diff --git a/libc/utils/MPFRWrapper/MPFRUtils.h b/libc/utils/MPFRWrapper/MPFRUtils.h
--- a/libc/utils/MPFRWrapper/MPFRUtils.h
+++ b/libc/utils/MPFRWrapper/MPFRUtils.h
@@ -48,6 +48,7 @@
   Floor,
   Round,
   Sin,
+  Sqrt,
   Trunc
 };
 
@@ -56,6 +57,9 @@
 template <typename T>
 bool compare(Operation op, T input, T libcOutput, const Tolerance &t);
 
+template <typename T>
+bool compare(Operation op, T input, T libcOutput, double t);
+
 template <typename T> class MPFRMatcher : public testing::Matcher<T> {
   static_assert(__llvm_libc::cpp::IsFloatingPointType<T>::Value,
                 "MPFRMatcher can only be used with floating point values.");
@@ -64,14 +68,21 @@
   T input;
   Tolerance tolerance;
   T matchValue;
+  double ulpTolerance;
+  bool useULP;
 
 public:
   MPFRMatcher(Operation op, T testInput, Tolerance &t)
-      : operation(op), input(testInput), tolerance(t) {}
+      : operation(op), input(testInput), tolerance(t), useULP(false) {}
+  MPFRMatcher(Operation op, T testInput, double ulpTolerance)
+      : operation(op), input(testInput), ulpTolerance(ulpTolerance),
+        useULP(true) {}
 
   bool match(T libcResult) {
     matchValue = libcResult;
-    return internal::compare(operation, input, libcResult, tolerance);
+    return (useULP
+                ? internal::compare(operation, input, libcResult, ulpTolerance)
+                : internal::compare(operation, input, libcResult, tolerance));
   }
 
   void explainError(testutils::StreamWrapper &OS) override;
@@ -79,9 +90,12 @@
 
 } // namespace internal
 
-template <typename T>
+template <typename T, typename U>
 __attribute__((no_sanitize("address")))
-internal::MPFRMatcher<T> getMPFRMatcher(Operation op, T input, Tolerance t) {
+typename cpp::EnableIfType<cpp::IsSameV<U, Tolerance> ||
+                               cpp::IsSameV<U, double>,
+                           internal::MPFRMatcher<T>>
+getMPFRMatcher(Operation op, T input, U t) {
   static_assert(
       __llvm_libc::cpp::IsFloatingPointType<T>::Value,
       "getMPFRMatcher can only be used to match floating point results.");
diff --git a/libc/utils/MPFRWrapper/MPFRUtils.cpp b/libc/utils/MPFRWrapper/MPFRUtils.cpp
--- a/libc/utils/MPFRWrapper/MPFRUtils.cpp
+++ b/libc/utils/MPFRWrapper/MPFRUtils.cpp
@@ -119,6 +119,9 @@
     case Operation::Sin:
       mpfr_sin(value, mpfrInput.value, MPFR_RNDN);
       break;
+    case Operation::Sqrt:
+      mpfr_sqrt(value, mpfrInput.value, MPFR_RNDN);
+      break;
     case Operation::Trunc:
       mpfr_trunc(value, mpfrInput.value);
       break;
@@ -157,29 +160,87 @@
   // These functions are useful for debugging.
   float asFloat() const { return mpfr_get_flt(value, MPFR_RNDN); }
   double asDouble() const { return mpfr_get_d(value, MPFR_RNDN); }
+  long double asLongDouble() const { return mpfr_get_ld(value, MPFR_RNDN); }
+
   void dump(const char *msg) const { mpfr_printf("%s%.128Rf\n", msg, value); }
+
+  // Return the ULP (units-in-the-last-place) difference between the
+  // stored MPFR and a floating point number.
+  // We define:
+  // ULP(mpfr_value, value) = abs(mpfr_value - value) / eps(value)
+  // ULP < 0.5 will imply that the value is correctly rounded.
+  template <typename T>
+  cpp::EnableIfType<cpp::IsFloatingPointType<T>::Value, double> ulp(T input) {
+    fputil::FPBits<T> bits(input);
+    MPFRNumber mpfrInput(input);
+
+    // abs(value - input)
+    mpfr_sub(mpfrInput.value, value, mpfrInput.value, MPFR_RNDN);
+    mpfr_abs(mpfrInput.value, mpfrInput.value, MPFR_RNDN);
+
+    // get eps(input)
+    int epsExponent =
+        bits.getExponent() - __llvm_libc::fputil::MantissaWidth<T>::value;
+    if (bits.exponent == 0) {
+      // correcting denormal exponent
+      ++epsExponent;
+    }
+
+    // Since eps(value) is of the form 2^e, instead of dividing such number,
+    // we multiply by its inverse 2^{-e}.
+    mpfr_mul_2si(mpfrInput.value, mpfrInput.value, -epsExponent, MPFR_RNDN);
+
+    return mpfrInput.asDouble();
+  }
 };
 
