diff --git a/mlir/include/mlir/Analysis/Presburger/MPInt.h b/mlir/include/mlir/Analysis/Presburger/MPInt.h
new file mode 100644
--- /dev/null
+++ b/mlir/include/mlir/Analysis/Presburger/MPInt.h
@@ -0,0 +1,580 @@
+//===- MPInt.h - MLIR MPInt Class -------------------------------*- 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
+//
+//===----------------------------------------------------------------------===//
+//
+// This is a simple class to represent arbitrary precision signed integers.
+// Unlike APInt, one does not have to specify a fixed maximum size, and the
+// integer can take on any arbitrary values. This is optimized for small-values
+// by providing fast-paths for the cases when the value stored fits in 64-bits.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef MLIR_ANALYSIS_PRESBURGER_MPINT_H
+#define MLIR_ANALYSIS_PRESBURGER_MPINT_H
+
+#include "mlir/Analysis/Presburger/SlowMPInt.h"
+#include "mlir/Support/MathExtras.h"
+#include "llvm/Support/raw_ostream.h"
+
+namespace mlir {
+namespace presburger {
+
+namespace detail {
+// If builtin intrinsics for overflow-checked arithmetic are available,
+// use them. Otherwise, call through to LLVM's overflow-checked arithmetic
+// functionality. Those functions also have such macro-gated uses of intrinsics,
+// however they are not always_inlined, which is important for us to achieve
+// high-performance; calling the functions directly would result in a slowdown
+// of 1.15x.
+__attribute__((always_inline)) inline bool addOverflow(int64_t x, int64_t y,
+                                                       int64_t &result) {
+#if __has_builtin(__builtin_add_overflow)
+  return __builtin_add_overflow(x, y, &result);
+#else
+  return llvm::AddOverflow(x, y, result);
+#endif
+}
+__attribute__((always_inline)) inline bool subOverflow(int64_t x, int64_t y,
+                                                       int64_t &result) {
+#if __has_builtin(__builtin_sub_overflow)
+  return __builtin_sub_overflow(x, y, &result);
+#else
+  return llvm::subOverflow(x, y, result);
+#endif
+}
+__attribute__((always_inline)) inline bool mulOverflow(int64_t x, int64_t y,
+                                                       int64_t &result) {
+#if __has_builtin(__builtin_mul_overflow)
+  return __builtin_mul_overflow(x, y, &result);
+#else
+  return llvm::MulOverflow(x, y, result);
+#endif
+}
+} // namespace detail
+
+/// This class provides support for multi-precision arithmetic.
+///
+/// Unlike APInt, this extends the precision as necessary to prevent overflows
+/// and supports operations between objects with differing internal precisions.
+///
+/// This is optimized for small-values by providing fast-paths for the cases
+/// when the value stored fits in 64-bits. We annotate all fastpaths by using
+/// the LLVM_LIKELY/LLVM_UNLIKELY annotations. Removing these would result in
+/// a 1.2x performance slowdown.
+///
+/// We always_inline all operations; removing these results in a 1.5x
+/// performance slowdown.
+///
+/// When holdsSlow is true, a SlowMPInt is held in the union. If it is false,
+/// the int64_t is held. Using std::variant instead would significantly impact
+/// performance.
+class MPInt {
+private:
+  union {
+    int64_t val64;
+    detail::SlowMPInt valSlow;
+  };
+  unsigned holdsSlow;
+
+  __attribute__((always_inline)) void init64(int64_t o) {
+    if (LLVM_UNLIKELY(isLarge()))
+      valSlow.detail::SlowMPInt::~SlowMPInt();
+    val64 = o;
+    holdsSlow = false;
+  }
+  __attribute__((always_inline)) void initAP(const detail::SlowMPInt &o) {
+    if (LLVM_LIKELY(isSmall())) {
+      // The data in memory could be in an arbitrary state, not necessarily
+      // corresponding to any valid state of valSlow; we cannot call any member
+      // functions, e.g. the assignment operator on it, as they may access the
+      // invalid internal state. We instead construct a new object using
+      // placement new.
