized(false);
 }
 
 // Delegate to the previous constructor, because later copy constructor may
@@ -1245,7 +1284,8 @@ IEEEFloat::integerPart IEEEFloat::subtractSignificand(const IEEEFloat &rhs,
    on to the full-precision result of the multiplication.  Returns the
    lost fraction.  */
 lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs,
-                                            IEEEFloat addend) {
+                                            IEEEFloat addend,
+                                            bool ignoreAddend) {
   unsigned int omsb;        // One, not zero, based MSB.
   unsigned int partsCount, newPartsCount, precision;
   integerPart *lhsSignificand;
@@ -1289,7 +1329,7 @@ lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs,
   // toward left by two bits, and adjust exponent accordingly.
   exponent += 2;
 
-  if (addend.isNonZero()) {
+  if (!ignoreAddend && addend.isNonZero()) {
     // The intermediate result of the multiplication has "2 * precision"
     // signicant bit; adjust the addend to be consistent with mul result.
     //
@@ -1377,7 +1417,12 @@ lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs,
 }
 
 lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs) {
-  return multiplySignificand(rhs, IEEEFloat(*semantics));
+  // When the given semantics has zero, the addend here is a zero.
+  // i.e . it belongs to the 'fcZero' category.
+  // But when the semantics does not support zero, we need to
+  // explicitly convey that this addend should be ignored
+  // for multiplication.
+  return multiplySignificand(rhs, IEEEFloat(*semantics), !semantics->hasZero);
 }
 
 /* Multiply the significands of LHS and RHS to DST.  */
@@ -1483,7 +1528,8 @@ lostFraction IEEEFloat::shiftSignificandRight(unsigned int bits) {
 
 /* Shift the significand left BITS bits, subtract BITS from its exponent.  */
 void IEEEFloat::shiftSignificandLeft(unsigned int bits) {
-  assert(bits < semantics->precision);
+  assert(bits < semantics->precision ||
+         (semantics->precision == 1 && bits <= 1));
 
   if (bits) {
     unsigned int partsCount = partCount();
@@ -1678,6 +1724,8 @@ IEEEFloat::opStatus IEEEFloat::normalize(roundingMode rounding_mode,
       category = fcZero;
       if (semantics->nanEncoding == fltNanEncoding::NegativeZero)
         sign = false;
+      if (!semantics->hasZero)
+        makeSmallestNormalized(false);
     }
 
     return opOK;
@@ -1729,6 +1777,11 @@ IEEEFloat::opStatus IEEEFloat::normalize(roundingMode rounding_mode,
     category = fcZero;
     if (semantics->nanEncoding == fltNanEncoding::NegativeZero)
       sign = false;
+    // This condition handles the case where the semantics
+    // does not have zero but uses the all-zero encoding
+    // to represent the smallest normal value.
+    if (!semantics->hasZero)
+      makeSmallestNormalized(false);
   }
 
   /* The fcZero case is a denormal that underflowed to zero.  */
@@ -1807,6 +1860,10 @@ lostFraction IEEEFloat::addOrSubtractSignificand(const IEEEFloat &rhs,
 
   /* Subtraction is more subtle than one might naively expect.  */
   if (subtract) {
+    if ((bits < 0) && !semantics->hasSignedRepr)
+      llvm_unreachable(
+          "This floating point format does not support signed values");
+
     IEEEFloat temp_rhs(rhs);
 
     if (bits == 0)
@@ -2252,6 +2309,17 @@ IEEEFloat::opStatus IEEEFloat::mod(const IEEEFloat &rhs) {
     V.sign = sign;
 
     fs = subtract(V, rmNearestTiesToEven);
+
+    // When the semantics supports zero, this loop's
+    // exit-condition is handled by the 'isFiniteNonZero'
+    // category check above. However, when the semantics
+    // does not have 'fcZero' and we have reached the
+    // minimum possible value, (and any further subtract
+    // will underflow to the same value) explicitly
+    // provide an exit-path here.
+    if (!semantics->hasZero && this->isSmallest())
+      break;
+
     assert(fs==opOK);
   }
   if (isZero()) {
@@ -2606,6 +2674,8 @@ IEEEFloat::opStatus IEEEFloat::convert(const fltSemantics &toSemantics,
     fs = opOK;
   }
 
+  if (category == fcZero && !semantics->hasZero)
+    makeSmallestNormalized(false);
   return fs;
 }
 
@@ -3070,6 +3140,8 @@ IEEEFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode) {
     fs = opOK;
     if (semantics->nanEncoding == fltNanEncoding::NegativeZero)
       sign = false;
+    if (!semantics->hasZero)
+      makeSmallestNormalized(false);
 
