diff --git a/libc/utils/FPUtil/CMakeLists.txt b/libc/utils/FPUtil/CMakeLists.txt
--- a/libc/utils/FPUtil/CMakeLists.txt
+++ b/libc/utils/FPUtil/CMakeLists.txt
@@ -17,6 +17,7 @@
     BasicOperations.h
     ManipulationFunctions.h
     NearestIntegerOperations.h
+    NormalFloat.h
   DEPENDS
     libc.utils.CPP.standalone_cpp
 )
diff --git a/libc/utils/FPUtil/ManipulationFunctions.h b/libc/utils/FPUtil/ManipulationFunctions.h
--- a/libc/utils/FPUtil/ManipulationFunctions.h
+++ b/libc/utils/FPUtil/ManipulationFunctions.h
@@ -6,37 +6,20 @@
 //
 //===----------------------------------------------------------------------===//
 
+#ifndef LLVM_LIBC_UTILS_FPUTIL_MANIPULATION_FUNCTIONS_H
+#define LLVM_LIBC_UTILS_FPUTIL_MANIPULATION_FUNCTIONS_H
+
 #include "FPBits.h"
 #include "NearestIntegerOperations.h"
+#include "NormalFloat.h"
 
 #include "utils/CPP/TypeTraits.h"
 
-#ifndef LLVM_LIBC_UTILS_FPUTIL_MANIPULATION_FUNCTIONS_H
-#define LLVM_LIBC_UTILS_FPUTIL_MANIPULATION_FUNCTIONS_H
-
 namespace __llvm_libc {
 namespace fputil {
 
-#if defined(__x86_64__) || defined(__i386__)
-template <typename T> struct Standard754Type {
-  static constexpr bool Value =
-      cpp::IsSame<float, cpp::RemoveCVType<T>>::Value ||
-      cpp::IsSame<double, cpp::RemoveCVType<T>>::Value;
-};
-#else
-template <typename T> struct Standard754Type {
-  static constexpr bool Value = cpp::IsFloatingPointType<T>::Value;
-};
-#endif
-
-template <typename T> static inline T frexp_impl(FPBits<T> &bits, int &exp) {
-  exp = bits.getExponent() + 1;
-  static constexpr uint16_t resultExponent = FPBits<T>::exponentBias - 1;
-  bits.exponent = resultExponent;
-  return bits;
-}
-
-template <typename T, cpp::EnableIfType<Standard754Type<T>::Value, int> = 0>
+template <typename T,
+          cpp::EnableIfType<cpp::IsFloatingPointType<T>::Value, int> = 0>
 static inline T frexp(T x, int &exp) {
   FPBits<T> bits(x);
   if (bits.isInfOrNaN())
@@ -46,42 +29,12 @@
     return x;
   }
 
-  return frexp_impl(bits, exp);
+  NormalFloat<T> normal(bits);
+  exp = normal.exponent + 1;
+  normal.exponent = -1;
+  return normal;
 }
 
-#if defined(__x86_64__) || defined(__i386__)
-static inline long double frexp(long double x, int &exp) {
-  FPBits<long double> bits(x);
-  if (bits.isInfOrNaN())
-    return x;
-  if (bits.isZero()) {
-    exp = 0;
-    return x;
-  }
-
-  if (bits.exponent != 0 || bits.implicitBit == 1)
-    return frexp_impl(bits, exp);
-
-  exp = bits.getExponent();
-  int shiftCount = 0;
-  uint64_t fullMantissa = *reinterpret_cast<uint64_t *>(&bits);
-  static constexpr uint64_t msBitMask = uint64_t(1) << 63;
-  for (; (fullMantissa & msBitMask) == uint64_t(0);
-       fullMantissa <<= 1, ++shiftCount) {
-    // This for loop will terminate as fullMantissa is != 0. If it were 0,
-    // then x will be NaN and handled before control reaches here.
-    // When the loop terminates, fullMantissa will represent the full mantissa
-    // of a normal long double value. That is, the implicit bit has the value
-    // of 1.
-  }
-
-  exp = exp - shiftCount + 1;
-  *reinterpret_cast<uint64_t *>(&bits) = fullMantissa;
-  bits.exponent = FPBits<long double>::exponentBias - 1;
-  return bits;
-}
-#endif
-
 template <typename T,
           cpp::EnableIfType<cpp::IsFloatingPointType<T>::Value, int> = 0>
 static inline T modf(T x, T &iptr) {
@@ -112,11 +65,8 @@
   return xbits;
 }
 
-template <typename T> static inline T logb_impl(const FPBits<T> &bits) {
-  return bits.getExponent();
-}
-
-template <typename T, cpp::EnableIfType<Standard754Type<T>::Value, int> = 0>
+template <typename T,
+          cpp::EnableIfType<cpp::IsFloatingPointType<T>::Value, int> = 0>
 static inline T logb(T x) {
   FPBits<T> bits(x);
   if (bits.isZero()) {
@@ -130,42 +80,9 @@
     return FPBits<T>::inf();
   }
 