+      new (&valSlow) detail::SlowMPInt(o);
+    } else {
+      // In this case, we need to use the assignment operator, because if we use
+      // placement-new as above we would lose track of allocated memory
+      // and leak it.
+      valSlow = o;
+    }
+    holdsSlow = true;
+  }
+
+  __attribute__((always_inline)) explicit MPInt(const detail::SlowMPInt &val)
+      : valSlow(val), holdsSlow(true) {}
+  __attribute__((always_inline)) bool isSmall() const { return !holdsSlow; }
+  __attribute__((always_inline)) bool isLarge() const { return holdsSlow; }
+  __attribute__((always_inline)) int64_t get64() const {
+    assert(isSmall());
+    return val64;
+  }
+  __attribute__((always_inline)) int64_t &get64() {
+    assert(isSmall());
+    return val64;
+  }
+  __attribute__((always_inline)) const detail::SlowMPInt &getAP() const {
+    assert(isLarge());
+    return valSlow;
+  }
+  __attribute__((always_inline)) detail::SlowMPInt &getAP() {
+    assert(isLarge());
+    return valSlow;
+  }
+  explicit operator detail::SlowMPInt() const {
+    if (isSmall())
+      return detail::SlowMPInt(get64());
+    return getAP();
+  }
+  __attribute__((always_inline)) detail::SlowMPInt getAsAP() const {
+    return detail::SlowMPInt(*this);
+  }
+
+public:
+  __attribute__((always_inline)) explicit MPInt(int64_t val)
+      : val64(val), holdsSlow(false) {}
+  __attribute__((always_inline)) MPInt() : MPInt(0) {}
+  __attribute__((always_inline)) ~MPInt() {
+    if (LLVM_UNLIKELY(isLarge()))
+      valSlow.detail::SlowMPInt::~SlowMPInt();
+  }
+  __attribute__((always_inline)) MPInt(const MPInt &o)
+      : val64(o.val64), holdsSlow(false) {
+    if (LLVM_UNLIKELY(o.isLarge()))
+      initAP(o.valSlow);
+  }
+  __attribute__((always_inline)) MPInt &operator=(const MPInt &o) {
+    if (LLVM_LIKELY(o.isSmall())) {
+      init64(o.val64);
+      return *this;
+    }
+    initAP(o.valSlow);
+    return *this;
+  }
+  __attribute__((always_inline)) MPInt &operator=(int x) {
+    init64(x);
+    return *this;
+  }
+  __attribute__((always_inline)) explicit operator int64_t() const {
+    if (isSmall())
+      return get64();
+    return static_cast<int64_t>(getAP());
+  }
+
+  bool operator==(const MPInt &o) const;
+  bool operator!=(const MPInt &o) const;
+  bool operator>(const MPInt &o) const;
+  bool operator<(const MPInt &o) const;
+  bool operator<=(const MPInt &o) const;
+  bool operator>=(const MPInt &o) const;
+  MPInt operator+(const MPInt &o) const;
+  MPInt operator-(const MPInt &o) const;
+  MPInt operator*(const MPInt &o) const;
+  MPInt operator/(const MPInt &o) const;
+  MPInt operator%(const MPInt &o) const;
+  MPInt &operator+=(const MPInt &o);
+  MPInt &operator-=(const MPInt &o);
+  MPInt &operator*=(const MPInt &o);
+  MPInt &operator/=(const MPInt &o);
+  MPInt &operator%=(const MPInt &o);
+  MPInt operator-() const;
+  MPInt &operator++();
+  MPInt &operator--();
+
+  // Divide by a number that is known to be positive.
+  // This is slightly more efficient because it saves an overflow check.