     /* Check whether the normalized exponent is high enough to overflow
        max during the log-rebasing in the max-exponent check below. */
@@ -3237,6 +3309,10 @@ IEEEFloat::convertFromString(StringRef str, roundingMode rounding_mode) {
   StringRef::iterator p = str.begin();
   size_t slen = str.size();
   sign = *p == '-' ? 1 : 0;
+  if (sign && !semantics->hasSignedRepr)
+    llvm_unreachable(
+        "This floating point format does not support signed values");
+
   if (*p == '-' || *p == '+') {
     p++;
     slen--;
@@ -3533,15 +3609,16 @@ APInt IEEEFloat::convertPPCDoubleDoubleAPFloatToAPInt() const {
 template <const fltSemantics &S>
 APInt IEEEFloat::convertIEEEFloatToAPInt() const {
   assert(semantics == &S);
-
-  constexpr int bias = -(S.minExponent - 1);
+  const int bias =
+      (semantics == &semFloat8E8M0FNU) ? -S.minExponent : -(S.minExponent - 1);
   constexpr unsigned int trailing_significand_bits = S.precision - 1;
   constexpr int integer_bit_part = trailing_significand_bits / integerPartWidth;
   constexpr integerPart integer_bit =
       integerPart{1} << (trailing_significand_bits % integerPartWidth);
   constexpr uint64_t significand_mask = integer_bit - 1;
   constexpr unsigned int exponent_bits =
-      S.sizeInBits - 1 - trailing_significand_bits;
+      trailing_significand_bits ? (S.sizeInBits - 1 - trailing_significand_bits)
+                                : S.sizeInBits;
   static_assert(exponent_bits < 64);
   constexpr uint64_t exponent_mask = (uint64_t{1} << exponent_bits) - 1;
 
@@ -3557,6 +3634,8 @@ APInt IEEEFloat::convertIEEEFloatToAPInt() const {
         !(significandParts()[integer_bit_part] & integer_bit))
       myexponent = 0; // denormal
   } else if (category == fcZero) {
+    if (!S.hasZero)
+      llvm_unreachable("semantics does not support zero!");
     myexponent = ::exponentZero(S) + bias;
     mysignificand.fill(0);
   } else if (category == fcInfinity) {
@@ -3659,6 +3738,11 @@ APInt IEEEFloat::convertFloatTF32APFloatToAPInt() const {
   return convertIEEEFloatToAPInt<semFloatTF32>();
 }
 
+APInt IEEEFloat::convertFloat8E8M0FNUAPFloatToAPInt() const {
+  assert(partCount() == 1);
+  return convertIEEEFloatToAPInt<semFloat8E8M0FNU>();
+}
+
 APInt IEEEFloat::convertFloat6E3M2FNAPFloatToAPInt() const {
   assert(partCount() == 1);
   return convertIEEEFloatToAPInt<semFloat6E3M2FN>();
@@ -3721,6 +3805,9 @@ APInt IEEEFloat::bitcastToAPInt() const {
   if (semantics == (const llvm::fltSemantics *)&semFloatTF32)
     return convertFloatTF32APFloatToAPInt();
 
+  if (semantics == (const llvm::fltSemantics *)&semFloat8E8M0FNU)
+    return convertFloat8E8M0FNUAPFloatToAPInt();
+
   if (semantics == (const llvm::fltSemantics *)&semFloat6E3M2FN)
     return convertFloat6E3M2FNAPFloatToAPInt();
 
@@ -3819,6 +3906,40 @@ void IEEEFloat::initFromPPCDoubleDoubleAPInt(const APInt &api) {
   }
 }
 
+// The E8M0 format has the following characteristics:
+// It is an 8-bit unsigned format with only exponents (no actual significand).
+// No encodings for {zero, infinities or denorms}.
+// NaN is represented by all 1's.
+// Bias is 127.
+void IEEEFloat::initFromFloat8E8M0FNUAPInt(const APInt &api) {
+  const uint64_t exponent_mask = 0xff;
+  uint64_t val = api.getRawData()[0];
+  uint64_t myexponent = (val & exponent_mask);
+
+  initialize(&semFloat8E8M0FNU);
+  assert(partCount() == 1);
+
+  // This format has unsigned representation only
+  sign = 0;
+
+  // Set the significand
+  // This format does not have any significand but the 'Pth' precision bit is
+  // always set to 1 for consistency in APFloat's internal representation.
+  uint64_t mysignificand = 1;
+  significandParts()[0] = mysignificand;
+
+  // This format can either have a NaN or fcNormal
+  // All 1's i.e. 255 is a NaN
+  if (val == exponent_mask) {
+    category = fcNaN;
+    exponent = exponentNaN();
+    return;
+  }
+  // Handle fcNormal...
+  category = fcNormal;
+  exponent = myexponent - 127; // 127 is bias
+  return;
+}
 template <const fltSemantics &S>
 void IEEEFloat::initFromIEEEAPInt(const APInt &api) {
   assert(api.getBitWidth() == S.sizeInBits);
@@ -3999,6 +4120,8 @@ void IEEEFloat::initFromAPInt(const fltSemantics *Sem, const APInt &api) {
     return initFromFloat8E3M4APInt(api);
   if (Sem == &semFloatTF32)
     return initFromFloatTF32APInt(api);
+  if (Sem == &semFloat8E8M0FNU)
+    return initFromFloat8E8M0FNUAPInt(api);
   if (Sem == &semFloat6E3M2FN)
     return initFromFloat6E3M2FNAPInt(api);
   if (Sem == &semFloat6E2M3FN)
@@ -4012,6 +4135,9 @@ void IEEEFloat::initFromAPInt(const fltSemantics *Sem, const APInt &api) {
 /// Make this number the largest magnitude normal number in the given
 /// semantics.
 void IEEEFloat::makeLargest(bool Negative) {
+  if (Negative && !semantics->hasSignedRepr)
+    llvm_unreachable(
+        "This floating point format does not support signed values");
   // We want (in interchange format):
   //   sign = {Negative}
   //   exponent = 1..10
@@ -4032,15 +4158,18 @@ void IEEEFloat::makeLargest(bool Negative) {
   significand[PartCount - 1] = (NumUnusedHighBits < integerPartWidth)
                                    ? (~integerPart(0) >> NumUnusedHighBits)
                                    : 0;
-
   if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly &&
-      semantics->nanEncoding == fltNanEncoding::AllOnes)
+      semantics->nanEncoding == fltNanEncoding::AllOnes &&
+      (semantics->precision > 1))
     significand[0] &= ~integerPart(1);
 }
 