-  return logb_impl(bits);
-}
-
-#if defined(__x86_64__) || defined(__i386__)
-static inline long double logb(long double x) {
-  FPBits<long double> bits(x);
-  if (bits.isZero()) {
-    // TODO(Floating point exception): Raise div-by-zero exception.
-    // TODO(errno): POSIX requires setting errno to ERANGE.
-    return FPBits<long double>::negInf();
-  } else if (bits.isNaN()) {
-    return x;
-  } else if (bits.isInf()) {
-    // Return positive infinity.
-    return FPBits<long double>::inf();
-  }
-
-  if (bits.exponent != 0 || bits.implicitBit == 1)
-    return logb_impl(bits);
-
-  int exp = bits.getExponent();
-  int shiftCount = 0;
-  uint64_t fullMantissa = *reinterpret_cast<uint64_t *>(&bits);
-  static constexpr uint64_t msBitMask = uint64_t(1) << 63;
-  for (; (fullMantissa & msBitMask) == uint64_t(0);
-       fullMantissa <<= 1, ++shiftCount) {
-    // This for loop will terminate as fullMantissa is != 0. If it were 0,
-    // then x will be NaN and handled before control reaches here.
-    // When the loop terminates, fullMantissa will represent the full mantissa
-    // of a normal long double value. That is, the implicit bit has the value
-    // of 1.
-  }
-
-  return exp - shiftCount;
+  NormalFloat<T> normal(bits);
+  return normal.exponent;
 }
-#endif
 