+  MPInt divByPositive(const MPInt &o) const;
+  MPInt &divByPositiveInPlace(const MPInt &o);
+
+  friend MPInt abs(const MPInt &x);
+  friend MPInt gcdRange(ArrayRef<MPInt> range);
+  friend MPInt ceilDiv(const MPInt &lhs, const MPInt &rhs);
+  friend MPInt floorDiv(const MPInt &lhs, const MPInt &rhs);
+  friend MPInt gcd(const MPInt &a, const MPInt &b);
+  friend MPInt lcm(const MPInt &a, const MPInt &b);
+  friend MPInt mod(const MPInt &lhs, const MPInt &rhs);
+
+  llvm::raw_ostream &print(llvm::raw_ostream &os) const;
+  void dump() const;
+
+  /// ---------------------------------------------------------------------------
+  /// Convenience operator overloads for int64_t.
+  /// ---------------------------------------------------------------------------
+  friend MPInt &operator+=(MPInt &a, int64_t b);
+  friend MPInt &operator-=(MPInt &a, int64_t b);
+  friend MPInt &operator*=(MPInt &a, int64_t b);
+  friend MPInt &operator/=(MPInt &a, int64_t b);
+  friend MPInt &operator%=(MPInt &a, int64_t b);
+
+  friend bool operator==(const MPInt &a, int64_t b);
+  friend bool operator!=(const MPInt &a, int64_t b);
+  friend bool operator>(const MPInt &a, int64_t b);
+  friend bool operator<(const MPInt &a, int64_t b);
+  friend bool operator<=(const MPInt &a, int64_t b);
+  friend bool operator>=(const MPInt &a, int64_t b);
+  friend MPInt operator+(const MPInt &a, int64_t b);
+  friend MPInt operator-(const MPInt &a, int64_t b);
+  friend MPInt operator*(const MPInt &a, int64_t b);
+  friend MPInt operator/(const MPInt &a, int64_t b);
+  friend MPInt operator%(const MPInt &a, int64_t b);
+
+  friend bool operator==(int64_t a, const MPInt &b);
+  friend bool operator!=(int64_t a, const MPInt &b);
+  friend bool operator>(int64_t a, const MPInt &b);
+  friend bool operator<(int64_t a, const MPInt &b);
+  friend bool operator<=(int64_t a, const MPInt &b);
+  friend bool operator>=(int64_t a, const MPInt &b);
+  friend MPInt operator+(int64_t a, const MPInt &b);
+  friend MPInt operator-(int64_t a, const MPInt &b);
+  friend MPInt operator*(int64_t a, const MPInt &b);
+  friend MPInt operator/(int64_t a, const MPInt &b);
+  friend MPInt operator%(int64_t a, const MPInt &b);
+
+  friend llvm::hash_code hash_value(const MPInt &x); // NOLINT
+};
+
+/// This just calls through to the operator int64_t, but it's useful when a
+/// function pointer is required. (Although this is marked inline, it is still
+/// possible to obtain and use a function pointer to this.)
+__attribute__((always_inline)) inline int64_t int64FromMPInt(const MPInt &x) {
+  return int64_t(x);
+}
+
+llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const MPInt &x);
+
+// The RHS is always expected to be positive, and the result
+/// is always non-negative.
+MPInt mod(const MPInt &lhs, const MPInt &rhs);
+
+/// We define the operations here in the header to facilitate inlining.
+
+/// ---------------------------------------------------------------------------
+/// Comparison operators.
+/// ---------------------------------------------------------------------------
+__attribute__((always_inline)) inline bool
+MPInt::operator==(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return get64() == o.get64();
+  return getAsAP() == o.getAsAP();
+}
+__attribute__((always_inline)) inline bool
+MPInt::operator!=(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return get64() != o.get64();
+  return getAsAP() != o.getAsAP();
+}
+__attribute__((always_inline)) inline bool
+MPInt::operator>(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return get64() > o.get64();
+  return getAsAP() > o.getAsAP();
+}
+__attribute__((always_inline)) inline bool
+MPInt::operator<(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return get64() < o.get64();
+  return getAsAP() < o.getAsAP();
+}
+__attribute__((always_inline)) inline bool
+MPInt::operator<=(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return get64() <= o.get64();
+  return getAsAP() <= o.getAsAP();
+}
+__attribute__((always_inline)) inline bool
+MPInt::operator>=(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return get64() >= o.get64();
+  return getAsAP() >= o.getAsAP();
+}
+
+/// ---------------------------------------------------------------------------
+/// Arithmetic operators.