 /// Make this number the smallest magnitude denormal number in the given
 /// semantics.
 void IEEEFloat::makeSmallest(bool Negative) {
+  if (Negative && !semantics->hasSignedRepr)
+    llvm_unreachable(
+        "This floating point format does not support signed values");
   // We want (in interchange format):
   //   sign = {Negative}
   //   exponent = 0..0
@@ -4052,6 +4181,9 @@ void IEEEFloat::makeSmallest(bool Negative) {
 }
 
 void IEEEFloat::makeSmallestNormalized(bool Negative) {
+  if (Negative && !semantics->hasSignedRepr)
+    llvm_unreachable(
+        "This floating point format does not support signed values");
   // We want (in interchange format):
   //   sign = {Negative}
   //   exponent = 0..0
@@ -4509,6 +4641,8 @@ IEEEFloat::opStatus IEEEFloat::next(bool nextDown) {
       exponent = 0;
       if (semantics->nanEncoding == fltNanEncoding::NegativeZero)
         sign = false;
+      if (!semantics->hasZero)
+        makeSmallestNormalized(false);
       break;
     }
 
@@ -4574,7 +4708,10 @@ IEEEFloat::opStatus IEEEFloat::next(bool nextDown) {
       // the integral bit to 1, and increment the exponent. If we have a
       // denormal always increment since moving denormals and the numbers in the
       // smallest normal binade have the same exponent in our representation.
-      bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
+      // If there are only exponents, any increment always crosses the
+      // BinadeBoundary.
+      bool WillCrossBinadeBoundary = !APFloat::hasSignificand(*semantics) ||
+                                     (!isDenormal() && isSignificandAllOnes());
 
       if (WillCrossBinadeBoundary) {
         integerPart *Parts = significandParts();
@@ -4626,6 +4763,9 @@ void IEEEFloat::makeInf(bool Negative) {
 }
 
 void IEEEFloat::makeZero(bool Negative) {
+  if (!semantics->hasZero)
+    llvm_unreachable("This floating point format does not support Zero");
+
   category = fcZero;
   sign = Negative;
   if (semantics->nanEncoding == fltNanEncoding::NegativeZero) {
diff --git a/llvm/unittests/ADT/APFloatTest.cpp b/llvm/unittests/ADT/APFloatTest.cpp
index cd8a00fb18d7fd..6008f00e42a989 100644
--- a/llvm/unittests/ADT/APFloatTest.cpp
+++ b/llvm/unittests/ADT/APFloatTest.cpp
@@ -824,6 +824,11 @@ TEST(APFloatTest, IsSmallestNormalized) {
     const fltSemantics &Semantics =
         APFloat::EnumToSemantics(static_cast<APFloat::Semantics>(I));
 
+    // For Float8E8M0FNU format, the below cases are tested
+    // through Float8E8M0FNUSmallest and Float8E8M0FNUNext tests.
+    if (I == APFloat::S_Float8E8M0FNU)
+      continue;
+
     EXPECT_FALSE(APFloat::getZero(Semantics, false).isSmallestNormalized());
     EXPECT_FALSE(APFloat::getZero(Semantics, true).isSmallestNormalized());
 
@@ -1917,6 +1922,57 @@ TEST(DoubleAPFloatTest, isInteger) {
   EXPECT_FALSE(T3.isInteger());
 }
 