 namespace internal {
 
+template <typename T> T toFloatingPoint(MPFRNumber mpfrInput);
+
+template <> float toFloatingPoint<float>(MPFRNumber mpfrInput) {
+  return mpfrInput.asFloat();
+}
+
+template <> double toFloatingPoint<double>(MPFRNumber mpfrInput) {
+  return mpfrInput.asDouble();
+}
+
+template <> long double toFloatingPoint<long double>(MPFRNumber mpfrInput) {
+  return mpfrInput.asLongDouble();
+}
+
 template <typename T>
 void MPFRMatcher<T>::explainError(testutils::StreamWrapper &OS) {
   MPFRNumber mpfrResult(operation, input);
   MPFRNumber mpfrInput(input);
   MPFRNumber mpfrMatchValue(matchValue);
-  MPFRNumber mpfrToleranceValue(matchValue, tolerance);
   FPBits<T> inputBits(input);
   FPBits<T> matchBits(matchValue);
+  FPBits<T> mpfrResultBits(toFloatingPoint<T>(mpfrResult));
   // TODO: Call to llvm::utohexstr implicitly converts __uint128_t values to
   // uint64_t values. This can be fixed using a custom wrapper for
   // llvm::utohexstr to handle __uint128_t values correctly.
   OS << "Match value not within tolerance value of MPFR result:\n"
      << "  Input decimal: " << mpfrInput.str() << '\n'
-     << "     Input bits: 0x" << llvm::utohexstr(inputBits.bitsAsUInt()) << '\n'
+     << "     Input bits: ";
+  __llvm_libc::testing::describeValue(OS, input);
+  OS << '\n'
      << "  Match decimal: " << mpfrMatchValue.str() << '\n'
-     << "     Match bits: 0x" << llvm::utohexstr(matchBits.bitsAsUInt()) << '\n'
+     << "     Match bits: ";
+  __llvm_libc::testing::describeValue(OS, matchValue);
+  OS << '\n'
      << "    MPFR result: " << mpfrResult.str() << '\n'
-     << "Tolerance value: " << mpfrToleranceValue.str() << '\n';
+     << "   MPFR rounded: ";
+  __llvm_libc::testing::describeValue(OS, toFloatingPoint<T>(mpfrResult));
+  OS << '\n';
+  if (useULP) {
+    OS << "     ULP errors: " << std::to_string(mpfrResult.ulp(matchValue))
+       << '\n';
+  } else {
+    MPFRNumber mpfrToleranceValue = MPFRNumber(matchValue, tolerance);
+    OS << "Tolerance value: " << mpfrToleranceValue.str() << '\n';
+  }
 }
 
 template void MPFRMatcher<float>::explainError(testutils::StreamWrapper &);
@@ -201,6 +262,16 @@
 template bool compare<long double>(Operation, long double, long double,
                                    const Tolerance &);
 
+template <typename T>
+bool compare(Operation op, T input, T libcResult, double ulpError) {
+  MPFRNumber mpfrResult(op, input);
+  return mpfrResult.ulp(libcResult) <= ulpError;
+}
+
+template bool compare<float>(Operation, float, float, double);
+template bool compare<double>(Operation, double, double, double);
+template bool compare<long double>(Operation, long double, long double, double);
+
 } // namespace internal
 
 } // namespace mpfr
diff --git a/libc/utils/UnitTest/Test.h b/libc/utils/UnitTest/Test.h
--- a/libc/utils/UnitTest/Test.h
+++ b/libc/utils/UnitTest/Test.h
@@ -36,6 +36,9 @@
   Cond_GE,
 };
 
+template <typename ValType>
+void describeValue(testutils::StreamWrapper &OS, ValType value);
+
 namespace internal {
 
 template <typename ValType>
diff --git a/libc/utils/UnitTest/Test.cpp b/libc/utils/UnitTest/Test.cpp
--- a/libc/utils/UnitTest/Test.cpp
+++ b/libc/utils/UnitTest/Test.cpp
@@ -181,6 +181,16 @@
 
 } // namespace internal
 
+template <typename ValType>
+void describeValue(testutils::StreamWrapper &OS, ValType value) {
+  OS << internal::describeValue<ValType>(value);
+}
+
+template void describeValue<float>(testutils::StreamWrapper &OS, float value);
+template void describeValue<double>(testutils::StreamWrapper &OS, double value);
+template void describeValue<long double>(testutils::StreamWrapper &OS,
+                                         long double value);
+
 Test *Test::Start = nullptr;
 Test *Test::End = nullptr;