+/// ---------------------------------------------------------------------------
+__attribute__((always_inline)) inline MPInt
+MPInt::operator+(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    MPInt result;
+    bool overflow = detail::addOverflow(get64(), o.get64(), result.get64());
+    if (LLVM_LIKELY(!overflow))
+      return result;
+    return MPInt(getAsAP() + o.getAsAP());
+  }
+  return MPInt(getAsAP() + o.getAsAP());
+}
+__attribute__((always_inline)) inline MPInt
+MPInt::operator-(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    MPInt result;
+    bool overflow = detail::subOverflow(get64(), o.get64(), result.get64());
+    if (LLVM_LIKELY(!overflow))
+      return result;
+    return MPInt(getAsAP() - o.getAsAP());
+  }
+  return MPInt(getAsAP() - o.getAsAP());
+}
+__attribute__((always_inline)) inline MPInt
+MPInt::operator*(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    MPInt result;
+    bool overflow = detail::mulOverflow(get64(), o.get64(), result.get64());
+    if (LLVM_LIKELY(!overflow))
+      return result;
+    return MPInt(getAsAP() * o.getAsAP());
+  }
+  return MPInt(getAsAP() * o.getAsAP());
+}
+
+__attribute__((always_inline)) inline MPInt
+MPInt::divByPositive(const MPInt &o) const {
+  assert(o > 0);
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return MPInt(get64() / o.get64());
+  return MPInt(getAsAP() / o.getAsAP());
+}
+
+__attribute__((always_inline)) inline MPInt
+MPInt::operator/(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    if (LLVM_UNLIKELY(o.get64() == -1))
+      return -*this;
+    return MPInt(get64() / o.get64());
+  }
+  return MPInt(getAsAP() / o.getAsAP());
+}
+
+inline MPInt abs(const MPInt &x) { return MPInt(x >= 0 ? x : -x); }
+inline MPInt ceilDiv(const MPInt &lhs, const MPInt &rhs) {
+  if (LLVM_LIKELY(lhs.isSmall() && rhs.isSmall())) {
+    if (rhs == -1)
+      return -lhs;
+    int64_t x = (rhs.get64() > 0) ? -1 : 1;
+    return MPInt(((lhs.get64() != 0) && (lhs.get64() > 0) == (rhs.get64() > 0))
+                     ? ((lhs.get64() + x) / rhs.get64()) + 1
+                     : -(-lhs.get64() / rhs.get64()));
+  }
+  return MPInt(ceilDiv(lhs.getAsAP(), rhs.getAsAP()));
+}
+inline MPInt floorDiv(const MPInt &lhs, const MPInt &rhs) {
+  if (LLVM_LIKELY(lhs.isSmall() && rhs.isSmall())) {
+    if (rhs == -1)
+      return -lhs;
+    int64_t x = (rhs.get64() < 0) ? 1 : -1;
+    return MPInt(
+        ((lhs.get64() != 0) && ((lhs.get64() < 0) != (rhs.get64() < 0)))
+            ? -((-lhs.get64() + x) / rhs.get64()) - 1
+            : lhs.get64() / rhs.get64());
+  }
+  return MPInt(floorDiv(lhs.getAsAP(), rhs.getAsAP()));
+}
+// The RHS is always expected to be positive, and the result
+/// is always non-negative.