+// Test to check if the full range of Float8E8M0FNU
+// values are being represented correctly.
+TEST(APFloatTest, Float8E8M0FNUValues) {
+  // High end of the range
+  auto test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p127");
+  EXPECT_EQ(0x1.0p127, test.convertToDouble());
+
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p126");
+  EXPECT_EQ(0x1.0p126, test.convertToDouble());
+
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p125");
+  EXPECT_EQ(0x1.0p125, test.convertToDouble());
+
+  // tests the fix in makeLargest()
+  test = APFloat::getLargest(APFloat::Float8E8M0FNU());
+  EXPECT_EQ(0x1.0p127, test.convertToDouble());
+
+  // tests overflow to nan
+  APFloat nan = APFloat(APFloat::Float8E8M0FNU(), "nan");
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p128");
+  EXPECT_TRUE(test.bitwiseIsEqual(nan));
+
+  // Mid of the range
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p0");
+  EXPECT_EQ(1.0, test.convertToDouble());
+
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p1");
+  EXPECT_EQ(2.0, test.convertToDouble());
+
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p2");
+  EXPECT_EQ(4.0, test.convertToDouble());
+
+  // Low end of the range
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p-125");
+  EXPECT_EQ(0x1.0p-125, test.convertToDouble());
+
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p-126");
+  EXPECT_EQ(0x1.0p-126, test.convertToDouble());
+
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p-127");
+  EXPECT_EQ(0x1.0p-127, test.convertToDouble());
+
+  // Smallest value
+  test = APFloat::getSmallest(APFloat::Float8E8M0FNU());
+  EXPECT_EQ(0x1.0p-127, test.convertToDouble());
+
+  // Value below the smallest, but clamped to the smallest
+  test = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p-128");
+  EXPECT_EQ(0x1.0p-127, test.convertToDouble());
+}
+
 TEST(APFloatTest, getLargest) {
   EXPECT_EQ(3.402823466e+38f, APFloat::getLargest(APFloat::IEEEsingle()).convertToFloat());
   EXPECT_EQ(1.7976931348623158e+308, APFloat::getLargest(APFloat::IEEEdouble()).convertToDouble());
@@ -1929,6 +1985,8 @@ TEST(APFloatTest, getLargest) {
       30, APFloat::getLargest(APFloat::Float8E4M3B11FNUZ()).convertToDouble());
   EXPECT_EQ(3.40116213421e+38f,
             APFloat::getLargest(APFloat::FloatTF32()).convertToFloat());
+  EXPECT_EQ(1.701411834e+38f,
+            APFloat::getLargest(APFloat::Float8E8M0FNU()).convertToDouble());
   EXPECT_EQ(28, APFloat::getLargest(APFloat::Float6E3M2FN()).convertToDouble());
   EXPECT_EQ(7.5,
             APFloat::getLargest(APFloat::Float6E2M3FN()).convertToDouble());
@@ -2012,6 +2070,13 @@ TEST(APFloatTest, getSmallest) {
   EXPECT_TRUE(test.isFiniteNonZero());
   EXPECT_TRUE(test.isDenormal());
   EXPECT_TRUE(test.bitwiseIsEqual(expected));
+
+  test = APFloat::getSmallest(APFloat::Float8E8M0FNU());
+  expected = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p-127");
+  EXPECT_FALSE(test.isNegative());
+  EXPECT_TRUE(test.isFiniteNonZero());
+  EXPECT_FALSE(test.isDenormal());
+  EXPECT_TRUE(test.bitwiseIsEqual(expected));
 }
 
 TEST(APFloatTest, getSmallestNormalized) {
@@ -2118,6 +2183,14 @@ TEST(APFloatTest, getSmallestNormalized) {
   EXPECT_FALSE(test.isDenormal());
   EXPECT_TRUE(test.bitwiseIsEqual(expected));
   EXPECT_TRUE(test.isSmallestNormalized());
+
+  test = APFloat::getSmallestNormalized(APFloat::Float8E8M0FNU(), false);
+  expected = APFloat(APFloat::Float8E8M0FNU(), "0x1.0p-127");
+  EXPECT_FALSE(test.isNegative());
+  EXPECT_TRUE(test.isFiniteNonZero());
+  EXPECT_FALSE(test.isDenormal());
+  EXPECT_TRUE(test.bitwiseIsEqual(expected));
+  EXPECT_TRUE(test.isSmallestNormalized());
 }
 
 TEST(APFloatTest, getZero) {
@@ -5326,6 +5399,104 @@ TEST(APFloatTest, Float8ExhaustivePair) {
   }
 }
 