 } // namespace fputil
 } // namespace __llvm_libc
diff --git a/libc/utils/FPUtil/NormalFloat.h b/libc/utils/FPUtil/NormalFloat.h
new file mode 100644
--- /dev/null
+++ b/libc/utils/FPUtil/NormalFloat.h
@@ -0,0 +1,231 @@
+//===-- A class to store a normalized floating point number -----*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_UTILS_FPUTIL_NORMAL_FLOAT_H
+#define LLVM_LIBC_UTILS_FPUTIL_NORMAL_FLOAT_H
+
+#include "FPBits.h"
+
+#include "utils/CPP/TypeTraits.h"
+
+#include <stdint.h>
+
+namespace __llvm_libc {
+namespace fputil {
+
+// A class which stores the normalized form of a floating point value.
+// The special IEEE-754 bits patterns of Zero, infinity and NaNs are
+// are not handled by this class.
+//
+// A normalized floating point number is of this form:
+//    (-1)*sign * 2^exponent * <mantissa>
+// where <mantissa> is of the form 1.<...>.
+template <typename T> struct NormalFloat {
+  static_assert(
+      cpp::IsFloatingPointType<T>::Value,
+      "NormalFloat template parameter has to be a floating point type.");
+
+  using UIntType = typename FPBits<T>::UIntType;
+  static constexpr UIntType one = (UIntType(1) << MantissaWidth<T>::value);
+
+  // Unbiased exponent value.
+  int32_t exponent;
+
+  UIntType mantissa;
+  // We want |UIntType| to have atleast one bit more than the actual mantissa
+  // bit width to accommodate the implicit 1 value.
+  static_assert(sizeof(UIntType) * 8 >= MantissaWidth<T>::value + 1,
+                "Bad type for mantissa in NormalFloat.");
+
+  bool sign;
+
+  NormalFloat(int32_t e, UIntType m, bool s)
+      : exponent(e), mantissa(m), sign(s) {
+    if (mantissa >= (one << 1) || (mantissa & one))
+      return;
+
+    for (unsigned i = 0;
+         (one & mantissa) == 0 && (i <= MantissaWidth<T>::value); ++i) {
+      mantissa <<= 1;
+      --exponent;
+    }
+  }
+
+  explicit NormalFloat(T x) { initFromBits(FPBits<T>(x)); }
+
+  explicit NormalFloat(FPBits<T> bits) { initFromBits(bits); }
+
+  // Compares this normalized number with another normalized number.
+  // Returns -1 is this number is less than |other|, 0 if this number is equal
+  // to |other|, and 1 if this number is greater than |other|.
+  int cmp(const NormalFloat<T> &other) const {
+    if (sign != other.sign)
+      return sign ? -1 : 1;
+
+    if (exponent > other.exponent) {
+      return sign ? -1 : 1;
+    } else if (exponent == other.exponent) {
+      if (mantissa > other.mantissa)
+        return sign ? -1 : 1;
+      else if (mantissa == other.mantissa)
+        return 0;
+      else
+        return sign ? 1 : -1;
+    } else {
+      return sign ? 1 : -1;
+    }
+  }
+
+  // Returns a new normalized floating point number which is equal in value
+  // to this number multiplied by 2^e. That is:
+  //     new = this *  2^e
+  NormalFloat<T> mul2(int e) const {
+    NormalFloat<T> result = *this;
+    result.exponent += e;
+    return result;
+  }
+
+  operator T() const {
+    int biasedExponent = exponent + FPBits<T>::exponentBias;
+    // Max exponent is of the form 0xFF...E. That is why -2 and not -1.
+    constexpr int maxExponentValue = (1 << ExponentWidth<T>::value) - 2;
+    if (biasedExponent > maxExponentValue) {
+      // TODO: Should infinity with the correct sign be returned?
+      return FPBits<T>::buildNaN(1);
+    }
+
+    FPBits<T> result(T(0.0));
+
+    constexpr int subnormalExponent = -FPBits<T>::exponentBias + 1;
+    if (exponent < subnormalExponent) {
+      unsigned shift = subnormalExponent - exponent;
+      if (shift <= MantissaWidth<T>::value) {
+        // Generate a subnormal number. Might lead to loss of precision.
+        result.exponent = 0;
+        result.mantissa = mantissa >> shift;
+        result.sign = sign;
+        return result;
+      } else {
+        // TODO: Should zero with the correct sign be returned?
+        return FPBits<T>::buildNaN(1);
+      }
+    }
+
+    result.exponent = exponent + FPBits<T>::exponentBias;
+    result.mantissa = mantissa;
+    result.sign = sign;
+    return result;
+  }
+
+private:
+  void initFromBits(FPBits<T> bits) {
+    sign = bits.sign;
+
+    if (bits.isInfOrNaN() || bits.isZero()) {
+      // Ignore special bit patterns. Implementations deal with them separately
+      // anyway so this should not be a problem.
+      exponent = 0;
+      mantissa = 0;
+      return;
+    }
+
+    // Normalize subnormal numbers.
+    if (bits.exponent == 0) {
+      unsigned shift = evaluateNormalizationShift(bits.mantissa);
+      mantissa = UIntType(bits.mantissa) << shift;
+      exponent = 1 - FPBits<T>::exponentBias - shift;
+      ;
+    } else {
+      exponent = bits.exponent - FPBits<T>::exponentBias;
+      mantissa = one | bits.mantissa;
+    }
+  }
+
+  unsigned evaluateNormalizationShift(UIntType m) {
+    unsigned shift = 0;
+    for (; (one & m) == 0 && (shift < MantissaWidth<T>::value);
+         m <<= 1, ++shift)
+      ;
+    return shift;
+  }
+};
+
+#if defined(__x86_64__) || defined(__i386__)
+template <>
+inline void NormalFloat<long double>::initFromBits(FPBits<long double> bits) {
+  sign = bits.sign;
+
+  if (bits.isInfOrNaN() || bits.isZero()) {
+    // Ignore special bit patterns. Implementations deal with them separately
+    // anyway so this should not be a problem.
+    exponent = 0;
+    mantissa = 0;
+    return;
+  }
+
+  if (bits.exponent == 0) {
+    if (bits.implicitBit == 0) {
+      // Since we ignore zero value, the mantissa in this case is non-zero.
+      int normalizationShift = evaluateNormalizationShift(bits.mantissa);
+      exponent = -16382 - normalizationShift;
+      mantissa = (bits.mantissa << normalizationShift);
+    } else {
+      exponent = -16382;
+      mantissa = one | bits.mantissa;
+    }
+  } else {
+    if (bits.implicitBit == 0) {
+      // Invalid number so just store 0 similar to a NaN.
+      exponent = 0;
+      mantissa = 0;
+    } else {
+      exponent = bits.exponent - 16383;
+      mantissa = one | bits.mantissa;
+    }
+  }
+}
+
+template <> inline NormalFloat<long double>::operator long double() const {
+  int biasedExponent = exponent + FPBits<long double>::exponentBias;
+  // Max exponent is of the form 0xFF...E. That is why -2 and not -1.
+  constexpr int maxExponentValue = (1 << ExponentWidth<long double>::value) - 2;
+  if (biasedExponent > maxExponentValue) {
+    // TODO: Should infinity with the correct sign be returned?
+    return FPBits<long double>::buildNaN(1);
+  }
+
+  FPBits<long double> result(0.0l);
+
+  constexpr int subnormalExponent = -FPBits<long double>::exponentBias + 1;
+  if (exponent < subnormalExponent) {
+    unsigned shift = subnormalExponent - exponent;
+    if (shift <= MantissaWidth<long double>::value) {
+      // Generate a subnormal number. Might lead to loss of precision.
+      result.exponent = 0;
+      result.mantissa = mantissa >> shift;
+      result.implicitBit = 0;
+      result.sign = sign;
+      return result;
+    } else {
+      // TODO: Should zero with the correct sign be returned?
+      return FPBits<long double>::buildNaN(1);
+    }
+  }
+
+  result.exponent = biasedExponent;
+  result.mantissa = mantissa;
+  result.implicitBit = 1;
+  result.sign = sign;
+  return result;
+}
+#endif
+
+} // namespace fputil
+} // namespace __llvm_libc
+
+#endif // LLVM_LIBC_UTILS_FPUTIL_NORMAL_FLOAT_H