+inline MPInt mod(const MPInt &lhs, const MPInt &rhs) {
+  if (LLVM_LIKELY(lhs.isSmall() && rhs.isSmall()))
+    return MPInt(lhs.get64() % rhs.get64() < 0
+                     ? lhs.get64() % rhs.get64() + rhs.get64()
+                     : lhs.get64() % rhs.get64());
+  return MPInt(mod(lhs.getAsAP(), rhs.getAsAP()));
+}
+
+__attribute__((always_inline)) inline MPInt gcd(const MPInt &a,
+                                                const MPInt &b) {
+  // TODO: fix unsigned/signed overflow issues
+  if (LLVM_LIKELY(a.isSmall() && b.isSmall()))
+    return MPInt(int64_t(llvm::GreatestCommonDivisor64(a.get64(), b.get64())));
+  return MPInt(gcd(a.getAsAP(), b.getAsAP()));
+}
+
+/// Returns the least common multiple of 'a' and 'b'.
+inline MPInt lcm(const MPInt &a, const MPInt &b) {
+  MPInt x = abs(a);
+  MPInt y = abs(b);
+  return (x * y) / gcd(x, y);
+}
+
+/// This operation cannot overflow.
+inline MPInt MPInt::operator%(const MPInt &o) const {
+  if (LLVM_LIKELY(isSmall() && o.isSmall()))
+    return MPInt(get64() % o.get64());
+  return MPInt(getAsAP() % o.getAsAP());
+}
+
+inline MPInt MPInt::operator-() const {
+  if (LLVM_LIKELY(isSmall())) {
+    if (LLVM_LIKELY(get64() != std::numeric_limits<int64_t>::min()))
+      return MPInt(-get64());
+    return MPInt(-getAsAP());
+  }
+  return MPInt(-getAsAP());
+}
+
+/// ---------------------------------------------------------------------------
+/// Assignment operators, preincrement, predecrement.
+/// ---------------------------------------------------------------------------
+__attribute__((always_inline)) inline MPInt &MPInt::operator+=(const MPInt &o) {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    int64_t result = get64();
+    bool overflow = detail::addOverflow(get64(), o.get64(), result);
+    if (LLVM_LIKELY(!overflow)) {
+      get64() = result;
+      return *this;
+    }
+    return *this = MPInt(getAsAP() + o.getAsAP());
+  }
+  return *this = MPInt(getAsAP() + o.getAsAP());
+}
+__attribute__((always_inline)) inline MPInt &MPInt::operator-=(const MPInt &o) {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    int64_t result = get64();
+    bool overflow = detail::subOverflow(get64(), o.get64(), result);
+    if (LLVM_LIKELY(!overflow)) {
+      get64() = result;
+      return *this;
+    }
+    return *this = MPInt(getAsAP() - o.getAsAP());
+  }
+  return *this = MPInt(getAsAP() - o.getAsAP());
+}
+__attribute__((always_inline)) inline MPInt &MPInt::operator*=(const MPInt &o) {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    int64_t result = get64();
+    bool overflow = detail::mulOverflow(get64(), o.get64(), result);
+    if (LLVM_LIKELY(!overflow)) {
+      get64() = result;
+      return *this;
+    }
+    return *this = MPInt(getAsAP() * o.getAsAP());
+  }
+  return *this = MPInt(getAsAP() * o.getAsAP());
+}
+__attribute__((always_inline)) inline MPInt &MPInt::operator/=(const MPInt &o) {
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    if (LLVM_UNLIKELY(o.get64() == -1))
+      return *this = -*this;
+    get64() /= o.get64();
+    return *this;
+  }
+  return *this = MPInt(getAsAP() / o.getAsAP());
+}
+
+__attribute__((always_inline)) inline MPInt &
+MPInt::divByPositiveInPlace(const MPInt &o) {
+  assert(o > 0);
+  if (LLVM_LIKELY(isSmall() && o.isSmall())) {
+    get64() /= o.get64();
+    return *this;
+  }
+  return *this = MPInt(getAsAP() / o.getAsAP());
+}
+
+__attribute__((always_inline)) inline MPInt &MPInt::operator%=(const MPInt &o) {
+  *this = *this % o;
+  return *this;
+}
+__attribute__((always_inline)) inline MPInt &MPInt::operator++() {
+  *this += 1;
+  return *this;
+}
+__attribute__((always_inline)) inline MPInt &MPInt::operator--() {
+  *this -= 1;
+  return *this;
+}
+
+/// ----------------------------------------------------------------------------
+/// Convenience operator overloads for int64_t.