+TEST(APFloatTest, Float8E8M0FNUExhaustivePair) {
+  // Test each pair of 8-bit values for Float8E8M0FNU format
+  APFloat::Semantics Sem = APFloat::S_Float8E8M0FNU;
+  const llvm::fltSemantics &S = APFloat::EnumToSemantics(Sem);
+  for (int i = 0; i < 256; i++) {
+    for (int j = 0; j < 256; j++) {
+      SCOPED_TRACE("sem=" + std::to_string(Sem) + ",i=" + std::to_string(i) +
+                   ",j=" + std::to_string(j));
+      APFloat x(S, APInt(8, i));
+      APFloat y(S, APInt(8, j));
+
+      bool losesInfo;
+      APFloat xd = x;
+      xd.convert(APFloat::IEEEdouble(), APFloat::rmNearestTiesToEven,
+                 &losesInfo);
+      EXPECT_FALSE(losesInfo);
+      APFloat yd = y;
+      yd.convert(APFloat::IEEEdouble(), APFloat::rmNearestTiesToEven,
+                 &losesInfo);
+      EXPECT_FALSE(losesInfo);
+
+      // Add
+      APFloat z = x;
+      z.add(y, APFloat::rmNearestTiesToEven);
+      APFloat zd = xd;
+      zd.add(yd, APFloat::rmNearestTiesToEven);
+      zd.convert(S, APFloat::rmNearestTiesToEven, &losesInfo);
+      EXPECT_TRUE(z.bitwiseIsEqual(zd))
+          << "sem=" << Sem << ", i=" << i << ", j=" << j;
+
+      // Subtract
+      if (i >= j) {
+        z = x;
+        z.subtract(y, APFloat::rmNearestTiesToEven);
+        zd = xd;
+        zd.subtract(yd, APFloat::rmNearestTiesToEven);
+        zd.convert(S, APFloat::rmNearestTiesToEven, &losesInfo);
+        EXPECT_TRUE(z.bitwiseIsEqual(zd))
+            << "sem=" << Sem << ", i=" << i << ", j=" << j;
+      }
+
+      // Multiply
+      z = x;
+      z.multiply(y, APFloat::rmNearestTiesToEven);
+      zd = xd;
+      zd.multiply(yd, APFloat::rmNearestTiesToEven);
+      zd.convert(S, APFloat::rmNearestTiesToEven, &losesInfo);
+      EXPECT_TRUE(z.bitwiseIsEqual(zd))
+          << "sem=" << Sem << ", i=" << i << ", j=" << j;
+
+      // Divide
+      z = x;
+      z.divide(y, APFloat::rmNearestTiesToEven);
+      zd = xd;
+      zd.divide(yd, APFloat::rmNearestTiesToEven);
+      zd.convert(S, APFloat::rmNearestTiesToEven, &losesInfo);
+      EXPECT_TRUE(z.bitwiseIsEqual(zd))
+          << "sem=" << Sem << ", i=" << i << ", j=" << j;
+
+      // Mod
+      z = x;
+      z.mod(y);
+      zd = xd;
+      zd.mod(yd);
+      zd.convert(S, APFloat::rmNearestTiesToEven, &losesInfo);
+      EXPECT_TRUE(z.bitwiseIsEqual(zd))
+          << "sem=" << Sem << ", i=" << i << ", j=" << j;
+      APFloat mod_cached = z;
+      // When one of them is a NaN, the result is a NaN.
+      // When i < j, the mod is 'i' since it is the smaller
+      // number. Otherwise the mod is always zero since
+      // both x and y are powers-of-two in this format.
+      // Since this format does not support zero and it is
+      // represented as the smallest normalized value, we
+      // test for isSmallestNormalized().
+      if (i == 255 || j == 255)
+        EXPECT_TRUE(z.isNaN());
+      else if (i >= j)
+        EXPECT_TRUE(z.isSmallestNormalized());
+      else
+        EXPECT_TRUE(z.bitwiseIsEqual(x));
+
+      // Remainder
+      z = x;
+      z.remainder(y);
+      zd = xd;
+      zd.remainder(yd);
+      zd.convert(S, APFloat::rmNearestTiesToEven, &losesInfo);
+      EXPECT_TRUE(z.bitwiseIsEqual(zd))
+          << "sem=" << Sem << ", i=" << i << ", j=" << j;
+      // Since this format has only exponents (i.e. no precision)
+      // we expect the remainder and mod to provide the same results.
+      EXPECT_TRUE(z.bitwiseIsEqual(mod_cached))
+          << "sem=" << Sem << ", i=" << i << ", j=" << j;
+    }
+  }
+}
+
 TEST(APFloatTest, Float6ExhaustivePair) {
   // Test each pair of 6-bit floats with non-standard semantics
   for (APFloat::Semantics Sem :
@@ -5801,6 +5972,46 @@ TEST(APFloatTest, Float8E4M3FNExhaustive) {
   }
 }
 