+/// ----------------------------------------------------------------------------
+__attribute__((always_inline)) inline MPInt &operator+=(MPInt &a, int64_t b) {
+  return a = a + b;
+}
+__attribute__((always_inline)) inline MPInt &operator-=(MPInt &a, int64_t b) {
+  return a = a - b;
+}
+__attribute__((always_inline)) inline MPInt &operator*=(MPInt &a, int64_t b) {
+  return a = a * b;
+}
+__attribute__((always_inline)) inline MPInt &operator/=(MPInt &a, int64_t b) {
+  return a = a / b;
+}
+__attribute__((always_inline)) inline MPInt &operator%=(MPInt &a, int64_t b) {
+  return a = a % b;
+}
+inline MPInt operator+(const MPInt &a, int64_t b) { return a + MPInt(b); }
+inline MPInt operator-(const MPInt &a, int64_t b) { return a - MPInt(b); }
+inline MPInt operator*(const MPInt &a, int64_t b) { return a * MPInt(b); }
+inline MPInt operator/(const MPInt &a, int64_t b) { return a / MPInt(b); }
+inline MPInt operator%(const MPInt &a, int64_t b) { return a % MPInt(b); }
+inline MPInt operator+(int64_t a, const MPInt &b) { return MPInt(a) + b; }
+inline MPInt operator-(int64_t a, const MPInt &b) { return MPInt(a) - b; }
+inline MPInt operator*(int64_t a, const MPInt &b) { return MPInt(a) * b; }
+inline MPInt operator/(int64_t a, const MPInt &b) { return MPInt(a) / b; }
+inline MPInt operator%(int64_t a, const MPInt &b) { return MPInt(a) % b; }
+
+/// We provide special implementations of the comparison operators rather than
+/// calling through as above, as this would result in a 1.2x slowdown.
+inline bool operator==(const MPInt &a, int64_t b) {
+  if (LLVM_LIKELY(a.isSmall()))
+    return a.get64() == b;
+  return a.getAP() == b;
+}
+inline bool operator!=(const MPInt &a, int64_t b) {
+  if (LLVM_LIKELY(a.isSmall()))
+    return a.get64() != b;
+  return a.getAP() != b;
+}
+inline bool operator>(const MPInt &a, int64_t b) {
+  if (LLVM_LIKELY(a.isSmall()))
+    return a.get64() > b;
+  return a.getAP() > b;
+}
+inline bool operator<(const MPInt &a, int64_t b) {
+  if (LLVM_LIKELY(a.isSmall()))
+    return a.get64() < b;
+  return a.getAP() < b;
+}
+inline bool operator<=(const MPInt &a, int64_t b) {
+  if (LLVM_LIKELY(a.isSmall()))
+    return a.get64() <= b;
+  return a.getAP() <= b;
+}
+inline bool operator>=(const MPInt &a, int64_t b) {
+  if (LLVM_LIKELY(a.isSmall()))
+    return a.get64() >= b;
+  return a.getAP() >= b;
+}
+inline bool operator==(int64_t a, const MPInt &b) {
+  if (LLVM_LIKELY(b.isSmall()))
+    return a == b.get64();
+  return a == b.getAP();
+}
+inline bool operator!=(int64_t a, const MPInt &b) {
+  if (LLVM_LIKELY(b.isSmall()))
+    return a != b.get64();
+  return a != b.getAP();
+}
+inline bool operator>(int64_t a, const MPInt &b) {
+  if (LLVM_LIKELY(b.isSmall()))
+    return a > b.get64();
+  return a > b.getAP();
+}
+inline bool operator<(int64_t a, const MPInt &b) {
+  if (LLVM_LIKELY(b.isSmall()))
+    return a < b.get64();
+  return a < b.getAP();
+}
+inline bool operator<=(int64_t a, const MPInt &b) {
+  if (LLVM_LIKELY(b.isSmall()))
+    return a <= b.get64();
+  return a <= b.getAP();
+}
+inline bool operator>=(int64_t a, const MPInt &b) {
+  if (LLVM_LIKELY(b.isSmall()))
+    return a >= b.get64();
+  return a >= b.getAP();
+}
+
+} // namespace presburger
+} // namespace mlir
+
+#endif // MLIR_ANALYSIS_PRESBURGER_MPINT_H
diff --git a/mlir/lib/Analysis/Presburger/CMakeLists.txt b/mlir/lib/Analysis/Presburger/CMakeLists.txt
--- a/mlir/lib/Analysis/Presburger/CMakeLists.txt
+++ b/mlir/lib/Analysis/Presburger/CMakeLists.txt
@@ -2,6 +2,7 @@
   IntegerRelation.cpp
   LinearTransform.cpp
   Matrix.cpp
+  MPInt.cpp
   PresburgerRelation.cpp
   PresburgerSpace.cpp
   PWMAFunction.cpp
diff --git a/mlir/lib/Analysis/Presburger/MPInt.cpp b/mlir/lib/Analysis/Presburger/MPInt.cpp
new file mode 100644
--- /dev/null
+++ b/mlir/lib/Analysis/Presburger/MPInt.cpp
@@ -0,0 +1,36 @@
+//===- MPInt.cpp - MLIR MPInt Class ---------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Analysis/Presburger/MPInt.h"
+#include "llvm/Support/MathExtras.h"
+
+using namespace mlir;
+using namespace presburger;
+
+llvm::hash_code mlir::presburger::hash_value(const MPInt &x) {
+  if (x.isSmall())
+    return llvm::hash_value(x.val64);
+  return detail::hash_value(x.valSlow);
+}
+
+/// ---------------------------------------------------------------------------
+/// Printing.
+/// ---------------------------------------------------------------------------
+llvm::raw_ostream &MPInt::print(llvm::raw_ostream &os) const {
+  if (isSmall())
+    return os << val64;
+  return os << valSlow;
+}
+
+void MPInt::dump() const { print(llvm::errs()); }
+
+llvm::raw_ostream &mlir::presburger::operator<<(llvm::raw_ostream &os,
+                                                const MPInt &x) {
+  x.print(os);
+  return os;
+}
diff --git a/mlir/unittests/Analysis/Presburger/CMakeLists.txt b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
--- a/mlir/unittests/Analysis/Presburger/CMakeLists.txt
+++ b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
@@ -3,6 +3,7 @@
   IntegerRelationTest.cpp
   LinearTransformTest.cpp
   MatrixTest.cpp
+  MPIntTest.cpp
   PresburgerSetTest.cpp
   PresburgerSpaceTest.cpp
   PWMAFunctionTest.cpp
diff --git a/mlir/unittests/Analysis/Presburger/MPIntTest.cpp b/mlir/unittests/Analysis/Presburger/MPIntTest.cpp