+TEST(APFloatTest, Float8E8M0FNUExhaustive) {
+  // Test each of the 256 Float8E8M0FNU values.
+  for (int i = 0; i < 256; i++) {
+    APFloat test(APFloat::Float8E8M0FNU(), APInt(8, i));
+    SCOPED_TRACE("i=" + std::to_string(i));
+
+    // isLargest
+    if (i == 254) {
+      EXPECT_TRUE(test.isLargest());
+      EXPECT_EQ(abs(test).convertToDouble(), 0x1.0p127);
+    } else {
+      EXPECT_FALSE(test.isLargest());
+    }
+
+    // isSmallest
+    if (i == 0) {
+      EXPECT_TRUE(test.isSmallest());
+      EXPECT_EQ(abs(test).convertToDouble(), 0x1.0p-127);
+    } else {
+      EXPECT_FALSE(test.isSmallest());
+    }
+
+    // convert to Double
+    bool losesInfo;
+    std::string val = std::to_string(i - 127); // 127 is the bias
+    llvm::SmallString<16> str("0x1.0p");
+    str += val;
+    APFloat test2(APFloat::IEEEdouble(), str);
+
+    APFloat::opStatus status = test.convert(
+        APFloat::IEEEdouble(), APFloat::rmNearestTiesToEven, &losesInfo);
+    EXPECT_EQ(status, APFloat::opOK);
+    EXPECT_FALSE(losesInfo);
+    if (i == 255)
+      EXPECT_TRUE(test.isNaN());
+    else
+      EXPECT_EQ(test.convertToDouble(), test2.convertToDouble());
+  }
+}
+
 TEST(APFloatTest, Float8E5M2FNUZNext) {
   APFloat test(APFloat::Float8E5M2FNUZ(), APFloat::uninitialized);
   APFloat expected(APFloat::Float8E5M2FNUZ(), APFloat::uninitialized);
@@ -7077,6 +7288,12 @@ TEST(APFloatTest, getExactLog2) {
     auto SemEnum = static_cast<APFloat::Semantics>(I);
     const fltSemantics &Semantics = APFloat::EnumToSemantics(SemEnum);
 
+    // For the Float8E8M0FNU format, the below cases along
+    // with some more corner cases are tested through
+    // Float8E8M0FNUGetExactLog2.
+    if (I == APFloat::S_Float8E8M0FNU)
+      continue;
+
     APFloat One(Semantics, "1.0");
 
     if (I == APFloat::S_PPCDoubleDouble) {
@@ -7146,6 +7363,250 @@ TEST(APFloatTest, getExactLog2) {
   }
 }
 
+TEST(APFloatTest, Float8E8M0FNUGetZero) {
+#ifdef GTEST_HAS_DEATH_TEST
+#ifndef NDEBUG
+  EXPECT_DEATH(APFloat::getZero(APFloat::Float8E8M0FNU(), false),
+               "This floating point format does not support Zero");
+  EXPECT_DEATH(APFloat::getZero(APFloat::Float8E8M0FNU(), true),
+               "This floating point format does not support Zero");
+#endif
+#endif
+}
+
+TEST(APFloatTest, Float8E8M0FNUGetSignedValues) {
+#ifdef GTEST_HAS_DEATH_TEST
+#ifndef NDEBUG
+  EXPECT_DEATH(APFloat(APFloat::Float8E8M0FNU(), "-64"),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat(APFloat::Float8E8M0FNU(), "-0x1.0p128"),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat(APFloat::Float8E8M0FNU(), "-inf"),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat::getNaN(APFloat::Float8E8M0FNU(), true),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat::getInf(APFloat::Float8E8M0FNU(), true),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat::getSmallest(APFloat::Float8E8M0FNU(), true),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat::getSmallestNormalized(APFloat::Float8E8M0FNU(), true),
+               "This floating point format does not support signed values");
+  EXPECT_DEATH(APFloat::getLargest(APFloat::Float8E8M0FNU(), true),
+               "This floating point format does not support signed values");
+  APFloat x = APFloat(APFloat::Float8E8M0FNU(), "4");
+  APFloat y = APFloat(APFloat::Float8E8M0FNU(), "8");
+  EXPECT_DEATH(x.subtract(y, APFloat::rmNearestTiesToEven),
+               "This floating point format does not support signed values");
+#endif
+#endif
+}
+
+TEST(APFloatTest, Float8E8M0FNUGetInf) {
+  // The E8M0 format does not support infinity and the
+  // all ones representation is treated as NaN.
+  APFloat t = APFloat::getInf(APFloat::Float8E8M0FNU());
+  EXPECT_TRUE(t.isNaN());
+  EXPECT_FALSE(t.isInfinity());
+}
+
+TEST(APFloatTest, Float8E8M0FNUFromString) {
+  // Exactly representable
+  EXPECT_EQ(64, APFloat(APFloat::Float8E8M0FNU(), "64").convertToDouble());
+  // Overflow to NaN
+  EXPECT_TRUE(APFloat(APFloat::Float8E8M0FNU(), "0x1.0p128").isNaN());
+  // Inf converted to NaN
+  EXPECT_TRUE(APFloat(APFloat::Float8E8M0FNU(), "inf").isNaN());
+  // NaN converted to NaN
+  EXPECT_TRUE(APFloat(APFloat::Float8E8M0FNU(), "nan").isNaN());
+}
+
+TEST(APFloatTest, Float8E8M0FNUDivideByZero) {
+  APFloat x(APFloat::Float8E8M0FNU(), "1");
+  APFloat zero(APFloat::Float8E8M0FNU(), "0");
+  x.divide(zero, APFloat::rmNearestTiesToEven);
+
+  // Zero is represented as the smallest normalized value
+  // in this format i.e 2^-127.
+  // This tests the fix in convertFromDecimalString() function.
+  EXPECT_EQ(0x1.0p-127, zero.convertToDouble());
+
+  // [1 / (2^-127)] = 2^127
+  EXPECT_EQ(0x1.0p127, x.convertToDouble());
+}
+
+TEST(APFloatTest, Float8E8M0FNUGetExactLog2) {
+  const fltSemantics &Semantics = APFloat::Float8E8M0FNU();
+  APFloat One(Semantics, "1.0");
+  EXPECT_EQ(0, One.getExactLog2());
+
+  // In the Float8E8M0FNU format, 3 is rounded-up to 4.
+  // So, we expect 2 as the result.
+  EXPECT_EQ(2, APFloat(Semantics, "3.0").getExactLog2());
+  EXPECT_EQ(2, APFloat(Semantics, "3.0").getExactLog2Abs());
+
+  // In the Float8E8M0FNU format, 5 is rounded-down to 4.
+  // So, we expect 2 as the result.
+  EXPECT_EQ(2, APFloat(Semantics, "5.0").getExactLog2());
+  EXPECT_EQ(2, APFloat(Semantics, "5.0").getExactLog2Abs());
+
+  // Exact power-of-two value.
+  EXPECT_EQ(3, APFloat(Semantics, "8.0").getExactLog2());
+  EXPECT_EQ(3, APFloat(Semantics, "8.0").getExactLog2Abs());
+
+  // Negative exponent value.
+  EXPECT_EQ(-2, APFloat(Semantics, "0.25").getExactLog2());
+  EXPECT_EQ(-2, APFloat(Semantics, "0.25").getExactLog2Abs());
+
+  int MinExp = APFloat::semanticsMinExponent(Semantics);
+  int MaxExp = APFloat::semanticsMaxExponent(Semantics);
+  int Precision = APFloat::semanticsPrecision(Semantics);
+
+  // Values below the minExp getting capped to minExp.
+  EXPECT_EQ(-127,
+            scalbn(One, MinExp - Precision - 1, APFloat::rmNearestTiesToEven)
+                .getExactLog2());
+  EXPECT_EQ(-127, scalbn(One, MinExp - Precision, APFloat::rmNearestTiesToEven)
+                      .getExactLog2());
+
+  // Values above the maxExp overflow to NaN, and getExactLog2() returns
+  // INT_MIN for these cases.
+  EXPECT_EQ(
+      INT_MIN,
+      scalbn(One, MaxExp + 1, APFloat::rmNearestTiesToEven).getExactLog2());
+
+  // This format can represent [minExp, maxExp].
+  // So, the result is the same as the 'Exp' of the scalbn.
+  for (int i = MinExp - Precision + 1; i <= MaxExp; ++i) {
+    EXPECT_EQ(i, scalbn(One, i, APFloat::rmNearestTiesToEven).getExactLog2());
+  }
+}
+