new file mode 100644
--- /dev/null
+++ b/mlir/unittests/Analysis/Presburger/MPIntTest.cpp
@@ -0,0 +1,111 @@
+//===- MPIntTest.cpp - Tests for MPInt ----------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Analysis/Presburger/MPInt.h"
+#include <gmock/gmock.h>
+#include <gtest/gtest.h>
+
+using namespace mlir;
+using namespace presburger;
+
+TEST(MPIntTest, ops) {
+  MPInt two(2), five(5), seven(7), ten(10);
+  EXPECT_EQ(five + five, ten);
+  EXPECT_EQ(five * five, 2 * ten + five);
+  EXPECT_EQ(five * five, 3 * ten - five);
+  EXPECT_EQ(five * two, ten);
+  EXPECT_EQ(five / two, two);
+  EXPECT_EQ(five % two, two / two);
+
+  EXPECT_EQ(-ten % seven, -10 % 7);
+  EXPECT_EQ(ten % -seven, 10 % -7);
+  EXPECT_EQ(-ten % -seven, -10 % -7);
+  EXPECT_EQ(ten % seven, 10 % 7);
+
+  EXPECT_EQ(-ten / seven, -10 / 7);
+  EXPECT_EQ(ten / -seven, 10 / -7);
+  EXPECT_EQ(-ten / -seven, -10 / -7);
+  EXPECT_EQ(ten / seven, 10 / 7);
+
+  MPInt x = ten;
+  x += five;
+  EXPECT_EQ(x, 15);
+  x *= two;
+  EXPECT_EQ(x, 30);
+  x /= seven;
+  EXPECT_EQ(x, 4);
+  x -= two * 10;
+  EXPECT_EQ(x, -16);
+  x *= 2 * two;
+  EXPECT_EQ(x, -64);
+  x /= two / -2;
+  EXPECT_EQ(x, 64);
+
+  EXPECT_LE(ten, ten);
+  EXPECT_GE(ten, ten);
+  EXPECT_EQ(ten, ten);
+  EXPECT_FALSE(ten != ten);
+  EXPECT_FALSE(ten < ten);
+  EXPECT_FALSE(ten > ten);
+  EXPECT_LT(five, ten);
+  EXPECT_GT(ten, five);
+}
+
+TEST(MPIntTest, ops64Overloads) {
+  MPInt two(2), five(5), seven(7), ten(10);
+  EXPECT_EQ(five + 5, ten);
+  EXPECT_EQ(five + 5, 5 + five);
+  EXPECT_EQ(five * 5, 2 * ten + 5);
+  EXPECT_EQ(five * 5, 3 * ten - 5);
+  EXPECT_EQ(five * two, ten);
+  EXPECT_EQ(5 / two, 2);
+  EXPECT_EQ(five / 2, 2);
+  EXPECT_EQ(2 % two, 0);
+  EXPECT_EQ(2 - two, 0);
+  EXPECT_EQ(2 % two, two % 2);
+
+  MPInt x = ten;
+  x += 5;
+  EXPECT_EQ(x, 15);
+  x *= 2;
+  EXPECT_EQ(x, 30);
+  x /= 7;
+  EXPECT_EQ(x, 4);
+  x -= 20;
+  EXPECT_EQ(x, -16);
+  x *= 4;
+  EXPECT_EQ(x, -64);
+  x /= -1;
+  EXPECT_EQ(x, 64);
+
+  EXPECT_LE(ten, 10);
+  EXPECT_GE(ten, 10);
+  EXPECT_EQ(ten, 10);
+  EXPECT_FALSE(ten != 10);
+  EXPECT_FALSE(ten < 10);
+  EXPECT_FALSE(ten > 10);
+  EXPECT_LT(five, 10);
+  EXPECT_GT(ten, 5);
+
+  EXPECT_LE(10, ten);
+  EXPECT_GE(10, ten);
+  EXPECT_EQ(10, ten);
+  EXPECT_FALSE(10 != ten);
+  EXPECT_FALSE(10 < ten);
+  EXPECT_FALSE(10 > ten);
+  EXPECT_LT(5, ten);
+  EXPECT_GT(10, five);
+}
+
+TEST(MPIntTest, overflows) {
+  MPInt x(1ll << 60);
+  EXPECT_EQ((x * x - x * x * x * x) / (x * x * x), 1 - (1ll << 60));
+  MPInt y(1ll << 62);
+  EXPECT_EQ((y + y + y + y + y + y) / y, 6);
+  EXPECT_EQ(-(2 * (-y)), 2 * y); // -(-2^63) overflow.
+}