+TEST(APFloatTest, Float8E8M0FNUSmallest) {
+  APFloat test(APFloat::getSmallest(APFloat::Float8E8M0FNU()));
+  EXPECT_EQ(0x1.0p-127, test.convertToDouble());
+
+  // For E8M0 format, there are no denorms.
+  // So, getSmallest is equal to isSmallestNormalized().
+  EXPECT_TRUE(test.isSmallestNormalized());
+  EXPECT_EQ(fcPosNormal, test.classify());
+
+  test = APFloat::getAllOnesValue(APFloat::Float8E8M0FNU());
+  EXPECT_FALSE(test.isSmallestNormalized());
+  EXPECT_TRUE(test.isNaN());
+}
+
+TEST(APFloatTest, Float8E8M0FNUNext) {
+  APFloat test(APFloat::getSmallest(APFloat::Float8E8M0FNU()));
+  // Increment of 1 should reach 2^-126
+  EXPECT_EQ(APFloat::opOK, test.next(false));
+  EXPECT_FALSE(test.isSmallestNormalized());
+  EXPECT_EQ(0x1.0p-126, test.convertToDouble());
+
+  // Decrement of 1, again, should reach 2^-127
+  // i.e. smallest normalized
+  EXPECT_EQ(APFloat::opOK, test.next(true));
+  EXPECT_TRUE(test.isSmallestNormalized());
+
+  // Decrement again, but gets capped at the smallest normalized
+  EXPECT_EQ(APFloat::opOK, test.next(true));
+  EXPECT_TRUE(test.isSmallestNormalized());
+}
+
+TEST(APFloatTest, Float8E8M0FNUFMA) {
+  APFloat f1(APFloat::Float8E8M0FNU(), "4.0");
+  APFloat f2(APFloat::Float8E8M0FNU(), "2.0");
+  APFloat f3(APFloat::Float8E8M0FNU(), "8.0");
+
+  // Exact value: 4*2 + 8 = 16.
+  f1.fusedMultiplyAdd(f2, f3, APFloat::rmNearestTiesToEven);
+  EXPECT_EQ(16.0, f1.convertToDouble());
+
+  // 4*2 + 4 = 12 but it gets rounded-up to 16.
+  f1 = APFloat(APFloat::Float8E8M0FNU(), "4.0");
+  f1.fusedMultiplyAdd(f2, f1, APFloat::rmNearestTiesToEven);
+  EXPECT_EQ(16.0, f1.convertToDouble());
+
+  // 4*2 + 2 = 10 but it gets rounded-down to 8.
+  f1 = APFloat(APFloat::Float8E8M0FNU(), "4.0");
+  f1.fusedMultiplyAdd(f2, f2, APFloat::rmNearestTiesToEven);
+  EXPECT_EQ(8.0, f1.convertToDouble());
+
+  // All of them using the same value.
+  f1 = APFloat(APFloat::Float8E8M0FNU(), "1.0");
+  f1.fusedMultiplyAdd(f1, f1, APFloat::rmNearestTiesToEven);
+  EXPECT_EQ(2.0, f1.convertToDouble());
+}
+
+TEST(APFloatTest, ConvertDoubleToE8M0FNU) {
+  bool losesInfo;
+  APFloat test(APFloat::IEEEdouble(), "1.0");
+  APFloat::opStatus status = test.convert(
+      APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven, &losesInfo);
+  EXPECT_EQ(1.0, test.convertToDouble());
+  EXPECT_FALSE(losesInfo);
+  EXPECT_EQ(status, APFloat::opOK);
+
+  // For E8M0, zero encoding is represented as the smallest normalized value.
+  test = APFloat(APFloat::IEEEdouble(), "0.0");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_TRUE(test.isSmallestNormalized());
+  EXPECT_EQ(0x1.0p-127, test.convertToDouble());
+  EXPECT_FALSE(losesInfo);
+  EXPECT_EQ(status, APFloat::opOK);
+
+  // Test that the conversion of a power-of-two value is precise.
+  test = APFloat(APFloat::IEEEdouble(), "8.0");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_EQ(8.0f, test.convertToDouble());
+  EXPECT_FALSE(losesInfo);
+  EXPECT_EQ(status, APFloat::opOK);
+
+  // Test to check round-down conversion to power-of-two.
+  // The fractional part of 9 is "001" (i.e. 1.125x2^3=9).
+  test = APFloat(APFloat::IEEEdouble(), "9.0");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_EQ(8.0f, test.convertToDouble());
+  EXPECT_TRUE(losesInfo);
+  EXPECT_EQ(status, APFloat::opInexact);
+
+  // Test to check round-up conversion to power-of-two.
+  // The fractional part of 13 is "101" (i.e. 1.625x2^3=13).
+  test = APFloat(APFloat::IEEEdouble(), "13.0");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_EQ(16.0f, test.convertToDouble());
+  EXPECT_TRUE(losesInfo);
+  EXPECT_EQ(status, APFloat::opInexact);
+
+  // Test to check round-up conversion to power-of-two.
+  // The fractional part of 12 is "100" (i.e. 1.5x2^3=12).
+  test = APFloat(APFloat::IEEEdouble(), "12.0");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_EQ(16.0f, test.convertToDouble());
+  EXPECT_TRUE(losesInfo);
+  EXPECT_EQ(status, APFloat::opInexact);
+
+  // Overflow to NaN.
+  test = APFloat(APFloat::IEEEdouble(), "0x1.0p128");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_TRUE(test.isNaN());
+  EXPECT_TRUE(losesInfo);
+  EXPECT_EQ(status, APFloat::opOverflow | APFloat::opInexact);
+
+  // Underflow to smallest normalized value.
+  test = APFloat(APFloat::IEEEdouble(), "0x1.0p-128");
+  status = test.convert(APFloat::Float8E8M0FNU(), APFloat::rmNearestTiesToEven,
+                        &losesInfo);
+  EXPECT_TRUE(test.isSmallestNormalized());
+  EXPECT_TRUE(losesInfo);
+  EXPECT_EQ(status, APFloat::opUnderflow | APFloat::opInexact);
+}
+
 TEST(APFloatTest, Float6E3M2FNFromString) {
   // Exactly representable
   EXPECT_EQ(28, APFloat(APFloat::Float6E3M2FN(), "28").convertToDouble());